Subgroups — C₂×C₆₇×#3519 #30742022

Order 17152.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	32	yes	maximal, direct product factor
2	C₂×#555×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	2	yes	maximal, complemented
5	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#546×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄²×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#540×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂²×#121×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#518×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
23	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
24	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
25	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
26	#555×C₆₇	C₂²	1	16	yes	complemented
27	#554×C₆₇	C₂²	1	16	yes	complemented
28	#553×C₆₇	C₂²	1	32	yes	complemented
29	#553×C₆₇	C₂²	1	32	yes	complemented
30	#550×C₆₇	C₂²	1	16	yes	complemented
31	#546×C₆₇	C₂²	1	64	yes	complemented
32	#546×C₆₇	C₂²	1	32	yes	complemented
33	D₄²×C₆₇	C₂²	1	16	yes	complemented
34	D₄²×C₆₇	C₂²	1	32	yes	complemented
35	#540×C₆₇	C₂²	1	32	yes	complemented
36	#538×C₆₇	C₂²	1	64	yes	complemented
37	#532×C₆₇	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#127×C₆₇	C₂²	1	2	yes	complemented
41	#529×C₆₇	C₂²	1	16	yes	complemented
42	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
44	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
48	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
49	#525×C₆₇	C₂²	1	32	yes	complemented
50	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
51	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
53	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
54	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
57	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
59	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
60	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
61	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
62	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
63	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
64	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
65	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
66	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
67	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
68	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
69	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
70	C₂×#121×C₆₇	C₂²	1	32	yes	complemented
71	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
72	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
73	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
74	#518×C₆₇	C₂²	1	32	yes	complemented
75	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
86	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄×C₆₇	C₂²	1	16	yes	complemented
92	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
93	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
94	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
97	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
99	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₆₇	C₂³	1	2	yes	—
102	C₂⁵×C₆₇	C₂³	1	4	yes	—
103	C₂×#41×C₆₇	—	4	8	no	—
104	C₂×#41×C₆₇	—	4	8	no	—
105	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
106	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	—	2	8	no	—
110	C₂²×D₄×C₆₇	—	2	16	no	—
111	C₂²×D₄×C₆₇	—	4	8	no	—
112	C₂²×D₄×C₆₇	—	4	16	no	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
130	C₂²×D₄×C₆₇	C₂³	1	32	yes	complemented
131	C₂³×C₄×C₆₇	—	4	8	no	—
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	16	yes	complemented
145	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
146	#127×C₆₇	C₂³	1	8	yes	complemented
147	#127×C₆₇	C₂³	1	16	yes	complemented
148	#126×C₆₇	C₂³	1	16	yes	complemented
149	#126×C₆₇	C₂³	1	32	yes	complemented
150	#125×C₆₇	C₂³	1	8	yes	complemented
151	#125×C₆₇	C₂³	1	16	yes	complemented
152	#124×C₆₇	C₂³	1	8	yes	complemented
153	#124×C₆₇	C₂³	1	16	yes	complemented
154	#124×C₆₇	C₂³	1	32	yes	complemented
155	#123×C₆₇	C₂³	1	32	yes	complemented
156	#123×C₆₇	C₂³	1	16	yes	complemented
157	#123×C₆₇	C₂³	1	32	yes	complemented
158	#123×C₆₇	C₂³	1	32	yes	complemented
159	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
160	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
161	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
162	#121×C₆₇	C₂³	1	8	yes	—
163	#121×C₆₇	C₂³	1	16	yes	complemented
164	#121×C₆₇	C₂³	1	32	yes	complemented
165	#121×C₆₇	C₂³	1	32	yes	complemented
166	#121×C₆₇	C₂³	1	16	yes	complemented
167	#121×C₆₇	C₂³	1	16	yes	complemented
168	#121×C₆₇	C₂³	1	16	yes	complemented
169	#121×C₆₇	C₂³	1	16	yes	complemented
170	#121×C₆₇	C₂³	1	32	yes	complemented
171	#121×C₆₇	C₂³	1	32	yes	complemented
172	#121×C₆₇	C₂³	1	16	yes	complemented
173	#121×C₆₇	C₂³	1	16	yes	complemented
174	#121×C₆₇	C₂³	1	32	yes	complemented
175	#120×C₆₇	C₂³	1	32	yes	complemented
176	#120×C₆₇	C₂³	1	32	yes	complemented
177	#120×C₆₇	C₂³	1	32	yes	complemented
178	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
179	C₄×D₄×C₆₇	C₂³	1	8	yes	—
180	C₄×D₄×C₆₇	C₂³	1	8	yes	—
181	C₄×D₄×C₆₇	C₂³	1	16	yes	—
182	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
183	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
184	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
185	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
186	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
187	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
188	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
189	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
190	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
191	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
192	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
193	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
194	#117×C₆₇	C₂³	1	16	yes	complemented
195	#117×C₆₇	C₂³	1	16	yes	complemented
196	#117×C₆₇	C₂³	1	16	yes	complemented
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
211	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
236	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
238	C₂⁴×C₆₇	—	2	8	no	—
239	C₂⁴×C₆₇	—	2	8	no	—
240	C₂⁴×C₆₇	—	2	16	no	—
241	C₂⁴×C₆₇	—	4	4	no	—
242	C₂⁴×C₆₇	—	4	8	no	—
243	C₂⁴×C₆₇	—	4	8	no	—
244	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
245	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
246	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
247	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
248	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
249	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₆₇	C₂⁴	1	16	yes	—
251	#41×C₆₇	—	4	32	no	—
252	#41×C₆₇	—	4	32	no	—
253	C₂×Q₈×C₆₇	—	2	4	no	—
254	C₂×Q₈×C₆₇	—	4	4	no	—
255	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
256	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
257	C₂×D₄×C₆₇	—	2	8	no	—
258	C₂×D₄×C₆₇	—	2	16	no	—
259	C₂×D₄×C₆₇	—	2	8	no	—
260	C₂×D₄×C₆₇	—	2	16	no	—
261	C₂×D₄×C₆₇	—	2	32	no	—
262	C₂×D₄×C₆₇	—	2	64	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	8	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	2	8	no	—
267	C₂×D₄×C₆₇	—	4	32	no	—
268	C₂×D₄×C₆₇	—	4	8	no	—
269	C₂×D₄×C₆₇	—	4	8	no	—
270	C₂×D₄×C₆₇	—	4	8	no	—
271	C₂×D₄×C₆₇	—	4	4	no	—
272	C₂×D₄×C₆₇	—	4	8	no	—
273	C₂×D₄×C₆₇	—	4	64	no	—
274	C₂×D₄×C₆₇	#41	1	8	yes	complemented
275	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
276	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
277	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
278	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
279	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
280	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
281	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
282	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
283	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
284	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
285	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
286	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
287	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
288	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₆₇	—	2	4	no	—
290	C₂²×C₄×C₆₇	—	2	4	no	—
291	C₂²×C₄×C₆₇	—	2	8	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	8	no	—
294	C₂²×C₄×C₆₇	—	2	8	no	—
295	C₂²×C₄×C₆₇	—	4	32	no	—
296	C₂²×C₄×C₆₇	—	4	4	no	—
297	C₂²×C₄×C₆₇	—	4	4	no	—
298	C₂²×C₄×C₆₇	—	4	4	no	—
299	C₂²×C₄×C₆₇	—	4	8	no	—
300	C₂²×C₄×C₆₇	—	4	8	no	—
301	C₂²×C₄×C₆₇	—	4	8	no	—
302	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
323	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
328	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
332	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
338	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
341	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
348	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
349	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
350	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
354	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
355	C₄²×C₆₇	C₂⁴	1	4	yes	—
356	C₄²×C₆₇	C₂⁴	1	4	yes	—
357	C₄²×C₆₇	C₂⁴	1	4	yes	—
358	C₄²×C₆₇	C₂⁴	1	4	yes	—
359	C₄²×C₆₇	C₂⁴	1	16	yes	—
360	C₄²×C₆₇	C₂⁴	1	8	yes	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	4	no	—
364	C₂³×C₆₇	—	2	4	no	—
365	C₂³×C₆₇	—	2	4	no	—
366	C₂³×C₆₇	—	2	16	no	—
367	C₂³×C₆₇	—	2	4	no	—
368	C₂³×C₆₇	—	2	8	no	—
369	C₂³×C₆₇	—	2	4	no	—
370	C₂³×C₆₇	—	2	8	no	—
371	C₂³×C₆₇	—	2	8	no	—
372	C₂³×C₆₇	—	2	4	no	—
373	C₂³×C₆₇	—	2	4	no	—
374	C₂³×C₆₇	—	2	16	no	—
375	C₂³×C₆₇	—	2	4	no	—
376	C₂³×C₆₇	—	2	32	no	—
377	C₂³×C₆₇	—	4	8	no	—
378	C₂³×C₆₇	—	4	16	no	—
379	C₂³×C₆₇	—	4	16	no	—
380	C₂³×C₆₇	—	4	32	no	—
381	C₂³×C₆₇	—	8	32	no	—
382	C₂³×C₆₇	C₂×#41	1	8	yes	—
383	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
384	C₂³×C₆₇	C₂⁵	1	4	yes	—
385	C₂³×C₆₇	C₂⁵	1	4	yes	—
386	C₂³×C₆₇	C₂⁵	1	8	yes	—
387	C₂³×C₆₇	C₂⁵	1	4	yes	—
388	C₂³×C₆₇	C₂⁵	1	2	yes	—
389	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
390	Q₈×C₆₇	—	2	8	no	—
391	Q₈×C₆₇	—	4	8	no	—
392	D₄×C₆₇	—	2	16	no	—
393	D₄×C₆₇	—	2	32	no	—
394	D₄×C₆₇	—	2	16	no	—
395	D₄×C₆₇	—	2	32	no	—
396	D₄×C₆₇	—	2	8	no	—
397	D₄×C₆₇	—	2	16	no	—
398	D₄×C₆₇	—	2	8	no	—
399	D₄×C₆₇	—	2	16	no	—
400	D₄×C₆₇	—	4	16	no	—
401	D₄×C₆₇	—	4	16	no	—
402	D₄×C₆₇	—	4	16	no	—
403	D₄×C₆₇	—	4	8	no	—
404	D₄×C₆₇	—	4	16	no	—
405	D₄×C₆₇	C₂×#41	1	16	yes	complemented
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	4	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	4	no	—
411	C₂×C₄×C₆₇	—	2	4	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	8	no	—
414	C₂×C₄×C₆₇	—	2	4	no	—
415	C₂×C₄×C₆₇	—	2	8	no	—
416	C₂×C₄×C₆₇	—	2	4	no	—
417	C₂×C₄×C₆₇	—	2	8	no	—
418	C₂×C₄×C₆₇	—	2	16	no	—
419	C₂×C₄×C₆₇	—	2	8	no	—
420	C₂×C₄×C₆₇	—	2	16	no	—
421	C₂×C₄×C₆₇	—	2	16	no	—
422	C₂×C₄×C₆₇	—	4	8	no	—
423	C₂×C₄×C₆₇	—	4	8	no	—
424	C₂×C₄×C₆₇	—	4	8	no	—
425	C₂×C₄×C₆₇	—	4	16	no	—
426	C₂×C₄×C₆₇	—	4	16	no	—
427	C₂×C₄×C₆₇	—	4	16	no	—
428	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
429	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
430	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
431	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
432	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
433	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
434	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
435	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
436	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
437	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
438	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
439	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
440	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
441	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	4	no	—
445	C₂²×C₆₇	—	2	4	no	—
446	C₂²×C₆₇	—	2	8	no	—
447	C₂²×C₆₇	—	2	16	no	—
448	C₂²×C₆₇	—	2	4	no	—
449	C₂²×C₆₇	—	2	4	no	—
450	C₂²×C₆₇	—	2	8	no	—
451	C₂²×C₆₇	—	2	4	no	—
452	C₂²×C₆₇	—	2	8	no	—
453	C₂²×C₆₇	—	2	8	no	—
454	C₂²×C₆₇	—	2	4	no	—
455	C₂²×C₆₇	—	2	4	no	—
456	C₂²×C₆₇	—	2	4	no	—
457	C₂²×C₆₇	—	4	32	no	—
458	C₂²×C₆₇	—	4	8	no	—
459	C₂²×C₆₇	—	4	16	no	—
460	C₂²×C₆₇	—	4	8	no	—
461	C₂²×C₆₇	—	8	32	no	—
462	C₂²×C₆₇	C₂²×#41	1	8	yes	—
463	C₂²×C₆₇	C₂²×#41	1	2	yes	—
464	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
465	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
466	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
467	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
468	C₄×C₆₇	—	2	2	no	—
469	C₄×C₆₇	—	2	4	no	—
470	C₄×C₆₇	—	2	2	no	—
471	C₄×C₆₇	—	2	2	no	—
472	C₄×C₆₇	—	2	4	no	—
473	C₄×C₆₇	—	2	4	no	—
474	C₄×C₆₇	—	2	2	no	—
475	C₄×C₆₇	—	2	4	no	—
476	C₄×C₆₇	—	2	8	no	—
477	C₄×C₆₇	—	2	4	no	—
478	C₄×C₆₇	C₂²×#41	1	4	yes	—
479	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
480	C₂×#3519	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
481	C₂×C₆₇	—	2	4	no	—
482	C₂×C₆₇	—	2	8	no	—
483	C₂×C₆₇	—	4	4	no	—
484	C₂×C₆₇	—	4	8	no	—
485	C₂×C₆₇	—	4	4	no	—
486	C₂×C₆₇	#3519	1	4	yes	direct product factor
487	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
488	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
489	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
490	#3519	C₂×C₆₇	1	32	yes	direct product factor
491	C₂×#555	C₂×C₆₇	1	1	yes	characteristic, complemented
492	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
493	C₂×#553	C₂×C₆₇	1	2	yes	complemented
494	C₂×#553	C₂×C₆₇	1	2	yes	complemented
495	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
496	C₂×#546	C₂×C₆₇	1	4	yes	complemented
497	C₂×#546	C₂×C₆₇	1	2	yes	complemented
498	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
499	C₂×D₄²	C₂×C₆₇	1	2	yes	complemented
500	C₂×#540	C₂×C₆₇	1	2	yes	complemented
501	C₂×#538	C₂×C₆₇	1	4	yes	complemented
502	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
503	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
504	C₂×#525	C₂×C₆₇	1	2	yes	complemented
505	C₂²×#121	C₂×C₆₇	1	2	yes	complemented
506	C₂×#518	C₂×C₆₇	1	2	yes	complemented
507	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
508	C₆₇	C₂×#3519	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
510	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
511	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
512	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
513	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
514	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
515	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	complemented
516	#555	C₂²×C₆₇	1	16	yes	complemented
517	#554	C₂²×C₆₇	1	16	yes	complemented
518	#553	C₂²×C₆₇	1	32	yes	complemented
519	#553	C₂²×C₆₇	1	32	yes	complemented
520	#550	C₂²×C₆₇	1	16	yes	complemented
521	#546	C₂²×C₆₇	1	64	yes	complemented
522	#546	C₂²×C₆₇	1	32	yes	complemented
523	D₄²	C₂²×C₆₇	1	16	yes	complemented
524	D₄²	C₂²×C₆₇	1	32	yes	complemented
525	#540	C₂²×C₆₇	1	32	yes	complemented
526	#538	C₂²×C₆₇	1	64	yes	complemented
527	#532	C₂²×C₆₇	1	16	yes	complemented
528	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
529	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
530	C₂×#127	C₂²×C₆₇	1	2	yes	complemented
531	#529	C₂²×C₆₇	1	16	yes	complemented
532	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
533	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
534	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
535	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
536	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
537	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
538	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
539	#525	C₂²×C₆₇	1	32	yes	complemented
540	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
541	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
542	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
543	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
544	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
545	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
546	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
547	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
549	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
550	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
551	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
552	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
553	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
554	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
555	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
556	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
557	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
558	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
559	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
560	C₂×#121	C₂²×C₆₇	1	32	yes	complemented
561	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
562	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
563	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
564	#518	C₂²×C₆₇	1	32	yes	complemented
565	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
566	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
569	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
570	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
572	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
573	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
574	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
575	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
576	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
577	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
578	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
579	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
581	C₂×C₄×D₄	C₂²×C₆₇	1	16	yes	complemented
582	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
583	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
584	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
585	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
587	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
588	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
589	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
590	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
591	C₂⁵	C₂³×C₆₇	1	2	yes	—
592	C₂⁵	C₂³×C₆₇	1	4	yes	—
593	C₂×#41	—	4	8	no	—
594	C₂×#41	—	4	8	no	—
595	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
596	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
597	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
598	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
599	C₂²×D₄	—	2	8	no	—
600	C₂²×D₄	—	2	16	no	—
601	C₂²×D₄	—	4	8	no	—
602	C₂²×D₄	—	4	16	no	—
603	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
604	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
605	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
607	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
608	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
609	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
610	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
612	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
613	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
614	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
615	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
616	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
617	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
618	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
620	C₂²×D₄	C₂³×C₆₇	1	32	yes	complemented
621	C₂³×C₄	—	4	8	no	—
622	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
624	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
626	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
627	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
629	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
630	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
631	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
632	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
633	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
634	C₂³×C₄	C₂³×C₆₇	1	16	yes	complemented
635	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
636	#127	C₂³×C₆₇	1	8	yes	complemented
637	#127	C₂³×C₆₇	1	16	yes	complemented
638	#126	C₂³×C₆₇	1	16	yes	complemented
639	#126	C₂³×C₆₇	1	32	yes	complemented
640	#125	C₂³×C₆₇	1	8	yes	complemented
641	#125	C₂³×C₆₇	1	16	yes	complemented
642	#124	C₂³×C₆₇	1	8	yes	complemented
643	#124	C₂³×C₆₇	1	16	yes	complemented
644	#124	C₂³×C₆₇	1	32	yes	complemented
645	#123	C₂³×C₆₇	1	32	yes	complemented
646	#123	C₂³×C₆₇	1	16	yes	complemented
647	#123	C₂³×C₆₇	1	32	yes	complemented
648	#123	C₂³×C₆₇	1	32	yes	complemented
649	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
650	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
651	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
652	#121	C₂³×C₆₇	1	8	yes	—
653	#121	C₂³×C₆₇	1	16	yes	complemented
654	#121	C₂³×C₆₇	1	32	yes	complemented
655	#121	C₂³×C₆₇	1	32	yes	complemented
656	#121	C₂³×C₆₇	1	16	yes	complemented
657	#121	C₂³×C₆₇	1	16	yes	complemented
658	#121	C₂³×C₆₇	1	16	yes	complemented
659	#121	C₂³×C₆₇	1	16	yes	complemented
660	#121	C₂³×C₆₇	1	32	yes	complemented
661	#121	C₂³×C₆₇	1	32	yes	complemented
662	#121	C₂³×C₆₇	1	16	yes	complemented
663	#121	C₂³×C₆₇	1	16	yes	complemented
664	#121	C₂³×C₆₇	1	32	yes	complemented
665	#120	C₂³×C₆₇	1	32	yes	complemented
666	#120	C₂³×C₆₇	1	32	yes	complemented
667	#120	C₂³×C₆₇	1	32	yes	complemented
668	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
669	C₄×D₄	C₂³×C₆₇	1	8	yes	—
670	C₄×D₄	C₂³×C₆₇	1	8	yes	—
671	C₄×D₄	C₂³×C₆₇	1	16	yes	—
672	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
673	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
674	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
675	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
676	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
677	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
678	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
679	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
680	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
681	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
682	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
683	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
684	#117	C₂³×C₆₇	1	16	yes	complemented
685	#117	C₂³×C₆₇	1	16	yes	complemented
686	#117	C₂³×C₆₇	1	16	yes	complemented
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
721	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
723	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
724	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
728	C₂⁴	—	2	8	no	—
729	C₂⁴	—	2	8	no	—
730	C₂⁴	—	2	16	no	—
731	C₂⁴	—	4	4	no	—
732	C₂⁴	—	4	8	no	—
733	C₂⁴	—	4	8	no	—
734	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
735	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
736	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
737	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
738	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
739	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₂⁴	C₂⁴×C₆₇	1	16	yes	—
741	#41	—	4	32	no	—
742	#41	—	4	32	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	4	no	—
745	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
746	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	16	no	—
749	C₂×D₄	—	2	8	no	—
750	C₂×D₄	—	2	16	no	—
751	C₂×D₄	—	2	32	no	—
752	C₂×D₄	—	2	64	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	8	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	8	no	—
757	C₂×D₄	—	4	32	no	—
758	C₂×D₄	—	4	8	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	4	8	no	—
761	C₂×D₄	—	4	4	no	—
762	C₂×D₄	—	4	8	no	—
763	C₂×D₄	—	4	64	no	—
764	C₂×D₄	#41×C₆₇	1	8	yes	complemented
765	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
766	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
767	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
768	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
769	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
770	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
771	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
772	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
773	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
774	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
775	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
776	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
777	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
778	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	8	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	8	no	—
784	C₂²×C₄	—	2	8	no	—
785	C₂²×C₄	—	4	32	no	—
786	C₂²×C₄	—	4	4	no	—
787	C₂²×C₄	—	4	4	no	—
788	C₂²×C₄	—	4	4	no	—
789	C₂²×C₄	—	4	8	no	—
790	C₂²×C₄	—	4	8	no	—
791	C₂²×C₄	—	4	8	no	—
792	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
799	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
802	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
803	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
804	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
806	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
807	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
809	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
810	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
811	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
812	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
813	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
814	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
817	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
818	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
819	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
820	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
821	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
822	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
823	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
824	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
825	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
826	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
827	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
828	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
829	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
830	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
831	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
832	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
834	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
835	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
836	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
837	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
838	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
839	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
840	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
841	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
842	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
843	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
844	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
845	C₄²	C₂⁴×C₆₇	1	4	yes	—
846	C₄²	C₂⁴×C₆₇	1	4	yes	—
847	C₄²	C₂⁴×C₆₇	1	4	yes	—
848	C₄²	C₂⁴×C₆₇	1	4	yes	—
849	C₄²	C₂⁴×C₆₇	1	16	yes	—
850	C₄²	C₂⁴×C₆₇	1	8	yes	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	4	no	—
856	C₂³	—	2	16	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	8	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	8	no	—
861	C₂³	—	2	8	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	2	16	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	2	32	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	16	no	—
869	C₂³	—	4	16	no	—
870	C₂³	—	4	32	no	—
871	C₂³	—	8	32	no	—
872	C₂³	C₂×#41×C₆₇	1	8	yes	—
873	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
874	C₂³	C₂⁵×C₆₇	1	4	yes	—
875	C₂³	C₂⁵×C₆₇	1	4	yes	—
876	C₂³	C₂⁵×C₆₇	1	8	yes	—
877	C₂³	C₂⁵×C₆₇	1	4	yes	—
878	C₂³	C₂⁵×C₆₇	1	2	yes	—
879	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	4	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	32	no	—
884	D₄	—	2	16	no	—
885	D₄	—	2	32	no	—
886	D₄	—	2	8	no	—
887	D₄	—	2	16	no	—
888	D₄	—	2	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	4	16	no	—
891	D₄	—	4	16	no	—
892	D₄	—	4	16	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	16	no	—
895	D₄	C₂×#41×C₆₇	1	16	yes	complemented
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	4	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	4	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	16	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	16	no	—
911	C₂×C₄	—	2	16	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	16	no	—
916	C₂×C₄	—	4	16	no	—
917	C₂×C₄	—	4	16	no	—
918	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
919	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
920	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
921	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
922	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
923	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
924	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
925	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
926	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
927	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
928	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
929	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
930	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
931	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	8	no	—
937	C₂²	—	2	16	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	8	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	4	32	no	—
948	C₂²	—	4	8	no	—
949	C₂²	—	4	8	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	8	32	no	—
952	C₂²	C₂²×#41×C₆₇	1	8	yes	—
953	C₂²	C₂²×#41×C₆₇	1	2	yes	—
954	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
955	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
956	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
957	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	4	no	—
966	C₄	—	2	8	no	—
967	C₄	—	2	4	no	—
968	C₄	C₂²×#41×C₆₇	1	4	yes	—
969	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	2	8	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	—	4	8	no	—
975	C₂	C₆₇×#3519	1	4	yes	direct product factor
976	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
977	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
978	C₂	C₂²×H(5,𝔽₂)×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×#3519	C₂	direct (N × H)
2. C₂×#555×C₆₇	C₂	semidirect
3. C₂×#554×C₆₇	C₂	semidirect
4. C₂×#553×C₆₇	C₂	semidirect
5. C₂×#553×C₆₇	C₂	semidirect
6. C₂×#550×C₆₇	C₂	semidirect
7. C₂×#546×C₆₇	C₂	semidirect
8. C₂×#546×C₆₇	C₂	semidirect
9. C₂×D₄²×C₆₇	C₂	semidirect
10. C₂×D₄²×C₆₇	C₂	semidirect
11. C₂×#540×C₆₇	C₂	semidirect
12. C₂×#538×C₆₇	C₂	semidirect
13. C₂×#532×C₆₇	C₂	semidirect
14. C₂×#529×C₆₇	C₂	semidirect
15. C₂×#525×C₆₇	C₂	semidirect
16. C₂²×#121×C₆₇	C₂	semidirect
17. C₂×#518×C₆₇	C₂	semidirect
18. C₂²×C₄×D₄×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
23. C₂³×D₄×C₆₇	C₂²	semidirect
24. C₂³×D₄×C₆₇	C₂²	semidirect
25. C₂⁴×C₄×C₆₇	C₂²	semidirect
26. #555×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
28. #553×C₆₇	C₂²	semidirect
29. #553×C₆₇	C₂²	semidirect
30. #550×C₆₇	C₂²	semidirect
31. #546×C₆₇	C₂²	semidirect
32. #546×C₆₇	C₂²	semidirect
33. D₄²×C₆₇	C₂²	semidirect
34. D₄²×C₆₇	C₂²	semidirect
35. #540×C₆₇	C₂²	semidirect
36. #538×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
39. C₂×#127×C₆₇	C₂²	semidirect
40. C₂×#127×C₆₇	C₂²	semidirect
41. #529×C₆₇	C₂²	semidirect
42. C₂×#126×C₆₇	C₂²	semidirect
43. C₂×#126×C₆₇	C₂²	semidirect
44. C₂×#125×C₆₇	C₂²	semidirect
45. C₂×#125×C₆₇	C₂²	semidirect
46. C₂×#124×C₆₇	C₂²	semidirect
47. C₂×#124×C₆₇	C₂²	semidirect
48. C₂×#124×C₆₇	C₂²	semidirect
49. #525×C₆₇	C₂²	semidirect
50. C₂×#123×C₆₇	C₂²	semidirect
51. C₂×#123×C₆₇	C₂²	semidirect
52. C₂×#123×C₆₇	C₂²	semidirect
53. C₂×#123×C₆₇	C₂²	semidirect
54. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
58. C₂×#121×C₆₇	C₂²	semidirect
59. C₂×#121×C₆₇	C₂²	semidirect
60. C₂×#121×C₆₇	C₂²	semidirect
61. C₂×#121×C₆₇	C₂²	semidirect
62. C₂×#121×C₆₇	C₂²	semidirect
63. C₂×#121×C₆₇	C₂²	semidirect
64. C₂×#121×C₆₇	C₂²	semidirect
65. C₂×#121×C₆₇	C₂²	semidirect
66. C₂×#121×C₆₇	C₂²	semidirect
67. C₂×#121×C₆₇	C₂²	semidirect
68. C₂×#121×C₆₇	C₂²	semidirect
69. C₂×#121×C₆₇	C₂²	semidirect
70. C₂×#121×C₆₇	C₂²	semidirect
71. C₂×#120×C₆₇	C₂²	semidirect
72. C₂×#120×C₆₇	C₂²	semidirect
73. C₂×#120×C₆₇	C₂²	semidirect
74. #518×C₆₇	C₂²	semidirect
75. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
79. C₂×C₄×D₄×C₆₇	C₂²	semidirect
80. C₂×C₄×D₄×C₆₇	C₂²	semidirect
81. C₂×C₄×D₄×C₆₇	C₂²	semidirect
82. C₂×C₄×D₄×C₆₇	C₂²	semidirect
83. C₂×C₄×D₄×C₆₇	C₂²	semidirect
84. C₂×C₄×D₄×C₆₇	C₂²	semidirect
85. C₂×C₄×D₄×C₆₇	C₂²	semidirect
86. C₂×C₄×D₄×C₆₇	C₂²	semidirect
87. C₂×C₄×D₄×C₆₇	C₂²	semidirect
88. C₂×C₄×D₄×C₆₇	C₂²	semidirect
89. C₂×C₄×D₄×C₆₇	C₂²	semidirect
90. C₂×C₄×D₄×C₆₇	C₂²	semidirect
91. C₂×C₄×D₄×C₆₇	C₂²	semidirect
92. C₂×#117×C₆₇	C₂²	semidirect
93. C₂×#117×C₆₇	C₂²	semidirect
94. C₂×#117×C₆₇	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
96. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
97. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
98. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
99. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
105. C₂×#41×C₆₇	C₂³	semidirect
106. C₂×#41×C₆₇	C₂³	semidirect
129. C₂²×D₄×C₆₇	C₂³	semidirect
130. C₂²×D₄×C₆₇	C₂³	semidirect
144. C₂³×C₄×C₆₇	C₂³	semidirect
145. C₄⋊Q₈×C₆₇	C₂³	semidirect
146. #127×C₆₇	C₂³	semidirect
147. #127×C₆₇	C₂³	semidirect
148. #126×C₆₇	C₂³	semidirect
149. #126×C₆₇	C₂³	semidirect
150. #125×C₆₇	C₂³	semidirect
151. #125×C₆₇	C₂³	semidirect
152. #124×C₆₇	C₂³	semidirect
153. #124×C₆₇	C₂³	semidirect
154. #124×C₆₇	C₂³	semidirect
155. #123×C₆₇	C₂³	semidirect
156. #123×C₆₇	C₂³	semidirect
157. #123×C₆₇	C₂³	semidirect
158. #123×C₆₇	C₂³	semidirect
159. C₂²⋊Q₈×C₆₇	C₂³	semidirect
160. C₂²⋊Q₈×C₆₇	C₂³	semidirect
161. C₂²⋊Q₈×C₆₇	C₂³	semidirect
163. #121×C₆₇	C₂³	semidirect
164. #121×C₆₇	C₂³	semidirect
165. #121×C₆₇	C₂³	semidirect
166. #121×C₆₇	C₂³	semidirect
167. #121×C₆₇	C₂³	semidirect
168. #121×C₆₇	C₂³	semidirect
169. #121×C₆₇	C₂³	semidirect
170. #121×C₆₇	C₂³	semidirect
171. #121×C₆₇	C₂³	semidirect
172. #121×C₆₇	C₂³	semidirect
173. #121×C₆₇	C₂³	semidirect
174. #121×C₆₇	C₂³	semidirect
175. #120×C₆₇	C₂³	semidirect
176. #120×C₆₇	C₂³	semidirect
177. #120×C₆₇	C₂³	semidirect
178. C₄×Q₈×C₆₇	C₂³	semidirect
182. C₄×D₄×C₆₇	C₂³	semidirect
183. C₄×D₄×C₆₇	C₂³	semidirect
184. C₄×D₄×C₆₇	C₂³	semidirect
185. C₄×D₄×C₆₇	C₂³	semidirect
186. C₄×D₄×C₆₇	C₂³	semidirect
187. C₄×D₄×C₆₇	C₂³	semidirect
188. C₄×D₄×C₆₇	C₂³	semidirect
189. C₄×D₄×C₆₇	C₂³	semidirect
190. C₄×D₄×C₆₇	C₂³	semidirect
191. C₄×D₄×C₆₇	C₂³	semidirect
192. C₄×D₄×C₆₇	C₂³	semidirect
193. C₄×D₄×C₆₇	C₂³	semidirect
194. #117×C₆₇	C₂³	semidirect
195. #117×C₆₇	C₂³	semidirect
196. #117×C₆₇	C₂³	semidirect
210. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
211. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
228. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
229. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
230. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
237. C₂×C₄²×C₆₇	C₂³	semidirect
274. C₂×D₄×C₆₇	#41	semidirect
405. D₄×C₆₇	C₂×#41	semidirect
480. C₂×#3519	C₆₇	direct (N × H)
486. C₂×C₆₇	#3519	direct (N × H)
490. #3519	C₂×C₆₇	direct (N × H)
491. C₂×#555	C₂×C₆₇	semidirect
492. C₂×#554	C₂×C₆₇	semidirect
493. C₂×#553	C₂×C₆₇	semidirect
494. C₂×#553	C₂×C₆₇	semidirect
495. C₂×#550	C₂×C₆₇	semidirect
496. C₂×#546	C₂×C₆₇	semidirect
497. C₂×#546	C₂×C₆₇	semidirect
498. C₂×D₄²	C₂×C₆₇	semidirect
499. C₂×D₄²	C₂×C₆₇	semidirect
500. C₂×#540	C₂×C₆₇	semidirect
501. C₂×#538	C₂×C₆₇	semidirect
502. C₂×#532	C₂×C₆₇	semidirect
503. C₂×#529	C₂×C₆₇	semidirect
504. C₂×#525	C₂×C₆₇	semidirect
505. C₂²×#121	C₂×C₆₇	semidirect
506. C₂×#518	C₂×C₆₇	semidirect
507. C₂²×C₄×D₄	C₂×C₆₇	semidirect
508. C₆₇	C₂×#3519	direct (N × H)
509. C₂²×#41	C₂²×C₆₇	semidirect
510. C₂²×#41	C₂²×C₆₇	semidirect
513. C₂³×D₄	C₂²×C₆₇	semidirect
514. C₂³×D₄	C₂²×C₆₇	semidirect
515. C₂⁴×C₄	C₂²×C₆₇	semidirect
516. #555	C₂²×C₆₇	semidirect
517. #554	C₂²×C₆₇	semidirect
518. #553	C₂²×C₆₇	semidirect
519. #553	C₂²×C₆₇	semidirect
520. #550	C₂²×C₆₇	semidirect
521. #546	C₂²×C₆₇	semidirect
522. #546	C₂²×C₆₇	semidirect
523. D₄²	C₂²×C₆₇	semidirect
524. D₄²	C₂²×C₆₇	semidirect
525. #540	C₂²×C₆₇	semidirect
526. #538	C₂²×C₆₇	semidirect
527. #532	C₂²×C₆₇	semidirect
528. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
529. C₂×#127	C₂²×C₆₇	semidirect
530. C₂×#127	C₂²×C₆₇	semidirect
531. #529	C₂²×C₆₇	semidirect
532. C₂×#126	C₂²×C₆₇	semidirect
533. C₂×#126	C₂²×C₆₇	semidirect
534. C₂×#125	C₂²×C₆₇	semidirect
535. C₂×#125	C₂²×C₆₇	semidirect
536. C₂×#124	C₂²×C₆₇	semidirect
537. C₂×#124	C₂²×C₆₇	semidirect
538. C₂×#124	C₂²×C₆₇	semidirect
539. #525	C₂²×C₆₇	semidirect
540. C₂×#123	C₂²×C₆₇	semidirect
541. C₂×#123	C₂²×C₆₇	semidirect
542. C₂×#123	C₂²×C₆₇	semidirect
543. C₂×#123	C₂²×C₆₇	semidirect
544. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
545. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
546. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
548. C₂×#121	C₂²×C₆₇	semidirect
549. C₂×#121	C₂²×C₆₇	semidirect
550. C₂×#121	C₂²×C₆₇	semidirect
551. C₂×#121	C₂²×C₆₇	semidirect
552. C₂×#121	C₂²×C₆₇	semidirect
553. C₂×#121	C₂²×C₆₇	semidirect
554. C₂×#121	C₂²×C₆₇	semidirect
555. C₂×#121	C₂²×C₆₇	semidirect
556. C₂×#121	C₂²×C₆₇	semidirect
557. C₂×#121	C₂²×C₆₇	semidirect
558. C₂×#121	C₂²×C₆₇	semidirect
559. C₂×#121	C₂²×C₆₇	semidirect
560. C₂×#121	C₂²×C₆₇	semidirect
561. C₂×#120	C₂²×C₆₇	semidirect
562. C₂×#120	C₂²×C₆₇	semidirect
563. C₂×#120	C₂²×C₆₇	semidirect
564. #518	C₂²×C₆₇	semidirect
565. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
569. C₂×C₄×D₄	C₂²×C₆₇	semidirect
570. C₂×C₄×D₄	C₂²×C₆₇	semidirect
571. C₂×C₄×D₄	C₂²×C₆₇	semidirect
572. C₂×C₄×D₄	C₂²×C₆₇	semidirect
573. C₂×C₄×D₄	C₂²×C₆₇	semidirect
574. C₂×C₄×D₄	C₂²×C₆₇	semidirect
575. C₂×C₄×D₄	C₂²×C₆₇	semidirect
576. C₂×C₄×D₄	C₂²×C₆₇	semidirect
577. C₂×C₄×D₄	C₂²×C₆₇	semidirect
578. C₂×C₄×D₄	C₂²×C₆₇	semidirect
579. C₂×C₄×D₄	C₂²×C₆₇	semidirect
580. C₂×C₄×D₄	C₂²×C₆₇	semidirect
581. C₂×C₄×D₄	C₂²×C₆₇	semidirect
582. C₂×#117	C₂²×C₆₇	semidirect
583. C₂×#117	C₂²×C₆₇	semidirect
584. C₂×#117	C₂²×C₆₇	semidirect
585. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
586. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
587. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
588. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
589. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
590. C₂²×C₄²	C₂²×C₆₇	semidirect
595. C₂×#41	C₂³×C₆₇	semidirect
596. C₂×#41	C₂³×C₆₇	semidirect
619. C₂²×D₄	C₂³×C₆₇	semidirect
620. C₂²×D₄	C₂³×C₆₇	semidirect
634. C₂³×C₄	C₂³×C₆₇	semidirect
635. C₄⋊Q₈	C₂³×C₆₇	semidirect
636. #127	C₂³×C₆₇	semidirect
637. #127	C₂³×C₆₇	semidirect
638. #126	C₂³×C₆₇	semidirect
639. #126	C₂³×C₆₇	semidirect
640. #125	C₂³×C₆₇	semidirect
641. #125	C₂³×C₆₇	semidirect
642. #124	C₂³×C₆₇	semidirect
643. #124	C₂³×C₆₇	semidirect
644. #124	C₂³×C₆₇	semidirect
645. #123	C₂³×C₆₇	semidirect
646. #123	C₂³×C₆₇	semidirect
647. #123	C₂³×C₆₇	semidirect
648. #123	C₂³×C₆₇	semidirect
649. C₂²⋊Q₈	C₂³×C₆₇	semidirect
650. C₂²⋊Q₈	C₂³×C₆₇	semidirect
651. C₂²⋊Q₈	C₂³×C₆₇	semidirect
653. #121	C₂³×C₆₇	semidirect
654. #121	C₂³×C₆₇	semidirect
655. #121	C₂³×C₆₇	semidirect
656. #121	C₂³×C₆₇	semidirect
657. #121	C₂³×C₆₇	semidirect
658. #121	C₂³×C₆₇	semidirect
659. #121	C₂³×C₆₇	semidirect
660. #121	C₂³×C₆₇	semidirect
661. #121	C₂³×C₆₇	semidirect
662. #121	C₂³×C₆₇	semidirect
663. #121	C₂³×C₆₇	semidirect
664. #121	C₂³×C₆₇	semidirect
665. #120	C₂³×C₆₇	semidirect
666. #120	C₂³×C₆₇	semidirect
667. #120	C₂³×C₆₇	semidirect
668. C₄×Q₈	C₂³×C₆₇	semidirect
672. C₄×D₄	C₂³×C₆₇	semidirect
673. C₄×D₄	C₂³×C₆₇	semidirect
674. C₄×D₄	C₂³×C₆₇	semidirect
675. C₄×D₄	C₂³×C₆₇	semidirect
676. C₄×D₄	C₂³×C₆₇	semidirect
677. C₄×D₄	C₂³×C₆₇	semidirect
678. C₄×D₄	C₂³×C₆₇	semidirect
679. C₄×D₄	C₂³×C₆₇	semidirect
680. C₄×D₄	C₂³×C₆₇	semidirect
681. C₄×D₄	C₂³×C₆₇	semidirect
682. C₄×D₄	C₂³×C₆₇	semidirect
683. C₄×D₄	C₂³×C₆₇	semidirect
684. #117	C₂³×C₆₇	semidirect
685. #117	C₂³×C₆₇	semidirect
686. #117	C₂³×C₆₇	semidirect
700. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
701. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
718. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
719. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
720. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
727. C₂×C₄²	C₂³×C₆₇	semidirect
764. C₂×D₄	#41×C₆₇	semidirect
895. D₄	C₂×#41×C₆₇	semidirect
975. C₂	C₆₇×#3519	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×#3519	2
C₂×#555×C₆₇	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#550×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#540×C₆₇	2
C₂×#538×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂×#525×C₆₇	2
C₂²×#121×C₆₇	2
C₂×#518×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₂×#3519	67

Subgroups — C2×C67×#3519 #30742022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3519 #30742022