Subgroups — C₆₇×#59808 #30739059

Order 17152.

3622 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2681	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2678	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2464	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2405	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2404	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
28	#547×C₆₇	—	2	8	no	—
29	#546×C₆₇	—	2	16	no	—
30	D₄²×C₆₇	—	2	8	no	—
31	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#123×C₆₇	C₂²	1	2	yes	—
35	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
37	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#121×C₆₇	C₂²	1	2	yes	—
43	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
47	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
48	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×#120×C₆₇	C₂²	1	2	yes	—
50	C₂×#120×C₆₇	C₂²	1	2	yes	—
51	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
64	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
65	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
66	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#398×C₆₇	C₂²	1	2	yes	complemented
68	#397×C₆₇	C₂²	1	2	yes	complemented
69	#396×C₆₇	C₂²	1	2	yes	complemented
70	#396×C₆₇	C₂²	1	2	yes	complemented
71	#394×C₆₇	C₂²	1	2	yes	complemented
72	#394×C₆₇	C₂²	1	2	yes	complemented
73	#394×C₆₇	C₂²	1	2	yes	complemented
74	#394×C₆₇	C₂²	1	2	yes	complemented
75	#394×C₆₇	C₂²	1	2	yes	complemented
76	#394×C₆₇	C₂²	1	2	yes	complemented
77	#394×C₆₇	C₂²	1	2	yes	complemented
78	#393×C₆₇	C₂²	1	2	yes	complemented
79	#393×C₆₇	C₂²	1	2	yes	complemented
80	#392×C₆₇	C₂²	1	2	yes	complemented
81	#392×C₆₇	C₂²	1	2	yes	complemented
82	#392×C₆₇	C₂²	1	2	yes	complemented
83	#390×C₆₇	C₂²	1	1	yes	characteristic
84	#390×C₆₇	C₂²	1	1	yes	characteristic
85	#390×C₆₇	C₂²	1	1	yes	characteristic
86	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#390×C₆₇	C₂²	1	2	yes	complemented
88	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#390×C₆₇	C₂²	1	2	yes	complemented
90	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#388×C₆₇	C₂²	1	2	yes	complemented
98	#388×C₆₇	C₂²	1	2	yes	complemented
99	#388×C₆₇	C₂²	1	2	yes	complemented
100	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#386×C₆₇	C₂²	1	1	yes	characteristic
103	#386×C₆₇	C₂²	1	2	yes	complemented
104	#386×C₆₇	C₂²	1	2	yes	complemented
105	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#386×C₆₇	C₂²	1	2	yes	complemented
107	#386×C₆₇	C₂²	1	2	yes	complemented
108	#386×C₆₇	C₂²	1	2	yes	complemented
109	#386×C₆₇	C₂²	1	2	yes	complemented
110	#386×C₆₇	C₂²	1	2	yes	complemented
111	#385×C₆₇	C₂²	1	2	yes	complemented
112	#385×C₆₇	C₂²	1	2	yes	complemented
113	#381×C₆₇	C₂²	1	2	yes	complemented
114	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#379×C₆₇	C₂²	1	2	yes	complemented
119	#379×C₆₇	C₂²	1	2	yes	complemented
120	#379×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
126	C₂⁵×C₆₇	C₂³	1	2	yes	—
127	C₂⁵×C₆₇	C₂³	1	2	yes	—
128	C₂×#41×C₆₇	—	2	8	no	—
129	C₂×#41×C₆₇	—	2	8	no	—
130	C₂×#41×C₆₇	—	4	4	no	—
131	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	—	2	8	no	—
133	C₂²×D₄×C₆₇	—	2	4	no	—
134	C₂²×D₄×C₆₇	—	2	8	no	—
135	C₂²×D₄×C₆₇	—	2	4	no	—
136	C₂²×D₄×C₆₇	—	2	4	no	—
137	C₂²×D₄×C₆₇	—	2	4	no	—
138	C₂²×D₄×C₆₇	—	4	2	no	—
139	C₂²×D₄×C₆₇	—	4	2	no	—
140	C₂²×D₄×C₆₇	—	4	4	no	—
141	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
147	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
148	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
151	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
154	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
155	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
157	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
160	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
161	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
162	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
165	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	—	2	4	no	—
167	#127×C₆₇	—	2	4	no	—
168	#124×C₆₇	—	2	8	no	—
169	#123×C₆₇	—	2	8	no	—
170	#123×C₆₇	—	2	8	no	—
171	#123×C₆₇	—	2	8	no	—
172	#123×C₆₇	—	2	8	no	—
173	C₂²⋊Q₈×C₆₇	—	2	8	no	—
174	C₂²⋊Q₈×C₆₇	—	2	8	no	—
175	#121×C₆₇	—	2	4	no	—
176	#121×C₆₇	—	2	8	no	—
177	#121×C₆₇	—	2	4	no	—
178	#121×C₆₇	—	2	4	no	—
179	#121×C₆₇	—	2	8	no	—
180	#121×C₆₇	—	2	8	no	—
181	#121×C₆₇	—	4	2	no	—
182	#121×C₆₇	D₄	1	8	yes	complemented
183	#121×C₆₇	D₄	1	8	yes	complemented
184	#120×C₆₇	—	2	8	no	—
185	#120×C₆₇	—	2	8	no	—
186	#120×C₆₇	—	2	8	no	—
187	#120×C₆₇	—	2	8	no	—
188	C₄×D₄×C₆₇	—	2	4	no	—
189	C₄×D₄×C₆₇	—	2	4	no	—
190	C₄×D₄×C₆₇	—	2	4	no	—
191	C₄×D₄×C₆₇	—	2	8	no	—
192	C₄×D₄×C₆₇	—	2	4	no	—
193	C₄×D₄×C₆₇	—	2	8	no	—
194	C₄×D₄×C₆₇	—	4	2	no	—
195	C₄×D₄×C₆₇	—	4	2	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
215	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
216	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
240	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
242	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
244	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
246	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
248	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
249	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
250	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄²×C₆₇	—	4	2	no	—
253	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
260	#95×C₆₇	C₂³	1	1	yes	characteristic
261	#95×C₆₇	C₂³	1	1	yes	characteristic
262	#95×C₆₇	C₂³	1	2	yes	—
263	#95×C₆₇	C₂³	1	1	yes	characteristic
264	#95×C₆₇	C₂³	1	2	yes	—
265	#95×C₆₇	C₂³	1	1	yes	characteristic
266	#95×C₆₇	C₂³	1	1	yes	characteristic
267	#95×C₆₇	C₂³	1	2	yes	—
268	#95×C₆₇	C₂³	1	1	yes	characteristic
269	#95×C₆₇	C₂³	1	2	yes	—
270	#95×C₆₇	C₂³	1	2	yes	—
271	#95×C₆₇	C₂³	1	2	yes	—
272	#95×C₆₇	C₂³	1	2	yes	—
273	C₂⁴×C₆₇	—	2	4	no	—
274	C₂⁴×C₆₇	—	2	4	no	—
275	C₂⁴×C₆₇	—	2	4	no	—
276	C₂⁴×C₆₇	—	2	4	no	—
277	C₂⁴×C₆₇	—	2	4	no	—
278	C₂⁴×C₆₇	—	2	4	no	—
279	C₂⁴×C₆₇	—	2	4	no	—
280	C₂⁴×C₆₇	—	4	2	no	—
281	C₂⁴×C₆₇	—	4	2	no	—
282	C₂⁴×C₆₇	—	4	2	no	—
283	C₂⁴×C₆₇	—	4	2	no	—
284	C₂⁴×C₆₇	—	4	2	no	—
285	C₂⁴×C₆₇	—	4	2	no	—
286	C₂⁴×C₆₇	—	4	2	no	—
287	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
288	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
290	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
292	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
293	#41×C₆₇	—	4	32	no	—
294	C₂×Q₈×C₆₇	—	2	4	no	—
295	C₂×Q₈×C₆₇	—	2	4	no	—
296	C₂×Q₈×C₆₇	—	4	2	no	—
297	C₂×D₄×C₆₇	—	2	2	no	—
298	C₂×D₄×C₆₇	—	2	4	no	—
299	C₂×D₄×C₆₇	—	2	2	no	—
300	C₂×D₄×C₆₇	—	2	2	no	—
301	C₂×D₄×C₆₇	—	2	4	no	—
302	C₂×D₄×C₆₇	—	2	2	no	—
303	C₂×D₄×C₆₇	—	2	4	no	—
304	C₂×D₄×C₆₇	—	2	4	no	—
305	C₂×D₄×C₆₇	—	2	4	no	—
306	C₂×D₄×C₆₇	—	2	4	no	—
307	C₂×D₄×C₆₇	—	2	4	no	—
308	C₂×D₄×C₆₇	—	2	4	no	—
309	C₂×D₄×C₆₇	—	2	4	no	—
310	C₂×D₄×C₆₇	—	2	4	no	—
311	C₂×D₄×C₆₇	—	2	4	no	—
312	C₂×D₄×C₆₇	—	2	4	no	—
313	C₂×D₄×C₆₇	—	2	4	no	—
314	C₂×D₄×C₆₇	—	2	2	no	—
315	C₂×D₄×C₆₇	—	2	4	no	—
316	C₂×D₄×C₆₇	—	2	4	no	—
317	C₂×D₄×C₆₇	—	2	4	no	—
318	C₂×D₄×C₆₇	—	2	2	no	—
319	C₂×D₄×C₆₇	—	2	2	no	—
320	C₂×D₄×C₆₇	—	2	2	no	—
321	C₂×D₄×C₆₇	—	2	2	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	2	2	no	—
324	C₂×D₄×C₆₇	—	4	16	no	—
325	C₂×D₄×C₆₇	—	4	1	no	—
326	C₂×D₄×C₆₇	—	4	2	no	—
327	C₂×D₄×C₆₇	—	4	2	no	—
328	C₂×D₄×C₆₇	—	4	2	no	—
329	C₂×D₄×C₆₇	—	4	2	no	—
330	C₂×D₄×C₆₇	—	4	1	no	—
331	C₂×D₄×C₆₇	—	4	2	no	—
332	C₂×D₄×C₆₇	—	4	2	no	—
333	C₂×D₄×C₆₇	—	4	2	no	—
334	C₂×D₄×C₆₇	—	4	2	no	—
335	C₂×D₄×C₆₇	—	4	2	no	—
336	C₂×D₄×C₆₇	—	4	2	no	—
337	C₂×D₄×C₆₇	—	4	32	no	—
338	C₂×D₄×C₆₇	—	4	16	no	—
339	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
340	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
341	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
342	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
343	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
344	C₂×D₄×C₆₇	#41	1	4	yes	complemented
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	4	no	—
348	C₂²×C₄×C₆₇	—	2	4	no	—
349	C₂²×C₄×C₆₇	—	2	4	no	—
350	C₂²×C₄×C₆₇	—	2	4	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	4	no	—
353	C₂²×C₄×C₆₇	—	2	4	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	4	no	—
356	C₂²×C₄×C₆₇	—	2	4	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	4	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	—	2	2	no	—
361	C₂²×C₄×C₆₇	—	2	2	no	—
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	4	no	—
364	C₂²×C₄×C₆₇	—	4	1	no	—
365	C₂²×C₄×C₆₇	—	4	1	no	—
366	C₂²×C₄×C₆₇	—	4	1	no	—
367	C₂²×C₄×C₆₇	—	4	1	no	—
368	C₂²×C₄×C₆₇	—	4	2	no	—
369	C₂²×C₄×C₆₇	—	4	2	no	—
370	C₂²×C₄×C₆₇	—	4	2	no	—
371	C₂²×C₄×C₆₇	—	4	2	no	—
372	C₂²×C₄×C₆₇	—	4	2	no	—
373	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	complemented
375	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	4	no	—
395	C₄⋊C₄×C₆₇	—	2	4	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	4	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	4	no	—
400	C₄⋊C₄×C₆₇	—	2	4	no	—
401	C₄⋊C₄×C₆₇	—	2	4	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	4	1	no	—
405	C₄⋊C₄×C₆₇	—	4	1	no	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
408	C₂²⋊C₄×C₆₇	—	2	4	no	—
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	4	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	4	no	—
413	C₂²⋊C₄×C₆₇	—	2	4	no	—
414	C₂²⋊C₄×C₆₇	—	2	4	no	—
415	C₂²⋊C₄×C₆₇	—	2	4	no	—
416	C₂²⋊C₄×C₆₇	—	2	4	no	—
417	C₂²⋊C₄×C₆₇	—	2	4	no	—
418	C₂²⋊C₄×C₆₇	—	2	4	no	—
419	C₂²⋊C₄×C₆₇	—	2	4	no	—
420	C₂²⋊C₄×C₆₇	—	2	4	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	4	no	—
423	C₂²⋊C₄×C₆₇	—	2	4	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	4	no	—
426	C₂²⋊C₄×C₆₇	—	2	4	no	—
427	C₂²⋊C₄×C₆₇	—	4	2	no	—
428	C₂²⋊C₄×C₆₇	—	4	2	no	—
429	C₂²⋊C₄×C₆₇	—	4	2	no	—
430	C₂²⋊C₄×C₆₇	—	4	2	no	—
431	C₂²⋊C₄×C₆₇	—	4	1	no	—
432	C₂²⋊C₄×C₆₇	—	4	2	no	—
433	C₂²⋊C₄×C₆₇	—	4	2	no	—
434	C₂²⋊C₄×C₆₇	—	4	2	no	—
435	C₂²⋊C₄×C₆₇	—	4	1	no	—
436	C₂²⋊C₄×C₆₇	—	4	1	no	—
437	C₂²⋊C₄×C₆₇	—	4	2	no	—
438	C₂²⋊C₄×C₆₇	—	4	1	no	—
439	C₂²⋊C₄×C₆₇	—	4	2	no	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
441	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	complemented
443	C₄²×C₆₇	—	2	4	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	4	1	no	—
449	C₄²×C₆₇	—	4	1	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	1	no	—
454	C₂³×C₆₇	—	2	2	no	—
455	C₂³×C₆₇	—	2	1	no	—
456	C₂³×C₆₇	—	2	2	no	—
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	2	2	no	—
459	C₂³×C₆₇	—	2	1	no	—
460	C₂³×C₆₇	—	2	1	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	2	2	no	—
463	C₂³×C₆₇	—	2	1	no	—
464	C₂³×C₆₇	—	2	1	no	—
465	C₂³×C₆₇	—	2	2	no	—
466	C₂³×C₆₇	—	2	1	no	—
467	C₂³×C₆₇	—	2	2	no	—
468	C₂³×C₆₇	—	2	1	no	—
469	C₂³×C₆₇	—	2	2	no	—
470	C₂³×C₆₇	—	2	1	no	—
471	C₂³×C₆₇	—	2	2	no	—
472	C₂³×C₆₇	—	2	1	no	—
473	C₂³×C₆₇	—	2	2	no	—
474	C₂³×C₆₇	—	2	2	no	—
475	C₂³×C₆₇	—	2	1	no	—
476	C₂³×C₆₇	—	2	2	no	—
477	C₂³×C₆₇	—	2	1	no	—
478	C₂³×C₆₇	—	2	2	no	—
479	C₂³×C₆₇	—	2	2	no	—
480	C₂³×C₆₇	—	2	2	no	—
481	C₂³×C₆₇	—	2	2	no	—
482	C₂³×C₆₇	—	2	2	no	—
483	C₂³×C₆₇	—	2	2	no	—
484	C₂³×C₆₇	—	2	2	no	—
485	C₂³×C₆₇	—	4	8	no	—
486	C₂³×C₆₇	—	4	8	no	—
487	C₂³×C₆₇	—	4	8	no	—
488	C₂³×C₆₇	—	4	8	no	—
489	C₂³×C₆₇	—	4	8	no	—
490	C₂³×C₆₇	—	4	8	no	—
491	C₂³×C₆₇	—	4	8	no	—
492	C₂³×C₆₇	—	8	4	no	—
493	C₂³×C₆₇	—	8	4	no	—
494	C₂³×C₆₇	—	8	4	no	—
495	C₂³×C₆₇	—	8	4	no	—
496	C₂³×C₆₇	—	8	4	no	—
497	C₂³×C₆₇	—	8	4	no	—
498	C₂³×C₆₇	—	8	4	no	—
499	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
500	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
501	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
502	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
503	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
504	C₂³×C₆₇	C₂×#41	1	4	yes	—
505	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
506	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
507	Q₈×C₆₇	—	4	8	no	—
508	D₄×C₆₇	—	2	8	no	—
509	D₄×C₆₇	—	2	16	no	—
510	D₄×C₆₇	—	2	8	no	—
511	D₄×C₆₇	—	2	8	no	—
512	D₄×C₆₇	—	2	8	no	—
513	D₄×C₆₇	—	4	4	no	—
514	D₄×C₆₇	—	4	8	no	—
515	D₄×C₆₇	—	4	8	no	—
516	D₄×C₆₇	—	4	8	no	—
517	D₄×C₆₇	—	4	8	no	—
518	D₄×C₆₇	—	4	8	no	—
519	D₄×C₆₇	—	4	8	no	—
520	D₄×C₆₇	—	4	4	no	—
521	D₄×C₆₇	—	8	4	no	—
522	D₄×C₆₇	—	8	4	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	1	no	—
533	C₂×C₄×C₆₇	—	2	1	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	8	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	2	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	2	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	2	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	2	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	4	4	no	—
567	C₂×C₄×C₆₇	—	4	8	no	—
568	C₂×C₄×C₆₇	—	4	8	no	—
569	C₂×C₄×C₆₇	—	4	8	no	—
570	C₂×C₄×C₆₇	—	4	4	no	—
571	C₂×C₄×C₆₇	—	4	8	no	—
572	C₂×C₄×C₆₇	—	4	4	no	—
573	C₂×C₄×C₆₇	—	4	4	no	—
574	C₂×C₄×C₆₇	—	8	4	no	—
575	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
576	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
577	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
580	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
581	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
582	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
583	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
584	C₂²×C₆₇	—	2	2	no	—
585	C₂²×C₆₇	—	2	2	no	—
586	C₂²×C₆₇	—	2	2	no	—
587	C₂²×C₆₇	—	2	2	no	—
588	C₂²×C₆₇	—	2	2	no	—
589	C₂²×C₆₇	—	2	2	no	—
590	C₂²×C₆₇	—	2	2	no	—
591	C₂²×C₆₇	—	2	4	no	—
592	C₂²×C₆₇	—	2	2	no	—
593	C₂²×C₆₇	—	2	4	no	—
594	C₂²×C₆₇	—	2	4	no	—
595	C₂²×C₆₇	—	2	2	no	—
596	C₂²×C₆₇	—	2	4	no	—
597	C₂²×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	2	2	no	—
600	C₂²×C₆₇	—	2	4	no	—
601	C₂²×C₆₇	—	2	4	no	—
602	C₂²×C₆₇	—	4	2	no	—
603	C₂²×C₆₇	—	4	1	no	—
604	C₂²×C₆₇	—	4	1	no	—
605	C₂²×C₆₇	—	4	2	no	—
606	C₂²×C₆₇	—	4	2	no	—
607	C₂²×C₆₇	—	4	2	no	—
608	C₂²×C₆₇	—	4	1	no	—
609	C₂²×C₆₇	—	4	1	no	—
610	C₂²×C₆₇	—	4	2	no	—
611	C₂²×C₆₇	—	4	1	no	—
612	C₂²×C₆₇	—	4	2	no	—
613	C₂²×C₆₇	—	4	1	no	—
614	C₂²×C₆₇	—	4	1	no	—
615	C₂²×C₆₇	—	4	2	no	—
616	C₂²×C₆₇	—	4	2	no	—
617	C₂²×C₆₇	—	4	1	no	—
618	C₂²×C₆₇	—	4	2	no	—
619	C₂²×C₆₇	—	4	2	no	—
620	C₂²×C₆₇	—	4	2	no	—
621	C₂²×C₆₇	—	4	2	no	—
622	C₂²×C₆₇	—	4	2	no	—
623	C₂²×C₆₇	—	4	2	no	—
624	C₂²×C₆₇	—	4	2	no	—
625	C₂²×C₆₇	—	8	16	no	—
626	C₂²×C₆₇	—	8	16	no	—
627	C₂²×C₆₇	D₄²	1	4	yes	—
628	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
629	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
630	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
631	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂²×C₆₇	#585	1	1	yes	characteristic
634	C₂²×C₆₇	#585	1	1	yes	characteristic
635	C₄×C₆₇	—	2	2	no	—
636	C₄×C₆₇	—	2	4	no	—
637	C₄×C₆₇	—	2	2	no	—
638	C₄×C₆₇	—	2	2	no	—
639	C₄×C₆₇	—	2	2	no	—
640	C₄×C₆₇	—	2	2	no	—
641	C₄×C₆₇	—	4	2	no	—
642	C₄×C₆₇	—	4	2	no	—
643	C₄×C₆₇	—	4	1	no	—
644	C₄×C₆₇	—	4	1	no	—
645	C₄×C₆₇	—	4	2	no	—
646	C₄×C₆₇	—	4	2	no	—
647	C₄×C₆₇	—	4	1	no	—
648	C₄×C₆₇	—	4	1	no	—
649	C₄×C₆₇	—	4	1	no	—
650	C₄×C₆₇	—	4	1	no	—
651	C₄×C₆₇	#546	1	4	yes	complemented
652	#59808	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
653	C₂×C₆₇	—	2	4	no	—
654	C₂×C₆₇	—	4	2	no	—
655	C₂×C₆₇	—	4	4	no	—
656	C₂×C₆₇	—	4	2	no	—
657	C₂×C₆₇	—	4	4	no	—
658	C₂×C₆₇	—	8	2	no	—
659	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
660	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
661	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
662	C₂×C₆₇	#3496	1	1	yes	characteristic
663	C₂×C₆₇	#3500	1	1	yes	characteristic
664	C₂×C₆₇	#3513	1	1	yes	characteristic
665	C₂×C₆₇	#3542	1	1	yes	characteristic
666	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
667	C₂×#546	C₂×C₆₇	1	2	yes	complemented
668	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#2681	C₂×C₆₇	1	2	yes	complemented
670	#2678	C₂×C₆₇	1	2	yes	complemented
671	#2534	C₂×C₆₇	1	2	yes	complemented
672	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
673	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#2472	C₂×C₆₇	1	2	yes	complemented
675	#2464	C₂×C₆₇	1	2	yes	complemented
676	#2452	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
678	#2428	C₂×C₆₇	1	1	yes	characteristic, complemented
679	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
680	#2408	C₂×C₆₇	1	1	yes	characteristic, complemented
681	#2408	C₂×C₆₇	1	1	yes	characteristic, complemented
682	#2405	C₂×C₆₇	1	2	yes	complemented
683	#2404	C₂×C₆₇	1	2	yes	complemented
684	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
685	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
686	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
687	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
688	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
689	C₆₇	#59808	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
691	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
692	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
693	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
694	#547	—	2	8	no	—
695	#546	—	2	16	no	—
696	D₄²	—	2	8	no	—
697	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
699	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
700	C₂×#123	C₂²×C₆₇	1	2	yes	—
701	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
702	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
703	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
704	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
705	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
706	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
708	C₂×#121	C₂²×C₆₇	1	2	yes	—
709	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
710	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
713	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
714	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	C₂×#120	C₂²×C₆₇	1	2	yes	—
716	C₂×#120	C₂²×C₆₇	1	2	yes	—
717	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
718	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
719	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
720	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
721	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
723	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
725	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
730	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
731	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
732	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	#398	C₂²×C₆₇	1	2	yes	complemented
734	#397	C₂²×C₆₇	1	2	yes	complemented
735	#396	C₂²×C₆₇	1	2	yes	complemented
736	#396	C₂²×C₆₇	1	2	yes	complemented
737	#394	C₂²×C₆₇	1	2	yes	complemented
738	#394	C₂²×C₆₇	1	2	yes	complemented
739	#394	C₂²×C₆₇	1	2	yes	complemented
740	#394	C₂²×C₆₇	1	2	yes	complemented
741	#394	C₂²×C₆₇	1	2	yes	complemented
742	#394	C₂²×C₆₇	1	2	yes	complemented
743	#394	C₂²×C₆₇	1	2	yes	complemented
744	#393	C₂²×C₆₇	1	2	yes	complemented
745	#393	C₂²×C₆₇	1	2	yes	complemented
746	#392	C₂²×C₆₇	1	2	yes	complemented
747	#392	C₂²×C₆₇	1	2	yes	complemented
748	#392	C₂²×C₆₇	1	2	yes	complemented
749	#390	C₂²×C₆₇	1	1	yes	characteristic
750	#390	C₂²×C₆₇	1	1	yes	characteristic
751	#390	C₂²×C₆₇	1	1	yes	characteristic
752	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	#390	C₂²×C₆₇	1	2	yes	complemented
757	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	#390	C₂²×C₆₇	1	2	yes	complemented
759	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
762	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	#388	C₂²×C₆₇	1	2	yes	complemented
764	#388	C₂²×C₆₇	1	2	yes	complemented
765	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#388	C₂²×C₆₇	1	2	yes	complemented
767	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	#386	C₂²×C₆₇	1	1	yes	characteristic
769	#386	C₂²×C₆₇	1	2	yes	complemented
770	#386	C₂²×C₆₇	1	2	yes	complemented
771	#386	C₂²×C₆₇	1	2	yes	complemented
772	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	#386	C₂²×C₆₇	1	2	yes	complemented
774	#386	C₂²×C₆₇	1	2	yes	complemented
775	#386	C₂²×C₆₇	1	2	yes	complemented
776	#386	C₂²×C₆₇	1	2	yes	complemented
777	#385	C₂²×C₆₇	1	2	yes	complemented
778	#385	C₂²×C₆₇	1	2	yes	complemented
779	#381	C₂²×C₆₇	1	2	yes	complemented
780	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#379	C₂²×C₆₇	1	2	yes	complemented
785	#379	C₂²×C₆₇	1	2	yes	complemented
786	#379	C₂²×C₆₇	1	2	yes	complemented
787	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
789	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
790	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
792	C₂⁵	C₂³×C₆₇	1	2	yes	—
793	C₂⁵	C₂³×C₆₇	1	2	yes	—
794	C₂×#41	—	2	8	no	—
795	C₂×#41	—	2	8	no	—
796	C₂×#41	—	4	4	no	—
797	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
798	C₂²×D₄	—	2	8	no	—
799	C₂²×D₄	—	2	4	no	—
800	C₂²×D₄	—	2	8	no	—
801	C₂²×D₄	—	2	4	no	—
802	C₂²×D₄	—	2	4	no	—
803	C₂²×D₄	—	2	4	no	—
804	C₂²×D₄	—	4	2	no	—
805	C₂²×D₄	—	4	2	no	—
806	C₂²×D₄	—	4	4	no	—
807	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
808	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
809	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
810	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
811	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
812	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
813	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
814	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
815	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
817	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
820	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
821	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
822	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
823	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
826	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
827	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
828	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
830	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
831	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₄⋊Q₈	—	2	4	no	—
833	#127	—	2	4	no	—
834	#124	—	2	8	no	—
835	#123	—	2	8	no	—
836	#123	—	2	8	no	—
837	#123	—	2	8	no	—
838	#123	—	2	8	no	—
839	C₂²⋊Q₈	—	2	8	no	—
840	C₂²⋊Q₈	—	2	8	no	—
841	#121	—	2	4	no	—
842	#121	—	2	8	no	—
843	#121	—	2	4	no	—
844	#121	—	2	4	no	—
845	#121	—	2	8	no	—
846	#121	—	2	8	no	—
847	#121	—	4	2	no	—
848	#121	D₄×C₆₇	1	8	yes	complemented
849	#121	D₄×C₆₇	1	8	yes	complemented
850	#120	—	2	8	no	—
851	#120	—	2	8	no	—
852	#120	—	2	8	no	—
853	#120	—	2	8	no	—
854	C₄×D₄	—	2	4	no	—
855	C₄×D₄	—	2	4	no	—
856	C₄×D₄	—	2	4	no	—
857	C₄×D₄	—	2	8	no	—
858	C₄×D₄	—	2	4	no	—
859	C₄×D₄	—	2	8	no	—
860	C₄×D₄	—	4	2	no	—
861	C₄×D₄	—	4	2	no	—
862	C₂×C₄⋊C₄	—	2	4	no	—
863	C₂×C₄⋊C₄	—	2	4	no	—
864	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
867	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
868	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
870	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
873	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
875	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
876	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
880	C₂×C₂²⋊C₄	—	2	8	no	—
881	C₂×C₂²⋊C₄	—	2	8	no	—
882	C₂×C₂²⋊C₄	—	4	4	no	—
883	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
884	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
885	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
886	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
887	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
888	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
889	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
891	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
893	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
894	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
896	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
897	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
898	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
899	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
900	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
901	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
902	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
903	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
904	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
905	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
906	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
907	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
908	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
910	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
912	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
913	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
914	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
915	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
916	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₂×C₄²	—	4	2	no	—
919	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
921	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
922	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
923	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
924	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
925	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
926	#95	C₂³×C₆₇	1	1	yes	characteristic
927	#95	C₂³×C₆₇	1	1	yes	characteristic
928	#95	C₂³×C₆₇	1	2	yes	—
929	#95	C₂³×C₆₇	1	1	yes	characteristic
930	#95	C₂³×C₆₇	1	2	yes	—
931	#95	C₂³×C₆₇	1	1	yes	characteristic
932	#95	C₂³×C₆₇	1	1	yes	characteristic
933	#95	C₂³×C₆₇	1	2	yes	—
934	#95	C₂³×C₆₇	1	1	yes	characteristic
935	#95	C₂³×C₆₇	1	2	yes	—
936	#95	C₂³×C₆₇	1	2	yes	—
937	#95	C₂³×C₆₇	1	2	yes	—
938	#95	C₂³×C₆₇	1	2	yes	—
939	C₂⁴	—	2	4	no	—
940	C₂⁴	—	2	4	no	—
941	C₂⁴	—	2	4	no	—
942	C₂⁴	—	2	4	no	—
943	C₂⁴	—	2	4	no	—
944	C₂⁴	—	2	4	no	—
945	C₂⁴	—	2	4	no	—
946	C₂⁴	—	4	2	no	—
947	C₂⁴	—	4	2	no	—
948	C₂⁴	—	4	2	no	—
949	C₂⁴	—	4	2	no	—
950	C₂⁴	—	4	2	no	—
951	C₂⁴	—	4	2	no	—
952	C₂⁴	—	4	2	no	—
953	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
954	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
955	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
956	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
958	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
959	#41	—	4	32	no	—
960	C₂×Q₈	—	2	4	no	—
961	C₂×Q₈	—	2	4	no	—
962	C₂×Q₈	—	4	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	4	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	4	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	4	no	—
970	C₂×D₄	—	2	4	no	—
971	C₂×D₄	—	2	4	no	—
972	C₂×D₄	—	2	4	no	—
973	C₂×D₄	—	2	4	no	—
974	C₂×D₄	—	2	4	no	—
975	C₂×D₄	—	2	4	no	—
976	C₂×D₄	—	2	4	no	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	2	4	no	—
979	C₂×D₄	—	2	4	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	4	no	—
982	C₂×D₄	—	2	4	no	—
983	C₂×D₄	—	2	4	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	4	16	no	—
991	C₂×D₄	—	4	1	no	—
992	C₂×D₄	—	4	2	no	—
993	C₂×D₄	—	4	2	no	—
994	C₂×D₄	—	4	2	no	—
995	C₂×D₄	—	4	2	no	—
996	C₂×D₄	—	4	2	no	—
997	C₂×D₄	—	4	1	no	—
998	C₂×D₄	—	4	2	no	—
999	C₂×D₄	—	4	2	no	—
1000	C₂×D₄	—	4	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	4	32	no	—
1004	C₂×D₄	—	4	16	no	—
1005	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
1006	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
1007	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
1008	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
1009	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
1010	C₂×D₄	#41×C₆₇	1	4	yes	complemented
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	4	no	—
1014	C₂²×C₄	—	2	4	no	—
1015	C₂²×C₄	—	2	4	no	—
1016	C₂²×C₄	—	2	4	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	4	no	—
1019	C₂²×C₄	—	2	4	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	4	no	—
1022	C₂²×C₄	—	2	4	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	4	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	2	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	4	no	—
1030	C₂²×C₄	—	4	1	no	—
1031	C₂²×C₄	—	4	1	no	—
1032	C₂²×C₄	—	4	2	no	—
1033	C₂²×C₄	—	4	2	no	—
1034	C₂²×C₄	—	4	2	no	—
1035	C₂²×C₄	—	4	1	no	—
1036	C₂²×C₄	—	4	1	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
1040	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	complemented
1041	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1046	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1047	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1050	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1051	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1055	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	4	no	—
1061	C₄⋊C₄	—	2	4	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	4	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	4	no	—
1066	C₄⋊C₄	—	2	4	no	—
1067	C₄⋊C₄	—	2	4	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	4	1	no	—
1071	C₄⋊C₄	—	4	1	no	—
1072	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
1073	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
1074	C₂²⋊C₄	—	2	4	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	4	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	4	no	—
1079	C₂²⋊C₄	—	2	4	no	—
1080	C₂²⋊C₄	—	2	4	no	—
1081	C₂²⋊C₄	—	2	4	no	—
1082	C₂²⋊C₄	—	2	4	no	—
1083	C₂²⋊C₄	—	2	4	no	—
1084	C₂²⋊C₄	—	2	4	no	—
1085	C₂²⋊C₄	—	2	4	no	—
1086	C₂²⋊C₄	—	2	4	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	4	no	—
1089	C₂²⋊C₄	—	2	4	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	4	no	—
1092	C₂²⋊C₄	—	2	4	no	—
1093	C₂²⋊C₄	—	4	2	no	—
1094	C₂²⋊C₄	—	4	2	no	—
1095	C₂²⋊C₄	—	4	2	no	—
1096	C₂²⋊C₄	—	4	2	no	—
1097	C₂²⋊C₄	—	4	1	no	—
1098	C₂²⋊C₄	—	4	2	no	—
1099	C₂²⋊C₄	—	4	1	no	—
1100	C₂²⋊C₄	—	4	2	no	—
1101	C₂²⋊C₄	—	4	1	no	—
1102	C₂²⋊C₄	—	4	2	no	—
1103	C₂²⋊C₄	—	4	2	no	—
1104	C₂²⋊C₄	—	4	2	no	—
1105	C₂²⋊C₄	—	4	1	no	—
1106	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
1107	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
1108	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	complemented
1109	C₄²	—	2	4	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	—	2	2	no	—
1112	C₄²	—	2	2	no	—
1113	C₄²	—	2	2	no	—
1114	C₄²	—	4	1	no	—
1115	C₄²	—	4	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	1	no	—
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	1	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	2	no	—
1123	C₂³	—	2	1	no	—
1124	C₂³	—	2	2	no	—
1125	C₂³	—	2	1	no	—
1126	C₂³	—	2	1	no	—
1127	C₂³	—	2	2	no	—
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	1	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	—	2	2	no	—
1132	C₂³	—	2	1	no	—
1133	C₂³	—	2	2	no	—
1134	C₂³	—	2	1	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	2	no	—
1140	C₂³	—	2	2	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	2	2	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	2	2	no	—
1145	C₂³	—	2	2	no	—
1146	C₂³	—	2	2	no	—
1147	C₂³	—	2	2	no	—
1148	C₂³	—	2	2	no	—
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	4	8	no	—
1152	C₂³	—	4	8	no	—
1153	C₂³	—	4	8	no	—
1154	C₂³	—	4	8	no	—
1155	C₂³	—	4	8	no	—
1156	C₂³	—	4	8	no	—
1157	C₂³	—	4	8	no	—
1158	C₂³	—	8	4	no	—
1159	C₂³	—	8	4	no	—
1160	C₂³	—	8	4	no	—
1161	C₂³	—	8	4	no	—
1162	C₂³	—	8	4	no	—
1163	C₂³	—	8	4	no	—
1164	C₂³	—	8	4	no	—
1165	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1166	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
1167	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1168	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1169	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1170	C₂³	C₂×#41×C₆₇	1	4	yes	—
1171	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
1172	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1173	Q₈	—	4	8	no	—
1174	D₄	—	2	8	no	—
1175	D₄	—	2	16	no	—
1176	D₄	—	2	8	no	—
1177	D₄	—	2	8	no	—
1178	D₄	—	2	8	no	—
1179	D₄	—	4	4	no	—
1180	D₄	—	4	8	no	—
1181	D₄	—	4	8	no	—
1182	D₄	—	4	8	no	—
1183	D₄	—	4	8	no	—
1184	D₄	—	4	8	no	—
1185	D₄	—	4	8	no	—
1186	D₄	—	4	4	no	—
1187	D₄	—	8	4	no	—
1188	D₄	—	8	4	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	8	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	2	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	4	4	no	—
1233	C₂×C₄	—	4	8	no	—
1234	C₂×C₄	—	4	8	no	—
1235	C₂×C₄	—	4	8	no	—
1236	C₂×C₄	—	4	4	no	—
1237	C₂×C₄	—	4	8	no	—
1238	C₂×C₄	—	4	4	no	—
1239	C₂×C₄	—	4	4	no	—
1240	C₂×C₄	—	8	4	no	—
1241	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1242	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1243	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1244	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1245	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1246	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1247	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1248	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1249	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	2	2	no	—
1252	C₂²	—	2	2	no	—
1253	C₂²	—	2	2	no	—
1254	C₂²	—	2	2	no	—
1255	C₂²	—	2	2	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	2	4	no	—
1258	C₂²	—	2	2	no	—
1259	C₂²	—	2	4	no	—
1260	C₂²	—	2	4	no	—
1261	C₂²	—	2	2	no	—
1262	C₂²	—	2	4	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	4	no	—
1267	C₂²	—	2	4	no	—
1268	C₂²	—	4	2	no	—
1269	C₂²	—	4	1	no	—
1270	C₂²	—	4	2	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	2	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	—	4	2	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	2	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	1	no	—
1282	C₂²	—	4	2	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	2	no	—
1285	C₂²	—	4	2	no	—
1286	C₂²	—	4	2	no	—
1287	C₂²	—	4	2	no	—
1288	C₂²	—	4	2	no	—
1289	C₂²	—	4	2	no	—
1290	C₂²	—	4	2	no	—
1291	C₂²	—	8	16	no	—
1292	C₂²	—	8	16	no	—
1293	C₂²	D₄²×C₆₇	1	4	yes	—
1294	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1295	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1296	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1297	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1298	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1299	C₂²	#585×C₆₇	1	1	yes	characteristic
1300	C₂²	#585×C₆₇	1	1	yes	characteristic
1301	C₄	—	2	2	no	—
1302	C₄	—	2	4	no	—
1303	C₄	—	2	2	no	—
1304	C₄	—	2	2	no	—
1305	C₄	—	2	2	no	—
1306	C₄	—	2	2	no	—
1307	C₄	—	4	1	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	2	no	—
1310	C₄	—	4	2	no	—
1311	C₄	—	4	1	no	—
1312	C₄	—	4	1	no	—
1313	C₄	—	4	2	no	—
1314	C₄	—	4	2	no	—
1315	C₄	—	4	1	no	—
1316	C₄	—	4	1	no	—
1317	C₄	#546×C₆₇	1	4	yes	complemented
1318	C₂	—	2	4	no	—
1319	C₂	—	4	2	no	—
1320	C₂	—	4	4	no	—
1321	C₂	—	4	4	no	—
1322	C₂	—	4	2	no	—
1323	C₂	—	8	2	no	—
1324	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1325	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1326	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1327	C₂	C₆₇×#3496	1	1	yes	characteristic
1328	C₂	C₆₇×#3500	1	1	yes	characteristic
1329	C₂	C₆₇×#3513	1	1	yes	characteristic
1330	C₂	C₆₇×#3542	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#547×C₆₇	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₂×D₄²×C₆₇	C₂	semidirect
4. C₆₇×#2681	C₂	semidirect
5. C₆₇×#2678	C₂	semidirect
6. C₆₇×#2534	C₂	semidirect
7. C₆₇×#2491	C₂	semidirect
8. C₆₇×#2486	C₂	semidirect
9. C₆₇×#2472	C₂	semidirect
10. C₆₇×#2464	C₂	semidirect
11. C₆₇×#2452	C₂	semidirect
12. C₆₇×#2445	C₂	semidirect
13. C₆₇×#2428	C₂	semidirect
14. C₆₇×#2416	C₂	semidirect
15. C₆₇×#2408	C₂	semidirect
16. C₆₇×#2408	C₂	semidirect
17. C₆₇×#2405	C₂	semidirect
18. C₆₇×#2404	C₂	semidirect
19. C₆₇×#2361	C₂	semidirect
20. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#390×C₆₇	C₂	semidirect
24. C₂²×#41×C₆₇	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
33. C₂×#124×C₆₇	C₂²	semidirect
35. C₂×#123×C₆₇	C₂²	semidirect
36. C₂×#123×C₆₇	C₂²	semidirect
37. C₂×#123×C₆₇	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
39. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
45. C₂×#121×C₆₇	C₂²	semidirect
46. C₂×#121×C₆₇	C₂²	semidirect
47. C₂×#121×C₆₇	C₂²	semidirect
48. C₂×#121×C₆₇	C₂²	semidirect
51. C₂×#120×C₆₇	C₂²	semidirect
52. C₂×#120×C₆₇	C₂²	semidirect
55. C₂×C₄×D₄×C₆₇	C₂²	semidirect
56. C₂×C₄×D₄×C₆₇	C₂²	semidirect
57. C₂×C₄×D₄×C₆₇	C₂²	semidirect
58. C₂×C₄×D₄×C₆₇	C₂²	semidirect
59. C₂×C₄×D₄×C₆₇	C₂²	semidirect
60. C₂×C₄×D₄×C₆₇	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
62. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
63. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
64. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
65. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
66. C₂²×C₄²×C₆₇	C₂²	semidirect
67. #398×C₆₇	C₂²	semidirect
68. #397×C₆₇	C₂²	semidirect
69. #396×C₆₇	C₂²	semidirect
70. #396×C₆₇	C₂²	semidirect
71. #394×C₆₇	C₂²	semidirect
72. #394×C₆₇	C₂²	semidirect
73. #394×C₆₇	C₂²	semidirect
74. #394×C₆₇	C₂²	semidirect
75. #394×C₆₇	C₂²	semidirect
76. #394×C₆₇	C₂²	semidirect
77. #394×C₆₇	C₂²	semidirect
78. #393×C₆₇	C₂²	semidirect
79. #393×C₆₇	C₂²	semidirect
80. #392×C₆₇	C₂²	semidirect
81. #392×C₆₇	C₂²	semidirect
82. #392×C₆₇	C₂²	semidirect
86. #390×C₆₇	C₂²	semidirect
87. #390×C₆₇	C₂²	semidirect
88. #390×C₆₇	C₂²	semidirect
89. #390×C₆₇	C₂²	semidirect
90. #390×C₆₇	C₂²	semidirect
91. #390×C₆₇	C₂²	semidirect
92. #390×C₆₇	C₂²	semidirect
93. #389×C₆₇	C₂²	semidirect
94. #389×C₆₇	C₂²	semidirect
95. #389×C₆₇	C₂²	semidirect
96. #389×C₆₇	C₂²	semidirect
97. #388×C₆₇	C₂²	semidirect
98. #388×C₆₇	C₂²	semidirect
99. #388×C₆₇	C₂²	semidirect
100. #388×C₆₇	C₂²	semidirect
101. #388×C₆₇	C₂²	semidirect
103. #386×C₆₇	C₂²	semidirect
104. #386×C₆₇	C₂²	semidirect
105. #386×C₆₇	C₂²	semidirect
106. #386×C₆₇	C₂²	semidirect
107. #386×C₆₇	C₂²	semidirect
108. #386×C₆₇	C₂²	semidirect
109. #386×C₆₇	C₂²	semidirect
110. #386×C₆₇	C₂²	semidirect
111. #385×C₆₇	C₂²	semidirect
112. #385×C₆₇	C₂²	semidirect
113. #381×C₆₇	C₂²	semidirect
114. #380×C₆₇	C₂²	semidirect
115. #380×C₆₇	C₂²	semidirect
116. #380×C₆₇	C₂²	semidirect
117. #380×C₆₇	C₂²	semidirect
118. #379×C₆₇	C₂²	semidirect
119. #379×C₆₇	C₂²	semidirect
120. #379×C₆₇	C₂²	semidirect
121. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
125. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
182. #121×C₆₇	D₄	semidirect
183. #121×C₆₇	D₄	semidirect
342. C₂×D₄×C₆₇	C₂×D₄	semidirect
343. C₂×D₄×C₆₇	C₂×D₄	semidirect
344. C₂×D₄×C₆₇	#41	semidirect
374. C₂²×C₄×C₆₇	C₂×D₄	semidirect
407. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
441. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
442. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
651. C₄×C₆₇	#546	semidirect
652. #59808	C₆₇	direct (N × H)
666. C₂×#547	C₂×C₆₇	semidirect
667. C₂×#546	C₂×C₆₇	semidirect
668. C₂×D₄²	C₂×C₆₇	semidirect
669. #2681	C₂×C₆₇	semidirect
670. #2678	C₂×C₆₇	semidirect
671. #2534	C₂×C₆₇	semidirect
672. #2491	C₂×C₆₇	semidirect
673. #2486	C₂×C₆₇	semidirect
674. #2472	C₂×C₆₇	semidirect
675. #2464	C₂×C₆₇	semidirect
676. #2452	C₂×C₆₇	semidirect
677. #2445	C₂×C₆₇	semidirect
678. #2428	C₂×C₆₇	semidirect
679. #2416	C₂×C₆₇	semidirect
680. #2408	C₂×C₆₇	semidirect
681. #2408	C₂×C₆₇	semidirect
682. #2405	C₂×C₆₇	semidirect
683. #2404	C₂×C₆₇	semidirect
684. #2361	C₂×C₆₇	semidirect
685. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
686. C₄×#121	C₂×C₆₇	semidirect
687. C₄×#121	C₂×C₆₇	semidirect
688. C₂×#390	C₂×C₆₇	semidirect
689. C₆₇	#59808	direct (N × H)
690. C₂²×#41	C₂²×C₆₇	semidirect
697. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
699. C₂×#124	C₂²×C₆₇	semidirect
701. C₂×#123	C₂²×C₆₇	semidirect
702. C₂×#123	C₂²×C₆₇	semidirect
703. C₂×#123	C₂²×C₆₇	semidirect
704. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
705. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
711. C₂×#121	C₂²×C₆₇	semidirect
712. C₂×#121	C₂²×C₆₇	semidirect
713. C₂×#121	C₂²×C₆₇	semidirect
714. C₂×#121	C₂²×C₆₇	semidirect
717. C₂×#120	C₂²×C₆₇	semidirect
718. C₂×#120	C₂²×C₆₇	semidirect
721. C₂×C₄×D₄	C₂²×C₆₇	semidirect
722. C₂×C₄×D₄	C₂²×C₆₇	semidirect
723. C₂×C₄×D₄	C₂²×C₆₇	semidirect
724. C₂×C₄×D₄	C₂²×C₆₇	semidirect
725. C₂×C₄×D₄	C₂²×C₆₇	semidirect
726. C₂×C₄×D₄	C₂²×C₆₇	semidirect
727. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
728. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
729. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
730. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
731. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
732. C₂²×C₄²	C₂²×C₆₇	semidirect
733. #398	C₂²×C₆₇	semidirect
734. #397	C₂²×C₆₇	semidirect
735. #396	C₂²×C₆₇	semidirect
736. #396	C₂²×C₆₇	semidirect
737. #394	C₂²×C₆₇	semidirect
738. #394	C₂²×C₆₇	semidirect
739. #394	C₂²×C₆₇	semidirect
740. #394	C₂²×C₆₇	semidirect
741. #394	C₂²×C₆₇	semidirect
742. #394	C₂²×C₆₇	semidirect
743. #394	C₂²×C₆₇	semidirect
744. #393	C₂²×C₆₇	semidirect
745. #393	C₂²×C₆₇	semidirect
746. #392	C₂²×C₆₇	semidirect
747. #392	C₂²×C₆₇	semidirect
748. #392	C₂²×C₆₇	semidirect
752. #390	C₂²×C₆₇	semidirect
753. #390	C₂²×C₆₇	semidirect
754. #390	C₂²×C₆₇	semidirect
755. #390	C₂²×C₆₇	semidirect
756. #390	C₂²×C₆₇	semidirect
757. #390	C₂²×C₆₇	semidirect
758. #390	C₂²×C₆₇	semidirect
759. #389	C₂²×C₆₇	semidirect
760. #389	C₂²×C₆₇	semidirect
761. #389	C₂²×C₆₇	semidirect
762. #389	C₂²×C₆₇	semidirect
763. #388	C₂²×C₆₇	semidirect
764. #388	C₂²×C₆₇	semidirect
765. #388	C₂²×C₆₇	semidirect
766. #388	C₂²×C₆₇	semidirect
767. #388	C₂²×C₆₇	semidirect
769. #386	C₂²×C₆₇	semidirect
770. #386	C₂²×C₆₇	semidirect
771. #386	C₂²×C₆₇	semidirect
772. #386	C₂²×C₆₇	semidirect
773. #386	C₂²×C₆₇	semidirect
774. #386	C₂²×C₆₇	semidirect
775. #386	C₂²×C₆₇	semidirect
776. #386	C₂²×C₆₇	semidirect
777. #385	C₂²×C₆₇	semidirect
778. #385	C₂²×C₆₇	semidirect
779. #381	C₂²×C₆₇	semidirect
780. #380	C₂²×C₆₇	semidirect
781. #380	C₂²×C₆₇	semidirect
782. #380	C₂²×C₆₇	semidirect
783. #380	C₂²×C₆₇	semidirect
784. #379	C₂²×C₆₇	semidirect
785. #379	C₂²×C₆₇	semidirect
786. #379	C₂²×C₆₇	semidirect
787. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
788. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
789. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
790. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
791. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
848. #121	D₄×C₆₇	semidirect
849. #121	D₄×C₆₇	semidirect
1008. C₂×D₄	C₂×D₄×C₆₇	semidirect
1009. C₂×D₄	C₂×D₄×C₆₇	semidirect
1010. C₂×D₄	#41×C₆₇	semidirect
1040. C₂²×C₄	C₂×D₄×C₆₇	semidirect
1073. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
1107. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
1108. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
1317. C₄	#546×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#547×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₆₇×#2681	2
C₆₇×#2678	2
C₆₇×#2534	2
C₆₇×#2491	2
C₆₇×#2486	2
C₆₇×#2472	2
C₆₇×#2464	2
C₆₇×#2452	2
C₆₇×#2445	2
C₆₇×#2428	2
C₆₇×#2416	2
C₆₇×#2408	2
C₆₇×#2405	2
C₆₇×#2404	2
C₆₇×#2361	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#121×C₆₇	2
C₂×#390×C₆₇	2
#59808	67

Subgroups — C67×#59808 #30739059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59808 #30739059