Subgroups — C₇×#61257 #13238473

Order 1792.

1828 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₇×#3350	C₂	1	4	yes	maximal, complemented
6	C₇×#3349	C₂	1	4	yes	maximal, complemented
7	C₇×#3342	C₂	1	2	yes	maximal, complemented
8	C₇×#3340	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3095	C₂	1	2	yes	maximal, complemented
11	C₇×#3093	C₂	1	2	yes	maximal, complemented
12	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3056	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2911	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₇×#556	—	2	1	no	—
21	C₇×#556	—	2	2	no	—
22	C₇×#556	—	2	1	no	—
23	C₇×#556	C₂²	1	2	yes	—
24	C₇×#556	C₂²	1	4	yes	—
25	C₇×#556	C₂²	1	2	yes	—
26	C₇×#556	C₂²	1	1	yes	characteristic
27	C₇×#555	C₂²	1	1	yes	characteristic
28	C₇×#554	C₂²	1	1	yes	characteristic
29	C₇×#553	C₂²	1	2	yes	—
30	C₇×#552	—	2	1	no	—
31	C₇×#552	C₂²	1	2	yes	—
32	C₇×#551	—	2	2	no	—
33	C₇×#547	C₂²	1	1	yes	characteristic
34	C₇×#546	—	2	1	no	—
35	C₇×#533	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₇×#529	—	2	2	no	—
38	C₇×#529	—	2	1	no	—
39	C₂×C₇×#126	—	2	2	no	—
40	C₂×C₇×#124	—	2	1	no	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₄×C₇×#41	—	2	1	no	—
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	—	2	1	no	—
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₇×#117	C₂²	1	2	yes	—
49	C₂×C₇×#117	C₂²	1	2	yes	—
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#500	C₂²	1	2	yes	complemented
52	C₇×#498	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	4	yes	complemented
54	C₇×#485	C₂²	1	4	yes	complemented
55	C₇×#485	C₂²	1	4	yes	complemented
56	C₇×#485	C₂²	1	4	yes	complemented
57	C₇×#484	C₂²	1	4	yes	complemented
58	C₇×#483	C₂²	1	4	yes	complemented
59	C₇×#482	C₂²	1	4	yes	complemented
60	C₇×#482	C₂²	1	4	yes	complemented
61	C₇×#479	C₂²	1	4	yes	complemented
62	C₇×#477	C₂²	1	2	yes	complemented
63	C₇×#477	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	2	yes	complemented
66	C₇×#475	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#470	C₂²	1	4	yes	complemented
69	C₇×#468	C₂²	1	4	yes	complemented
70	C₇×#467	C₂²	1	4	yes	complemented
71	C₇×#465	C₂²	1	4	yes	complemented
72	C₇×#441	C₂²	1	2	yes	complemented
73	C₇×#440	C₂²	1	2	yes	complemented
74	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
75	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
76	C₇×#436	C₂²	1	2	yes	—
77	C₇×#435	C₂²	1	4	yes	—
78	C₇×C₈×D₄	C₂²	1	2	yes	—
79	C₇×#428	C₂²	1	2	yes	—
80	C₇×#428	C₂²	1	2	yes	—
81	C₇×#428	C₂²	1	1	yes	characteristic
82	C₇×#428	C₂²	1	2	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	4	yes	complemented
85	C₇×#428	C₂²	1	4	yes	complemented
86	C₇×#427	C₂²	1	4	yes	complemented
87	C₇×#427	C₂²	1	4	yes	complemented
88	C₇×#423	C₂²	1	1	yes	characteristic
89	C₇×#419	C₂²	1	1	yes	characteristic
90	C₇×#419	C₂²	1	2	yes	—
91	C₇×#417	C₂²	1	1	yes	characteristic
92	C₇×#417	C₂²	1	2	yes	—
93	C₇×#407	C₂²	1	2	yes	—
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
95	#61257	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	1	no	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂²×C₇×Q₈	—	2	1	no	—
99	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
100	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₇	C₂³	1	2	yes	—
102	C₇×#137	—	2	4	no	—
103	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
104	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₇×M₁₆	—	2	8	no	—
106	C₂×C₇×M₁₆	C₂³	1	4	yes	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇×M₁₆	C₂³	1	2	yes	—
109	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	4	yes	—
111	C₇×C₄⋊Q₈	—	2	1	no	—
112	C₇×C₄⋊Q₈	—	2	1	no	—
113	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×#126	—	2	2	no	—
118	C₇×#126	—	2	4	no	—
119	C₇×#126	—	2	4	no	—
120	C₇×#126	—	2	4	no	—
121	C₇×#126	—	2	4	no	—
122	C₇×#126	—	2	2	no	—
123	C₇×#126	—	2	2	no	—
124	C₇×#125	—	2	2	no	—
125	C₇×#125	—	2	1	no	—
126	C₇×#125	C₂³	1	2	yes	—
127	C₇×#124	—	2	2	no	—
128	C₇×#124	—	2	2	no	—
129	C₇×#124	—	2	4	no	—
130	C₇×#124	—	2	1	no	—
131	C₇×#124	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	2	no	—
135	C₇×#123	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	2	no	—
137	C₇×C₂²⋊Q₈	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	1	no	—
140	C₇×C₂²⋊Q₈	—	2	1	no	—
141	C₇×C₂²⋊Q₈	—	2	2	no	—
142	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	1	no	—
148	C₇×#121	C₂³	1	2	yes	—
149	C₇×#121	C₂³	1	2	yes	—
150	C₇×#120	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	2	no	—
152	C₄×C₇×Q₈	—	2	2	no	—
153	C₄×C₇×Q₈	—	2	4	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
160	C₄×C₇×Q₈	C₂³	1	2	yes	—
161	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	D₄	1	1	yes	characteristic
170	C₄×C₇×D₄	D₄	1	1	yes	characteristic
171	C₄×C₇×D₄	D₄	1	2	yes	—
172	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
173	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
174	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
175	C₄×C₇×D₄	C₂³	1	2	yes	—
176	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
177	C₇×#117	—	2	2	no	—
178	C₇×#117	—	2	2	no	—
179	C₇×#117	—	2	2	no	—
180	C₇×#117	—	2	2	no	—
181	C₇×#117	—	2	1	no	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	—	2	1	no	—
184	C₇×#117	C₂³	1	4	yes	—
185	C₇×#117	C₂³	1	4	yes	—
186	C₇×#117	C₂³	1	2	yes	—
187	C₇×#117	C₂³	1	2	yes	—
188	C₇×#117	C₂³	1	1	yes	characteristic
189	C₇×#117	C₂³	1	2	yes	—
190	C₂×C₇×C₄⋊C₄	—	2	2	no	—
191	C₂×C₇×C₄⋊C₄	—	2	1	no	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
194	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
202	C₂×C₄²×C₇	—	2	2	no	—
203	C₂×C₄²×C₇	—	2	2	no	—
204	C₂×C₄²×C₇	—	2	1	no	—
205	C₂×C₄²×C₇	—	2	1	no	—
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₇×#107	C₂³	1	4	yes	—
208	C₇×#107	C₂³	1	4	yes	—
209	C₇×#107	C₂³	1	4	yes	—
210	C₇×#107	C₂³	1	4	yes	—
211	C₇×#107	C₂³	1	2	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#106	C₂³	1	4	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	4	yes	—
216	C₇×#106	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	4	yes	—
221	C₇×#103	C₂³	1	4	yes	—
222	C₇×#103	C₂³	1	2	yes	—
223	C₇×#103	C₂³	1	2	yes	—
224	C₇×#103	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	2	yes	—
227	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₇×#97	C₂³	1	2	yes	—
230	C₄×C₇×C₈	C₂³	1	2	yes	—
231	#3475	C₂×C₇	1	1	yes	characteristic
232	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
233	#3356	C₂×C₇	1	2	yes	complemented
234	#3353	C₂×C₇	1	2	yes	complemented
235	#3350	C₂×C₇	1	4	yes	complemented
236	#3349	C₂×C₇	1	4	yes	complemented
237	#3342	C₂×C₇	1	2	yes	complemented
238	#3340	C₂×C₇	1	2	yes	complemented
239	#3165	C₂×C₇	1	1	yes	characteristic, complemented
240	#3095	C₂×C₇	1	2	yes	complemented
241	#3093	C₂×C₇	1	2	yes	complemented
242	#3079	C₂×C₇	1	1	yes	characteristic, complemented
243	#3078	C₂×C₇	1	1	yes	characteristic, complemented
244	#3056	C₂×C₇	1	2	yes	complemented
245	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
246	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
247	#2911	C₂×C₇	1	2	yes	complemented
248	C₂⁴×C₇	C₂×D₄	1	2	yes	—
249	C₇×#41	—	2	2	no	—
250	C₇×#41	—	2	2	no	—
251	C₇×#41	—	4	4	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	1	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	1	no	—
257	C₂×C₇×Q₈	—	2	2	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	4	4	no	—
260	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
261	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×D₄	—	2	1	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	4	2	no	—
266	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
267	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
268	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
269	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇	—	2	4	no	—
271	C₂²×C₄×C₇	—	2	4	no	—
272	C₂²×C₄×C₇	—	2	1	no	—
273	C₂²×C₄×C₇	—	2	1	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	1	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₇×Q₁₆	—	2	4	no	—
289	C₇×SD₁₆	—	2	4	no	—
290	C₇×M₁₆	—	2	4	no	—
291	C₇×M₁₆	—	2	2	no	—
292	C₇×M₁₆	—	2	8	no	—
293	C₇×M₁₆	#41	1	4	yes	complemented
294	C₂×C₇×C₈	—	2	8	no	—
295	C₂×C₇×C₈	C₂⁴	1	2	yes	—
296	C₂×C₇×C₈	C₂⁴	1	4	yes	—
297	C₂×C₇×C₈	C₂⁴	1	2	yes	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	1	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	1	no	—
316	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
317	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₇×C₂²⋊C₄	—	2	1	no	—
326	C₇×C₂²⋊C₄	—	2	2	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	4	no	—
330	C₇×C₂²⋊C₄	—	2	4	no	—
331	C₇×C₂²⋊C₄	—	2	4	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	2	no	—
336	C₇×C₂²⋊C₄	—	2	1	no	—
337	C₇×C₂²⋊C₄	—	2	1	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₄²×C₇	—	2	1	no	—
344	C₄²×C₇	—	2	2	no	—
345	C₄²×C₇	—	2	1	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	4	no	—
349	C₄²×C₇	—	2	4	no	—
350	C₄²×C₇	—	2	1	no	—
351	C₄²×C₇	—	2	2	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₇	C₂⁴	1	1	yes	characteristic
356	C₄²×C₇	C₂⁴	1	1	yes	characteristic
357	C₂×#137	C₂²×C₇	1	1	yes	characteristic
358	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
359	#556	—	2	1	no	—
360	#556	—	2	2	no	—
361	#556	—	2	1	no	—
362	#556	C₂²×C₇	1	2	yes	—
363	#556	C₂²×C₇	1	1	yes	characteristic
364	#556	C₂²×C₇	1	4	yes	—
365	#556	C₂²×C₇	1	2	yes	—
366	#555	C₂²×C₇	1	1	yes	characteristic
367	#554	C₂²×C₇	1	1	yes	characteristic
368	#553	C₂²×C₇	1	2	yes	—
369	#552	—	2	1	no	—
370	#552	C₂²×C₇	1	2	yes	—
371	#551	—	2	2	no	—
372	#547	C₂²×C₇	1	1	yes	characteristic
373	#546	—	2	1	no	—
374	#533	C₂²×C₇	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
376	#529	—	2	2	no	—
377	#529	—	2	1	no	—
378	C₂×#126	—	2	2	no	—
379	C₂×#124	—	2	1	no	—
380	#525	C₂²×C₇	1	2	yes	—
381	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
382	C₄×#41	—	2	1	no	—
383	C₄×#41	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄×Q₈	—	2	1	no	—
385	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
387	C₂×#117	C₂²×C₇	1	2	yes	—
388	C₂×#117	C₂²×C₇	1	2	yes	—
389	#501	C₂²×C₇	1	4	yes	complemented
390	#500	C₂²×C₇	1	2	yes	complemented
391	#498	C₂²×C₇	1	2	yes	complemented
392	#485	C₂²×C₇	1	4	yes	complemented
393	#485	C₂²×C₇	1	4	yes	complemented
394	#485	C₂²×C₇	1	4	yes	complemented
395	#485	C₂²×C₇	1	4	yes	complemented
396	#484	C₂²×C₇	1	4	yes	complemented
397	#483	C₂²×C₇	1	4	yes	complemented
398	#482	C₂²×C₇	1	4	yes	complemented
399	#482	C₂²×C₇	1	4	yes	complemented
400	#479	C₂²×C₇	1	4	yes	complemented
401	#477	C₂²×C₇	1	2	yes	complemented
402	#477	C₂²×C₇	1	2	yes	complemented
403	#476	C₂²×C₇	1	2	yes	complemented
404	#475	C₂²×C₇	1	2	yes	complemented
405	#475	C₂²×C₇	1	2	yes	complemented
406	#474	C₂²×C₇	1	2	yes	complemented
407	#470	C₂²×C₇	1	4	yes	complemented
408	#468	C₂²×C₇	1	4	yes	complemented
409	#467	C₂²×C₇	1	4	yes	complemented
410	#465	C₂²×C₇	1	4	yes	complemented
411	#441	C₂²×C₇	1	2	yes	complemented
412	#440	C₂²×C₇	1	2	yes	complemented
413	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
414	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
415	#436	C₂²×C₇	1	2	yes	—
416	#435	C₂²×C₇	1	4	yes	—
417	C₈×D₄	C₂²×C₇	1	2	yes	—
418	#428	C₂²×C₇	1	2	yes	—
419	#428	C₂²×C₇	1	2	yes	—
420	#428	C₂²×C₇	1	2	yes	—
421	#428	C₂²×C₇	1	2	yes	—
422	#428	C₂²×C₇	1	1	yes	characteristic
423	#428	C₂²×C₇	1	4	yes	complemented
424	#428	C₂²×C₇	1	4	yes	complemented
425	#427	C₂²×C₇	1	4	yes	complemented
426	#427	C₂²×C₇	1	4	yes	complemented
427	#423	C₂²×C₇	1	1	yes	characteristic
428	#419	C₂²×C₇	1	2	yes	—
429	#419	C₂²×C₇	1	1	yes	characteristic
430	#417	C₂²×C₇	1	2	yes	—
431	#417	C₂²×C₇	1	1	yes	characteristic
432	#407	C₂²×C₇	1	2	yes	—
433	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
434	C₂³×C₇	—	2	4	no	—
435	C₂³×C₇	—	2	1	no	—
436	C₂³×C₇	—	4	2	no	—
437	C₂³×C₇	—	4	2	no	—
438	C₂³×C₇	C₂²×D₄	1	2	yes	—
439	C₂³×C₇	C₂²×D₄	1	2	yes	—
440	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₇×Q₈	—	2	2	no	—
442	C₇×Q₈	—	2	1	no	—
443	C₇×Q₈	—	2	2	no	—
444	C₇×Q₈	—	2	1	no	—
445	C₇×Q₈	—	4	4	no	—
446	C₇×Q₈	—	4	2	no	—
447	C₇×Q₈	—	4	4	no	—
448	C₇×Q₈	—	4	2	no	—
449	C₇×Q₈	—	8	1	no	—
450	C₇×D₄	—	2	2	no	—
451	C₇×D₄	—	2	2	no	—
452	C₇×D₄	—	2	1	no	—
453	C₇×D₄	—	2	1	no	—
454	C₇×D₄	—	4	2	no	—
455	C₇×D₄	—	4	4	no	—
456	C₇×D₄	—	4	2	no	—
457	C₇×D₄	—	8	2	no	—
458	C₂×C₄×C₇	—	2	4	no	—
459	C₂×C₄×C₇	—	2	4	no	—
460	C₂×C₄×C₇	—	2	4	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	2	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	1	no	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	1	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	4	no	—
474	C₂×C₄×C₇	—	4	1	no	—
475	C₂×C₄×C₇	—	4	2	no	—
476	C₂×C₄×C₇	—	4	4	no	—
477	C₂×C₄×C₇	—	4	4	no	—
478	C₂×C₄×C₇	—	4	2	no	—
479	C₂×C₄×C₇	—	4	2	no	—
480	C₂×C₄×C₇	—	4	2	no	—
481	C₂×C₄×C₇	—	8	1	no	—
482	C₂×C₄×C₇	—	8	2	no	—
483	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇	C₂×#41	1	2	yes	—
491	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
492	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
493	C₇×C₈	—	2	4	no	—
494	C₇×C₈	—	2	2	no	—
495	C₇×C₈	C₂×#41	1	4	yes	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	C₂³×C₇	1	1	yes	characteristic
498	C₂²×Q₈	—	2	1	no	—
499	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
500	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₇	1	2	yes	—
502	#137	—	2	4	no	—
503	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
505	C₂×M₁₆	—	2	8	no	—
506	C₂×M₁₆	C₂³×C₇	1	2	yes	—
507	C₂×M₁₆	C₂³×C₇	1	4	yes	—
508	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
509	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₇	1	4	yes	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	#126	—	2	2	no	—
518	#126	—	2	4	no	—
519	#126	—	2	4	no	—
520	#126	—	2	4	no	—
521	#126	—	2	4	no	—
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#125	C₂³×C₇	1	2	yes	—
527	#124	—	2	2	no	—
528	#124	—	2	2	no	—
529	#124	—	2	4	no	—
530	#124	—	2	1	no	—
531	#124	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
543	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
545	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
546	#121	—	2	2	no	—
547	#121	—	2	1	no	—
548	#121	C₂³×C₇	1	2	yes	—
549	#121	C₂³×C₇	1	2	yes	—
550	#120	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	4	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	C₂³×C₇	1	2	yes	—
560	C₄×Q₈	C₂³×C₇	1	2	yes	—
561	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	C₇×D₄	1	1	yes	characteristic
570	C₄×D₄	C₇×D₄	1	1	yes	characteristic
571	C₄×D₄	C₇×D₄	1	2	yes	—
572	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
573	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
574	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
575	C₄×D₄	C₂³×C₇	1	2	yes	—
576	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	2	1	no	—
582	#117	—	2	2	no	—
583	#117	—	2	1	no	—
584	#117	C₂³×C₇	1	1	yes	characteristic
585	#117	C₂³×C₇	1	2	yes	—
586	#117	C₂³×C₇	1	2	yes	—
587	#117	C₂³×C₇	1	2	yes	—
588	#117	C₂³×C₇	1	4	yes	—
589	#117	C₂³×C₇	1	4	yes	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₂²⋊C₄	—	2	2	no	—
599	C₂×C₂²⋊C₄	—	2	2	no	—
600	C₂×C₂²⋊C₄	—	2	2	no	—
601	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	2	2	no	—
604	C₂×C₄²	—	2	1	no	—
605	C₂×C₄²	—	2	1	no	—
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	#107	C₂³×C₇	1	2	yes	—
608	#107	C₂³×C₇	1	4	yes	—
609	#107	C₂³×C₇	1	4	yes	—
610	#107	C₂³×C₇	1	4	yes	—
611	#107	C₂³×C₇	1	4	yes	—
612	#106	C₂³×C₇	1	2	yes	—
613	#106	C₂³×C₇	1	4	yes	—
614	#106	C₂³×C₇	1	4	yes	—
615	#106	C₂³×C₇	1	4	yes	—
616	#106	C₂³×C₇	1	4	yes	—
617	C₄⋊C₈	C₂³×C₇	1	2	yes	—
618	C₄⋊C₈	C₂³×C₇	1	2	yes	—
619	#103	C₂³×C₇	1	2	yes	—
620	#103	C₂³×C₇	1	4	yes	—
621	#103	C₂³×C₇	1	2	yes	—
622	#103	C₂³×C₇	1	2	yes	—
623	#103	C₂³×C₇	1	4	yes	—
624	#103	C₂³×C₇	1	4	yes	—
625	#102	C₂³×C₇	1	2	yes	—
626	#102	C₂³×C₇	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
628	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
629	#97	C₂³×C₇	1	2	yes	—
630	C₄×C₈	C₂³×C₇	1	2	yes	—
631	C₂²×C₇	—	2	1	no	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	2	no	—
634	C₂²×C₇	—	2	2	no	—
635	C₂²×C₇	—	2	2	no	—
636	C₂²×C₇	—	2	2	no	—
637	C₂²×C₇	—	2	2	no	—
638	C₂²×C₇	—	2	2	no	—
639	C₂²×C₇	—	4	1	no	—
640	C₂²×C₇	—	4	1	no	—
641	C₂²×C₇	—	4	1	no	—
642	C₂²×C₇	—	8	4	no	—
643	C₂²×C₇	#547	1	2	yes	—
644	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	2	no	—
648	C₄×C₇	—	2	2	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	4	2	no	—
651	C₄×C₇	—	4	1	no	—
652	C₄×C₇	—	4	2	no	—
653	C₄×C₇	—	4	1	no	—
654	C₄×C₇	—	4	2	no	—
655	C₄×C₇	—	4	1	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	—	4	4	no	—
658	C₄×C₇	#547	1	2	yes	—
659	C₄×C₇	#575	1	2	yes	—
660	C₄×C₇	C₂²×#41	1	1	yes	characteristic
661	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
662	C₂⁴	C₂×C₇×D₄	1	2	yes	—
663	#41	—	2	2	no	—
664	#41	—	2	2	no	—
665	#41	—	4	4	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
681	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
682	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
683	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
696	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
697	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
698	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
702	Q₁₆	—	2	4	no	—
703	SD₁₆	—	2	4	no	—
704	M₁₆	—	2	4	no	—
705	M₁₆	—	2	2	no	—
706	M₁₆	—	2	8	no	—
707	M₁₆	C₇×#41	1	4	yes	complemented
708	C₂×C₈	—	2	8	no	—
709	C₂×C₈	C₂⁴×C₇	1	2	yes	—
710	C₂×C₈	C₂⁴×C₇	1	4	yes	—
711	C₂×C₈	C₂⁴×C₇	1	2	yes	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
731	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
732	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
735	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
754	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
755	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
756	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
769	C₄²	C₂⁴×C₇	1	1	yes	characteristic
770	C₄²	C₂⁴×C₇	1	1	yes	characteristic
771	C₂×C₇	—	2	2	no	—
772	C₂×C₇	—	4	2	no	—
773	C₂×C₇	—	4	2	no	—
774	C₂×C₇	—	8	1	no	—
775	C₂×C₇	C₂×#547	1	1	yes	characteristic
776	C₂×C₇	C₂×#575	1	1	yes	characteristic
777	C₂×C₇	#3586	1	1	yes	characteristic
778	C₂³	—	2	4	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	4	2	no	—
781	C₂³	—	4	2	no	—
782	C₂³	C₂²×C₇×D₄	1	2	yes	—
783	C₂³	C₂²×C₇×D₄	1	2	yes	—
784	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
785	Q₈	—	2	2	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	2	1	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	4	2	no	—
791	Q₈	—	4	4	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	8	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	4	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
828	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
830	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
831	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
832	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂×C₇×#41	1	2	yes	—
835	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
836	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
837	C₈	—	2	4	no	—
838	C₈	—	2	2	no	—
839	C₈	C₂×C₇×#41	1	4	yes	—
840	C₇	#61257	1	1	yes	characteristic, direct product factor, Sylow
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₇×#547	1	2	yes	—
854	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₇×#547	1	2	yes	—
869	C₄	C₇×#575	1	2	yes	—
870	C₄	C₂²×C₇×#41	1	1	yes	characteristic
871	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
872	C₂	—	2	2	no	—
873	C₂	—	4	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	1	no	—
876	C₂	C₂×C₇×#547	1	1	yes	characteristic
877	C₂	C₂×C₇×#575	1	1	yes	characteristic
878	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×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#556	C₂	semidirect
3. C₇×#3356	C₂	semidirect
4. C₇×#3353	C₂	semidirect
5. C₇×#3350	C₂	semidirect
6. C₇×#3349	C₂	semidirect
7. C₇×#3342	C₂	semidirect
8. C₇×#3340	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3095	C₂	semidirect
11. C₇×#3093	C₂	semidirect
12. C₇×#3079	C₂	semidirect
13. C₇×#3078	C₂	semidirect
14. C₇×#3056	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₇×#2911	C₂	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#500	C₂²	semidirect
52. C₇×#498	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#485	C₂²	semidirect
55. C₇×#485	C₂²	semidirect
56. C₇×#485	C₂²	semidirect
57. C₇×#484	C₂²	semidirect
58. C₇×#483	C₂²	semidirect
59. C₇×#482	C₂²	semidirect
60. C₇×#482	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#477	C₂²	semidirect
63. C₇×#477	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#470	C₂²	semidirect
69. C₇×#468	C₂²	semidirect
70. C₇×#467	C₂²	semidirect
71. C₇×#465	C₂²	semidirect
72. C₇×#441	C₂²	semidirect
73. C₇×#440	C₂²	semidirect
74. C₄×C₇×Q₁₆	C₂²	semidirect
75. C₄×C₇×SD₁₆	C₂²	semidirect
84. C₇×#428	C₂²	semidirect
85. C₇×#428	C₂²	semidirect
86. C₇×#427	C₂²	semidirect
87. C₇×#427	C₂²	semidirect
95. #61257	C₇	direct (N × H)
232. C₂×#556	C₂×C₇	semidirect
233. #3356	C₂×C₇	semidirect
234. #3353	C₂×C₇	semidirect
235. #3350	C₂×C₇	semidirect
236. #3349	C₂×C₇	semidirect
237. #3342	C₂×C₇	semidirect
238. #3340	C₂×C₇	semidirect
239. #3165	C₂×C₇	semidirect
240. #3095	C₂×C₇	semidirect
241. #3093	C₂×C₇	semidirect
242. #3079	C₂×C₇	semidirect
243. #3078	C₂×C₇	semidirect
244. #3056	C₂×C₇	semidirect
245. C₄×#137	C₂×C₇	semidirect
246. D₄×M₁₆	C₂×C₇	semidirect
247. #2911	C₂×C₇	semidirect
293. C₇×M₁₆	#41	semidirect
389. #501	C₂²×C₇	semidirect
390. #500	C₂²×C₇	semidirect
391. #498	C₂²×C₇	semidirect
392. #485	C₂²×C₇	semidirect
393. #485	C₂²×C₇	semidirect
394. #485	C₂²×C₇	semidirect
395. #485	C₂²×C₇	semidirect
396. #484	C₂²×C₇	semidirect
397. #483	C₂²×C₇	semidirect
398. #482	C₂²×C₇	semidirect
399. #482	C₂²×C₇	semidirect
400. #479	C₂²×C₇	semidirect
401. #477	C₂²×C₇	semidirect
402. #477	C₂²×C₇	semidirect
403. #476	C₂²×C₇	semidirect
404. #475	C₂²×C₇	semidirect
405. #475	C₂²×C₇	semidirect
406. #474	C₂²×C₇	semidirect
407. #470	C₂²×C₇	semidirect
408. #468	C₂²×C₇	semidirect
409. #467	C₂²×C₇	semidirect
410. #465	C₂²×C₇	semidirect
411. #441	C₂²×C₇	semidirect
412. #440	C₂²×C₇	semidirect
413. C₄×Q₁₆	C₂²×C₇	semidirect
414. C₄×SD₁₆	C₂²×C₇	semidirect
423. #428	C₂²×C₇	semidirect
424. #428	C₂²×C₇	semidirect
425. #427	C₂²×C₇	semidirect
426. #427	C₂²×C₇	semidirect
707. M₁₆	C₇×#41	semidirect
840. C₇	#61257	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×#3475	2
C₂×C₇×#556	2
C₇×#3356	2
C₇×#3353	2
C₇×#3350	2
C₇×#3349	2
C₇×#3342	2
C₇×#3340	2
C₇×#3165	2
C₇×#3095	2
C₇×#3093	2
C₇×#3079	2
C₇×#3078	2
C₇×#3056	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₇×#2911	2
#61257	7

Subgroups — C7×#61257 #13238473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61257 #13238473