Subgroups — C₂×C₆₇×#3513 #30742021

Order 17152.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3513	C₂	1	32	yes	maximal, direct product factor
2	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#540×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#539×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#538×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
21	C₂²×#123×C₆₇	C₂	1	2	yes	maximal, complemented
22	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
27	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
31	#559×C₆₇	C₂²	1	16	yes	complemented
32	#554×C₆₇	C₂²	1	16	yes	complemented
33	#553×C₆₇	C₂²	1	16	yes	complemented
34	#553×C₆₇	C₂²	1	32	yes	complemented
35	#552×C₆₇	C₂²	1	16	yes	complemented
36	#551×C₆₇	C₂²	1	32	yes	complemented
37	#551×C₆₇	C₂²	1	32	yes	complemented
38	#547×C₆₇	C₂²	1	16	yes	complemented
39	#546×C₆₇	C₂²	1	16	yes	complemented
40	#546×C₆₇	C₂²	1	16	yes	complemented
41	#546×C₆₇	C₂²	1	32	yes	complemented
42	D₄²×C₆₇	C₂²	1	16	yes	complemented
43	#542×C₆₇	C₂²	1	16	yes	complemented
44	#540×C₆₇	C₂²	1	16	yes	complemented
45	#539×C₆₇	C₂²	1	32	yes	complemented
46	#538×C₆₇	C₂²	1	32	yes	complemented
47	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
49	#529×C₆₇	C₂²	1	16	yes	complemented
50	#529×C₆₇	C₂²	1	16	yes	complemented
51	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
55	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
56	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
57	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
60	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
64	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
65	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#525×C₆₇	C₂²	1	32	yes	complemented
67	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#123×C₆₇	C₂²	1	2	yes	—
69	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
70	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
72	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
73	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
74	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
75	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
77	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
78	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
79	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
81	C₂×#123×C₆₇	C₂²	1	32	yes	complemented
82	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
91	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
92	C₂×#121×C₆₇	C₂²	1	2	yes	—
93	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
94	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
96	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
97	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
98	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
100	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂×#120×C₆₇	C₂²	1	2	yes	—
102	C₂×#120×C₆₇	C₂²	1	2	yes	—
103	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
104	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
105	#520×C₆₇	C₂²	1	16	yes	complemented
106	#518×C₆₇	C₂²	1	16	yes	complemented
107	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
116	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
118	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
120	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
124	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
126	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
127	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
129	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×D₄×C₆₇	C₂²	1	16	yes	complemented
131	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
136	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
137	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
139	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
140	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
141	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
142	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
143	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
144	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
145	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
146	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁵×C₆₇	C₂³	1	2	yes	—
148	C₂⁵×C₆₇	C₂³	1	2	yes	—
149	C₂×#41×C₆₇	—	2	8	no	—
150	C₂×#41×C₆₇	—	4	8	no	—
151	C₂×#41×C₆₇	C₂³	1	8	yes	—
152	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
153	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₂²×D₄×C₆₇	—	2	8	no	—
157	C₂²×D₄×C₆₇	—	2	8	no	—
158	C₂²×D₄×C₆₇	—	4	8	no	—
159	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
161	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
162	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
163	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
166	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
167	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
169	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
170	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
172	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
173	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
174	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
175	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
176	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂³×C₄×C₆₇	—	4	8	no	—
178	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
181	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
182	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
186	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
187	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
188	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
189	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
190	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
191	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
192	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
193	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
194	C₂³×C₄×C₆₇	C₂³	1	16	yes	complemented
195	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
196	#127×C₆₇	C₂³	1	8	yes	—
197	#126×C₆₇	C₂³	1	16	yes	complemented
198	#126×C₆₇	C₂³	1	8	yes	complemented
199	#126×C₆₇	C₂³	1	8	yes	complemented
200	#126×C₆₇	C₂³	1	16	yes	complemented
201	#126×C₆₇	C₂³	1	16	yes	complemented
202	#126×C₆₇	C₂³	1	16	yes	complemented
203	#125×C₆₇	C₂³	1	8	yes	complemented
204	#125×C₆₇	C₂³	1	8	yes	complemented
205	#125×C₆₇	C₂³	1	16	yes	complemented
206	#125×C₆₇	C₂³	1	8	yes	complemented
207	#124×C₆₇	C₂³	1	8	yes	complemented
208	#124×C₆₇	C₂³	1	8	yes	complemented
209	#124×C₆₇	C₂³	1	16	yes	complemented
210	#124×C₆₇	C₂³	1	16	yes	complemented
211	#124×C₆₇	C₂³	1	8	yes	complemented
212	#123×C₆₇	C₂³	1	8	yes	—
213	#123×C₆₇	C₂³	1	16	yes	—
214	#123×C₆₇	C₂³	1	16	yes	complemented
215	#123×C₆₇	C₂³	1	16	yes	complemented
216	#123×C₆₇	C₂³	1	16	yes	complemented
217	#123×C₆₇	C₂³	1	16	yes	complemented
218	#123×C₆₇	C₂³	1	16	yes	complemented
219	#123×C₆₇	C₂³	1	16	yes	complemented
220	#123×C₆₇	C₂³	1	8	yes	complemented
221	#123×C₆₇	C₂³	1	16	yes	complemented
222	#123×C₆₇	C₂³	1	16	yes	complemented
223	#123×C₆₇	C₂³	1	16	yes	complemented
224	#123×C₆₇	C₂³	1	16	yes	complemented
225	#123×C₆₇	C₂³	1	16	yes	complemented
226	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
227	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
228	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
229	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
230	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
231	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
232	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
233	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
234	#121×C₆₇	C₂³	1	8	yes	—
235	#121×C₆₇	C₂³	1	8	yes	—
236	#121×C₆₇	C₂³	1	16	yes	—
237	#121×C₆₇	C₂³	1	8	yes	—
238	#121×C₆₇	C₂³	1	16	yes	complemented
239	#121×C₆₇	C₂³	1	16	yes	complemented
240	#121×C₆₇	C₂³	1	16	yes	complemented
241	#121×C₆₇	C₂³	1	16	yes	complemented
242	#121×C₆₇	C₂³	1	8	yes	complemented
243	#121×C₆₇	C₂³	1	16	yes	complemented
244	#121×C₆₇	C₂³	1	8	yes	complemented
245	#120×C₆₇	C₂³	1	16	yes	—
246	#120×C₆₇	C₂³	1	16	yes	—
247	#120×C₆₇	C₂³	1	16	yes	complemented
248	#120×C₆₇	C₂³	1	16	yes	complemented
249	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
250	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
251	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
252	C₄×D₄×C₆₇	C₂³	1	8	yes	—
253	C₄×D₄×C₆₇	C₂³	1	8	yes	—
254	C₄×D₄×C₆₇	C₂³	1	8	yes	—
255	C₄×D₄×C₆₇	C₂³	1	8	yes	—
256	C₄×D₄×C₆₇	C₂³	1	8	yes	—
257	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
258	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
259	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
260	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
261	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
262	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
263	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
264	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
265	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
266	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
267	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
268	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
269	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
270	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
271	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
272	#117×C₆₇	C₂³	1	8	yes	complemented
273	#117×C₆₇	C₂³	1	8	yes	complemented
274	#117×C₆₇	C₂³	1	8	yes	complemented
275	#117×C₆₇	C₂³	1	16	yes	complemented
276	#117×C₆₇	C₂³	1	16	yes	complemented
277	#117×C₆₇	C₂³	1	16	yes	complemented
278	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
304	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
305	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
306	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
307	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
310	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
314	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
315	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
320	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
321	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
322	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
325	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
327	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
334	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
335	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
337	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
341	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
346	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
347	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
348	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
351	C₂⁴×C₆₇	—	2	8	no	—
352	C₂⁴×C₆₇	—	2	8	no	—
353	C₂⁴×C₆₇	—	2	8	no	—
354	C₂⁴×C₆₇	—	4	4	no	—
355	C₂⁴×C₆₇	—	4	4	no	—
356	C₂⁴×C₆₇	—	4	4	no	—
357	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
359	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
360	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
362	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
363	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
365	#41×C₆₇	—	2	32	no	—
366	#41×C₆₇	—	4	32	no	—
367	C₂×Q₈×C₆₇	—	2	4	no	—
368	C₂×Q₈×C₆₇	—	4	2	no	—
369	C₂×Q₈×C₆₇	—	4	4	no	—
370	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
371	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
372	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
373	C₂×D₄×C₆₇	—	2	8	no	—
374	C₂×D₄×C₆₇	—	2	8	no	—
375	C₂×D₄×C₆₇	—	2	8	no	—
376	C₂×D₄×C₆₇	—	2	4	no	—
377	C₂×D₄×C₆₇	—	2	8	no	—
378	C₂×D₄×C₆₇	—	2	4	no	—
379	C₂×D₄×C₆₇	—	2	32	no	—
380	C₂×D₄×C₆₇	—	2	32	no	—
381	C₂×D₄×C₆₇	—	2	4	no	—
382	C₂×D₄×C₆₇	—	2	4	no	—
383	C₂×D₄×C₆₇	—	4	4	no	—
384	C₂×D₄×C₆₇	—	4	4	no	—
385	C₂×D₄×C₆₇	—	4	4	no	—
386	C₂×D₄×C₆₇	—	4	2	no	—
387	C₂×D₄×C₆₇	—	4	4	no	—
388	C₂×D₄×C₆₇	—	4	4	no	—
389	C₂×D₄×C₆₇	—	4	32	no	—
390	C₂×D₄×C₆₇	#41	1	8	yes	complemented
391	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
392	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
393	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
394	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
395	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
396	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
397	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
398	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
399	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
400	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
401	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
402	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
403	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
404	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
405	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
406	C₂²×C₄×C₆₇	—	2	8	no	—
407	C₂²×C₄×C₆₇	—	2	4	no	—
408	C₂²×C₄×C₆₇	—	2	8	no	—
409	C₂²×C₄×C₆₇	—	2	4	no	—
410	C₂²×C₄×C₆₇	—	2	4	no	—
411	C₂²×C₄×C₆₇	—	2	4	no	—
412	C₂²×C₄×C₆₇	—	4	4	no	—
413	C₂²×C₄×C₆₇	—	4	4	no	—
414	C₂²×C₄×C₆₇	—	4	4	no	—
415	C₂²×C₄×C₆₇	—	4	4	no	—
416	C₂²×C₄×C₆₇	—	4	32	no	—
417	C₂²×C₄×C₆₇	—	4	4	no	—
418	C₂²×C₄×C₆₇	—	4	2	no	—
419	C₂²×C₄×C₆₇	—	4	4	no	—
420	C₂²×C₄×C₆₇	—	4	4	no	—
421	C₂²×C₄×C₆₇	—	4	4	no	—
422	C₂²×C₄×C₆₇	—	4	4	no	—
423	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
424	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
427	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
428	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
429	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
432	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
440	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
445	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
446	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
448	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
449	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
450	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
451	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
452	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
453	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
454	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
455	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
457	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
458	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
459	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
460	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
461	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
462	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
463	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
465	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
466	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
467	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
468	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
469	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
470	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
471	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
472	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
473	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
474	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
475	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
476	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
477	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
478	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
479	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
480	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
481	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
482	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
483	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
484	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
485	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
486	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
487	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
488	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
489	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
490	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
491	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
492	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
493	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
497	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
499	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
500	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
501	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
502	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
503	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
504	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
505	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
506	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
507	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
508	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
509	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
510	C₄²×C₆₇	C₂⁴	1	4	yes	—
511	C₄²×C₆₇	C₂⁴	1	4	yes	—
512	C₄²×C₆₇	C₂⁴	1	4	yes	—
513	C₄²×C₆₇	C₂⁴	1	4	yes	—
514	C₄²×C₆₇	C₂⁴	1	8	yes	—
515	C₄²×C₆₇	C₂⁴	1	8	yes	—
516	C₄²×C₆₇	C₂⁴	1	8	yes	—
517	C₄²×C₆₇	C₂⁴	1	4	yes	—
518	C₄²×C₆₇	C₂⁴	1	4	yes	—
519	C₂³×C₆₇	—	2	2	no	—
520	C₂³×C₆₇	—	2	4	no	—
521	C₂³×C₆₇	—	2	2	no	—
522	C₂³×C₆₇	—	2	4	no	—
523	C₂³×C₆₇	—	2	2	no	—
524	C₂³×C₆₇	—	2	2	no	—
525	C₂³×C₆₇	—	2	16	no	—
526	C₂³×C₆₇	—	2	4	no	—
527	C₂³×C₆₇	—	2	4	no	—
528	C₂³×C₆₇	—	2	2	no	—
529	C₂³×C₆₇	—	2	16	no	—
530	C₂³×C₆₇	—	2	4	no	—
531	C₂³×C₆₇	—	2	4	no	—
532	C₂³×C₆₇	—	2	2	no	—
533	C₂³×C₆₇	—	2	4	no	—
534	C₂³×C₆₇	—	2	2	no	—
535	C₂³×C₆₇	—	2	4	no	—
536	C₂³×C₆₇	—	2	2	no	—
537	C₂³×C₆₇	—	2	16	no	—
538	C₂³×C₆₇	—	4	8	no	—
539	C₂³×C₆₇	—	4	8	no	—
540	C₂³×C₆₇	—	4	8	no	—
541	C₂³×C₆₇	—	4	32	no	—
542	C₂³×C₆₇	—	8	16	no	—
543	C₂³×C₆₇	C₂×#41	1	8	yes	—
544	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
545	C₂³×C₆₇	C₂⁵	1	2	yes	—
546	C₂³×C₆₇	C₂⁵	1	4	yes	—
547	C₂³×C₆₇	C₂⁵	1	4	yes	—
548	C₂³×C₆₇	C₂⁵	1	2	yes	—
549	C₂³×C₆₇	C₂⁵	1	4	yes	—
550	C₂³×C₆₇	C₂⁵	1	2	yes	—
551	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
552	Q₈×C₆₇	—	2	8	no	—
553	Q₈×C₆₇	—	4	4	no	—
554	Q₈×C₆₇	—	4	8	no	—
555	D₄×C₆₇	—	2	16	no	—
556	D₄×C₆₇	—	2	16	no	—
557	D₄×C₆₇	—	2	16	no	—
558	D₄×C₆₇	—	2	8	no	—
559	D₄×C₆₇	—	2	16	no	—
560	D₄×C₆₇	—	2	8	no	—
561	D₄×C₆₇	—	2	8	no	—
562	D₄×C₆₇	—	2	8	no	—
563	D₄×C₆₇	—	4	8	no	—
564	D₄×C₆₇	—	4	8	no	—
565	D₄×C₆₇	—	4	8	no	—
566	D₄×C₆₇	—	4	4	no	—
567	D₄×C₆₇	—	4	8	no	—
568	D₄×C₆₇	—	4	8	no	—
569	D₄×C₆₇	C₂×#41	1	16	yes	complemented
570	C₂×C₄×C₆₇	—	2	2	no	—
571	C₂×C₄×C₆₇	—	2	2	no	—
572	C₂×C₄×C₆₇	—	2	2	no	—
573	C₂×C₄×C₆₇	—	2	4	no	—
574	C₂×C₄×C₆₇	—	2	16	no	—
575	C₂×C₄×C₆₇	—	2	8	no	—
576	C₂×C₄×C₆₇	—	2	2	no	—
577	C₂×C₄×C₆₇	—	2	2	no	—
578	C₂×C₄×C₆₇	—	2	4	no	—
579	C₂×C₄×C₆₇	—	2	4	no	—
580	C₂×C₄×C₆₇	—	2	16	no	—
581	C₂×C₄×C₆₇	—	2	2	no	—
582	C₂×C₄×C₆₇	—	2	4	no	—
583	C₂×C₄×C₆₇	—	2	2	no	—
584	C₂×C₄×C₆₇	—	2	2	no	—
585	C₂×C₄×C₆₇	—	2	4	no	—
586	C₂×C₄×C₆₇	—	2	2	no	—
587	C₂×C₄×C₆₇	—	2	2	no	—
588	C₂×C₄×C₆₇	—	2	2	no	—
589	C₂×C₄×C₆₇	—	2	8	no	—
590	C₂×C₄×C₆₇	—	2	8	no	—
591	C₂×C₄×C₆₇	—	2	8	no	—
592	C₂×C₄×C₆₇	—	4	8	no	—
593	C₂×C₄×C₆₇	—	4	8	no	—
594	C₂×C₄×C₆₇	—	4	8	no	—
595	C₂×C₄×C₆₇	—	4	8	no	—
596	C₂×C₄×C₆₇	—	4	8	no	—
597	C₂×C₄×C₆₇	—	4	4	no	—
598	C₂×C₄×C₆₇	—	4	8	no	—
599	C₂×C₄×C₆₇	—	4	8	no	—
600	C₂×C₄×C₆₇	—	4	8	no	—
601	C₂×C₄×C₆₇	—	4	8	no	—
602	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
603	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
604	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
605	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
606	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
607	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
608	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
609	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
610	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
611	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
612	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
613	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
614	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
615	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
616	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
617	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
618	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
619	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
620	C₂²×C₆₇	—	2	2	no	—
621	C₂²×C₆₇	—	2	4	no	—
622	C₂²×C₆₇	—	2	2	no	—
623	C₂²×C₆₇	—	2	4	no	—
624	C₂²×C₆₇	—	2	8	no	—
625	C₂²×C₆₇	—	2	16	no	—
626	C₂²×C₆₇	—	2	2	no	—
627	C₂²×C₆₇	—	2	2	no	—
628	C₂²×C₆₇	—	2	4	no	—
629	C₂²×C₆₇	—	2	4	no	—
630	C₂²×C₆₇	—	2	2	no	—
631	C₂²×C₆₇	—	2	4	no	—
632	C₂²×C₆₇	—	2	4	no	—
633	C₂²×C₆₇	—	2	2	no	—
634	C₂²×C₆₇	—	2	4	no	—
635	C₂²×C₆₇	—	2	2	no	—
636	C₂²×C₆₇	—	2	4	no	—
637	C₂²×C₆₇	—	2	2	no	—
638	C₂²×C₆₇	—	4	32	no	—
639	C₂²×C₆₇	—	4	4	no	—
640	C₂²×C₆₇	—	4	8	no	—
641	C₂²×C₆₇	—	4	8	no	—
642	C₂²×C₆₇	—	4	4	no	—
643	C₂²×C₆₇	—	8	16	no	—
644	C₂²×C₆₇	C₂²×#41	1	8	yes	—
645	C₂²×C₆₇	C₂²×#41	1	2	yes	—
646	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
647	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
648	C₂²×C₆₇	#585	1	2	yes	—
649	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
650	C₄×C₆₇	—	2	2	no	—
651	C₄×C₆₇	—	2	2	no	—
652	C₄×C₆₇	—	2	2	no	—
653	C₄×C₆₇	—	2	4	no	—
654	C₄×C₆₇	—	2	2	no	—
655	C₄×C₆₇	—	2	2	no	—
656	C₄×C₆₇	—	2	4	no	—
657	C₄×C₆₇	—	2	4	no	—
658	C₄×C₆₇	—	2	2	no	—
659	C₄×C₆₇	—	2	4	no	—
660	C₄×C₆₇	—	2	2	no	—
661	C₄×C₆₇	—	2	2	no	—
662	C₄×C₆₇	—	2	4	no	—
663	C₄×C₆₇	—	2	2	no	—
664	C₄×C₆₇	—	2	2	no	—
665	C₄×C₆₇	—	2	2	no	—
666	C₄×C₆₇	C₂²×#41	1	4	yes	—
667	C₂×#3513	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
668	C₂×C₆₇	—	2	4	no	—
669	C₂×C₆₇	—	2	8	no	—
670	C₂×C₆₇	—	4	2	no	—
671	C₂×C₆₇	—	4	4	no	—
672	C₂×C₆₇	—	4	4	no	—
673	C₂×C₆₇	—	4	2	no	—
674	C₂×C₆₇	#3513	1	4	yes	direct product factor
675	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
676	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
678	#3513	C₂×C₆₇	1	32	yes	direct product factor
679	C₂×#559	C₂×C₆₇	1	1	yes	characteristic, complemented
680	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
681	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
682	C₂×#553	C₂×C₆₇	1	2	yes	complemented
683	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
684	C₂×#551	C₂×C₆₇	1	2	yes	complemented
685	C₂×#551	C₂×C₆₇	1	2	yes	complemented
686	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
687	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
688	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
689	C₂×#546	C₂×C₆₇	1	2	yes	complemented
690	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
691	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
692	C₂×#540	C₂×C₆₇	1	1	yes	characteristic, complemented
693	C₂×#539	C₂×C₆₇	1	2	yes	complemented
694	C₂×#538	C₂×C₆₇	1	2	yes	complemented
695	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
696	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
697	C₂×#525	C₂×C₆₇	1	2	yes	complemented
698	C₂²×#123	C₂×C₆₇	1	2	yes	complemented
699	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
700	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
701	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
702	C₆₇	C₂×#3513	1	1	yes	characteristic, direct product factor, Sylow
703	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
704	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
705	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
706	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
707	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
708	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	complemented
709	#559	C₂²×C₆₇	1	16	yes	complemented
710	#554	C₂²×C₆₇	1	16	yes	complemented
711	#553	C₂²×C₆₇	1	16	yes	complemented
712	#553	C₂²×C₆₇	1	32	yes	complemented
713	#552	C₂²×C₆₇	1	16	yes	complemented
714	#551	C₂²×C₆₇	1	32	yes	complemented
715	#551	C₂²×C₆₇	1	32	yes	complemented
716	#547	C₂²×C₆₇	1	16	yes	complemented
717	#546	C₂²×C₆₇	1	16	yes	complemented
718	#546	C₂²×C₆₇	1	16	yes	complemented
719	#546	C₂²×C₆₇	1	32	yes	complemented
720	D₄²	C₂²×C₆₇	1	16	yes	complemented
721	#542	C₂²×C₆₇	1	16	yes	complemented
722	#540	C₂²×C₆₇	1	16	yes	complemented
723	#539	C₂²×C₆₇	1	32	yes	complemented
724	#538	C₂²×C₆₇	1	32	yes	complemented
725	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
727	#529	C₂²×C₆₇	1	16	yes	complemented
728	#529	C₂²×C₆₇	1	16	yes	complemented
729	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
730	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
733	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
734	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
735	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
737	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
738	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
742	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
743	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	#525	C₂²×C₆₇	1	32	yes	complemented
745	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
746	C₂×#123	C₂²×C₆₇	1	2	yes	—
747	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
748	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
749	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
750	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
751	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
752	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
753	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
755	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
756	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
757	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
758	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
759	C₂×#123	C₂²×C₆₇	1	32	yes	complemented
760	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
761	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
762	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
765	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
766	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
767	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
769	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
770	C₂×#121	C₂²×C₆₇	1	2	yes	—
771	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
772	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
773	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
774	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
775	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
776	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
777	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
778	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	C₂×#120	C₂²×C₆₇	1	2	yes	—
780	C₂×#120	C₂²×C₆₇	1	2	yes	—
781	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
782	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
783	#520	C₂²×C₆₇	1	16	yes	complemented
784	#518	C₂²×C₆₇	1	16	yes	complemented
785	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
787	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
789	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
790	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
791	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
792	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
793	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
794	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
795	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
796	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
797	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
798	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
799	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
800	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
801	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
802	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
803	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
804	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
805	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
807	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
808	C₂×C₄×D₄	C₂²×C₆₇	1	16	yes	complemented
809	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
812	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
813	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
814	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
815	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
816	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
817	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
818	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
819	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
820	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
821	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
822	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
823	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
824	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
825	C₂⁵	C₂³×C₆₇	1	2	yes	—
826	C₂⁵	C₂³×C₆₇	1	2	yes	—
827	C₂×#41	—	2	8	no	—
828	C₂×#41	—	4	8	no	—
829	C₂×#41	C₂³×C₆₇	1	8	yes	—
830	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
831	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
832	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
833	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
834	C₂²×D₄	—	2	8	no	—
835	C₂²×D₄	—	2	8	no	—
836	C₂²×D₄	—	4	8	no	—
837	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
838	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
839	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
840	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
841	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
844	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
845	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
846	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
847	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
848	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
849	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
850	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
851	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
852	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
853	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
854	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
855	C₂³×C₄	—	4	8	no	—
856	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
857	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
858	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
859	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
860	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
861	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
862	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
863	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
864	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
865	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
866	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
867	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
868	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
869	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
870	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
871	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
872	C₂³×C₄	C₂³×C₆₇	1	16	yes	complemented
873	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
874	#127	C₂³×C₆₇	1	8	yes	—
875	#126	C₂³×C₆₇	1	16	yes	complemented
876	#126	C₂³×C₆₇	1	8	yes	complemented
877	#126	C₂³×C₆₇	1	8	yes	complemented
878	#126	C₂³×C₆₇	1	16	yes	complemented
879	#126	C₂³×C₆₇	1	16	yes	complemented
880	#126	C₂³×C₆₇	1	16	yes	complemented
881	#125	C₂³×C₆₇	1	8	yes	complemented
882	#125	C₂³×C₆₇	1	8	yes	complemented
883	#125	C₂³×C₆₇	1	16	yes	complemented
884	#125	C₂³×C₆₇	1	8	yes	complemented
885	#124	C₂³×C₆₇	1	8	yes	complemented
886	#124	C₂³×C₆₇	1	8	yes	complemented
887	#124	C₂³×C₆₇	1	16	yes	complemented
888	#124	C₂³×C₆₇	1	16	yes	complemented
889	#124	C₂³×C₆₇	1	8	yes	complemented
890	#123	C₂³×C₆₇	1	8	yes	—
891	#123	C₂³×C₆₇	1	16	yes	—
892	#123	C₂³×C₆₇	1	16	yes	complemented
893	#123	C₂³×C₆₇	1	16	yes	complemented
894	#123	C₂³×C₆₇	1	16	yes	complemented
895	#123	C₂³×C₆₇	1	16	yes	complemented
896	#123	C₂³×C₆₇	1	16	yes	complemented
897	#123	C₂³×C₆₇	1	16	yes	complemented
898	#123	C₂³×C₆₇	1	8	yes	complemented
899	#123	C₂³×C₆₇	1	16	yes	complemented
900	#123	C₂³×C₆₇	1	16	yes	complemented
901	#123	C₂³×C₆₇	1	16	yes	complemented
902	#123	C₂³×C₆₇	1	16	yes	complemented
903	#123	C₂³×C₆₇	1	16	yes	complemented
904	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
905	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
906	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
907	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
908	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
909	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
910	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
911	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
912	#121	C₂³×C₆₇	1	8	yes	—
913	#121	C₂³×C₆₇	1	8	yes	—
914	#121	C₂³×C₆₇	1	16	yes	—
915	#121	C₂³×C₆₇	1	8	yes	—
916	#121	C₂³×C₆₇	1	16	yes	complemented
917	#121	C₂³×C₆₇	1	16	yes	complemented
918	#121	C₂³×C₆₇	1	16	yes	complemented
919	#121	C₂³×C₆₇	1	16	yes	complemented
920	#121	C₂³×C₆₇	1	8	yes	complemented
921	#121	C₂³×C₆₇	1	16	yes	complemented
922	#121	C₂³×C₆₇	1	8	yes	complemented
923	#120	C₂³×C₆₇	1	16	yes	—
924	#120	C₂³×C₆₇	1	16	yes	—
925	#120	C₂³×C₆₇	1	16	yes	complemented
926	#120	C₂³×C₆₇	1	16	yes	complemented
927	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
928	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
929	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
930	C₄×D₄	C₂³×C₆₇	1	8	yes	—
931	C₄×D₄	C₂³×C₆₇	1	8	yes	—
932	C₄×D₄	C₂³×C₆₇	1	8	yes	—
933	C₄×D₄	C₂³×C₆₇	1	8	yes	—
934	C₄×D₄	C₂³×C₆₇	1	8	yes	—
935	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
936	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
937	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
938	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
939	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
940	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
941	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
942	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
943	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
944	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
945	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
946	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
947	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
948	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
949	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
950	#117	C₂³×C₆₇	1	8	yes	complemented
951	#117	C₂³×C₆₇	1	8	yes	complemented
952	#117	C₂³×C₆₇	1	8	yes	complemented
953	#117	C₂³×C₆₇	1	16	yes	complemented
954	#117	C₂³×C₆₇	1	16	yes	complemented
955	#117	C₂³×C₆₇	1	16	yes	complemented
956	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
958	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
961	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
964	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
965	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
966	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
967	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
968	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
973	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
974	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
975	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
978	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
982	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
983	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
984	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
985	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
986	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
988	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
992	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
993	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
994	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
995	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
996	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
997	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
998	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
999	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1000	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1001	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1002	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1003	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1005	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1008	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1011	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1012	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
1013	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
1015	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
1016	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
1017	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
1018	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
1019	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1021	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1022	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1023	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1025	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1026	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1027	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1028	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
1029	C₂⁴	—	2	8	no	—
1030	C₂⁴	—	2	8	no	—
1031	C₂⁴	—	2	8	no	—
1032	C₂⁴	—	4	4	no	—
1033	C₂⁴	—	4	4	no	—
1034	C₂⁴	—	4	4	no	—
1035	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1036	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
1037	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
1038	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1039	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
1040	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
1041	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
1043	#41	—	2	32	no	—
1044	#41	—	4	32	no	—
1045	C₂×Q₈	—	2	4	no	—
1046	C₂×Q₈	—	4	4	no	—
1047	C₂×Q₈	—	4	2	no	—
1048	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1049	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1050	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
1051	C₂×D₄	—	2	8	no	—
1052	C₂×D₄	—	2	8	no	—
1053	C₂×D₄	—	2	8	no	—
1054	C₂×D₄	—	2	4	no	—
1055	C₂×D₄	—	2	8	no	—
1056	C₂×D₄	—	2	4	no	—
1057	C₂×D₄	—	2	32	no	—
1058	C₂×D₄	—	2	32	no	—
1059	C₂×D₄	—	2	4	no	—
1060	C₂×D₄	—	2	4	no	—
1061	C₂×D₄	—	4	4	no	—
1062	C₂×D₄	—	4	4	no	—
1063	C₂×D₄	—	4	4	no	—
1064	C₂×D₄	—	4	4	no	—
1065	C₂×D₄	—	4	2	no	—
1066	C₂×D₄	—	4	4	no	—
1067	C₂×D₄	—	4	32	no	—
1068	C₂×D₄	#41×C₆₇	1	8	yes	complemented
1069	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1070	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1071	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1072	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1073	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1074	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1075	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1076	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1077	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1078	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1079	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1080	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1081	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1082	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1083	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1084	C₂²×C₄	—	2	8	no	—
1085	C₂²×C₄	—	2	4	no	—
1086	C₂²×C₄	—	2	8	no	—
1087	C₂²×C₄	—	2	4	no	—
1088	C₂²×C₄	—	2	4	no	—
1089	C₂²×C₄	—	2	4	no	—
1090	C₂²×C₄	—	4	4	no	—
1091	C₂²×C₄	—	4	4	no	—
1092	C₂²×C₄	—	4	4	no	—
1093	C₂²×C₄	—	4	4	no	—
1094	C₂²×C₄	—	4	32	no	—
1095	C₂²×C₄	—	4	4	no	—
1096	C₂²×C₄	—	4	4	no	—
1097	C₂²×C₄	—	4	4	no	—
1098	C₂²×C₄	—	4	4	no	—
1099	C₂²×C₄	—	4	2	no	—
1100	C₂²×C₄	—	4	4	no	—
1101	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1102	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1103	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1104	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1105	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1106	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1107	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1109	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1111	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1112	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1113	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1114	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1115	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1116	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1117	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1118	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1119	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1120	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1121	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1122	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1123	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1124	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1125	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1126	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1127	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1128	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1129	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1130	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1131	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1132	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1133	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1134	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1135	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1136	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1137	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1138	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1139	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1140	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1141	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1142	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1143	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1144	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1145	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1146	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1147	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1148	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1149	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1150	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1151	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1152	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1153	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1154	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1155	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1156	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1157	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1158	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1159	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1160	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1161	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1162	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1163	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1164	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1165	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1166	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1167	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1168	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1169	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1170	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1171	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1172	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1173	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1174	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1175	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1176	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1177	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1178	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1179	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1180	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1181	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1182	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1183	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1184	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1185	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1186	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1187	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1188	C₄²	C₂⁴×C₆₇	1	4	yes	—
1189	C₄²	C₂⁴×C₆₇	1	4	yes	—
1190	C₄²	C₂⁴×C₆₇	1	4	yes	—
1191	C₄²	C₂⁴×C₆₇	1	4	yes	—
1192	C₄²	C₂⁴×C₆₇	1	8	yes	—
1193	C₄²	C₂⁴×C₆₇	1	8	yes	—
1194	C₄²	C₂⁴×C₆₇	1	8	yes	—
1195	C₄²	C₂⁴×C₆₇	1	4	yes	—
1196	C₄²	C₂⁴×C₆₇	1	4	yes	—
1197	C₂³	—	2	2	no	—
1198	C₂³	—	2	4	no	—
1199	C₂³	—	2	2	no	—
1200	C₂³	—	2	4	no	—
1201	C₂³	—	2	2	no	—
1202	C₂³	—	2	2	no	—
1203	C₂³	—	2	16	no	—
1204	C₂³	—	2	4	no	—
1205	C₂³	—	2	4	no	—
1206	C₂³	—	2	2	no	—
1207	C₂³	—	2	16	no	—
1208	C₂³	—	2	4	no	—
1209	C₂³	—	2	4	no	—
1210	C₂³	—	2	2	no	—
1211	C₂³	—	2	4	no	—
1212	C₂³	—	2	2	no	—
1213	C₂³	—	2	4	no	—
1214	C₂³	—	2	2	no	—
1215	C₂³	—	2	16	no	—
1216	C₂³	—	4	8	no	—
1217	C₂³	—	4	8	no	—
1218	C₂³	—	4	8	no	—
1219	C₂³	—	4	32	no	—
1220	C₂³	—	8	16	no	—
1221	C₂³	C₂×#41×C₆₇	1	8	yes	—
1222	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
1223	C₂³	C₂⁵×C₆₇	1	2	yes	—
1224	C₂³	C₂⁵×C₆₇	1	4	yes	—
1225	C₂³	C₂⁵×C₆₇	1	4	yes	—
1226	C₂³	C₂⁵×C₆₇	1	2	yes	—
1227	C₂³	C₂⁵×C₆₇	1	4	yes	—
1228	C₂³	C₂⁵×C₆₇	1	2	yes	—
1229	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1230	Q₈	—	2	8	no	—
1231	Q₈	—	4	8	no	—
1232	Q₈	—	4	4	no	—
1233	D₄	—	2	16	no	—
1234	D₄	—	2	16	no	—
1235	D₄	—	2	16	no	—
1236	D₄	—	2	8	no	—
1237	D₄	—	2	16	no	—
1238	D₄	—	2	8	no	—
1239	D₄	—	2	8	no	—
1240	D₄	—	2	8	no	—
1241	D₄	—	4	8	no	—
1242	D₄	—	4	8	no	—
1243	D₄	—	4	8	no	—
1244	D₄	—	4	8	no	—
1245	D₄	—	4	4	no	—
1246	D₄	—	4	8	no	—
1247	D₄	C₂×#41×C₆₇	1	16	yes	complemented
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	16	no	—
1253	C₂×C₄	—	2	8	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	4	no	—
1257	C₂×C₄	—	2	4	no	—
1258	C₂×C₄	—	2	16	no	—
1259	C₂×C₄	—	2	2	no	—
1260	C₂×C₄	—	2	4	no	—
1261	C₂×C₄	—	2	2	no	—
1262	C₂×C₄	—	2	2	no	—
1263	C₂×C₄	—	2	4	no	—
1264	C₂×C₄	—	2	2	no	—
1265	C₂×C₄	—	2	2	no	—
1266	C₂×C₄	—	2	2	no	—
1267	C₂×C₄	—	2	8	no	—
1268	C₂×C₄	—	2	8	no	—
1269	C₂×C₄	—	2	8	no	—
1270	C₂×C₄	—	4	8	no	—
1271	C₂×C₄	—	4	8	no	—
1272	C₂×C₄	—	4	8	no	—
1273	C₂×C₄	—	4	8	no	—
1274	C₂×C₄	—	4	8	no	—
1275	C₂×C₄	—	4	8	no	—
1276	C₂×C₄	—	4	8	no	—
1277	C₂×C₄	—	4	8	no	—
1278	C₂×C₄	—	4	4	no	—
1279	C₂×C₄	—	4	8	no	—
1280	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1281	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1282	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1283	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1284	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1285	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1286	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1287	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1288	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1289	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1290	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1291	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1292	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1293	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1294	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1295	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1296	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1297	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1298	C₂²	—	2	2	no	—
1299	C₂²	—	2	4	no	—
1300	C₂²	—	2	2	no	—
1301	C₂²	—	2	4	no	—
1302	C₂²	—	2	8	no	—
1303	C₂²	—	2	16	no	—
1304	C₂²	—	2	2	no	—
1305	C₂²	—	2	2	no	—
1306	C₂²	—	2	4	no	—
1307	C₂²	—	2	4	no	—
1308	C₂²	—	2	2	no	—
1309	C₂²	—	2	4	no	—
1310	C₂²	—	2	4	no	—
1311	C₂²	—	2	2	no	—
1312	C₂²	—	2	4	no	—
1313	C₂²	—	2	2	no	—
1314	C₂²	—	2	4	no	—
1315	C₂²	—	2	2	no	—
1316	C₂²	—	4	32	no	—
1317	C₂²	—	4	8	no	—
1318	C₂²	—	4	4	no	—
1319	C₂²	—	4	8	no	—
1320	C₂²	—	4	4	no	—
1321	C₂²	—	8	16	no	—
1322	C₂²	C₂²×#41×C₆₇	1	8	yes	—
1323	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1324	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
1325	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1326	C₂²	#585×C₆₇	1	2	yes	—
1327	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1328	C₄	—	2	2	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	4	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	4	no	—
1335	C₄	—	2	4	no	—
1336	C₄	—	2	2	no	—
1337	C₄	—	2	4	no	—
1338	C₄	—	2	2	no	—
1339	C₄	—	2	2	no	—
1340	C₄	—	2	4	no	—
1341	C₄	—	2	2	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	C₂²×#41×C₆₇	1	4	yes	—
1345	C₂	—	2	4	no	—
1346	C₂	—	2	8	no	—
1347	C₂	—	4	4	no	—
1348	C₂	—	4	2	no	—
1349	C₂	—	4	4	no	—
1350	C₂	—	4	2	no	—
1351	C₂	C₆₇×#3513	1	4	yes	direct product factor
1352	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
1353	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1354	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3513	C₂	direct (N × H)
2. C₂×#559×C₆₇	C₂	semidirect
3. C₂×#554×C₆₇	C₂	semidirect
4. C₂×#553×C₆₇	C₂	semidirect
5. C₂×#553×C₆₇	C₂	semidirect
6. C₂×#552×C₆₇	C₂	semidirect
7. C₂×#551×C₆₇	C₂	semidirect
8. C₂×#551×C₆₇	C₂	semidirect
9. C₂×#547×C₆₇	C₂	semidirect
10. C₂×#546×C₆₇	C₂	semidirect
11. C₂×#546×C₆₇	C₂	semidirect
12. C₂×#546×C₆₇	C₂	semidirect
13. C₂×D₄²×C₆₇	C₂	semidirect
14. C₂×#542×C₆₇	C₂	semidirect
15. C₂×#540×C₆₇	C₂	semidirect
16. C₂×#539×C₆₇	C₂	semidirect
17. C₂×#538×C₆₇	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂×#529×C₆₇	C₂	semidirect
20. C₂×#525×C₆₇	C₂	semidirect
21. C₂²×#123×C₆₇	C₂	semidirect
22. C₂×#520×C₆₇	C₂	semidirect
23. C₂×#518×C₆₇	C₂	semidirect
24. C₂²×C₄×D₄×C₆₇	C₂	semidirect
26. C₂²×#41×C₆₇	C₂²	semidirect
30. C₂⁴×C₄×C₆₇	C₂²	semidirect
31. #559×C₆₇	C₂²	semidirect
32. #554×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
36. #551×C₆₇	C₂²	semidirect
37. #551×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
39. #546×C₆₇	C₂²	semidirect
40. #546×C₆₇	C₂²	semidirect
41. #546×C₆₇	C₂²	semidirect
42. D₄²×C₆₇	C₂²	semidirect
43. #542×C₆₇	C₂²	semidirect
44. #540×C₆₇	C₂²	semidirect
45. #539×C₆₇	C₂²	semidirect
46. #538×C₆₇	C₂²	semidirect
47. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
49. #529×C₆₇	C₂²	semidirect
50. #529×C₆₇	C₂²	semidirect
51. C₂×#126×C₆₇	C₂²	semidirect
52. C₂×#126×C₆₇	C₂²	semidirect
53. C₂×#126×C₆₇	C₂²	semidirect
54. C₂×#126×C₆₇	C₂²	semidirect
55. C₂×#126×C₆₇	C₂²	semidirect
56. C₂×#126×C₆₇	C₂²	semidirect
57. C₂×#125×C₆₇	C₂²	semidirect
58. C₂×#125×C₆₇	C₂²	semidirect
59. C₂×#125×C₆₇	C₂²	semidirect
60. C₂×#125×C₆₇	C₂²	semidirect
61. C₂×#124×C₆₇	C₂²	semidirect
62. C₂×#124×C₆₇	C₂²	semidirect
63. C₂×#124×C₆₇	C₂²	semidirect
64. C₂×#124×C₆₇	C₂²	semidirect
65. C₂×#124×C₆₇	C₂²	semidirect
66. #525×C₆₇	C₂²	semidirect
69. C₂×#123×C₆₇	C₂²	semidirect
70. C₂×#123×C₆₇	C₂²	semidirect
71. C₂×#123×C₆₇	C₂²	semidirect
72. C₂×#123×C₆₇	C₂²	semidirect
73. C₂×#123×C₆₇	C₂²	semidirect
74. C₂×#123×C₆₇	C₂²	semidirect
75. C₂×#123×C₆₇	C₂²	semidirect
76. C₂×#123×C₆₇	C₂²	semidirect
77. C₂×#123×C₆₇	C₂²	semidirect
78. C₂×#123×C₆₇	C₂²	semidirect
79. C₂×#123×C₆₇	C₂²	semidirect
80. C₂×#123×C₆₇	C₂²	semidirect
81. C₂×#123×C₆₇	C₂²	semidirect
82. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
83. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
87. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
94. C₂×#121×C₆₇	C₂²	semidirect
95. C₂×#121×C₆₇	C₂²	semidirect
96. C₂×#121×C₆₇	C₂²	semidirect
97. C₂×#121×C₆₇	C₂²	semidirect
98. C₂×#121×C₆₇	C₂²	semidirect
99. C₂×#121×C₆₇	C₂²	semidirect
100. C₂×#121×C₆₇	C₂²	semidirect
103. C₂×#120×C₆₇	C₂²	semidirect
104. C₂×#120×C₆₇	C₂²	semidirect
105. #520×C₆₇	C₂²	semidirect
106. #518×C₆₇	C₂²	semidirect
107. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
108. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
109. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
115. C₂×C₄×D₄×C₆₇	C₂²	semidirect
116. C₂×C₄×D₄×C₆₇	C₂²	semidirect
117. C₂×C₄×D₄×C₆₇	C₂²	semidirect
118. C₂×C₄×D₄×C₆₇	C₂²	semidirect
119. C₂×C₄×D₄×C₆₇	C₂²	semidirect
120. C₂×C₄×D₄×C₆₇	C₂²	semidirect
121. C₂×C₄×D₄×C₆₇	C₂²	semidirect
122. C₂×C₄×D₄×C₆₇	C₂²	semidirect
123. C₂×C₄×D₄×C₆₇	C₂²	semidirect
124. C₂×C₄×D₄×C₆₇	C₂²	semidirect
125. C₂×C₄×D₄×C₆₇	C₂²	semidirect
126. C₂×C₄×D₄×C₆₇	C₂²	semidirect
127. C₂×C₄×D₄×C₆₇	C₂²	semidirect
128. C₂×C₄×D₄×C₆₇	C₂²	semidirect
129. C₂×C₄×D₄×C₆₇	C₂²	semidirect
130. C₂×C₄×D₄×C₆₇	C₂²	semidirect
131. C₂×#117×C₆₇	C₂²	semidirect
132. C₂×#117×C₆₇	C₂²	semidirect
133. C₂×#117×C₆₇	C₂²	semidirect
134. C₂×#117×C₆₇	C₂²	semidirect
135. C₂×#117×C₆₇	C₂²	semidirect
136. C₂×#117×C₆₇	C₂²	semidirect
137. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
138. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
139. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
140. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
141. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
142. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
143. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
144. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
145. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
146. C₂²×C₄²×C₆₇	C₂²	semidirect
152. C₂×#41×C₆₇	C₂³	semidirect
194. C₂³×C₄×C₆₇	C₂³	semidirect
195. C₄⋊Q₈×C₆₇	C₂³	semidirect
197. #126×C₆₇	C₂³	semidirect
198. #126×C₆₇	C₂³	semidirect
199. #126×C₆₇	C₂³	semidirect
200. #126×C₆₇	C₂³	semidirect
201. #126×C₆₇	C₂³	semidirect
202. #126×C₆₇	C₂³	semidirect
203. #125×C₆₇	C₂³	semidirect
204. #125×C₆₇	C₂³	semidirect
205. #125×C₆₇	C₂³	semidirect
206. #125×C₆₇	C₂³	semidirect
207. #124×C₆₇	C₂³	semidirect
208. #124×C₆₇	C₂³	semidirect
209. #124×C₆₇	C₂³	semidirect
210. #124×C₆₇	C₂³	semidirect
211. #124×C₆₇	C₂³	semidirect
214. #123×C₆₇	C₂³	semidirect
215. #123×C₆₇	C₂³	semidirect
216. #123×C₆₇	C₂³	semidirect
217. #123×C₆₇	C₂³	semidirect
218. #123×C₆₇	C₂³	semidirect
219. #123×C₆₇	C₂³	semidirect
220. #123×C₆₇	C₂³	semidirect
221. #123×C₆₇	C₂³	semidirect
222. #123×C₆₇	C₂³	semidirect
223. #123×C₆₇	C₂³	semidirect
224. #123×C₆₇	C₂³	semidirect
225. #123×C₆₇	C₂³	semidirect
226. C₂²⋊Q₈×C₆₇	C₂³	semidirect
227. C₂²⋊Q₈×C₆₇	C₂³	semidirect
228. C₂²⋊Q₈×C₆₇	C₂³	semidirect
229. C₂²⋊Q₈×C₆₇	C₂³	semidirect
230. C₂²⋊Q₈×C₆₇	C₂³	semidirect
231. C₂²⋊Q₈×C₆₇	C₂³	semidirect
232. C₂²⋊Q₈×C₆₇	C₂³	semidirect
233. C₂²⋊Q₈×C₆₇	C₂³	semidirect
238. #121×C₆₇	C₂³	semidirect
239. #121×C₆₇	C₂³	semidirect
240. #121×C₆₇	C₂³	semidirect
241. #121×C₆₇	C₂³	semidirect
242. #121×C₆₇	C₂³	semidirect
243. #121×C₆₇	C₂³	semidirect
244. #121×C₆₇	C₂³	semidirect
247. #120×C₆₇	C₂³	semidirect
248. #120×C₆₇	C₂³	semidirect
249. C₄×Q₈×C₆₇	C₂³	semidirect
250. C₄×Q₈×C₆₇	C₂³	semidirect
251. C₄×Q₈×C₆₇	C₂³	semidirect
257. C₄×D₄×C₆₇	C₂³	semidirect
258. C₄×D₄×C₆₇	C₂³	semidirect
259. C₄×D₄×C₆₇	C₂³	semidirect
260. C₄×D₄×C₆₇	C₂³	semidirect
261. C₄×D₄×C₆₇	C₂³	semidirect
262. C₄×D₄×C₆₇	C₂³	semidirect
263. C₄×D₄×C₆₇	C₂³	semidirect
264. C₄×D₄×C₆₇	C₂³	semidirect
265. C₄×D₄×C₆₇	C₂³	semidirect
266. C₄×D₄×C₆₇	C₂³	semidirect
267. C₄×D₄×C₆₇	C₂³	semidirect
268. C₄×D₄×C₆₇	C₂³	semidirect
269. C₄×D₄×C₆₇	C₂³	semidirect
270. C₄×D₄×C₆₇	C₂³	semidirect
271. C₄×D₄×C₆₇	C₂³	semidirect
272. #117×C₆₇	C₂³	semidirect
273. #117×C₆₇	C₂³	semidirect
274. #117×C₆₇	C₂³	semidirect
275. #117×C₆₇	C₂³	semidirect
276. #117×C₆₇	C₂³	semidirect
277. #117×C₆₇	C₂³	semidirect
303. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
304. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
305. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
306. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
336. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
337. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
338. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
339. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
340. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
350. C₂×C₄²×C₆₇	C₂³	semidirect
390. C₂×D₄×C₆₇	#41	semidirect
569. D₄×C₆₇	C₂×#41	semidirect
667. C₂×#3513	C₆₇	direct (N × H)
674. C₂×C₆₇	#3513	direct (N × H)
678. #3513	C₂×C₆₇	direct (N × H)
679. C₂×#559	C₂×C₆₇	semidirect
680. C₂×#554	C₂×C₆₇	semidirect
681. C₂×#553	C₂×C₆₇	semidirect
682. C₂×#553	C₂×C₆₇	semidirect
683. C₂×#552	C₂×C₆₇	semidirect
684. C₂×#551	C₂×C₆₇	semidirect
685. C₂×#551	C₂×C₆₇	semidirect
686. C₂×#547	C₂×C₆₇	semidirect
687. C₂×#546	C₂×C₆₇	semidirect
688. C₂×#546	C₂×C₆₇	semidirect
689. C₂×#546	C₂×C₆₇	semidirect
690. C₂×D₄²	C₂×C₆₇	semidirect
691. C₂×#542	C₂×C₆₇	semidirect
692. C₂×#540	C₂×C₆₇	semidirect
693. C₂×#539	C₂×C₆₇	semidirect
694. C₂×#538	C₂×C₆₇	semidirect
695. C₂×#529	C₂×C₆₇	semidirect
696. C₂×#529	C₂×C₆₇	semidirect
697. C₂×#525	C₂×C₆₇	semidirect
698. C₂²×#123	C₂×C₆₇	semidirect
699. C₂×#520	C₂×C₆₇	semidirect
700. C₂×#518	C₂×C₆₇	semidirect
701. C₂²×C₄×D₄	C₂×C₆₇	semidirect
702. C₆₇	C₂×#3513	direct (N × H)
704. C₂²×#41	C₂²×C₆₇	semidirect
708. C₂⁴×C₄	C₂²×C₆₇	semidirect
709. #559	C₂²×C₆₇	semidirect
710. #554	C₂²×C₆₇	semidirect
711. #553	C₂²×C₆₇	semidirect
712. #553	C₂²×C₆₇	semidirect
713. #552	C₂²×C₆₇	semidirect
714. #551	C₂²×C₆₇	semidirect
715. #551	C₂²×C₆₇	semidirect
716. #547	C₂²×C₆₇	semidirect
717. #546	C₂²×C₆₇	semidirect
718. #546	C₂²×C₆₇	semidirect
719. #546	C₂²×C₆₇	semidirect
720. D₄²	C₂²×C₆₇	semidirect
721. #542	C₂²×C₆₇	semidirect
722. #540	C₂²×C₆₇	semidirect
723. #539	C₂²×C₆₇	semidirect
724. #538	C₂²×C₆₇	semidirect
725. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
727. #529	C₂²×C₆₇	semidirect
728. #529	C₂²×C₆₇	semidirect
729. C₂×#126	C₂²×C₆₇	semidirect
730. C₂×#126	C₂²×C₆₇	semidirect
731. C₂×#126	C₂²×C₆₇	semidirect
732. C₂×#126	C₂²×C₆₇	semidirect
733. C₂×#126	C₂²×C₆₇	semidirect
734. C₂×#126	C₂²×C₆₇	semidirect
735. C₂×#125	C₂²×C₆₇	semidirect
736. C₂×#125	C₂²×C₆₇	semidirect
737. C₂×#125	C₂²×C₆₇	semidirect
738. C₂×#125	C₂²×C₆₇	semidirect
739. C₂×#124	C₂²×C₆₇	semidirect
740. C₂×#124	C₂²×C₆₇	semidirect
741. C₂×#124	C₂²×C₆₇	semidirect
742. C₂×#124	C₂²×C₆₇	semidirect
743. C₂×#124	C₂²×C₆₇	semidirect
744. #525	C₂²×C₆₇	semidirect
747. C₂×#123	C₂²×C₆₇	semidirect
748. C₂×#123	C₂²×C₆₇	semidirect
749. C₂×#123	C₂²×C₆₇	semidirect
750. C₂×#123	C₂²×C₆₇	semidirect
751. C₂×#123	C₂²×C₆₇	semidirect
752. C₂×#123	C₂²×C₆₇	semidirect
753. C₂×#123	C₂²×C₆₇	semidirect
754. C₂×#123	C₂²×C₆₇	semidirect
755. C₂×#123	C₂²×C₆₇	semidirect
756. C₂×#123	C₂²×C₆₇	semidirect
757. C₂×#123	C₂²×C₆₇	semidirect
758. C₂×#123	C₂²×C₆₇	semidirect
759. C₂×#123	C₂²×C₆₇	semidirect
760. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
761. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
762. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
763. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
764. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
765. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
766. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
767. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
772. C₂×#121	C₂²×C₆₇	semidirect
773. C₂×#121	C₂²×C₆₇	semidirect
774. C₂×#121	C₂²×C₆₇	semidirect
775. C₂×#121	C₂²×C₆₇	semidirect
776. C₂×#121	C₂²×C₆₇	semidirect
777. C₂×#121	C₂²×C₆₇	semidirect
778. C₂×#121	C₂²×C₆₇	semidirect
781. C₂×#120	C₂²×C₆₇	semidirect
782. C₂×#120	C₂²×C₆₇	semidirect
783. #520	C₂²×C₆₇	semidirect
784. #518	C₂²×C₆₇	semidirect
785. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
786. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
787. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
793. C₂×C₄×D₄	C₂²×C₆₇	semidirect
794. C₂×C₄×D₄	C₂²×C₆₇	semidirect
795. C₂×C₄×D₄	C₂²×C₆₇	semidirect
796. C₂×C₄×D₄	C₂²×C₆₇	semidirect
797. C₂×C₄×D₄	C₂²×C₆₇	semidirect
798. C₂×C₄×D₄	C₂²×C₆₇	semidirect
799. C₂×C₄×D₄	C₂²×C₆₇	semidirect
800. C₂×C₄×D₄	C₂²×C₆₇	semidirect
801. C₂×C₄×D₄	C₂²×C₆₇	semidirect
802. C₂×C₄×D₄	C₂²×C₆₇	semidirect
803. C₂×C₄×D₄	C₂²×C₆₇	semidirect
804. C₂×C₄×D₄	C₂²×C₆₇	semidirect
805. C₂×C₄×D₄	C₂²×C₆₇	semidirect
806. C₂×C₄×D₄	C₂²×C₆₇	semidirect
807. C₂×C₄×D₄	C₂²×C₆₇	semidirect
808. C₂×C₄×D₄	C₂²×C₆₇	semidirect
809. C₂×#117	C₂²×C₆₇	semidirect
810. C₂×#117	C₂²×C₆₇	semidirect
811. C₂×#117	C₂²×C₆₇	semidirect
812. C₂×#117	C₂²×C₆₇	semidirect
813. C₂×#117	C₂²×C₆₇	semidirect
814. C₂×#117	C₂²×C₆₇	semidirect
815. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
816. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
817. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
818. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
819. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
820. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
821. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
822. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
823. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
824. C₂²×C₄²	C₂²×C₆₇	semidirect
830. C₂×#41	C₂³×C₆₇	semidirect
872. C₂³×C₄	C₂³×C₆₇	semidirect
873. C₄⋊Q₈	C₂³×C₆₇	semidirect
875. #126	C₂³×C₆₇	semidirect
876. #126	C₂³×C₆₇	semidirect
877. #126	C₂³×C₆₇	semidirect
878. #126	C₂³×C₆₇	semidirect
879. #126	C₂³×C₆₇	semidirect
880. #126	C₂³×C₆₇	semidirect
881. #125	C₂³×C₆₇	semidirect
882. #125	C₂³×C₆₇	semidirect
883. #125	C₂³×C₆₇	semidirect
884. #125	C₂³×C₆₇	semidirect
885. #124	C₂³×C₆₇	semidirect
886. #124	C₂³×C₆₇	semidirect
887. #124	C₂³×C₆₇	semidirect
888. #124	C₂³×C₆₇	semidirect
889. #124	C₂³×C₆₇	semidirect
892. #123	C₂³×C₆₇	semidirect
893. #123	C₂³×C₆₇	semidirect
894. #123	C₂³×C₆₇	semidirect
895. #123	C₂³×C₆₇	semidirect
896. #123	C₂³×C₆₇	semidirect
897. #123	C₂³×C₆₇	semidirect
898. #123	C₂³×C₆₇	semidirect
899. #123	C₂³×C₆₇	semidirect
900. #123	C₂³×C₆₇	semidirect
901. #123	C₂³×C₆₇	semidirect
902. #123	C₂³×C₆₇	semidirect
903. #123	C₂³×C₆₇	semidirect
904. C₂²⋊Q₈	C₂³×C₆₇	semidirect
905. C₂²⋊Q₈	C₂³×C₆₇	semidirect
906. C₂²⋊Q₈	C₂³×C₆₇	semidirect
907. C₂²⋊Q₈	C₂³×C₆₇	semidirect
908. C₂²⋊Q₈	C₂³×C₆₇	semidirect
909. C₂²⋊Q₈	C₂³×C₆₇	semidirect
910. C₂²⋊Q₈	C₂³×C₆₇	semidirect
911. C₂²⋊Q₈	C₂³×C₆₇	semidirect
916. #121	C₂³×C₆₇	semidirect
917. #121	C₂³×C₆₇	semidirect
918. #121	C₂³×C₆₇	semidirect
919. #121	C₂³×C₆₇	semidirect
920. #121	C₂³×C₆₇	semidirect
921. #121	C₂³×C₆₇	semidirect
922. #121	C₂³×C₆₇	semidirect
925. #120	C₂³×C₆₇	semidirect
926. #120	C₂³×C₆₇	semidirect
927. C₄×Q₈	C₂³×C₆₇	semidirect
928. C₄×Q₈	C₂³×C₆₇	semidirect
929. C₄×Q₈	C₂³×C₆₇	semidirect
935. C₄×D₄	C₂³×C₆₇	semidirect
936. C₄×D₄	C₂³×C₆₇	semidirect
937. C₄×D₄	C₂³×C₆₇	semidirect
938. C₄×D₄	C₂³×C₆₇	semidirect
939. C₄×D₄	C₂³×C₆₇	semidirect
940. C₄×D₄	C₂³×C₆₇	semidirect
941. C₄×D₄	C₂³×C₆₇	semidirect
942. C₄×D₄	C₂³×C₆₇	semidirect
943. C₄×D₄	C₂³×C₆₇	semidirect
944. C₄×D₄	C₂³×C₆₇	semidirect
945. C₄×D₄	C₂³×C₆₇	semidirect
946. C₄×D₄	C₂³×C₆₇	semidirect
947. C₄×D₄	C₂³×C₆₇	semidirect
948. C₄×D₄	C₂³×C₆₇	semidirect
949. C₄×D₄	C₂³×C₆₇	semidirect
950. #117	C₂³×C₆₇	semidirect
951. #117	C₂³×C₆₇	semidirect
952. #117	C₂³×C₆₇	semidirect
953. #117	C₂³×C₆₇	semidirect
954. #117	C₂³×C₆₇	semidirect
955. #117	C₂³×C₆₇	semidirect
981. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
982. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
983. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
984. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
1014. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
1015. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
1016. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
1017. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
1018. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
1028. C₂×C₄²	C₂³×C₆₇	semidirect
1068. C₂×D₄	#41×C₆₇	semidirect
1247. D₄	C₂×#41×C₆₇	semidirect
1351. C₂	C₆₇×#3513	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3513	2
C₂×#559×C₆₇	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#552×C₆₇	2
C₂×#551×C₆₇	2
C₂×#547×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#542×C₆₇	2
C₂×#540×C₆₇	2
C₂×#539×C₆₇	2
C₂×#538×C₆₇	2
C₂×#529×C₆₇	2
C₂×#525×C₆₇	2
C₂²×#123×C₆₇	2
C₂×#520×C₆₇	2
C₂×#518×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂×#3513	67

Subgroups — C2×C67×#3513 #30742021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3513 #30742021