Subgroups — C₇×#60932 #13238148

Order 1792.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3261	C₂	1	2	yes	maximal, complemented
4	C₇×#3260	C₂	1	2	yes	maximal, complemented
5	C₇×#3258	C₂	1	2	yes	maximal, complemented
6	C₇×#3257	C₂	1	2	yes	maximal, complemented
7	C₇×#3256	C₂	1	2	yes	maximal, complemented
8	C₇×#3252	C₂	1	2	yes	maximal, complemented
9	C₇×#3250	C₂	1	2	yes	maximal, complemented
10	C₇×#3248	C₂	1	2	yes	maximal, complemented
11	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₇×#137	C₂²	1	1	yes	characteristic
26	C₂×C₇×#135	C₂²	1	1	yes	characteristic
27	C₂×C₇×#135	C₂²	1	1	yes	characteristic
28	C₂×C₇×#131	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₇×#553	—	2	2	no	—
31	C₇×#553	—	2	2	no	—
32	C₇×#553	—	2	1	no	—
33	C₇×#553	—	2	1	no	—
34	C₇×#552	—	2	1	no	—
35	C₇×#552	—	2	1	no	—
36	C₇×#544	C₂²	1	1	yes	characteristic
37	C₇×#542	—	2	1	no	—
38	C₇×#542	C₂²	1	2	yes	—
39	C₇×#541	—	2	1	no	—
40	C₇×#541	C₂²	1	2	yes	—
41	C₇×#541	C₂²	1	2	yes	—
42	C₇×#540	C₂²	1	2	yes	—
43	C₇×#539	—	2	2	no	—
44	C₇×#537	C₂²	1	1	yes	characteristic
45	C₇×#537	C₂²	1	1	yes	characteristic
46	C₇×#537	C₂²	1	1	yes	characteristic
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#536	C₂²	1	1	yes	characteristic
49	C₇×#533	—	2	1	no	—
50	C₇×#533	C₂²	1	2	yes	—
51	C₇×#532	C₂²	1	1	yes	characteristic
52	C₇×#529	—	2	2	no	—
53	C₇×#529	—	2	1	no	—
54	C₇×#529	C₂²	1	2	yes	—
55	C₇×#529	C₂²	1	2	yes	—
56	C₇×#529	C₂²	1	2	yes	—
57	C₂×C₇×#125	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₄×C₇×#41	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
63	C₇×#479	C₂²	1	2	yes	—
64	C₇×#479	C₂²	1	2	yes	—
65	C₇×#479	C₂²	1	2	yes	—
66	C₇×#479	C₂²	1	2	yes	—
67	C₇×#479	C₂²	1	2	yes	—
68	C₇×#479	C₂²	1	2	yes	—
69	C₇×#479	C₂²	1	2	yes	—
70	C₇×#479	C₂²	1	2	yes	—
71	C₇×#478	C₂²	1	2	yes	—
72	C₇×#478	C₂²	1	2	yes	—
73	C₇×#478	C₂²	1	2	yes	—
74	C₇×#478	C₂²	1	2	yes	—
75	C₇×#477	C₂²	1	2	yes	—
76	C₇×#476	C₂²	1	2	yes	—
77	C₇×#475	C₂²	1	2	yes	—
78	C₇×#474	C₂²	1	2	yes	—
79	C₇×#470	C₂²	1	2	yes	—
80	C₇×#470	C₂²	1	2	yes	—
81	C₇×#470	C₂²	1	2	yes	—
82	C₇×#469	C₂²	1	2	yes	—
83	C₇×#468	C₂²	1	2	yes	—
84	C₇×#468	C₂²	1	2	yes	—
85	C₇×#468	C₂²	1	2	yes	—
86	C₇×#468	C₂²	1	2	yes	—
87	C₇×#467	C₂²	1	2	yes	—
88	C₇×#467	C₂²	1	2	yes	—
89	C₇×#467	C₂²	1	2	yes	—
90	C₇×#466	C₂²	1	2	yes	—
91	C₇×#465	C₂²	1	2	yes	—
92	C₇×#465	C₂²	1	2	yes	—
93	C₇×#465	C₂²	1	2	yes	—
94	C₇×#465	C₂²	1	2	yes	—
95	C₇×#464	C₂²	1	1	yes	characteristic
96	C₇×#464	C₂²	1	2	yes	—
97	C₇×#464	C₂²	1	2	yes	—
98	C₇×#464	C₂²	1	2	yes	—
99	C₇×#464	C₂²	1	1	yes	characteristic
100	C₇×#464	C₂²	1	2	yes	—
101	C₇×#463	C₂²	1	1	yes	characteristic
102	C₇×#463	C₂²	1	2	yes	—
103	C₇×#463	C₂²	1	1	yes	characteristic
104	C₇×#463	C₂²	1	2	yes	—
105	C₇×#462	C₂²	1	2	yes	—
106	C₇×#462	C₂²	1	2	yes	—
107	C₇×#462	C₂²	1	2	yes	—
108	C₇×#462	C₂²	1	1	yes	characteristic
109	C₇×#461	C₂²	1	2	yes	—
110	C₇×#461	C₂²	1	2	yes	—
111	C₇×#461	C₂²	1	1	yes	characteristic
112	C₇×#460	C₂²	1	2	yes	—
113	C₇×#460	C₂²	1	1	yes	characteristic
114	C₇×#459	C₂²	1	1	yes	characteristic
115	C₇×#428	C₂²	1	1	yes	characteristic
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₂×C₇×#107	C₂²	1	1	yes	characteristic
118	C₂×C₇×#106	C₂²	1	1	yes	characteristic
119	C₇×#424	C₂²	1	2	yes	—
120	C₇×#424	C₂²	1	2	yes	—
121	C₇×#424	C₂²	1	1	yes	characteristic
122	C₇×#424	C₂²	1	1	yes	characteristic
123	C₇×#423	C₂²	1	2	yes	—
124	C₇×#423	C₂²	1	1	yes	characteristic
125	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
126	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#417	C₂²	1	1	yes	characteristic
129	C₇×#417	C₂²	1	1	yes	characteristic
130	C₇×#417	C₂²	1	1	yes	characteristic
131	C₇×#416	C₂²	1	1	yes	characteristic
132	C₇×#416	C₂²	1	1	yes	characteristic
133	C₂×C₇×#103	C₂²	1	1	yes	characteristic
134	C₂×C₇×#103	C₂²	1	1	yes	characteristic
135	#60932	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂×C₇×#41	C₂³	1	1	yes	characteristic
140	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
141	C₇×#137	—	4	2	no	—
142	C₇×#137	—	4	2	no	—
143	C₇×#135	—	4	2	no	—
144	C₇×#135	—	4	2	no	—
145	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
156	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
157	C₇×#131	—	4	2	no	—
158	C₇×#131	—	4	2	no	—
159	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₇×M₁₆	C₂³	1	2	yes	—
162	C₂×C₇×M₁₆	C₂³	1	2	yes	—
163	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
165	C₂²×C₇×C₈	C₂³	1	2	yes	—
166	C₂²×C₇×C₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	—	2	1	no	—
168	C₇×C₄⋊Q₈	—	2	1	no	—
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×#127	C₂³	1	1	yes	characteristic
173	C₇×#126	—	2	2	no	—
174	C₇×#126	—	2	2	no	—
175	C₇×#126	—	2	2	no	—
176	C₇×#126	—	2	2	no	—
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	1	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	2	no	—
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#125	C₂³	1	2	yes	—
191	C₇×#125	C₂³	1	2	yes	—
192	C₇×#124	—	2	1	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	C₂³	1	1	yes	characteristic
195	C₇×#124	C₂³	1	1	yes	characteristic
196	C₇×#124	C₂³	1	2	yes	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	1	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	—	2	2	no	—
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₄×C₇×Q₈	—	2	1	no	—
232	C₄×C₇×Q₈	—	2	1	no	—
233	C₄×C₇×Q₈	—	2	2	no	—
234	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
235	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
236	C₄×C₇×Q₈	C₂³	1	2	yes	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	2	yes	—
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	2	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	D₄	1	1	yes	characteristic
252	C₄×C₇×D₄	D₄	1	2	yes	—
253	C₄×C₇×D₄	D₄	1	2	yes	—
254	C₄×C₇×D₄	D₄	1	1	yes	characteristic
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₇×#117	—	2	2	no	—
260	C₇×#117	—	2	1	no	—
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₇×#117	C₂³	1	2	yes	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₇×C₄⋊C₄	—	2	1	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₇	—	2	1	no	—
278	C₂×C₄²×C₇	—	2	1	no	—
279	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₇	C₂³	1	2	yes	—
281	C₇×#107	C₂³	1	2	yes	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×#106	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	2	yes	—
292	C₇×C₄⋊C₈	C₂³	1	2	yes	—
293	C₇×C₄⋊C₈	C₂³	1	2	yes	—
294	C₇×C₄⋊C₈	C₂³	1	2	yes	—
295	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
296	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
297	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
298	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	1	yes	characteristic
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#103	C₂³	1	2	yes	—
304	C₇×#103	C₂³	1	2	yes	—
305	C₇×#103	C₂³	1	2	yes	—
306	C₇×#103	C₂³	1	2	yes	—
307	C₇×#103	C₂³	1	1	yes	characteristic
308	C₇×#103	C₂³	1	1	yes	characteristic
309	C₇×#103	C₂³	1	2	yes	—
310	C₇×#103	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	2	yes	—
313	C₇×#102	C₂³	1	1	yes	characteristic
314	C₇×#102	C₂³	1	1	yes	characteristic
315	C₇×#102	C₂³	1	2	yes	—
316	C₇×#102	C₂³	1	2	yes	—
317	C₇×#102	C₂³	1	1	yes	characteristic
318	C₇×#102	C₂³	1	1	yes	characteristic
319	#3512	C₂×C₇	1	1	yes	characteristic, complemented
320	#3461	C₂×C₇	1	1	yes	characteristic, complemented
321	#3261	C₂×C₇	1	2	yes	complemented
322	#3260	C₂×C₇	1	2	yes	complemented
323	#3258	C₂×C₇	1	2	yes	complemented
324	#3257	C₂×C₇	1	2	yes	complemented
325	#3256	C₂×C₇	1	2	yes	complemented
326	#3252	C₂×C₇	1	2	yes	complemented
327	#3250	C₂×C₇	1	2	yes	complemented
328	#3248	C₂×C₇	1	2	yes	complemented
329	#3084	C₂×C₇	1	1	yes	characteristic, complemented
330	#3083	C₂×C₇	1	1	yes	characteristic, complemented
331	#3080	C₂×C₇	1	1	yes	characteristic, complemented
332	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
333	#3063	C₂×C₇	1	1	yes	characteristic, complemented
334	#3063	C₂×C₇	1	1	yes	characteristic, complemented
335	#3061	C₂×C₇	1	1	yes	characteristic, complemented
336	#3060	C₂×C₇	1	1	yes	characteristic, complemented
337	#3046	C₂×C₇	1	1	yes	characteristic, complemented
338	#3046	C₂×C₇	1	1	yes	characteristic, complemented
339	#3037	C₂×C₇	1	1	yes	characteristic, complemented
340	#3035	C₂×C₇	1	1	yes	characteristic, complemented
341	#2906	C₂×C₇	1	1	yes	characteristic, complemented
342	C₇×#41	—	2	2	no	—
343	C₇×#41	—	2	2	no	—
344	C₇×#41	—	2	2	no	—
345	C₇×#41	—	2	2	no	—
346	C₇×#41	—	2	2	no	—
347	C₇×#41	—	2	2	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₂×C₇×Q₈	—	2	1	no	—
351	C₂×C₇×Q₈	—	2	2	no	—
352	C₂×C₇×Q₈	—	2	2	no	—
353	C₂×C₇×Q₈	—	2	2	no	—
354	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
356	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	2	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	1	no	—
367	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
368	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
369	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
370	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
371	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	1	no	—
375	C₂²×C₄×C₇	—	2	1	no	—
376	C₂²×C₄×C₇	—	2	1	no	—
377	C₂²×C₄×C₇	—	2	1	no	—
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	1	no	—
380	C₂²×C₄×C₇	—	2	1	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	2	no	—
383	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
388	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
389	C₇×Q₁₆	—	4	1	no	—
390	C₇×Q₁₆	—	4	1	no	—
391	C₇×Q₁₆	—	4	2	no	—
392	C₇×Q₁₆	—	4	2	no	—
393	C₇×SD₁₆	—	4	1	no	—
394	C₇×SD₁₆	—	4	1	no	—
395	C₇×SD₁₆	—	4	1	no	—
396	C₇×SD₁₆	—	4	1	no	—
397	C₇×SD₁₆	—	4	2	no	—
398	C₇×SD₁₆	—	4	2	no	—
399	C₇×D₈	—	4	1	no	—
400	C₇×D₈	—	4	1	no	—
401	C₇×M₁₆	—	2	2	no	—
402	C₇×M₁₆	—	2	2	no	—
403	C₇×M₁₆	—	4	2	no	—
404	C₇×M₁₆	—	4	2	no	—
405	C₂×C₇×C₈	—	2	2	no	—
406	C₂×C₇×C₈	—	2	2	no	—
407	C₂×C₇×C₈	—	4	2	no	—
408	C₂×C₇×C₈	—	4	2	no	—
409	C₂×C₇×C₈	C₂⁴	1	2	yes	—
410	C₂×C₇×C₈	C₂⁴	1	2	yes	—
411	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
415	C₇×C₄⋊C₄	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	1	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	2	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	1	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	1	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	2	no	—
430	C₇×C₄⋊C₄	—	2	2	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	1	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
448	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	1	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	1	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	1	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	2	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	1	no	—
466	C₇×C₂²⋊C₄	—	2	1	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₄²×C₇	—	2	2	no	—
472	C₄²×C₇	—	2	1	no	—
473	C₄²×C₇	—	2	1	no	—
474	C₄²×C₇	—	2	1	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	—	2	2	no	—
478	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
479	C₄²×C₇	C₂×D₄	1	2	yes	—
480	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₇	C₂×D₄	1	2	yes	—
482	C₄²×C₇	C₂⁴	1	1	yes	characteristic
483	C₄²×C₇	C₂⁴	1	2	yes	—
484	C₄²×C₇	C₂⁴	1	1	yes	characteristic
485	C₂×#137	C₂²×C₇	1	1	yes	characteristic
486	C₂×#137	C₂²×C₇	1	1	yes	characteristic
487	C₂×#135	C₂²×C₇	1	1	yes	characteristic
488	C₂×#135	C₂²×C₇	1	1	yes	characteristic
489	C₂×#131	C₂²×C₇	1	1	yes	characteristic
490	C₂×#131	C₂²×C₇	1	1	yes	characteristic
491	#553	—	2	2	no	—
492	#553	—	2	2	no	—
493	#553	—	2	1	no	—
494	#553	—	2	1	no	—
495	#552	—	2	1	no	—
496	#552	—	2	1	no	—
497	#544	C₂²×C₇	1	1	yes	characteristic
498	#542	—	2	1	no	—
499	#542	C₂²×C₇	1	2	yes	—
500	#541	—	2	1	no	—
501	#541	C₂²×C₇	1	2	yes	—
502	#541	C₂²×C₇	1	2	yes	—
503	#540	C₂²×C₇	1	2	yes	—
504	#539	—	2	2	no	—
505	#537	C₂²×C₇	1	1	yes	characteristic
506	#537	C₂²×C₇	1	1	yes	characteristic
507	#537	C₂²×C₇	1	1	yes	characteristic
508	#536	C₂²×C₇	1	1	yes	characteristic
509	#536	C₂²×C₇	1	1	yes	characteristic
510	#533	—	2	1	no	—
511	#533	C₂²×C₇	1	2	yes	—
512	#532	C₂²×C₇	1	1	yes	characteristic
513	#529	—	2	2	no	—
514	#529	—	2	1	no	—
515	#529	C₂²×C₇	1	2	yes	—
516	#529	C₂²×C₇	1	2	yes	—
517	#529	C₂²×C₇	1	2	yes	—
518	C₂×#125	C₂²×C₇	1	1	yes	characteristic
519	#520	C₂²×C₇	1	1	yes	characteristic
520	#520	C₂²×C₇	1	1	yes	characteristic
521	C₄×#41	C₂²×C₇	1	1	yes	characteristic
522	C₄×#41	C₂²×C₇	1	1	yes	characteristic
523	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
524	#479	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#479	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#479	C₂²×C₇	1	2	yes	—
529	#479	C₂²×C₇	1	2	yes	—
530	#479	C₂²×C₇	1	2	yes	—
531	#479	C₂²×C₇	1	2	yes	—
532	#478	C₂²×C₇	1	2	yes	—
533	#478	C₂²×C₇	1	2	yes	—
534	#478	C₂²×C₇	1	2	yes	—
535	#478	C₂²×C₇	1	2	yes	—
536	#477	C₂²×C₇	1	2	yes	—
537	#476	C₂²×C₇	1	2	yes	—
538	#475	C₂²×C₇	1	2	yes	—
539	#474	C₂²×C₇	1	2	yes	—
540	#470	C₂²×C₇	1	2	yes	—
541	#470	C₂²×C₇	1	2	yes	—
542	#470	C₂²×C₇	1	2	yes	—
543	#469	C₂²×C₇	1	2	yes	—
544	#468	C₂²×C₇	1	2	yes	—
545	#468	C₂²×C₇	1	2	yes	—
546	#468	C₂²×C₇	1	2	yes	—
547	#468	C₂²×C₇	1	2	yes	—
548	#467	C₂²×C₇	1	2	yes	—
549	#467	C₂²×C₇	1	2	yes	—
550	#467	C₂²×C₇	1	2	yes	—
551	#466	C₂²×C₇	1	2	yes	—
552	#465	C₂²×C₇	1	2	yes	—
553	#465	C₂²×C₇	1	2	yes	—
554	#465	C₂²×C₇	1	2	yes	—
555	#465	C₂²×C₇	1	2	yes	—
556	#464	C₂²×C₇	1	1	yes	characteristic
557	#464	C₂²×C₇	1	2	yes	—
558	#464	C₂²×C₇	1	2	yes	—
559	#464	C₂²×C₇	1	2	yes	—
560	#464	C₂²×C₇	1	1	yes	characteristic
561	#464	C₂²×C₇	1	2	yes	—
562	#463	C₂²×C₇	1	1	yes	characteristic
563	#463	C₂²×C₇	1	2	yes	—
564	#463	C₂²×C₇	1	1	yes	characteristic
565	#463	C₂²×C₇	1	2	yes	—
566	#462	C₂²×C₇	1	2	yes	—
567	#462	C₂²×C₇	1	2	yes	—
568	#462	C₂²×C₇	1	2	yes	—
569	#462	C₂²×C₇	1	1	yes	characteristic
570	#461	C₂²×C₇	1	2	yes	—
571	#461	C₂²×C₇	1	2	yes	—
572	#461	C₂²×C₇	1	1	yes	characteristic
573	#460	C₂²×C₇	1	2	yes	—
574	#460	C₂²×C₇	1	1	yes	characteristic
575	#459	C₂²×C₇	1	1	yes	characteristic
576	#428	C₂²×C₇	1	1	yes	characteristic
577	#428	C₂²×C₇	1	1	yes	characteristic
578	C₂×#107	C₂²×C₇	1	1	yes	characteristic
579	C₂×#106	C₂²×C₇	1	1	yes	characteristic
580	#424	C₂²×C₇	1	1	yes	characteristic
581	#424	C₂²×C₇	1	1	yes	characteristic
582	#424	C₂²×C₇	1	2	yes	—
583	#424	C₂²×C₇	1	2	yes	—
584	#423	C₂²×C₇	1	1	yes	characteristic
585	#423	C₂²×C₇	1	2	yes	—
586	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
587	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
588	#417	C₂²×C₇	1	1	yes	characteristic
589	#417	C₂²×C₇	1	1	yes	characteristic
590	#417	C₂²×C₇	1	1	yes	characteristic
591	#417	C₂²×C₇	1	1	yes	characteristic
592	#416	C₂²×C₇	1	1	yes	characteristic
593	#416	C₂²×C₇	1	1	yes	characteristic
594	C₂×#103	C₂²×C₇	1	1	yes	characteristic
595	C₂×#103	C₂²×C₇	1	1	yes	characteristic
596	C₂³×C₇	—	2	1	no	—
597	C₂³×C₇	—	2	1	no	—
598	C₂³×C₇	—	2	1	no	—
599	C₂³×C₇	C₂²×D₄	1	2	yes	—
600	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₇×Q₈	—	2	2	no	—
602	C₇×Q₈	—	2	2	no	—
603	C₇×Q₈	—	2	1	no	—
604	C₇×Q₈	—	2	1	no	—
605	C₇×Q₈	—	2	1	no	—
606	C₇×Q₈	—	2	2	no	—
607	C₇×Q₈	—	2	1	no	—
608	C₇×Q₈	—	2	1	no	—
609	C₇×Q₈	—	2	1	no	—
610	C₇×Q₈	—	4	2	no	—
611	C₇×Q₈	—	8	2	no	—
612	C₇×D₄	—	2	4	no	—
613	C₇×D₄	—	2	2	no	—
614	C₇×D₄	—	2	1	no	—
615	C₇×D₄	—	2	1	no	—
616	C₇×D₄	—	2	1	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	2	1	no	—
619	C₇×D₄	—	2	1	no	—
620	C₇×D₄	—	4	2	no	—
621	C₇×D₄	—	4	2	no	—
622	C₇×D₄	—	4	2	no	—
623	C₇×D₄	—	8	1	no	—
624	C₇×D₄	—	8	1	no	—
625	C₇×D₄	—	8	2	no	—
626	C₇×D₄	—	8	2	no	—
627	C₇×D₄	—	8	2	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	2	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	2	no	—
637	C₂×C₄×C₇	—	2	2	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	4	1	no	—
640	C₂×C₄×C₇	—	4	2	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	1	no	—
643	C₂×C₄×C₇	—	4	2	no	—
644	C₂×C₄×C₇	—	4	2	no	—
645	C₂×C₄×C₇	—	4	2	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	—	4	2	no	—
648	C₂×C₄×C₇	—	8	1	no	—
649	C₂×C₄×C₇	—	8	2	no	—
650	C₂×C₄×C₇	—	8	2	no	—
651	C₂×C₄×C₇	—	8	1	no	—
652	C₂×C₄×C₇	—	8	1	no	—
653	C₂×C₄×C₇	—	8	1	no	—
654	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
655	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
657	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
660	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
661	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
663	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
664	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
665	C₇×C₈	—	2	1	no	—
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	—	2	1	no	—
668	C₇×C₈	—	2	1	no	—
669	C₇×C₈	—	2	2	no	—
670	C₇×C₈	—	2	2	no	—
671	C₂×#41	C₂³×C₇	1	1	yes	characteristic
672	C₂×#41	C₂³×C₇	1	1	yes	characteristic
673	C₂×#41	C₂³×C₇	1	1	yes	characteristic
674	C₂×#41	C₂³×C₇	1	1	yes	characteristic
675	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
676	#137	—	4	2	no	—
677	#137	—	4	2	no	—
678	#135	—	4	2	no	—
679	#135	—	4	2	no	—
680	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
681	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
685	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
690	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
691	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
692	#131	—	4	2	no	—
693	#131	—	4	2	no	—
694	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
696	C₂×M₁₆	C₂³×C₇	1	2	yes	—
697	C₂×M₁₆	C₂³×C₇	1	2	yes	—
698	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
699	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
700	C₂²×C₈	C₂³×C₇	1	2	yes	—
701	C₂²×C₈	C₂³×C₇	1	2	yes	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	1	no	—
704	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
707	#127	C₂³×C₇	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	1	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	C₂³×C₇	1	2	yes	—
725	#125	C₂³×C₇	1	2	yes	—
726	#125	C₂³×C₇	1	2	yes	—
727	#124	—	2	1	no	—
728	#124	—	2	2	no	—
729	#124	C₂³×C₇	1	1	yes	characteristic
730	#124	C₂³×C₇	1	1	yes	characteristic
731	#124	C₂³×C₇	1	2	yes	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
750	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
751	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
753	#121	—	2	2	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	2	no	—
758	#121	—	2	2	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	C₂³×C₇	1	2	yes	—
764	#121	C₂³×C₇	1	2	yes	—
765	#121	C₂³×C₇	1	2	yes	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
770	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₇	1	2	yes	—
772	C₄×Q₈	C₂³×C₇	1	2	yes	—
773	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₇	1	2	yes	—
776	C₄×Q₈	C₂³×C₇	1	2	yes	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	C₇×D₄	1	1	yes	characteristic
787	C₄×D₄	C₇×D₄	1	2	yes	—
788	C₄×D₄	C₇×D₄	1	2	yes	—
789	C₄×D₄	C₇×D₄	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₇	1	2	yes	—
793	C₄×D₄	C₂³×C₇	1	2	yes	—
794	#117	—	2	2	no	—
795	#117	—	2	1	no	—
796	#117	—	2	1	no	—
797	#117	—	2	1	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	C₂³×C₇	1	1	yes	characteristic
802	#117	C₂³×C₇	1	1	yes	characteristic
803	#117	C₂³×C₇	1	2	yes	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
810	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	—	2	1	no	—
814	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₇	1	2	yes	—
816	#107	C₂³×C₇	1	2	yes	—
817	#107	C₂³×C₇	1	2	yes	—
818	#107	C₂³×C₇	1	2	yes	—
819	#107	C₂³×C₇	1	2	yes	—
820	#106	C₂³×C₇	1	2	yes	—
821	#106	C₂³×C₇	1	2	yes	—
822	#106	C₂³×C₇	1	2	yes	—
823	#106	C₂³×C₇	1	2	yes	—
824	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₇	1	2	yes	—
827	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₇	1	2	yes	—
830	C₄⋊C₈	C₂³×C₇	1	2	yes	—
831	C₄⋊C₈	C₂³×C₇	1	2	yes	—
832	C₄⋊C₈	C₂³×C₇	1	2	yes	—
833	C₄⋊C₈	C₂³×C₇	1	2	yes	—
834	#103	C₂³×C₇	1	2	yes	—
835	#103	C₂³×C₇	1	2	yes	—
836	#103	C₂³×C₇	1	2	yes	—
837	#103	C₂³×C₇	1	2	yes	—
838	#103	C₂³×C₇	1	1	yes	characteristic
839	#103	C₂³×C₇	1	1	yes	characteristic
840	#103	C₂³×C₇	1	1	yes	characteristic
841	#103	C₂³×C₇	1	1	yes	characteristic
842	#103	C₂³×C₇	1	2	yes	—
843	#103	C₂³×C₇	1	2	yes	—
844	#103	C₂³×C₇	1	2	yes	—
845	#103	C₂³×C₇	1	2	yes	—
846	#102	C₂³×C₇	1	1	yes	characteristic
847	#102	C₂³×C₇	1	1	yes	characteristic
848	#102	C₂³×C₇	1	1	yes	characteristic
849	#102	C₂³×C₇	1	1	yes	characteristic
850	#102	C₂³×C₇	1	2	yes	—
851	#102	C₂³×C₇	1	2	yes	—
852	#102	C₂³×C₇	1	2	yes	—
853	#102	C₂³×C₇	1	2	yes	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	2	no	—
857	C₂²×C₇	—	2	2	no	—
858	C₂²×C₇	—	2	2	no	—
859	C₂²×C₇	—	4	1	no	—
860	C₂²×C₇	—	4	1	no	—
861	C₂²×C₇	—	4	1	no	—
862	C₂²×C₇	—	4	1	no	—
863	C₂²×C₇	—	4	1	no	—
864	C₂²×C₇	—	4	1	no	—
865	C₂²×C₇	—	4	1	no	—
866	C₂²×C₇	—	4	1	no	—
867	C₂²×C₇	—	4	1	no	—
868	C₂²×C₇	#537	1	2	yes	—
869	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
870	C₄×C₇	—	2	1	no	—
871	C₄×C₇	—	2	1	no	—
872	C₄×C₇	—	2	2	no	—
873	C₄×C₇	—	2	1	no	—
874	C₄×C₇	—	2	2	no	—
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	2	no	—
877	C₄×C₇	—	4	2	no	—
878	C₄×C₇	—	4	2	no	—
879	C₄×C₇	—	4	1	no	—
880	C₄×C₇	—	4	1	no	—
881	C₄×C₇	—	4	2	no	—
882	C₄×C₇	—	4	1	no	—
883	C₄×C₇	—	4	1	no	—
884	C₄×C₇	—	4	1	no	—
885	C₄×C₇	—	4	2	no	—
886	C₄×C₇	#537	1	2	yes	—
887	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
888	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
889	#41	—	2	2	no	—
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
915	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
918	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
931	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
932	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
933	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
936	Q₁₆	—	4	1	no	—
937	Q₁₆	—	4	1	no	—
938	Q₁₆	—	4	2	no	—
939	Q₁₆	—	4	2	no	—
940	SD₁₆	—	4	1	no	—
941	SD₁₆	—	4	1	no	—
942	SD₁₆	—	4	1	no	—
943	SD₁₆	—	4	1	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	—	4	2	no	—
946	D₈	—	4	1	no	—
947	D₈	—	4	1	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	4	2	no	—
951	M₁₆	—	4	2	no	—
952	C₂×C₈	—	2	2	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	—	4	2	no	—
956	C₂×C₈	C₂⁴×C₇	1	2	yes	—
957	C₂×C₈	C₂⁴×C₇	1	2	yes	—
958	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
988	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
990	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1026	C₄²	C₂×C₇×D₄	1	2	yes	—
1027	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1028	C₄²	C₂×C₇×D₄	1	2	yes	—
1029	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₇	1	2	yes	—
1031	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1032	C₂×C₇	—	2	2	no	—
1033	C₂×C₇	—	4	2	no	—
1034	C₂×C₇	—	8	1	no	—
1035	C₂×C₇	—	8	1	no	—
1036	C₂×C₇	—	8	1	no	—
1037	C₂×C₇	C₂×#537	1	1	yes	characteristic
1038	C₂×C₇	#3584	1	1	yes	characteristic
1039	C₂×C₇	#3586	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	C₂²×C₇×D₄	1	2	yes	—
1044	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	1	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1099	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1101	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1102	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1105	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1106	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1107	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1108	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	—	2	2	no	—
1115	C₇	#60932	1	1	yes	characteristic, direct product factor, Sylow
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	C₇×#537	1	2	yes	—
1131	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₇×#537	1	2	yes	—
1149	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1150	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₂×C₇×#537	1	1	yes	characteristic
1157	C₂	C₇×#3584	1	1	yes	characteristic
1158	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3461	C₂	semidirect
3. C₇×#3261	C₂	semidirect
4. C₇×#3260	C₂	semidirect
5. C₇×#3258	C₂	semidirect
6. C₇×#3257	C₂	semidirect
7. C₇×#3256	C₂	semidirect
8. C₇×#3252	C₂	semidirect
9. C₇×#3250	C₂	semidirect
10. C₇×#3248	C₂	semidirect
11. C₇×#3084	C₂	semidirect
12. C₇×#3083	C₂	semidirect
13. C₇×#3080	C₂	semidirect
14. C₂×C₇×#479	C₂	semidirect
15. C₇×#3063	C₂	semidirect
16. C₇×#3063	C₂	semidirect
17. C₇×#3061	C₂	semidirect
18. C₇×#3060	C₂	semidirect
19. C₇×#3046	C₂	semidirect
20. C₇×#3046	C₂	semidirect
21. C₇×#3037	C₂	semidirect
22. C₇×#3035	C₂	semidirect
23. C₇×#2906	C₂	semidirect
135. #60932	C₇	direct (N × H)
319. #3512	C₂×C₇	semidirect
320. #3461	C₂×C₇	semidirect
321. #3261	C₂×C₇	semidirect
322. #3260	C₂×C₇	semidirect
323. #3258	C₂×C₇	semidirect
324. #3257	C₂×C₇	semidirect
325. #3256	C₂×C₇	semidirect
326. #3252	C₂×C₇	semidirect
327. #3250	C₂×C₇	semidirect
328. #3248	C₂×C₇	semidirect
329. #3084	C₂×C₇	semidirect
330. #3083	C₂×C₇	semidirect
331. #3080	C₂×C₇	semidirect
332. C₂×#479	C₂×C₇	semidirect
333. #3063	C₂×C₇	semidirect
334. #3063	C₂×C₇	semidirect
335. #3061	C₂×C₇	semidirect
336. #3060	C₂×C₇	semidirect
337. #3046	C₂×C₇	semidirect
338. #3046	C₂×C₇	semidirect
339. #3037	C₂×C₇	semidirect
340. #3035	C₂×C₇	semidirect
341. #2906	C₂×C₇	semidirect
1115. C₇	#60932	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×#3512	2
C₇×#3461	2
C₇×#3261	2
C₇×#3260	2
C₇×#3258	2
C₇×#3257	2
C₇×#3256	2
C₇×#3252	2
C₇×#3250	2
C₇×#3248	2
C₇×#3084	2
C₇×#3083	2
C₇×#3080	2
C₂×C₇×#479	2
C₇×#3063	2
C₇×#3061	2
C₇×#3060	2
C₇×#3046	2
C₇×#3037	2
C₇×#3035	2
C₇×#2906	2
#60932	7

Subgroups — C7×#60932 #13238148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60932 #13238148