Subgroups — C₇×#62880 #13240096

Order 1792.

7362 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3562	C₂	1	8	yes	maximal, complemented
2	C₇×#3543	C₂	1	8	yes	maximal, complemented
3	C₇×#3542	C₂	1	8	yes	maximal, complemented
4	C₇×#3539	C₂	1	4	yes	maximal, complemented
5	C₇×#3537	C₂	1	8	yes	maximal, complemented
6	C₇×#3537	C₂	1	4	yes	maximal, complemented
7	C₇×#3534	C₂	1	8	yes	maximal, complemented
8	C₇×#3512	C₂	1	2	yes	maximal, complemented
9	C₇×#3506	C₂	1	2	yes	maximal, complemented
10	C₇×#3498	C₂	1	2	yes	maximal, complemented
11	C₇×#3496	C₂	1	2	yes	maximal, complemented
12	C₇×#3488	C₂	1	4	yes	maximal, complemented
13	C₇×#3455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×H(5,𝔽₂)	C₂²	1	4	yes	complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	complemented
18	C₇×#562	C₂²	1	16	yes	complemented
19	C₇×#560	C₂²	1	16	yes	complemented
20	C₇×#560	C₂²	1	16	yes	complemented
21	C₇×#560	C₂²	1	16	yes	complemented
22	C₇×#559	C₂²	1	8	yes	complemented
23	C₇×#556	C₂²	1	4	yes	complemented
24	C₇×#555	C₂²	1	4	yes	complemented
25	C₇×#553	C₂²	1	16	yes	complemented
26	C₇×#553	C₂²	1	8	yes	complemented
27	C₇×#553	C₂²	1	16	yes	complemented
28	C₇×#553	C₂²	1	8	yes	complemented
29	C₇×#552	C₂²	1	8	yes	complemented
30	C₇×#551	C₂²	1	16	yes	complemented
31	C₇×#550	C₂²	1	8	yes	complemented
32	C₇×#550	C₂²	1	8	yes	complemented
33	C₇×#550	C₂²	1	4	yes	complemented
34	C₇×#548	C₂²	1	8	yes	complemented
35	C₇×#547	C₂²	1	4	yes	complemented
36	C₇×#547	C₂²	1	4	yes	complemented
37	C₇×#547	C₂²	1	4	yes	complemented
38	C₇×#546	C₂²	1	8	yes	complemented
39	C₇×#546	C₂²	1	8	yes	complemented
40	C₇×#546	C₂²	1	16	yes	complemented
41	C₇×#546	C₂²	1	8	yes	complemented
42	C₇×#546	C₂²	1	16	yes	complemented
43	C₇×D₄²	C₂²	1	16	yes	complemented
44	C₇×D₄²	C₂²	1	8	yes	complemented
45	C₇×D₄²	C₂²	1	4	yes	complemented
46	C₇×D₄²	C₂²	1	4	yes	complemented
47	C₇×D₄²	C₂²	1	16	yes	complemented
48	C₇×D₄²	C₂²	1	8	yes	complemented
49	C₇×D₄²	C₂²	1	16	yes	complemented
50	C₇×#542	C₂²	1	4	yes	complemented
51	C₇×#541	C₂²	1	4	yes	complemented
52	C₇×#541	C₂²	1	2	yes	complemented
53	C₇×#540	C₂²	1	8	yes	complemented
54	C₇×#540	C₂²	1	16	yes	complemented
55	C₇×#540	C₂²	1	4	yes	complemented
56	C₇×#540	C₂²	1	4	yes	complemented
57	C₇×#540	C₂²	1	2	yes	complemented
58	C₇×#540	C₂²	1	4	yes	complemented
59	C₇×#540	C₂²	1	16	yes	complemented
60	C₇×#539	C₂²	1	16	yes	complemented
61	C₇×#539	C₂²	1	4	yes	complemented
62	C₇×#538	C₂²	1	16	yes	complemented
63	C₇×#538	C₂²	1	16	yes	complemented
64	C₇×#538	C₂²	1	4	yes	complemented
65	C₇×#538	C₂²	1	8	yes	complemented
66	C₇×#537	C₂²	1	4	yes	complemented
67	C₇×#537	C₂²	1	4	yes	complemented
68	C₇×#537	C₂²	1	8	yes	complemented
69	C₇×#536	C₂²	1	4	yes	complemented
70	C₇×#535	C₂²	1	8	yes	complemented
71	C₇×#535	C₂²	1	4	yes	complemented
72	C₇×#535	C₂²	1	4	yes	complemented
73	C₇×#535	C₂²	1	8	yes	complemented
74	C₇×#535	C₂²	1	16	yes	complemented
75	C₇×#534	C₂²	1	4	yes	complemented
76	C₇×#534	C₂²	1	8	yes	complemented
77	C₇×#534	C₂²	1	16	yes	complemented
78	C₇×#534	C₂²	1	16	yes	complemented
79	C₇×#533	C₂²	1	1	yes	characteristic, complemented
80	C₇×#532	C₂²	1	4	yes	complemented
81	C₇×#532	C₂²	1	2	yes	complemented
82	C₇×#532	C₂²	1	2	yes	complemented
83	C₇×#532	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₇×#127	C₂²	1	4	yes	complemented
86	C₇×#529	C₂²	1	8	yes	complemented
87	C₇×#529	C₂²	1	8	yes	complemented
88	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
89	C₇×#525	C₂²	1	4	yes	complemented
90	C₇×#525	C₂²	1	4	yes	complemented
91	C₇×#525	C₂²	1	2	yes	complemented
92	C₇×#525	C₂²	1	8	yes	complemented
93	C₇×#525	C₂²	1	8	yes	complemented
94	C₂×C₇×#123	C₂²	1	4	yes	complemented
95	C₂×C₇×#121	C₂²	1	2	yes	complemented
96	C₂×C₇×#121	C₂²	1	4	yes	complemented
97	C₂×C₇×#121	C₂²	1	8	yes	complemented
98	C₂×C₇×#121	C₂²	1	8	yes	complemented
99	C₇×#520	C₂²	1	4	yes	complemented
100	C₄×C₇×#41	C₂²	1	2	yes	complemented
101	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
102	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
103	#62880	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₇×H(5,𝔽₂)	—	4	16	no	—
105	C₂×C₇×#41	—	4	8	no	—
106	C₂×C₇×#41	C₂³	1	4	yes	—
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂×C₇×#41	C₂³	1	4	yes	—
109	C₂×C₇×#41	C₂³	1	4	yes	—
110	C₂×C₇×#41	C₂³	1	4	yes	—
111	C₂×C₇×#41	C₂³	1	8	yes	—
112	C₂×C₇×#41	C₂³	1	8	yes	—
113	C₂×C₇×#41	C₂³	1	8	yes	—
114	C₂²×C₇×Q₈	C₂³	1	2	yes	—
115	C₂²×C₇×D₄	C₂³	1	2	yes	—
116	C₂²×C₇×D₄	C₂³	1	4	yes	—
117	C₂²×C₇×D₄	C₂³	1	2	yes	—
118	C₂²×C₇×D₄	C₂³	1	16	yes	—
119	C₂²×C₇×D₄	C₂³	1	8	yes	—
120	C₂²×C₇×D₄	C₂³	1	8	yes	—
121	C₂²×C₇×D₄	C₂³	1	4	yes	—
122	C₂²×C₇×D₄	C₂³	1	4	yes	—
123	C₂²×C₇×D₄	C₂³	1	8	yes	—
124	C₂²×C₇×D₄	C₂³	1	16	yes	—
125	C₂²×C₇×D₄	C₂³	1	16	yes	—
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₇	C₂³	1	4	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₇×#127	C₂³	1	4	yes	—
134	C₇×#127	C₂³	1	2	yes	—
135	C₇×#127	C₂³	1	8	yes	—
136	C₇×#127	C₂³	1	16	yes	—
137	C₇×#127	C₂³	1	4	yes	—
138	C₇×#127	C₂³	1	2	yes	—
139	C₇×#127	C₂³	1	1	yes	characteristic
140	C₇×#127	C₂³	1	16	yes	—
141	C₇×#126	C₂³	1	16	yes	—
142	C₇×#126	C₂³	1	8	yes	—
143	C₇×#126	C₂³	1	8	yes	—
144	C₇×#126	C₂³	1	16	yes	—
145	C₇×#126	C₂³	1	16	yes	—
146	C₇×#125	C₂³	1	4	yes	—
147	C₇×#125	C₂³	1	4	yes	—
148	C₇×#125	C₂³	1	8	yes	—
149	C₇×#125	C₂³	1	2	yes	—
150	C₇×#125	C₂³	1	16	yes	—
151	C₇×#124	C₂³	1	4	yes	—
152	C₇×#124	C₂³	1	8	yes	—
153	C₇×#124	C₂³	1	8	yes	—
154	C₇×#124	C₂³	1	4	yes	—
155	C₇×#124	C₂³	1	2	yes	—
156	C₇×#124	C₂³	1	16	yes	—
157	C₇×#124	C₂³	1	16	yes	—
158	C₇×#123	C₂³	1	16	yes	—
159	C₇×#123	C₂³	1	16	yes	—
160	C₇×#123	C₂³	1	8	yes	—
161	C₇×#123	C₂³	1	8	yes	—
162	C₇×#123	C₂³	1	16	yes	—
163	C₇×#123	C₂³	1	4	yes	—
164	C₇×#123	C₂³	1	16	yes	—
165	C₇×#123	C₂³	1	8	yes	—
166	C₇×#123	C₂³	1	8	yes	—
167	C₇×#123	C₂³	1	16	yes	—
168	C₇×#123	C₂³	1	16	yes	—
169	C₇×#123	C₂³	1	16	yes	—
170	C₇×#123	C₂³	1	16	yes	—
171	C₇×#123	C₂³	1	16	yes	—
172	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
174	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
181	C₇×#121	C₂³	1	4	yes	—
182	C₇×#121	C₂³	1	8	yes	—
183	C₇×#121	C₂³	1	4	yes	—
184	C₇×#121	C₂³	1	4	yes	—
185	C₇×#121	C₂³	1	16	yes	—
186	C₇×#121	C₂³	1	16	yes	—
187	C₇×#121	C₂³	1	16	yes	—
188	C₇×#121	C₂³	1	8	yes	—
189	C₇×#121	C₂³	1	8	yes	—
190	C₇×#121	C₂³	1	16	yes	—
191	C₇×#121	C₂³	1	8	yes	—
192	C₇×#121	C₂³	1	16	yes	—
193	C₇×#121	C₂³	1	8	yes	—
194	C₇×#121	C₂³	1	8	yes	—
195	C₇×#121	C₂³	1	16	yes	—
196	C₇×#121	C₂³	1	4	yes	—
197	C₇×#121	C₂³	1	8	yes	—
198	C₇×#121	C₂³	1	8	yes	—
199	C₇×#121	C₂³	1	8	yes	—
200	C₇×#121	C₂³	1	8	yes	—
201	C₇×#121	C₂³	1	8	yes	—
202	C₇×#121	C₂³	1	8	yes	—
203	C₇×#121	C₂³	1	8	yes	—
204	C₇×#121	C₂³	1	16	yes	—
205	C₇×#121	C₂³	1	16	yes	—
206	C₇×#121	C₂³	1	16	yes	—
207	C₇×#121	C₂³	1	16	yes	—
208	C₇×#121	C₂³	1	16	yes	—
209	C₇×#121	C₂³	1	16	yes	—
210	C₇×#121	C₂³	1	16	yes	—
211	C₇×#121	C₂³	1	16	yes	—
212	C₇×#120	C₂³	1	8	yes	—
213	C₇×#120	C₂³	1	8	yes	—
214	C₇×#120	C₂³	1	16	yes	—
215	C₇×#120	C₂³	1	16	yes	—
216	C₇×#120	C₂³	1	4	yes	—
217	C₇×#120	C₂³	1	16	yes	—
218	C₇×#120	C₂³	1	16	yes	—
219	C₇×#120	C₂³	1	16	yes	—
220	C₇×#120	C₂³	1	16	yes	—
221	C₇×#120	C₂³	1	16	yes	—
222	C₇×#120	C₂³	1	16	yes	—
223	C₄×C₇×Q₈	C₂³	1	4	yes	—
224	C₄×C₇×Q₈	C₂³	1	8	yes	—
225	C₄×C₇×Q₈	C₂³	1	4	yes	—
226	C₄×C₇×D₄	C₂³	1	4	yes	—
227	C₄×C₇×D₄	C₂³	1	4	yes	—
228	C₄×C₇×D₄	C₂³	1	4	yes	—
229	C₄×C₇×D₄	C₂³	1	4	yes	—
230	C₄×C₇×D₄	C₂³	1	8	yes	—
231	C₄×C₇×D₄	C₂³	1	4	yes	—
232	C₄×C₇×D₄	C₂³	1	16	yes	—
233	C₄×C₇×D₄	C₂³	1	8	yes	—
234	C₄×C₇×D₄	C₂³	1	4	yes	—
235	C₄×C₇×D₄	C₂³	1	8	yes	—
236	C₄×C₇×D₄	C₂³	1	4	yes	—
237	C₄×C₇×D₄	C₂³	1	8	yes	—
238	C₄×C₇×D₄	C₂³	1	16	yes	—
239	C₄×C₇×D₄	C₂³	1	16	yes	—
240	C₄×C₇×D₄	C₂³	1	16	yes	—
241	C₄×C₇×D₄	C₂³	1	4	yes	—
242	C₄×C₇×D₄	C₂³	1	16	yes	—
243	C₄×C₇×D₄	C₂³	1	16	yes	—
244	C₇×#117	C₂³	1	2	yes	—
245	C₇×#117	C₂³	1	2	yes	—
246	C₇×#117	C₂³	1	4	yes	—
247	C₇×#117	C₂³	1	2	yes	—
248	C₇×#117	C₂³	1	4	yes	—
249	C₇×#117	C₂³	1	8	yes	—
250	C₇×#117	C₂³	1	8	yes	—
251	C₇×#117	C₂³	1	16	yes	—
252	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
255	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
257	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
259	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
260	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
261	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
262	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
263	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₇	C₂³	1	4	yes	—
265	#3562	C₂×C₇	1	8	yes	complemented
266	#3543	C₂×C₇	1	8	yes	complemented
267	#3542	C₂×C₇	1	8	yes	complemented
268	#3539	C₂×C₇	1	4	yes	complemented
269	#3537	C₂×C₇	1	8	yes	complemented
270	#3537	C₂×C₇	1	4	yes	complemented
271	#3534	C₂×C₇	1	8	yes	complemented
272	#3512	C₂×C₇	1	2	yes	complemented
273	#3506	C₂×C₇	1	2	yes	complemented
274	#3498	C₂×C₇	1	2	yes	complemented
275	#3496	C₂×C₇	1	2	yes	complemented
276	#3488	C₂×C₇	1	4	yes	complemented
277	#3455	C₂×C₇	1	1	yes	characteristic, complemented
278	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
279	#3449	C₂×C₇	1	1	yes	characteristic, complemented
280	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₇	C₂⁴	1	4	yes	—
282	C₂⁴×C₇	C₂⁴	1	16	yes	—
283	C₂⁴×C₇	C₂⁴	1	4	yes	—
284	C₇×#41	—	2	16	no	—
285	C₇×#41	—	2	8	no	—
286	C₇×#41	—	4	8	no	—
287	C₇×#41	—	4	8	no	—
288	C₇×#41	—	4	8	no	—
289	C₇×#41	—	4	16	no	—
290	C₇×#41	—	4	16	no	—
291	C₇×#41	—	8	8	no	—
292	C₂×C₇×Q₈	—	4	4	no	—
293	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
294	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
295	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
296	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
297	C₂×C₇×D₄	—	2	8	no	—
298	C₂×C₇×D₄	—	4	4	no	—
299	C₂×C₇×D₄	—	4	16	no	—
300	C₂×C₇×D₄	—	4	16	no	—
301	C₂×C₇×D₄	—	4	8	no	—
302	C₂×C₇×D₄	—	4	32	no	—
303	C₂×C₇×D₄	—	8	4	no	—
304	C₂×C₇×D₄	—	8	8	no	—
305	C₂×C₇×D₄	—	8	4	no	—
306	C₂×C₇×D₄	—	8	16	no	—
307	C₂×C₇×D₄	—	8	16	no	—
308	C₂×C₇×D₄	C₂⁴	1	8	yes	—
309	C₂×C₇×D₄	C₂⁴	1	4	yes	—
310	C₂×C₇×D₄	C₂⁴	1	2	yes	—
311	C₂×C₇×D₄	C₂⁴	1	4	yes	—
312	C₂×C₇×D₄	C₂⁴	1	4	yes	—
313	C₂×C₇×D₄	C₂⁴	1	4	yes	—
314	C₂×C₇×D₄	C₂⁴	1	4	yes	—
315	C₂×C₇×D₄	C₂⁴	1	4	yes	—
316	C₂×C₇×D₄	C₂⁴	1	16	yes	—
317	C₂×C₇×D₄	C₂⁴	1	16	yes	—
318	C₂×C₇×D₄	C₂⁴	1	8	yes	—
319	C₂×C₇×D₄	C₂⁴	1	4	yes	—
320	C₂×C₇×D₄	C₂⁴	1	16	yes	—
321	C₂×C₇×D₄	C₂⁴	1	16	yes	—
322	C₂×C₇×D₄	C₂⁴	1	8	yes	—
323	C₂×C₇×D₄	C₂⁴	1	16	yes	—
324	C₂×C₇×D₄	C₂⁴	1	4	yes	—
325	C₂×C₇×D₄	C₂⁴	1	8	yes	—
326	C₂×C₇×D₄	C₂⁴	1	16	yes	—
327	C₂×C₇×D₄	C₂⁴	1	16	yes	—
328	C₂²×C₄×C₇	—	2	4	no	—
329	C₂²×C₄×C₇	—	4	8	no	—
330	C₂²×C₄×C₇	—	8	4	no	—
331	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
342	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
343	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
344	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
347	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
349	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
350	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
351	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
352	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
353	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
354	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
355	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
356	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
357	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
358	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
359	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
360	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
361	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
362	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
363	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
364	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
365	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
366	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
367	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
368	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
369	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
370	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
371	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
372	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
373	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
374	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
375	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
376	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
377	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
378	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
379	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
380	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
381	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₄²×C₇	C₂⁴	1	2	yes	—
383	C₄²×C₇	C₂⁴	1	1	yes	characteristic
384	C₄²×C₇	C₂⁴	1	1	yes	characteristic
385	C₄²×C₇	C₂⁴	1	2	yes	—
386	C₄²×C₇	C₂⁴	1	2	yes	—
387	C₄²×C₇	C₂⁴	1	4	yes	—
388	C₄²×C₇	C₂⁴	1	8	yes	—
389	C₄²×C₇	C₂⁴	1	16	yes	—
390	C₂×H(5,𝔽₂)	C₂²×C₇	1	4	yes	complemented
391	C₂²×#41	C₂²×C₇	1	2	yes	complemented
392	#562	C₂²×C₇	1	16	yes	complemented
393	#560	C₂²×C₇	1	16	yes	complemented
394	#560	C₂²×C₇	1	16	yes	complemented
395	#560	C₂²×C₇	1	16	yes	complemented
396	#559	C₂²×C₇	1	8	yes	complemented
397	#556	C₂²×C₇	1	4	yes	complemented
398	#555	C₂²×C₇	1	4	yes	complemented
399	#553	C₂²×C₇	1	8	yes	complemented
400	#553	C₂²×C₇	1	16	yes	complemented
401	#553	C₂²×C₇	1	8	yes	complemented
402	#553	C₂²×C₇	1	16	yes	complemented
403	#552	C₂²×C₇	1	8	yes	complemented
404	#551	C₂²×C₇	1	16	yes	complemented
405	#550	C₂²×C₇	1	8	yes	complemented
406	#550	C₂²×C₇	1	8	yes	complemented
407	#550	C₂²×C₇	1	4	yes	complemented
408	#548	C₂²×C₇	1	8	yes	complemented
409	#547	C₂²×C₇	1	4	yes	complemented
410	#547	C₂²×C₇	1	4	yes	complemented
411	#547	C₂²×C₇	1	4	yes	complemented
412	#546	C₂²×C₇	1	16	yes	complemented
413	#546	C₂²×C₇	1	8	yes	complemented
414	#546	C₂²×C₇	1	8	yes	complemented
415	#546	C₂²×C₇	1	8	yes	complemented
416	#546	C₂²×C₇	1	16	yes	complemented
417	D₄²	C₂²×C₇	1	16	yes	complemented
418	D₄²	C₂²×C₇	1	8	yes	complemented
419	D₄²	C₂²×C₇	1	4	yes	complemented
420	D₄²	C₂²×C₇	1	4	yes	complemented
421	D₄²	C₂²×C₇	1	16	yes	complemented
422	D₄²	C₂²×C₇	1	8	yes	complemented
423	D₄²	C₂²×C₇	1	16	yes	complemented
424	#542	C₂²×C₇	1	4	yes	complemented
425	#541	C₂²×C₇	1	2	yes	complemented
426	#541	C₂²×C₇	1	4	yes	complemented
427	#540	C₂²×C₇	1	4	yes	complemented
428	#540	C₂²×C₇	1	4	yes	complemented
429	#540	C₂²×C₇	1	8	yes	complemented
430	#540	C₂²×C₇	1	2	yes	complemented
431	#540	C₂²×C₇	1	4	yes	complemented
432	#540	C₂²×C₇	1	16	yes	complemented
433	#540	C₂²×C₇	1	16	yes	complemented
434	#539	C₂²×C₇	1	4	yes	complemented
435	#539	C₂²×C₇	1	16	yes	complemented
436	#538	C₂²×C₇	1	4	yes	complemented
437	#538	C₂²×C₇	1	8	yes	complemented
438	#538	C₂²×C₇	1	16	yes	complemented
439	#538	C₂²×C₇	1	16	yes	complemented
440	#537	C₂²×C₇	1	4	yes	complemented
441	#537	C₂²×C₇	1	4	yes	complemented
442	#537	C₂²×C₇	1	8	yes	complemented
443	#536	C₂²×C₇	1	4	yes	complemented
444	#535	C₂²×C₇	1	4	yes	complemented
445	#535	C₂²×C₇	1	4	yes	complemented
446	#535	C₂²×C₇	1	8	yes	complemented
447	#535	C₂²×C₇	1	8	yes	complemented
448	#535	C₂²×C₇	1	16	yes	complemented
449	#534	C₂²×C₇	1	4	yes	complemented
450	#534	C₂²×C₇	1	8	yes	complemented
451	#534	C₂²×C₇	1	16	yes	complemented
452	#534	C₂²×C₇	1	16	yes	complemented
453	#533	C₂²×C₇	1	1	yes	characteristic, complemented
454	#532	C₂²×C₇	1	2	yes	complemented
455	#532	C₂²×C₇	1	2	yes	complemented
456	#532	C₂²×C₇	1	1	yes	characteristic, complemented
457	#532	C₂²×C₇	1	4	yes	complemented
458	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
459	C₂×#127	C₂²×C₇	1	4	yes	complemented
460	#529	C₂²×C₇	1	8	yes	complemented
461	#529	C₂²×C₇	1	8	yes	complemented
462	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
463	#525	C₂²×C₇	1	4	yes	complemented
464	#525	C₂²×C₇	1	4	yes	complemented
465	#525	C₂²×C₇	1	2	yes	complemented
466	#525	C₂²×C₇	1	8	yes	complemented
467	#525	C₂²×C₇	1	8	yes	complemented
468	C₂×#123	C₂²×C₇	1	4	yes	complemented
469	C₂×#121	C₂²×C₇	1	2	yes	complemented
470	C₂×#121	C₂²×C₇	1	4	yes	complemented
471	C₂×#121	C₂²×C₇	1	8	yes	complemented
472	C₂×#121	C₂²×C₇	1	8	yes	complemented
473	#520	C₂²×C₇	1	4	yes	complemented
474	C₄×#41	C₂²×C₇	1	2	yes	complemented
475	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
476	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
477	C₂³×C₇	—	2	2	no	—
478	C₂³×C₇	—	2	8	no	—
479	C₂³×C₇	—	4	4	no	—
480	C₂³×C₇	—	4	4	no	—
481	C₂³×C₇	—	4	2	no	—
482	C₂³×C₇	—	4	4	no	—
483	C₂³×C₇	—	4	8	no	—
484	C₂³×C₇	—	4	16	no	—
485	C₂³×C₇	—	4	16	no	—
486	C₂³×C₇	—	4	16	no	—
487	C₂³×C₇	C₂⁵	1	4	yes	—
488	C₂³×C₇	C₂⁵	1	2	yes	—
489	C₂³×C₇	C₂⁵	1	8	yes	—
490	C₂³×C₇	C₂⁵	1	8	yes	—
491	C₂³×C₇	C₂⁵	1	1	yes	characteristic
492	C₇×Q₈	—	2	8	no	—
493	C₇×Q₈	—	2	4	no	—
494	C₇×Q₈	—	4	4	no	—
495	C₇×Q₈	—	4	4	no	—
496	C₇×D₄	—	2	8	no	—
497	C₇×D₄	—	2	16	no	—
498	C₇×D₄	—	2	8	no	—
499	C₇×D₄	—	2	8	no	—
500	C₇×D₄	—	2	4	no	—
501	C₇×D₄	—	2	8	no	—
502	C₇×D₄	—	4	16	no	—
503	C₇×D₄	—	4	16	no	—
504	C₇×D₄	—	4	4	no	—
505	C₇×D₄	—	4	8	no	—
506	C₇×D₄	—	4	4	no	—
507	C₇×D₄	—	4	16	no	—
508	C₇×D₄	—	4	4	no	—
509	C₇×D₄	—	4	16	no	—
510	C₇×D₄	—	4	16	no	—
511	C₇×D₄	—	4	8	no	—
512	C₇×D₄	—	4	8	no	—
513	C₇×D₄	—	4	16	no	—
514	C₇×D₄	—	4	16	no	—
515	C₇×D₄	—	4	4	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	4	no	—
518	C₂×C₄×C₇	—	2	4	no	—
519	C₂×C₄×C₇	—	2	16	no	—
520	C₂×C₄×C₇	—	2	8	no	—
521	C₂×C₄×C₇	—	4	4	no	—
522	C₂×C₄×C₇	—	4	8	no	—
523	C₂×C₄×C₇	—	4	2	no	—
524	C₂×C₄×C₇	—	4	4	no	—
525	C₂×C₄×C₇	—	4	8	no	—
526	C₂×C₄×C₇	—	4	8	no	—
527	C₂×C₄×C₇	—	4	16	no	—
528	C₂×C₄×C₇	—	4	2	no	—
529	C₂×C₄×C₇	—	4	8	no	—
530	C₂×C₄×C₇	—	4	16	no	—
531	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
532	C₂×C₄×C₇	C₂⁵	1	8	yes	—
533	C₂×C₄×C₇	C₂⁵	1	4	yes	—
534	C₂×C₄×C₇	C₂⁵	1	2	yes	—
535	C₂×C₄×C₇	C₂⁵	1	2	yes	—
536	C₂×C₄×C₇	C₂⁵	1	8	yes	—
537	C₂×C₄×C₇	C₂⁵	1	8	yes	—
538	C₂×C₄×C₇	C₂⁵	1	4	yes	—
539	C₂×C₄×C₇	C₂⁵	1	2	yes	—
540	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
541	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
542	H(5,𝔽₂)	—	4	16	no	—
543	C₂×#41	—	4	8	no	—
544	C₂×#41	C₂³×C₇	1	2	yes	—
545	C₂×#41	C₂³×C₇	1	4	yes	—
546	C₂×#41	C₂³×C₇	1	4	yes	—
547	C₂×#41	C₂³×C₇	1	8	yes	—
548	C₂×#41	C₂³×C₇	1	8	yes	—
549	C₂×#41	C₂³×C₇	1	4	yes	—
550	C₂×#41	C₂³×C₇	1	4	yes	—
551	C₂×#41	C₂³×C₇	1	8	yes	—
552	C₂²×Q₈	C₂³×C₇	1	2	yes	—
553	C₂²×D₄	C₂³×C₇	1	2	yes	—
554	C₂²×D₄	C₂³×C₇	1	16	yes	—
555	C₂²×D₄	C₂³×C₇	1	8	yes	—
556	C₂²×D₄	C₂³×C₇	1	8	yes	—
557	C₂²×D₄	C₂³×C₇	1	4	yes	—
558	C₂²×D₄	C₂³×C₇	1	2	yes	—
559	C₂²×D₄	C₂³×C₇	1	4	yes	—
560	C₂²×D₄	C₂³×C₇	1	4	yes	—
561	C₂²×D₄	C₂³×C₇	1	8	yes	—
562	C₂²×D₄	C₂³×C₇	1	16	yes	—
563	C₂²×D₄	C₂³×C₇	1	16	yes	—
564	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₇	1	4	yes	—
566	C₂³×C₄	C₂³×C₇	1	4	yes	—
567	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
570	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
571	#127	C₂³×C₇	1	4	yes	—
572	#127	C₂³×C₇	1	2	yes	—
573	#127	C₂³×C₇	1	8	yes	—
574	#127	C₂³×C₇	1	16	yes	—
575	#127	C₂³×C₇	1	4	yes	—
576	#127	C₂³×C₇	1	2	yes	—
577	#127	C₂³×C₇	1	1	yes	characteristic
578	#127	C₂³×C₇	1	16	yes	—
579	#126	C₂³×C₇	1	16	yes	—
580	#126	C₂³×C₇	1	8	yes	—
581	#126	C₂³×C₇	1	8	yes	—
582	#126	C₂³×C₇	1	16	yes	—
583	#126	C₂³×C₇	1	16	yes	—
584	#125	C₂³×C₇	1	4	yes	—
585	#125	C₂³×C₇	1	4	yes	—
586	#125	C₂³×C₇	1	8	yes	—
587	#125	C₂³×C₇	1	2	yes	—
588	#125	C₂³×C₇	1	16	yes	—
589	#124	C₂³×C₇	1	4	yes	—
590	#124	C₂³×C₇	1	8	yes	—
591	#124	C₂³×C₇	1	8	yes	—
592	#124	C₂³×C₇	1	4	yes	—
593	#124	C₂³×C₇	1	2	yes	—
594	#124	C₂³×C₇	1	16	yes	—
595	#124	C₂³×C₇	1	16	yes	—
596	#123	C₂³×C₇	1	16	yes	—
597	#123	C₂³×C₇	1	16	yes	—
598	#123	C₂³×C₇	1	8	yes	—
599	#123	C₂³×C₇	1	8	yes	—
600	#123	C₂³×C₇	1	16	yes	—
601	#123	C₂³×C₇	1	4	yes	—
602	#123	C₂³×C₇	1	16	yes	—
603	#123	C₂³×C₇	1	8	yes	—
604	#123	C₂³×C₇	1	8	yes	—
605	#123	C₂³×C₇	1	16	yes	—
606	#123	C₂³×C₇	1	16	yes	—
607	#123	C₂³×C₇	1	16	yes	—
608	#123	C₂³×C₇	1	16	yes	—
609	#123	C₂³×C₇	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
611	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
612	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
613	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
614	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
615	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
616	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
617	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
618	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
619	#121	C₂³×C₇	1	4	yes	—
620	#121	C₂³×C₇	1	8	yes	—
621	#121	C₂³×C₇	1	4	yes	—
622	#121	C₂³×C₇	1	4	yes	—
623	#121	C₂³×C₇	1	16	yes	—
624	#121	C₂³×C₇	1	16	yes	—
625	#121	C₂³×C₇	1	16	yes	—
626	#121	C₂³×C₇	1	8	yes	—
627	#121	C₂³×C₇	1	8	yes	—
628	#121	C₂³×C₇	1	16	yes	—
629	#121	C₂³×C₇	1	8	yes	—
630	#121	C₂³×C₇	1	16	yes	—
631	#121	C₂³×C₇	1	8	yes	—
632	#121	C₂³×C₇	1	8	yes	—
633	#121	C₂³×C₇	1	16	yes	—
634	#121	C₂³×C₇	1	4	yes	—
635	#121	C₂³×C₇	1	8	yes	—
636	#121	C₂³×C₇	1	8	yes	—
637	#121	C₂³×C₇	1	8	yes	—
638	#121	C₂³×C₇	1	8	yes	—
639	#121	C₂³×C₇	1	8	yes	—
640	#121	C₂³×C₇	1	8	yes	—
641	#121	C₂³×C₇	1	8	yes	—
642	#121	C₂³×C₇	1	16	yes	—
643	#121	C₂³×C₇	1	16	yes	—
644	#121	C₂³×C₇	1	16	yes	—
645	#121	C₂³×C₇	1	16	yes	—
646	#121	C₂³×C₇	1	16	yes	—
647	#121	C₂³×C₇	1	16	yes	—
648	#121	C₂³×C₇	1	16	yes	—
649	#121	C₂³×C₇	1	16	yes	—
650	#120	C₂³×C₇	1	8	yes	—
651	#120	C₂³×C₇	1	8	yes	—
652	#120	C₂³×C₇	1	16	yes	—
653	#120	C₂³×C₇	1	16	yes	—
654	#120	C₂³×C₇	1	4	yes	—
655	#120	C₂³×C₇	1	16	yes	—
656	#120	C₂³×C₇	1	16	yes	—
657	#120	C₂³×C₇	1	16	yes	—
658	#120	C₂³×C₇	1	16	yes	—
659	#120	C₂³×C₇	1	16	yes	—
660	#120	C₂³×C₇	1	16	yes	—
661	C₄×Q₈	C₂³×C₇	1	4	yes	—
662	C₄×Q₈	C₂³×C₇	1	8	yes	—
663	C₄×Q₈	C₂³×C₇	1	4	yes	—
664	C₄×D₄	C₂³×C₇	1	4	yes	—
665	C₄×D₄	C₂³×C₇	1	4	yes	—
666	C₄×D₄	C₂³×C₇	1	4	yes	—
667	C₄×D₄	C₂³×C₇	1	4	yes	—
668	C₄×D₄	C₂³×C₇	1	8	yes	—
669	C₄×D₄	C₂³×C₇	1	4	yes	—
670	C₄×D₄	C₂³×C₇	1	16	yes	—
671	C₄×D₄	C₂³×C₇	1	8	yes	—
672	C₄×D₄	C₂³×C₇	1	4	yes	—
673	C₄×D₄	C₂³×C₇	1	8	yes	—
674	C₄×D₄	C₂³×C₇	1	4	yes	—
675	C₄×D₄	C₂³×C₇	1	8	yes	—
676	C₄×D₄	C₂³×C₇	1	16	yes	—
677	C₄×D₄	C₂³×C₇	1	16	yes	—
678	C₄×D₄	C₂³×C₇	1	16	yes	—
679	C₄×D₄	C₂³×C₇	1	4	yes	—
680	C₄×D₄	C₂³×C₇	1	16	yes	—
681	C₄×D₄	C₂³×C₇	1	16	yes	—
682	#117	C₂³×C₇	1	2	yes	—
683	#117	C₂³×C₇	1	2	yes	—
684	#117	C₂³×C₇	1	4	yes	—
685	#117	C₂³×C₇	1	2	yes	—
686	#117	C₂³×C₇	1	4	yes	—
687	#117	C₂³×C₇	1	8	yes	—
688	#117	C₂³×C₇	1	8	yes	—
689	#117	C₂³×C₇	1	16	yes	—
690	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
693	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
694	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₇	1	4	yes	—
703	C₂²×C₇	—	2	2	no	—
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	8	no	—
706	C₂²×C₇	—	2	4	no	—
707	C₂²×C₇	—	2	8	no	—
708	C₂²×C₇	—	2	8	no	—
709	C₂²×C₇	—	2	8	no	—
710	C₂²×C₇	—	2	8	no	—
711	C₂²×C₇	—	2	4	no	—
712	C₂²×C₇	—	2	8	no	—
713	C₂²×C₇	—	2	8	no	—
714	C₂²×C₇	—	8	2	no	—
715	C₂²×C₇	—	8	8	no	—
716	C₂²×C₇	—	8	8	no	—
717	C₂²×C₇	—	16	16	no	—
718	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
719	C₂²×C₇	C₂⁶	1	1	yes	characteristic
720	C₄×C₇	—	2	2	no	—
721	C₄×C₇	—	2	4	no	—
722	C₄×C₇	—	2	8	no	—
723	C₄×C₇	—	2	2	no	—
724	C₄×C₇	—	2	8	no	—
725	C₄×C₇	—	2	2	no	—
726	C₄×C₇	—	2	4	no	—
727	C₄×C₇	—	2	8	no	—
728	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
729	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
730	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₇	1	4	yes	—
732	C₂⁴	C₂⁴×C₇	1	16	yes	—
733	C₂⁴	C₂⁴×C₇	1	4	yes	—
734	#41	—	2	16	no	—
735	#41	—	2	8	no	—
736	#41	—	4	8	no	—
737	#41	—	4	8	no	—
738	#41	—	4	8	no	—
739	#41	—	4	16	no	—
740	#41	—	4	16	no	—
741	#41	—	8	8	no	—
742	C₂×Q₈	—	4	4	no	—
743	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
744	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
745	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
746	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	16	no	—
750	C₂×D₄	—	4	16	no	—
751	C₂×D₄	—	4	8	no	—
752	C₂×D₄	—	4	32	no	—
753	C₂×D₄	—	8	4	no	—
754	C₂×D₄	—	8	8	no	—
755	C₂×D₄	—	8	4	no	—
756	C₂×D₄	—	8	16	no	—
757	C₂×D₄	—	8	16	no	—
758	C₂×D₄	C₂⁴×C₇	1	8	yes	—
759	C₂×D₄	C₂⁴×C₇	1	4	yes	—
760	C₂×D₄	C₂⁴×C₇	1	2	yes	—
761	C₂×D₄	C₂⁴×C₇	1	4	yes	—
762	C₂×D₄	C₂⁴×C₇	1	4	yes	—
763	C₂×D₄	C₂⁴×C₇	1	4	yes	—
764	C₂×D₄	C₂⁴×C₇	1	4	yes	—
765	C₂×D₄	C₂⁴×C₇	1	4	yes	—
766	C₂×D₄	C₂⁴×C₇	1	16	yes	—
767	C₂×D₄	C₂⁴×C₇	1	16	yes	—
768	C₂×D₄	C₂⁴×C₇	1	8	yes	—
769	C₂×D₄	C₂⁴×C₇	1	4	yes	—
770	C₂×D₄	C₂⁴×C₇	1	16	yes	—
771	C₂×D₄	C₂⁴×C₇	1	16	yes	—
772	C₂×D₄	C₂⁴×C₇	1	8	yes	—
773	C₂×D₄	C₂⁴×C₇	1	16	yes	—
774	C₂×D₄	C₂⁴×C₇	1	4	yes	—
775	C₂×D₄	C₂⁴×C₇	1	8	yes	—
776	C₂×D₄	C₂⁴×C₇	1	16	yes	—
777	C₂×D₄	C₂⁴×C₇	1	16	yes	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	4	8	no	—
780	C₂²×C₄	—	8	4	no	—
781	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
782	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
790	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
791	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
792	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
793	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
794	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
795	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
796	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
798	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
799	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
800	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
801	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
802	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
803	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
804	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
805	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
806	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
807	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
808	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
809	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
810	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
811	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
812	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
813	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
814	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
815	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
816	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
817	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
818	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
819	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
820	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
822	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
823	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
825	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
826	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
827	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
828	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
829	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
830	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
831	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
832	C₄²	C₂⁴×C₇	1	2	yes	—
833	C₄²	C₂⁴×C₇	1	1	yes	characteristic
834	C₄²	C₂⁴×C₇	1	1	yes	characteristic
835	C₄²	C₂⁴×C₇	1	2	yes	—
836	C₄²	C₂⁴×C₇	1	2	yes	—
837	C₄²	C₂⁴×C₇	1	4	yes	—
838	C₄²	C₂⁴×C₇	1	8	yes	—
839	C₄²	C₂⁴×C₇	1	16	yes	—
840	C₂×C₇	—	2	2	no	—
841	C₂×C₇	—	4	2	no	—
842	C₂×C₇	—	4	8	no	—
843	C₂×C₇	—	4	8	no	—
844	C₂×C₇	—	4	4	no	—
845	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
846	C₂×C₇	H(7,𝔽₂)	1	2	yes	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	8	no	—
849	C₂³	—	4	4	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	2	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	8	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	16	no	—
857	C₂³	C₂⁵×C₇	1	4	yes	—
858	C₂³	C₂⁵×C₇	1	2	yes	—
859	C₂³	C₂⁵×C₇	1	8	yes	—
860	C₂³	C₂⁵×C₇	1	8	yes	—
861	C₂³	C₂⁵×C₇	1	1	yes	characteristic
862	Q₈	—	2	8	no	—
863	Q₈	—	2	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	—	4	4	no	—
866	D₄	—	2	8	no	—
867	D₄	—	2	16	no	—
868	D₄	—	2	8	no	—
869	D₄	—	2	8	no	—
870	D₄	—	2	4	no	—
871	D₄	—	2	8	no	—
872	D₄	—	4	16	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	16	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	16	no	—
880	D₄	—	4	16	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	D₄	—	4	16	no	—
884	D₄	—	4	16	no	—
885	D₄	—	4	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	4	no	—
889	C₂×C₄	—	2	16	no	—
890	C₂×C₄	—	2	8	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	8	no	—
896	C₂×C₄	—	4	8	no	—
897	C₂×C₄	—	4	16	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	16	no	—
901	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
902	C₂×C₄	C₂⁵×C₇	1	8	yes	—
903	C₂×C₄	C₂⁵×C₇	1	4	yes	—
904	C₂×C₄	C₂⁵×C₇	1	2	yes	—
905	C₂×C₄	C₂⁵×C₇	1	2	yes	—
906	C₂×C₄	C₂⁵×C₇	1	8	yes	—
907	C₂×C₄	C₂⁵×C₇	1	8	yes	—
908	C₂×C₄	C₂⁵×C₇	1	4	yes	—
909	C₂×C₄	C₂⁵×C₇	1	2	yes	—
910	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
911	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
912	C₇	#62880	1	1	yes	characteristic, direct product factor, Sylow
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	8	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	8	no	—
918	C₂²	—	2	8	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	8	no	—
924	C₂²	—	8	2	no	—
925	C₂²	—	8	8	no	—
926	C₂²	—	8	8	no	—
927	C₂²	—	16	16	no	—
928	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
929	C₂²	C₂⁶×C₇	1	1	yes	characteristic
930	C₄	—	2	2	no	—
931	C₄	—	2	4	no	—
932	C₄	—	2	8	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	8	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	8	no	—
938	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
939	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
940	C₂	—	2	2	no	—
941	C₂	—	4	2	no	—
942	C₂	—	4	8	no	—
943	C₂	—	4	8	no	—
944	C₂	—	4	4	no	—
945	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂	C₇×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3562	C₂	semidirect
2. C₇×#3543	C₂	semidirect
3. C₇×#3542	C₂	semidirect
4. C₇×#3539	C₂	semidirect
5. C₇×#3537	C₂	semidirect
6. C₇×#3537	C₂	semidirect
7. C₇×#3534	C₂	semidirect
8. C₇×#3512	C₂	semidirect
9. C₇×#3506	C₂	semidirect
10. C₇×#3498	C₂	semidirect
11. C₇×#3496	C₂	semidirect
12. C₇×#3488	C₂	semidirect
13. C₇×#3455	C₂	semidirect
14. C₂×C₇×#540	C₂	semidirect
15. C₇×#3449	C₂	semidirect
16. C₂×C₇×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₇×#562	C₂²	semidirect
19. C₇×#560	C₂²	semidirect
20. C₇×#560	C₂²	semidirect
21. C₇×#560	C₂²	semidirect
22. C₇×#559	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#553	C₂²	semidirect
26. C₇×#553	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#552	C₂²	semidirect
30. C₇×#551	C₂²	semidirect
31. C₇×#550	C₂²	semidirect
32. C₇×#550	C₂²	semidirect
33. C₇×#550	C₂²	semidirect
34. C₇×#548	C₂²	semidirect
35. C₇×#547	C₂²	semidirect
36. C₇×#547	C₂²	semidirect
37. C₇×#547	C₂²	semidirect
38. C₇×#546	C₂²	semidirect
39. C₇×#546	C₂²	semidirect
40. C₇×#546	C₂²	semidirect
41. C₇×#546	C₂²	semidirect
42. C₇×#546	C₂²	semidirect
43. C₇×D₄²	C₂²	semidirect
44. C₇×D₄²	C₂²	semidirect
45. C₇×D₄²	C₂²	semidirect
46. C₇×D₄²	C₂²	semidirect
47. C₇×D₄²	C₂²	semidirect
48. C₇×D₄²	C₂²	semidirect
49. C₇×D₄²	C₂²	semidirect
50. C₇×#542	C₂²	semidirect
51. C₇×#541	C₂²	semidirect
52. C₇×#541	C₂²	semidirect
53. C₇×#540	C₂²	semidirect
54. C₇×#540	C₂²	semidirect
55. C₇×#540	C₂²	semidirect
56. C₇×#540	C₂²	semidirect
57. C₇×#540	C₂²	semidirect
58. C₇×#540	C₂²	semidirect
59. C₇×#540	C₂²	semidirect
60. C₇×#539	C₂²	semidirect
61. C₇×#539	C₂²	semidirect
62. C₇×#538	C₂²	semidirect
63. C₇×#538	C₂²	semidirect
64. C₇×#538	C₂²	semidirect
65. C₇×#538	C₂²	semidirect
66. C₇×#537	C₂²	semidirect
67. C₇×#537	C₂²	semidirect
68. C₇×#537	C₂²	semidirect
69. C₇×#536	C₂²	semidirect
70. C₇×#535	C₂²	semidirect
71. C₇×#535	C₂²	semidirect
72. C₇×#535	C₂²	semidirect
73. C₇×#535	C₂²	semidirect
74. C₇×#535	C₂²	semidirect
75. C₇×#534	C₂²	semidirect
76. C₇×#534	C₂²	semidirect
77. C₇×#534	C₂²	semidirect
78. C₇×#534	C₂²	semidirect
79. C₇×#533	C₂²	semidirect
80. C₇×#532	C₂²	semidirect
81. C₇×#532	C₂²	semidirect
82. C₇×#532	C₂²	semidirect
83. C₇×#532	C₂²	semidirect
84. C₂×C₇×#127	C₂²	semidirect
85. C₂×C₇×#127	C₂²	semidirect
86. C₇×#529	C₂²	semidirect
87. C₇×#529	C₂²	semidirect
88. C₂×C₇×#125	C₂²	semidirect
89. C₇×#525	C₂²	semidirect
90. C₇×#525	C₂²	semidirect
91. C₇×#525	C₂²	semidirect
92. C₇×#525	C₂²	semidirect
93. C₇×#525	C₂²	semidirect
94. C₂×C₇×#123	C₂²	semidirect
95. C₂×C₇×#121	C₂²	semidirect
96. C₂×C₇×#121	C₂²	semidirect
97. C₂×C₇×#121	C₂²	semidirect
98. C₂×C₇×#121	C₂²	semidirect
99. C₇×#520	C₂²	semidirect
100. C₄×C₇×#41	C₂²	semidirect
101. C₂×C₄×C₇×D₄	C₂²	semidirect
102. C₂×C₇×#117	C₂²	semidirect
103. #62880	C₇	direct (N × H)
265. #3562	C₂×C₇	semidirect
266. #3543	C₂×C₇	semidirect
267. #3542	C₂×C₇	semidirect
268. #3539	C₂×C₇	semidirect
269. #3537	C₂×C₇	semidirect
270. #3537	C₂×C₇	semidirect
271. #3534	C₂×C₇	semidirect
272. #3512	C₂×C₇	semidirect
273. #3506	C₂×C₇	semidirect
274. #3498	C₂×C₇	semidirect
275. #3496	C₂×C₇	semidirect
276. #3488	C₂×C₇	semidirect
277. #3455	C₂×C₇	semidirect
278. C₂×#540	C₂×C₇	semidirect
279. #3449	C₂×C₇	semidirect
390. C₂×H(5,𝔽₂)	C₂²×C₇	semidirect
391. C₂²×#41	C₂²×C₇	semidirect
392. #562	C₂²×C₇	semidirect
393. #560	C₂²×C₇	semidirect
394. #560	C₂²×C₇	semidirect
395. #560	C₂²×C₇	semidirect
396. #559	C₂²×C₇	semidirect
397. #556	C₂²×C₇	semidirect
398. #555	C₂²×C₇	semidirect
399. #553	C₂²×C₇	semidirect
400. #553	C₂²×C₇	semidirect
401. #553	C₂²×C₇	semidirect
402. #553	C₂²×C₇	semidirect
403. #552	C₂²×C₇	semidirect
404. #551	C₂²×C₇	semidirect
405. #550	C₂²×C₇	semidirect
406. #550	C₂²×C₇	semidirect
407. #550	C₂²×C₇	semidirect
408. #548	C₂²×C₇	semidirect
409. #547	C₂²×C₇	semidirect
410. #547	C₂²×C₇	semidirect
411. #547	C₂²×C₇	semidirect
412. #546	C₂²×C₇	semidirect
413. #546	C₂²×C₇	semidirect
414. #546	C₂²×C₇	semidirect
415. #546	C₂²×C₇	semidirect
416. #546	C₂²×C₇	semidirect
417. D₄²	C₂²×C₇	semidirect
418. D₄²	C₂²×C₇	semidirect
419. D₄²	C₂²×C₇	semidirect
420. D₄²	C₂²×C₇	semidirect
421. D₄²	C₂²×C₇	semidirect
422. D₄²	C₂²×C₇	semidirect
423. D₄²	C₂²×C₇	semidirect
424. #542	C₂²×C₇	semidirect
425. #541	C₂²×C₇	semidirect
426. #541	C₂²×C₇	semidirect
427. #540	C₂²×C₇	semidirect
428. #540	C₂²×C₇	semidirect
429. #540	C₂²×C₇	semidirect
430. #540	C₂²×C₇	semidirect
431. #540	C₂²×C₇	semidirect
432. #540	C₂²×C₇	semidirect
433. #540	C₂²×C₇	semidirect
434. #539	C₂²×C₇	semidirect
435. #539	C₂²×C₇	semidirect
436. #538	C₂²×C₇	semidirect
437. #538	C₂²×C₇	semidirect
438. #538	C₂²×C₇	semidirect
439. #538	C₂²×C₇	semidirect
440. #537	C₂²×C₇	semidirect
441. #537	C₂²×C₇	semidirect
442. #537	C₂²×C₇	semidirect
443. #536	C₂²×C₇	semidirect
444. #535	C₂²×C₇	semidirect
445. #535	C₂²×C₇	semidirect
446. #535	C₂²×C₇	semidirect
447. #535	C₂²×C₇	semidirect
448. #535	C₂²×C₇	semidirect
449. #534	C₂²×C₇	semidirect
450. #534	C₂²×C₇	semidirect
451. #534	C₂²×C₇	semidirect
452. #534	C₂²×C₇	semidirect
453. #533	C₂²×C₇	semidirect
454. #532	C₂²×C₇	semidirect
455. #532	C₂²×C₇	semidirect
456. #532	C₂²×C₇	semidirect
457. #532	C₂²×C₇	semidirect
458. C₂×#127	C₂²×C₇	semidirect
459. C₂×#127	C₂²×C₇	semidirect
460. #529	C₂²×C₇	semidirect
461. #529	C₂²×C₇	semidirect
462. C₂×#125	C₂²×C₇	semidirect
463. #525	C₂²×C₇	semidirect
464. #525	C₂²×C₇	semidirect
465. #525	C₂²×C₇	semidirect
466. #525	C₂²×C₇	semidirect
467. #525	C₂²×C₇	semidirect
468. C₂×#123	C₂²×C₇	semidirect
469. C₂×#121	C₂²×C₇	semidirect
470. C₂×#121	C₂²×C₇	semidirect
471. C₂×#121	C₂²×C₇	semidirect
472. C₂×#121	C₂²×C₇	semidirect
473. #520	C₂²×C₇	semidirect
474. C₄×#41	C₂²×C₇	semidirect
475. C₂×C₄×D₄	C₂²×C₇	semidirect
476. C₂×#117	C₂²×C₇	semidirect
912. C₇	#62880	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3562	2
C₇×#3543	2
C₇×#3542	2
C₇×#3539	2
C₇×#3537	2
C₇×#3534	2
C₇×#3512	2
C₇×#3506	2
C₇×#3498	2
C₇×#3496	2
C₇×#3488	2
C₇×#3455	2
C₂×C₇×#540	2
C₇×#3449	2
#62880	7

Subgroups — C7×#62880 #13240096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62880 #13240096