Subgroups — C₇×#61277 #13238493

Order 1792.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3493	C₂	1	1	yes	maximal, characteristic
3	C₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₇×#3352	C₂	1	2	yes	maximal, complemented
5	C₇×#3350	C₂	1	2	yes	maximal, complemented
6	C₇×#3349	C₂	1	2	yes	maximal, complemented
7	C₇×#3348	C₂	1	2	yes	maximal, complemented
8	C₇×#3344	C₂	1	2	yes	maximal, complemented
9	C₇×#3342	C₂	1	2	yes	maximal, complemented
10	C₇×#3337	C₂	1	2	yes	maximal, complemented
11	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₇×#131	C₂²	1	1	yes	characteristic
26	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
27	C₇×#556	—	2	1	no	—
28	C₇×#556	C₂²	1	2	yes	—
29	C₇×#556	C₂²	1	2	yes	—
30	C₇×#555	—	2	1	no	—
31	C₇×#555	C₂²	1	2	yes	—
32	C₇×#554	C₂²	1	2	yes	—
33	C₇×#553	—	2	1	no	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#552	—	2	2	no	—
36	C₇×#552	—	2	1	no	—
37	C₇×#552	C₂²	1	2	yes	—
38	C₇×#552	C₂²	1	2	yes	—
39	C₇×#552	C₂²	1	2	yes	—
40	C₇×#551	—	2	2	no	—
41	C₇×#544	C₂²	1	1	yes	characteristic
42	C₇×#544	C₂²	1	1	yes	characteristic
43	C₇×#542	—	2	1	no	—
44	C₇×#541	—	2	1	no	—
45	C₇×#538	—	2	2	no	—
46	C₇×#537	C₂²	1	1	yes	characteristic
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#533	—	2	1	no	—
49	C₇×#529	—	2	2	no	—
50	C₇×#529	—	2	1	no	—
51	C₇×#525	C₂²	1	1	yes	characteristic
52	C₇×#525	C₂²	1	1	yes	characteristic
53	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	1	yes	characteristic
56	C₇×#520	C₂²	1	1	yes	characteristic
57	C₇×#519	C₂²	1	1	yes	characteristic
58	C₂×C₇×#117	C₂²	1	1	yes	characteristic
59	C₂×C₇×#117	C₂²	1	1	yes	characteristic
60	C₇×#501	C₂²	1	2	yes	complemented
61	C₇×#501	C₂²	1	2	yes	complemented
62	C₇×#500	C₂²	1	2	yes	complemented
63	C₇×#499	C₂²	1	2	yes	complemented
64	C₇×#485	C₂²	1	2	yes	—
65	C₇×#485	C₂²	1	1	yes	characteristic
66	C₇×#485	C₂²	1	2	yes	—
67	C₇×#485	C₂²	1	2	yes	—
68	C₇×#485	C₂²	1	2	yes	—
69	C₇×#485	C₂²	1	1	yes	characteristic
70	C₇×#485	C₂²	1	2	yes	complemented
71	C₇×#485	C₂²	1	2	yes	complemented
72	C₇×#485	C₂²	1	2	yes	complemented
73	C₇×#484	C₂²	1	1	yes	characteristic
74	C₇×#484	C₂²	1	2	yes	complemented
75	C₇×#484	C₂²	1	2	yes	complemented
76	C₇×#483	C₂²	1	1	yes	characteristic
77	C₇×#483	C₂²	1	2	yes	complemented
78	C₇×#482	C₂²	1	1	yes	characteristic
79	C₇×#482	C₂²	1	1	yes	characteristic
80	C₇×#482	C₂²	1	2	yes	complemented
81	C₇×#481	C₂²	1	1	yes	characteristic
82	C₇×#480	C₂²	1	1	yes	characteristic
83	C₇×#480	C₂²	1	2	yes	complemented
84	C₇×#479	C₂²	1	2	yes	complemented
85	C₇×#479	C₂²	1	2	yes	complemented
86	C₇×#479	C₂²	1	2	yes	complemented
87	C₇×#478	C₂²	1	2	yes	complemented
88	C₇×#477	C₂²	1	2	yes	complemented
89	C₇×#476	C₂²	1	2	yes	complemented
90	C₇×#475	C₂²	1	2	yes	complemented
91	C₇×#475	C₂²	1	2	yes	complemented
92	C₇×#470	C₂²	1	2	yes	—
93	C₇×#470	C₂²	1	2	yes	complemented
94	C₇×#468	C₂²	1	2	yes	—
95	C₇×#468	C₂²	1	2	yes	complemented
96	C₇×#467	C₂²	1	2	yes	—
97	C₇×#467	C₂²	1	2	yes	complemented
98	C₇×#465	C₂²	1	2	yes	—
99	C₇×#465	C₂²	1	2	yes	complemented
100	C₇×#441	C₂²	1	2	yes	complemented
101	C₇×#440	C₂²	1	2	yes	complemented
102	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
104	C₇×#436	C₂²	1	2	yes	—
105	C₇×#435	C₂²	1	2	yes	—
106	C₇×#435	C₂²	1	2	yes	—
107	C₇×C₈×D₄	C₂²	1	2	yes	—
108	C₇×#428	C₂²	1	1	yes	characteristic
109	C₇×#428	C₂²	1	1	yes	characteristic
110	C₇×#428	C₂²	1	1	yes	characteristic
111	C₇×#428	C₂²	1	1	yes	characteristic
112	C₇×#428	C₂²	1	1	yes	characteristic
113	C₇×#428	C₂²	1	2	yes	—
114	C₇×#428	C₂²	1	2	yes	—
115	C₇×#428	C₂²	1	2	yes	complemented
116	C₇×#428	C₂²	1	2	yes	complemented
117	C₇×#427	C₂²	1	1	yes	characteristic
118	C₇×#427	C₂²	1	2	yes	—
119	C₇×#427	C₂²	1	2	yes	—
120	C₇×#427	C₂²	1	1	yes	characteristic
121	C₇×#427	C₂²	1	2	yes	complemented
122	C₂×C₇×#107	C₂²	1	1	yes	characteristic
123	C₂×C₇×#106	C₂²	1	1	yes	characteristic
124	C₂×C₇×#106	C₂²	1	2	yes	complemented
125	C₇×#424	C₂²	1	1	yes	characteristic
126	C₇×#419	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₇×#416	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₇×#103	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#61277	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	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₇×#137	—	2	4	no	—
141	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
143	C₇×#131	—	2	4	no	—
144	C₂×C₇×M₁₆	—	2	4	no	—
145	C₂×C₇×M₁₆	C₂³	1	2	yes	—
146	C₂×C₇×M₁₆	C₂³	1	2	yes	—
147	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	2	yes	—
150	C₂²×C₇×C₈	C₂³	1	2	yes	—
151	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	—	2	1	no	—
154	C₇×C₄⋊Q₈	—	2	1	no	—
155	C₇×C₄⋊Q₈	—	2	1	no	—
156	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₇×#126	—	2	2	no	—
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	—	2	2	no	—
162	C₇×#126	—	2	2	no	—
163	C₇×#126	—	2	2	no	—
164	C₇×#126	—	2	2	no	—
165	C₇×#126	—	2	2	no	—
166	C₇×#125	—	2	1	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	2	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	—	2	1	no	—
172	C₇×#125	C₂³	1	2	yes	—
173	C₇×#125	C₂³	1	2	yes	—
174	C₇×#124	—	2	1	no	—
175	C₇×#124	—	2	2	no	—
176	C₇×#124	—	2	2	no	—
177	C₇×#124	—	2	2	no	—
178	C₇×#124	—	2	2	no	—
179	C₇×#123	—	2	2	no	—
180	C₇×#123	—	2	2	no	—
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	1	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	D₄	1	2	yes	—
186	C₇×C₂²⋊Q₈	—	2	1	no	—
187	C₇×C₂²⋊Q₈	—	2	1	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	1	no	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	D₄	1	1	yes	characteristic
207	C₇×#121	D₄	1	1	yes	characteristic
208	C₇×#121	C₂³	1	1	yes	characteristic
209	C₇×#121	C₂³	1	2	yes	—
210	C₇×#121	C₂³	1	1	yes	characteristic
211	C₇×#120	—	2	1	no	—
212	C₇×#120	D₄	1	2	yes	—
213	C₄×C₇×Q₈	—	2	1	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	2	no	—
218	C₄×C₇×Q₈	—	2	2	no	—
219	C₄×C₇×Q₈	C₂³	1	2	yes	—
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×D₄	—	2	2	no	—
223	C₄×C₇×D₄	—	2	1	no	—
224	C₄×C₇×D₄	—	2	2	no	—
225	C₄×C₇×D₄	—	2	1	no	—
226	C₄×C₇×D₄	—	2	2	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	1	no	—
229	C₄×C₇×D₄	—	2	2	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	C₂³	1	2	yes	—
232	C₄×C₇×D₄	C₂³	1	2	yes	—
233	C₄×C₇×D₄	C₂³	1	2	yes	—
234	C₇×#117	—	2	1	no	—
235	C₇×#117	—	2	1	no	—
236	C₇×#117	—	2	1	no	—
237	C₇×#117	—	2	1	no	—
238	C₇×#117	—	2	1	no	—
239	C₇×#117	—	2	2	no	—
240	C₇×#117	—	2	2	no	—
241	C₇×#117	—	2	2	no	—
242	C₇×#117	—	2	2	no	—
243	C₇×#117	—	2	2	no	—
244	C₇×#117	C₂³	1	1	yes	characteristic
245	C₇×#117	C₂³	1	1	yes	characteristic
246	C₇×#117	C₂³	1	2	yes	—
247	C₇×#117	C₂³	1	2	yes	—
248	C₇×#117	C₂³	1	2	yes	—
249	C₇×#117	C₂³	1	2	yes	—
250	C₇×#117	C₂³	1	1	yes	characteristic
251	C₇×#117	C₂³	1	1	yes	characteristic
252	C₇×#117	C₂³	1	1	yes	characteristic
253	C₇×#117	C₂³	1	1	yes	characteristic
254	C₂×C₇×C₄⋊C₄	—	2	1	no	—
255	C₂×C₇×C₄⋊C₄	—	2	1	no	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²×C₇	—	2	1	no	—
267	C₂×C₄²×C₇	—	2	1	no	—
268	C₇×#107	C₂³	1	2	yes	—
269	C₇×#107	C₂³	1	2	yes	—
270	C₇×#107	C₂³	1	1	yes	characteristic
271	C₇×#107	C₂³	1	2	yes	—
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	1	yes	characteristic
274	C₇×#107	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	2	yes	—
278	C₇×#107	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	2	yes	—
280	C₇×#106	C₂³	1	2	yes	—
281	C₇×#106	C₂³	1	1	yes	characteristic
282	C₇×#106	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×#106	C₂³	1	1	yes	characteristic
287	C₇×#106	C₂³	1	1	yes	characteristic
288	C₇×#106	C₂³	1	1	yes	characteristic
289	C₇×#106	C₂³	1	2	yes	—
290	C₇×C₄⋊C₈	C₂³	1	2	yes	—
291	C₇×C₄⋊C₈	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	1	yes	characteristic
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	1	yes	characteristic
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₇×#97	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3495	C₂×C₇	1	1	yes	characteristic, complemented
317	#3493	C₂×C₇	1	1	yes	characteristic
318	#3357	C₂×C₇	1	2	yes	complemented
319	#3352	C₂×C₇	1	2	yes	complemented
320	#3350	C₂×C₇	1	2	yes	complemented
321	#3349	C₂×C₇	1	2	yes	complemented
322	#3348	C₂×C₇	1	2	yes	complemented
323	#3344	C₂×C₇	1	2	yes	complemented
324	#3342	C₂×C₇	1	2	yes	complemented
325	#3337	C₂×C₇	1	2	yes	complemented
326	#3164	C₂×C₇	1	1	yes	characteristic, complemented
327	#3098	C₂×C₇	1	1	yes	characteristic, complemented
328	#3097	C₂×C₇	1	1	yes	characteristic, complemented
329	#3091	C₂×C₇	1	1	yes	characteristic, complemented
330	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
331	#3084	C₂×C₇	1	1	yes	characteristic, complemented
332	#3082	C₂×C₇	1	1	yes	characteristic, complemented
333	#3063	C₂×C₇	1	1	yes	characteristic, complemented
334	#3056	C₂×C₇	1	1	yes	characteristic, complemented
335	#2947	C₂×C₇	1	1	yes	characteristic, complemented
336	#2933	C₂×C₇	1	1	yes	characteristic, complemented
337	#2912	C₂×C₇	1	1	yes	characteristic, complemented
338	#2911	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	2	2	no	—
342	C₇×#41	—	2	2	no	—
343	C₇×#41	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	1	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
350	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
351	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₇×D₄	—	2	1	no	—
353	C₂×C₇×D₄	—	2	1	no	—
354	C₂×C₇×D₄	—	2	1	no	—
355	C₂×C₇×D₄	—	2	2	no	—
356	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
357	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
358	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
359	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
360	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₇	—	2	2	no	—
362	C₂²×C₄×C₇	—	2	2	no	—
363	C₂²×C₄×C₇	—	2	1	no	—
364	C₂²×C₄×C₇	—	2	1	no	—
365	C₂²×C₄×C₇	—	2	1	no	—
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	1	no	—
368	C₂²×C₄×C₇	—	2	1	no	—
369	C₂²×C₄×C₇	—	2	2	no	—
370	C₂²×C₄×C₇	—	2	2	no	—
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	2	no	—
373	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
380	C₇×Q₁₆	—	2	4	no	—
381	C₇×SD₁₆	—	2	4	no	—
382	C₇×M₁₆	—	2	2	no	—
383	C₇×M₁₆	—	2	4	no	—
384	C₇×M₁₆	—	2	4	no	—
385	C₇×M₁₆	#41	1	4	yes	—
386	C₂×C₇×C₈	—	2	2	no	—
387	C₂×C₇×C₈	—	2	2	no	—
388	C₂×C₇×C₈	—	2	4	no	—
389	C₂×C₇×C₈	—	2	4	no	—
390	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
394	C₂×C₇×C₈	C₂⁴	1	2	yes	—
395	C₂×C₇×C₈	C₂⁴	1	2	yes	—
396	C₇×C₄⋊C₄	—	2	1	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	no	—
399	C₇×C₄⋊C₄	—	2	2	no	—
400	C₇×C₄⋊C₄	—	2	1	no	—
401	C₇×C₄⋊C₄	—	2	1	no	—
402	C₇×C₄⋊C₄	—	2	1	no	—
403	C₇×C₄⋊C₄	—	2	1	no	—
404	C₇×C₄⋊C₄	—	2	2	no	—
405	C₇×C₄⋊C₄	—	2	2	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	2	no	—
418	C₇×C₄⋊C₄	—	2	2	no	—
419	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
431	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
432	C₇×C₂²⋊C₄	—	2	1	no	—
433	C₇×C₂²⋊C₄	—	2	2	no	—
434	C₇×C₂²⋊C₄	—	2	2	no	—
435	C₇×C₂²⋊C₄	—	2	1	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	1	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	1	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	—	2	2	no	—
445	C₇×C₂²⋊C₄	—	2	1	no	—
446	C₇×C₂²⋊C₄	—	2	1	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
453	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
456	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
457	C₄²×C₇	—	2	2	no	—
458	C₄²×C₇	—	2	1	no	—
459	C₄²×C₇	—	2	1	no	—
460	C₄²×C₇	—	2	2	no	—
461	C₄²×C₇	—	2	1	no	—
462	C₄²×C₇	—	2	1	no	—
463	C₄²×C₇	—	2	2	no	—
464	C₄²×C₇	—	2	2	no	—
465	C₄²×C₇	—	2	2	no	—
466	C₄²×C₇	—	2	2	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	—	2	1	no	—
469	C₄²×C₇	C₂⁴	1	2	yes	—
470	C₂×#137	C₂²×C₇	1	1	yes	characteristic
471	C₂×#131	C₂²×C₇	1	1	yes	characteristic
472	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
473	#556	—	2	1	no	—
474	#556	C₂²×C₇	1	2	yes	—
475	#556	C₂²×C₇	1	2	yes	—
476	#555	—	2	1	no	—
477	#555	C₂²×C₇	1	2	yes	—
478	#554	C₂²×C₇	1	2	yes	—
479	#553	—	2	1	no	—
480	#553	C₂²×C₇	1	2	yes	—
481	#552	—	2	2	no	—
482	#552	—	2	1	no	—
483	#552	C₂²×C₇	1	2	yes	—
484	#552	C₂²×C₇	1	2	yes	—
485	#552	C₂²×C₇	1	2	yes	—
486	#551	—	2	2	no	—
487	#544	C₂²×C₇	1	1	yes	characteristic
488	#544	C₂²×C₇	1	1	yes	characteristic
489	#542	—	2	1	no	—
490	#541	—	2	1	no	—
491	#538	—	2	2	no	—
492	#537	C₂²×C₇	1	1	yes	characteristic
493	#536	C₂²×C₇	1	1	yes	characteristic
494	#533	—	2	1	no	—
495	#529	—	2	2	no	—
496	#529	—	2	1	no	—
497	#525	C₂²×C₇	1	1	yes	characteristic
498	#525	C₂²×C₇	1	1	yes	characteristic
499	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
500	#520	C₂²×C₇	1	1	yes	characteristic
501	#520	C₂²×C₇	1	1	yes	characteristic
502	#520	C₂²×C₇	1	1	yes	characteristic
503	#519	C₂²×C₇	1	1	yes	characteristic
504	C₂×#117	C₂²×C₇	1	1	yes	characteristic
505	C₂×#117	C₂²×C₇	1	1	yes	characteristic
506	#501	C₂²×C₇	1	2	yes	complemented
507	#501	C₂²×C₇	1	2	yes	complemented
508	#500	C₂²×C₇	1	2	yes	complemented
509	#499	C₂²×C₇	1	2	yes	complemented
510	#485	C₂²×C₇	1	2	yes	—
511	#485	C₂²×C₇	1	1	yes	characteristic
512	#485	C₂²×C₇	1	2	yes	—
513	#485	C₂²×C₇	1	2	yes	—
514	#485	C₂²×C₇	1	2	yes	—
515	#485	C₂²×C₇	1	1	yes	characteristic
516	#485	C₂²×C₇	1	2	yes	complemented
517	#485	C₂²×C₇	1	2	yes	complemented
518	#485	C₂²×C₇	1	2	yes	complemented
519	#484	C₂²×C₇	1	1	yes	characteristic
520	#484	C₂²×C₇	1	2	yes	complemented
521	#484	C₂²×C₇	1	2	yes	complemented
522	#483	C₂²×C₇	1	1	yes	characteristic
523	#483	C₂²×C₇	1	2	yes	complemented
524	#482	C₂²×C₇	1	1	yes	characteristic
525	#482	C₂²×C₇	1	1	yes	characteristic
526	#482	C₂²×C₇	1	2	yes	complemented
527	#481	C₂²×C₇	1	1	yes	characteristic
528	#480	C₂²×C₇	1	1	yes	characteristic
529	#480	C₂²×C₇	1	2	yes	complemented
530	#479	C₂²×C₇	1	2	yes	complemented
531	#479	C₂²×C₇	1	2	yes	complemented
532	#479	C₂²×C₇	1	2	yes	complemented
533	#478	C₂²×C₇	1	2	yes	complemented
534	#477	C₂²×C₇	1	2	yes	complemented
535	#476	C₂²×C₇	1	2	yes	complemented
536	#475	C₂²×C₇	1	2	yes	complemented
537	#475	C₂²×C₇	1	2	yes	complemented
538	#470	C₂²×C₇	1	2	yes	—
539	#470	C₂²×C₇	1	2	yes	complemented
540	#468	C₂²×C₇	1	2	yes	—
541	#468	C₂²×C₇	1	2	yes	complemented
542	#467	C₂²×C₇	1	2	yes	—
543	#467	C₂²×C₇	1	2	yes	complemented
544	#465	C₂²×C₇	1	2	yes	—
545	#465	C₂²×C₇	1	2	yes	complemented
546	#441	C₂²×C₇	1	2	yes	complemented
547	#440	C₂²×C₇	1	2	yes	complemented
548	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
549	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
550	#436	C₂²×C₇	1	2	yes	—
551	#435	C₂²×C₇	1	2	yes	—
552	#435	C₂²×C₇	1	2	yes	—
553	C₈×D₄	C₂²×C₇	1	2	yes	—
554	#428	C₂²×C₇	1	1	yes	characteristic
555	#428	C₂²×C₇	1	1	yes	characteristic
556	#428	C₂²×C₇	1	2	yes	—
557	#428	C₂²×C₇	1	2	yes	—
558	#428	C₂²×C₇	1	1	yes	characteristic
559	#428	C₂²×C₇	1	1	yes	characteristic
560	#428	C₂²×C₇	1	1	yes	characteristic
561	#428	C₂²×C₇	1	2	yes	complemented
562	#428	C₂²×C₇	1	2	yes	complemented
563	#427	C₂²×C₇	1	2	yes	—
564	#427	C₂²×C₇	1	1	yes	characteristic
565	#427	C₂²×C₇	1	2	yes	—
566	#427	C₂²×C₇	1	1	yes	characteristic
567	#427	C₂²×C₇	1	2	yes	complemented
568	C₂×#107	C₂²×C₇	1	1	yes	characteristic
569	C₂×#106	C₂²×C₇	1	1	yes	characteristic
570	C₂×#106	C₂²×C₇	1	2	yes	complemented
571	#424	C₂²×C₇	1	1	yes	characteristic
572	#419	C₂²×C₇	1	1	yes	characteristic
573	#417	C₂²×C₇	1	1	yes	characteristic
574	#416	C₂²×C₇	1	1	yes	characteristic
575	#416	C₂²×C₇	1	1	yes	characteristic
576	C₂×#103	C₂²×C₇	1	1	yes	characteristic
577	C₂×#103	C₂²×C₇	1	1	yes	characteristic
578	#408	C₂²×C₇	1	1	yes	characteristic
579	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
580	#405	C₂²×C₇	1	1	yes	characteristic
581	C₂³×C₇	—	2	2	no	—
582	C₂³×C₇	—	2	1	no	—
583	C₂³×C₇	—	4	1	no	—
584	C₂³×C₇	—	4	1	no	—
585	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
586	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
587	C₂³×C₇	C₂²×D₄	1	2	yes	—
588	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
589	C₇×Q₈	—	2	2	no	—
590	C₇×Q₈	—	2	2	no	—
591	C₇×Q₈	—	2	1	no	—
592	C₇×Q₈	—	2	2	no	—
593	C₇×Q₈	—	2	1	no	—
594	C₇×Q₈	—	4	2	no	—
595	C₇×Q₈	—	8	2	no	—
596	C₇×Q₈	—	8	2	no	—
597	C₇×D₄	—	2	4	no	—
598	C₇×D₄	—	2	2	no	—
599	C₇×D₄	—	2	1	no	—
600	C₇×D₄	—	2	1	no	—
601	C₇×D₄	—	4	2	no	—
602	C₇×D₄	—	4	2	no	—
603	C₇×D₄	—	4	2	no	—
604	C₇×D₄	—	8	2	no	—
605	C₇×D₄	—	8	1	no	—
606	C₇×D₄	—	8	1	no	—
607	C₂×C₄×C₇	—	2	2	no	—
608	C₂×C₄×C₇	—	2	2	no	—
609	C₂×C₄×C₇	—	2	2	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	2	2	no	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	2	1	no	—
614	C₂×C₄×C₇	—	2	1	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	1	no	—
617	C₂×C₄×C₇	—	2	2	no	—
618	C₂×C₄×C₇	—	2	1	no	—
619	C₂×C₄×C₇	—	2	1	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	1	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	2	no	—
624	C₂×C₄×C₇	—	2	1	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	2	no	—
627	C₂×C₄×C₇	—	4	2	no	—
628	C₂×C₄×C₇	—	4	2	no	—
629	C₂×C₄×C₇	—	4	2	no	—
630	C₂×C₄×C₇	—	8	2	no	—
631	C₂×C₄×C₇	—	8	2	no	—
632	C₂×C₄×C₇	—	8	1	no	—
633	C₂×C₄×C₇	—	8	1	no	—
634	C₂×C₄×C₇	—	8	1	no	—
635	C₂×C₄×C₇	—	8	1	no	—
636	C₂×C₄×C₇	—	8	2	no	—
637	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
639	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
641	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
642	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₇	C₂×#41	1	2	yes	—
644	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
645	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
646	C₇×C₈	—	2	1	no	—
647	C₇×C₈	—	2	1	no	—
648	C₇×C₈	—	2	2	no	—
649	C₇×C₈	—	2	1	no	—
650	C₇×C₈	—	2	1	no	—
651	C₇×C₈	C₂×#41	1	4	yes	—
652	C₂×#41	C₂³×C₇	1	1	yes	characteristic
653	C₂×#41	C₂³×C₇	1	1	yes	characteristic
654	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
656	#137	—	2	4	no	—
657	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
659	#131	—	2	4	no	—
660	C₂×M₁₆	—	2	4	no	—
661	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
662	C₂×M₁₆	C₂³×C₇	1	2	yes	—
663	C₂×M₁₆	C₂³×C₇	1	2	yes	—
664	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
665	C₂²×C₈	C₂³×C₇	1	2	yes	—
666	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
667	C₂²×C₈	C₂³×C₇	1	2	yes	—
668	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
669	C₄⋊Q₈	—	2	1	no	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
673	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
674	#126	—	2	2	no	—
675	#126	—	2	2	no	—
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#125	—	2	1	no	—
683	#125	—	2	2	no	—
684	#125	—	2	2	no	—
685	#125	—	2	2	no	—
686	#125	—	2	2	no	—
687	#125	—	2	1	no	—
688	#125	C₂³×C₇	1	2	yes	—
689	#125	C₂³×C₇	1	2	yes	—
690	#124	—	2	1	no	—
691	#124	—	2	2	no	—
692	#124	—	2	2	no	—
693	#124	—	2	2	no	—
694	#124	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	1	no	—
700	#123	—	2	2	no	—
701	#123	C₇×D₄	1	2	yes	—
702	C₂²⋊Q₈	—	2	1	no	—
703	C₂²⋊Q₈	—	2	1	no	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
710	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
711	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
713	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
714	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
717	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
718	#121	—	2	2	no	—
719	#121	—	2	1	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	C₇×D₄	1	1	yes	characteristic
723	#121	C₇×D₄	1	1	yes	characteristic
724	#121	C₂³×C₇	1	1	yes	characteristic
725	#121	C₂³×C₇	1	1	yes	characteristic
726	#121	C₂³×C₇	1	2	yes	—
727	#120	—	2	1	no	—
728	#120	C₇×D₄	1	2	yes	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	—	2	1	no	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	2	no	—
735	C₄×Q₈	C₂³×C₇	1	2	yes	—
736	C₄×Q₈	C₂³×C₇	1	2	yes	—
737	C₄×Q₈	C₂³×C₇	1	2	yes	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	1	no	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	1	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	C₂³×C₇	1	2	yes	—
748	C₄×D₄	C₂³×C₇	1	2	yes	—
749	C₄×D₄	C₂³×C₇	1	2	yes	—
750	#117	—	2	1	no	—
751	#117	—	2	1	no	—
752	#117	—	2	1	no	—
753	#117	—	2	1	no	—
754	#117	—	2	1	no	—
755	#117	—	2	2	no	—
756	#117	—	2	2	no	—
757	#117	—	2	2	no	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	C₂³×C₇	1	1	yes	characteristic
761	#117	C₂³×C₇	1	1	yes	characteristic
762	#117	C₂³×C₇	1	1	yes	characteristic
763	#117	C₂³×C₇	1	2	yes	—
764	#117	C₂³×C₇	1	2	yes	—
765	#117	C₂³×C₇	1	1	yes	characteristic
766	#117	C₂³×C₇	1	1	yes	characteristic
767	#117	C₂³×C₇	1	2	yes	—
768	#117	C₂³×C₇	1	2	yes	—
769	#117	C₂³×C₇	1	1	yes	characteristic
770	C₂×C₄⋊C₄	—	2	1	no	—
771	C₂×C₄⋊C₄	—	2	1	no	—
772	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
773	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
774	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
775	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
779	C₂×C₂²⋊C₄	—	2	1	no	—
780	C₂×C₂²⋊C₄	—	2	1	no	—
781	C₂×C₂²⋊C₄	—	2	1	no	—
782	C₂×C₄²	—	2	1	no	—
783	C₂×C₄²	—	2	1	no	—
784	#107	C₂³×C₇	1	2	yes	—
785	#107	C₂³×C₇	1	2	yes	—
786	#107	C₂³×C₇	1	2	yes	—
787	#107	C₂³×C₇	1	2	yes	—
788	#107	C₂³×C₇	1	2	yes	—
789	#107	C₂³×C₇	1	2	yes	—
790	#107	C₂³×C₇	1	1	yes	characteristic
791	#107	C₂³×C₇	1	1	yes	characteristic
792	#107	C₂³×C₇	1	1	yes	characteristic
793	#107	C₂³×C₇	1	1	yes	characteristic
794	#107	C₂³×C₇	1	2	yes	—
795	#106	C₂³×C₇	1	2	yes	—
796	#106	C₂³×C₇	1	2	yes	—
797	#106	C₂³×C₇	1	1	yes	characteristic
798	#106	C₂³×C₇	1	2	yes	—
799	#106	C₂³×C₇	1	2	yes	—
800	#106	C₂³×C₇	1	1	yes	characteristic
801	#106	C₂³×C₇	1	2	yes	—
802	#106	C₂³×C₇	1	2	yes	—
803	#106	C₂³×C₇	1	2	yes	—
804	#106	C₂³×C₇	1	1	yes	characteristic
805	#106	C₂³×C₇	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₇	1	2	yes	—
807	C₄⋊C₈	C₂³×C₇	1	2	yes	—
808	#103	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	2	yes	—
810	#103	C₂³×C₇	1	2	yes	—
811	#103	C₂³×C₇	1	2	yes	—
812	#103	C₂³×C₇	1	1	yes	characteristic
813	#103	C₂³×C₇	1	1	yes	characteristic
814	#103	C₂³×C₇	1	1	yes	characteristic
815	#103	C₂³×C₇	1	1	yes	characteristic
816	#103	C₂³×C₇	1	2	yes	—
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	2	yes	—
819	#102	C₂³×C₇	1	1	yes	characteristic
820	#102	C₂³×C₇	1	1	yes	characteristic
821	#102	C₂³×C₇	1	1	yes	characteristic
822	#102	C₂³×C₇	1	1	yes	characteristic
823	#102	C₂³×C₇	1	2	yes	—
824	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
827	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
830	#97	C₂³×C₇	1	2	yes	—
831	C₄×C₈	C₂³×C₇	1	2	yes	—
832	C₂²×C₇	—	2	1	no	—
833	C₂²×C₇	—	2	1	no	—
834	C₂²×C₇	—	2	2	no	—
835	C₂²×C₇	—	2	1	no	—
836	C₂²×C₇	—	2	1	no	—
837	C₂²×C₇	—	2	1	no	—
838	C₂²×C₇	—	2	2	no	—
839	C₂²×C₇	—	2	1	no	—
840	C₂²×C₇	—	2	1	no	—
841	C₂²×C₇	—	2	1	no	—
842	C₂²×C₇	—	2	2	no	—
843	C₂²×C₇	—	4	1	no	—
844	C₂²×C₇	—	4	1	no	—
845	C₂²×C₇	—	4	1	no	—
846	C₂²×C₇	—	8	2	no	—
847	C₂²×C₇	#547	1	2	yes	—
848	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
849	C₄×C₇	—	2	2	no	—
850	C₄×C₇	—	2	2	no	—
851	C₄×C₇	—	2	1	no	—
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	2	no	—
854	C₄×C₇	—	4	1	no	—
855	C₄×C₇	—	4	2	no	—
856	C₄×C₇	—	4	2	no	—
857	C₄×C₇	—	4	1	no	—
858	C₄×C₇	—	4	1	no	—
859	C₄×C₇	—	4	1	no	—
860	C₄×C₇	—	4	1	no	—
861	C₄×C₇	—	4	2	no	—
862	C₄×C₇	—	4	1	no	—
863	C₄×C₇	—	4	1	no	—
864	C₄×C₇	—	4	2	no	—
865	C₄×C₇	#547	1	2	yes	—
866	C₄×C₇	C₂²×#41	1	1	yes	characteristic
867	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
868	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
869	#41	—	2	2	no	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
886	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
887	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
888	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
889	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
904	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
909	Q₁₆	—	2	4	no	—
910	SD₁₆	—	2	4	no	—
911	M₁₆	—	2	2	no	—
912	M₁₆	—	2	4	no	—
913	M₁₆	—	2	4	no	—
914	M₁₆	C₇×#41	1	4	yes	—
915	C₂×C₈	—	2	2	no	—
916	C₂×C₈	—	2	2	no	—
917	C₂×C₈	—	2	4	no	—
918	C₂×C₈	—	2	4	no	—
919	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₇	1	2	yes	—
924	C₂×C₈	C₂⁴×C₇	1	2	yes	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
949	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
950	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
951	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
982	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
983	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
984	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
985	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	C₂⁴×C₇	1	2	yes	—
999	C₂×C₇	—	2	2	no	—
1000	C₂×C₇	—	4	2	no	—
1001	C₂×C₇	—	4	1	no	—
1002	C₂×C₇	—	4	1	no	—
1003	C₂×C₇	—	8	1	no	—
1004	C₂×C₇	C₂×#547	1	1	yes	characteristic
1005	C₂×C₇	#3584	1	1	yes	characteristic
1006	C₂×C₇	#3586	1	1	yes	characteristic
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	4	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1012	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1013	C₂³	C₂²×C₇×D₄	1	2	yes	—
1014	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	8	2	no	—
1022	Q₈	—	8	2	no	—
1023	D₄	—	2	4	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	2	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	8	2	no	—
1031	D₄	—	8	1	no	—
1032	D₄	—	8	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1065	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1066	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1067	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1068	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1069	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1070	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1071	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	C₂×C₇×#41	1	4	yes	—
1078	C₇	#61277	1	1	yes	characteristic, direct product factor, Sylow
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	2	no	—
1094	C₂²	C₇×#547	1	2	yes	—
1095	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	C₇×#547	1	2	yes	—
1113	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1114	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₂×C₇×#547	1	1	yes	characteristic
1121	C₂	C₇×#3584	1	1	yes	characteristic
1122	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
3. C₇×#3357	C₂	semidirect
4. C₇×#3352	C₂	semidirect
5. C₇×#3350	C₂	semidirect
6. C₇×#3349	C₂	semidirect
7. C₇×#3348	C₂	semidirect
8. C₇×#3344	C₂	semidirect
9. C₇×#3342	C₂	semidirect
10. C₇×#3337	C₂	semidirect
11. C₇×#3164	C₂	semidirect
12. C₇×#3098	C₂	semidirect
13. C₇×#3097	C₂	semidirect
14. C₇×#3091	C₂	semidirect
15. C₂×C₇×#485	C₂	semidirect
16. C₇×#3084	C₂	semidirect
17. C₇×#3082	C₂	semidirect
18. C₇×#3063	C₂	semidirect
19. C₇×#3056	C₂	semidirect
20. C₇×#2947	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2912	C₂	semidirect
23. C₇×#2911	C₂	semidirect
60. C₇×#501	C₂²	semidirect
61. C₇×#501	C₂²	semidirect
62. C₇×#500	C₂²	semidirect
63. C₇×#499	C₂²	semidirect
70. C₇×#485	C₂²	semidirect
71. C₇×#485	C₂²	semidirect
72. C₇×#485	C₂²	semidirect
74. C₇×#484	C₂²	semidirect
75. C₇×#484	C₂²	semidirect
77. C₇×#483	C₂²	semidirect
80. C₇×#482	C₂²	semidirect
83. C₇×#480	C₂²	semidirect
84. C₇×#479	C₂²	semidirect
85. C₇×#479	C₂²	semidirect
86. C₇×#479	C₂²	semidirect
87. C₇×#478	C₂²	semidirect
88. C₇×#477	C₂²	semidirect
89. C₇×#476	C₂²	semidirect
90. C₇×#475	C₂²	semidirect
91. C₇×#475	C₂²	semidirect
93. C₇×#470	C₂²	semidirect
95. C₇×#468	C₂²	semidirect
97. C₇×#467	C₂²	semidirect
99. C₇×#465	C₂²	semidirect
100. C₇×#441	C₂²	semidirect
101. C₇×#440	C₂²	semidirect
102. C₄×C₇×Q₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
115. C₇×#428	C₂²	semidirect
116. C₇×#428	C₂²	semidirect
121. C₇×#427	C₂²	semidirect
124. C₂×C₇×#106	C₂²	semidirect
135. #61277	C₇	direct (N × H)
316. #3495	C₂×C₇	semidirect
318. #3357	C₂×C₇	semidirect
319. #3352	C₂×C₇	semidirect
320. #3350	C₂×C₇	semidirect
321. #3349	C₂×C₇	semidirect
322. #3348	C₂×C₇	semidirect
323. #3344	C₂×C₇	semidirect
324. #3342	C₂×C₇	semidirect
325. #3337	C₂×C₇	semidirect
326. #3164	C₂×C₇	semidirect
327. #3098	C₂×C₇	semidirect
328. #3097	C₂×C₇	semidirect
329. #3091	C₂×C₇	semidirect
330. C₂×#485	C₂×C₇	semidirect
331. #3084	C₂×C₇	semidirect
332. #3082	C₂×C₇	semidirect
333. #3063	C₂×C₇	semidirect
334. #3056	C₂×C₇	semidirect
335. #2947	C₂×C₇	semidirect
336. #2933	C₂×C₇	semidirect
337. #2912	C₂×C₇	semidirect
338. #2911	C₂×C₇	semidirect
506. #501	C₂²×C₇	semidirect
507. #501	C₂²×C₇	semidirect
508. #500	C₂²×C₇	semidirect
509. #499	C₂²×C₇	semidirect
516. #485	C₂²×C₇	semidirect
517. #485	C₂²×C₇	semidirect
518. #485	C₂²×C₇	semidirect
520. #484	C₂²×C₇	semidirect
521. #484	C₂²×C₇	semidirect
523. #483	C₂²×C₇	semidirect
526. #482	C₂²×C₇	semidirect
529. #480	C₂²×C₇	semidirect
530. #479	C₂²×C₇	semidirect
531. #479	C₂²×C₇	semidirect
532. #479	C₂²×C₇	semidirect
533. #478	C₂²×C₇	semidirect
534. #477	C₂²×C₇	semidirect
535. #476	C₂²×C₇	semidirect
536. #475	C₂²×C₇	semidirect
537. #475	C₂²×C₇	semidirect
539. #470	C₂²×C₇	semidirect
541. #468	C₂²×C₇	semidirect
543. #467	C₂²×C₇	semidirect
545. #465	C₂²×C₇	semidirect
546. #441	C₂²×C₇	semidirect
547. #440	C₂²×C₇	semidirect
548. C₄×Q₁₆	C₂²×C₇	semidirect
549. C₄×SD₁₆	C₂²×C₇	semidirect
561. #428	C₂²×C₇	semidirect
562. #428	C₂²×C₇	semidirect
567. #427	C₂²×C₇	semidirect
570. C₂×#106	C₂²×C₇	semidirect
1078. C₇	#61277	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×#3495	2
C₇×#3493	2
C₇×#3357	2
C₇×#3352	2
C₇×#3350	2
C₇×#3349	2
C₇×#3348	2
C₇×#3344	2
C₇×#3342	2
C₇×#3337	2
C₇×#3164	2
C₇×#3098	2
C₇×#3097	2
C₇×#3091	2
C₂×C₇×#485	2
C₇×#3084	2
C₇×#3082	2
C₇×#3063	2
C₇×#3056	2
C₇×#2947	2
C₇×#2933	2
C₇×#2912	2
C₇×#2911	2
#61277	7

Subgroups — C7×#61277 #13238493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61277 #13238493