Subgroups — C₇×#61243 #13238459

Order 1792.

1848 conjugacy classes of subgroups.

The subgroup lattice has 978 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	2	yes	maximal, complemented
2	C₇×#3350	C₂	1	2	yes	maximal, complemented
3	C₇×#3349	C₂	1	2	yes	maximal, complemented
4	C₇×#3348	C₂	1	2	yes	maximal, complemented
5	C₇×#3347	C₂	1	2	yes	maximal, complemented
6	C₇×#3346	C₂	1	2	yes	maximal, complemented
7	C₇×#3345	C₂	1	2	yes	maximal, complemented
8	C₇×#3344	C₂	1	2	yes	maximal, complemented
9	C₇×#3343	C₂	1	2	yes	maximal, complemented
10	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3091	C₂	1	2	yes	maximal, complemented
12	C₇×#3091	C₂	1	2	yes	maximal, complemented
13	C₇×#3076	C₂	1	2	yes	maximal, complemented
14	C₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3050	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#135	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#556	C₂²	1	2	yes	—
24	C₇×#555	C₂²	1	2	yes	—
25	C₇×#554	C₂²	1	2	yes	—
26	C₇×#553	C₂²	1	2	yes	—
27	C₇×#553	C₂²	1	2	yes	—
28	C₇×#552	—	2	2	no	—
29	C₇×#552	C₂²	1	2	yes	—
30	C₇×#552	C₂²	1	2	yes	—
31	C₇×#551	—	2	2	no	—
32	C₇×#551	—	2	2	no	—
33	C₇×#547	C₂²	1	2	yes	—
34	C₇×#546	—	2	2	no	—
35	C₇×#533	C₂²	1	2	yes	—
36	C₇×#529	—	2	2	no	—
37	C₇×#529	—	2	2	no	—
38	C₇×#529	—	2	2	no	—
39	C₇×#525	C₂²	1	2	yes	—
40	C₇×#525	C₂²	1	2	yes	—
41	C₄×C₇×#41	—	2	2	no	—
42	C₄×C₇×#41	C₂²	1	2	yes	—
43	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
44	C₂×C₇×#117	C₂²	1	2	yes	—
45	C₂×C₇×#117	C₂²	1	2	yes	—
46	C₇×#501	C₂²	1	2	yes	complemented
47	C₇×#501	C₂²	1	2	yes	complemented
48	C₇×#501	C₂²	1	2	yes	complemented
49	C₇×#501	C₂²	1	2	yes	complemented
50	C₇×#485	C₂²	1	2	yes	complemented
51	C₇×#485	C₂²	1	2	yes	complemented
52	C₇×#485	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	2	yes	complemented
54	C₇×#484	C₂²	1	2	yes	complemented
55	C₇×#484	C₂²	1	2	yes	complemented
56	C₇×#483	C₂²	1	2	yes	complemented
57	C₇×#483	C₂²	1	2	yes	complemented
58	C₇×#482	C₂²	1	2	yes	complemented
59	C₇×#482	C₂²	1	2	yes	complemented
60	C₇×#482	C₂²	1	2	yes	complemented
61	C₇×#482	C₂²	1	2	yes	complemented
62	C₇×#481	C₂²	1	2	yes	complemented
63	C₇×#481	C₂²	1	2	yes	complemented
64	C₇×#480	C₂²	1	2	yes	complemented
65	C₇×#480	C₂²	1	2	yes	complemented
66	C₇×#479	C₂²	1	2	yes	complemented
67	C₇×#479	C₂²	1	2	yes	complemented
68	C₇×#478	C₂²	1	2	yes	complemented
69	C₇×#478	C₂²	1	2	yes	complemented
70	C₇×#477	C₂²	1	2	yes	complemented
71	C₇×#476	C₂²	1	2	yes	complemented
72	C₇×#475	C₂²	1	2	yes	complemented
73	C₇×#474	C₂²	1	2	yes	complemented
74	C₇×#470	C₂²	1	2	yes	complemented
75	C₇×#469	C₂²	1	2	yes	complemented
76	C₇×#468	C₂²	1	2	yes	complemented
77	C₇×#468	C₂²	1	2	yes	complemented
78	C₇×#467	C₂²	1	1	yes	characteristic, complemented
79	C₇×#467	C₂²	1	1	yes	characteristic, complemented
80	C₇×#466	C₂²	1	1	yes	characteristic, complemented
81	C₇×#466	C₂²	1	1	yes	characteristic, complemented
82	C₇×#465	C₂²	1	2	yes	complemented
83	C₇×#465	C₂²	1	2	yes	complemented
84	C₇×#442	C₂²	1	2	yes	complemented
85	C₇×#441	C₂²	1	2	yes	complemented
86	C₇×#440	C₂²	1	2	yes	complemented
87	C₇×#440	C₂²	1	2	yes	complemented
88	C₇×#435	C₂²	1	2	yes	—
89	C₇×#435	C₂²	1	2	yes	—
90	C₇×#435	C₂²	1	2	yes	—
91	C₇×#435	C₂²	1	2	yes	—
92	C₇×#428	C₂²	1	2	yes	complemented
93	C₇×#428	C₂²	1	2	yes	complemented
94	C₇×#428	C₂²	1	2	yes	complemented
95	C₇×#428	C₂²	1	2	yes	complemented
96	C₇×#427	C₂²	1	1	yes	characteristic
97	C₇×#427	C₂²	1	1	yes	characteristic
98	C₇×#427	C₂²	1	2	yes	—
99	C₇×#427	C₂²	1	1	yes	characteristic
100	C₇×#427	C₂²	1	2	yes	—
101	C₇×#427	C₂²	1	2	yes	—
102	C₇×#427	C₂²	1	2	yes	complemented
103	C₇×#427	C₂²	1	1	yes	characteristic, complemented
104	C₇×#427	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₇×#106	C₂²	1	2	yes	complemented
108	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
109	C₇×#416	C₂²	1	2	yes	—
110	C₇×#416	C₂²	1	2	yes	—
111	C₇×#416	C₂²	1	2	yes	—
112	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
114	C₂×C₇×#97	C₂²	1	1	yes	characteristic
115	#61243	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	—	2	2	no	—
117	C₂×C₇×#41	C₂³	1	2	yes	—
118	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₇×#135	—	2	4	no	—
122	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
125	C₂×C₇×M₁₆	—	2	4	no	—
126	C₂×C₇×M₁₆	C₂³	1	2	yes	—
127	C₂×C₇×M₁₆	C₂³	1	2	yes	—
128	C₂²×C₇×C₈	—	2	4	no	—
129	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
130	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
131	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
134	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
135	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
136	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₇×#126	—	2	2	no	—
140	C₇×#126	—	2	2	no	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#125	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#125	C₂³	1	2	yes	—
149	C₇×#125	C₂³	1	2	yes	—
150	C₇×#124	—	2	2	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	—	2	2	no	—
153	C₇×#123	—	2	2	no	—
154	C₇×#123	—	2	2	no	—
155	C₇×#123	—	2	2	no	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×C₂²⋊Q₈	—	2	2	no	—
162	C₇×C₂²⋊Q₈	—	2	2	no	—
163	C₇×C₂²⋊Q₈	—	2	2	no	—
164	C₇×C₂²⋊Q₈	—	2	2	no	—
165	C₇×C₂²⋊Q₈	—	2	2	no	—
166	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₇×#121	—	2	2	no	—
171	C₇×#121	—	2	2	no	—
172	C₇×#121	—	2	2	no	—
173	C₇×#121	C₂³	1	2	yes	—
174	C₇×#121	C₂³	1	2	yes	—
175	C₇×#121	C₂³	1	2	yes	—
176	C₇×#121	C₂³	1	2	yes	—
177	C₇×#120	—	2	2	no	—
178	C₇×#120	—	2	2	no	—
179	C₄×C₇×Q₈	—	2	2	no	—
180	C₄×C₇×Q₈	—	2	2	no	—
181	C₄×C₇×Q₈	—	2	2	no	—
182	C₄×C₇×Q₈	C₂³	1	2	yes	—
183	C₄×C₇×Q₈	C₂³	1	2	yes	—
184	C₄×C₇×D₄	—	2	2	no	—
185	C₄×C₇×D₄	—	2	2	no	—
186	C₄×C₇×D₄	—	2	2	no	—
187	C₄×C₇×D₄	—	2	2	no	—
188	C₄×C₇×D₄	—	2	2	no	—
189	C₄×C₇×D₄	—	2	2	no	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	D₄	1	2	yes	—
194	C₄×C₇×D₄	D₄	1	2	yes	—
195	C₄×C₇×D₄	C₂³	1	2	yes	—
196	C₄×C₇×D₄	C₂³	1	2	yes	—
197	C₄×C₇×D₄	C₂³	1	2	yes	—
198	C₄×C₇×D₄	C₂³	1	2	yes	—
199	C₇×#117	—	2	2	no	—
200	C₇×#117	—	2	2	no	—
201	C₇×#117	—	2	2	no	—
202	C₇×#117	—	2	2	no	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	C₂³	1	2	yes	—
208	C₇×#117	C₂³	1	2	yes	—
209	C₇×#117	C₂³	1	2	yes	—
210	C₇×#117	C₂³	1	2	yes	—
211	C₇×#117	C₂³	1	2	yes	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
215	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
222	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₇	—	2	2	no	—
224	C₂×C₄²×C₇	—	2	2	no	—
225	C₂×C₄²×C₇	—	2	2	no	—
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₇×#107	C₂³	1	1	yes	characteristic
228	C₇×#107	C₂³	1	1	yes	characteristic
229	C₇×#107	C₂³	1	1	yes	characteristic
230	C₇×#107	C₂³	1	1	yes	characteristic
231	C₇×#107	C₂³	1	2	yes	—
232	C₇×#107	C₂³	1	2	yes	—
233	C₇×#107	C₂³	1	2	yes	—
234	C₇×#107	C₂³	1	2	yes	—
235	C₇×#107	C₂³	1	2	yes	—
236	C₇×#107	C₂³	1	2	yes	—
237	C₇×#107	C₂³	1	1	yes	characteristic
238	C₇×#107	C₂³	1	1	yes	characteristic
239	C₇×#106	C₂³	1	2	yes	—
240	C₇×#106	C₂³	1	2	yes	—
241	C₇×#106	C₂³	1	2	yes	—
242	C₇×#106	C₂³	1	2	yes	—
243	C₇×#106	C₂³	1	2	yes	—
244	C₇×#106	C₂³	1	2	yes	—
245	C₇×#106	C₂³	1	2	yes	—
246	C₇×#106	C₂³	1	2	yes	—
247	C₇×#106	C₂³	1	2	yes	—
248	C₇×C₄⋊C₈	C₂³	1	2	yes	—
249	C₇×C₄⋊C₈	C₂³	1	2	yes	—
250	C₇×#103	C₂³	1	2	yes	—
251	C₇×#103	C₂³	1	2	yes	—
252	C₇×#103	C₂³	1	2	yes	—
253	C₇×#103	C₂³	1	2	yes	—
254	C₇×#103	C₂³	1	2	yes	—
255	C₇×#103	C₂³	1	2	yes	—
256	C₇×#102	C₂³	1	2	yes	—
257	C₇×#102	C₂³	1	2	yes	—
258	C₇×#102	C₂³	1	2	yes	—
259	C₇×#102	C₂³	1	2	yes	—
260	C₇×#102	C₂³	1	2	yes	—
261	C₇×#102	C₂³	1	2	yes	—
262	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₇×#97	C₂³	1	2	yes	—
267	C₇×#97	C₂³	1	2	yes	—
268	#3475	C₂×C₇	1	2	yes	complemented
269	#3350	C₂×C₇	1	2	yes	complemented
270	#3349	C₂×C₇	1	2	yes	complemented
271	#3348	C₂×C₇	1	2	yes	complemented
272	#3347	C₂×C₇	1	2	yes	complemented
273	#3346	C₂×C₇	1	2	yes	complemented
274	#3345	C₂×C₇	1	2	yes	complemented
275	#3344	C₂×C₇	1	2	yes	complemented
276	#3343	C₂×C₇	1	2	yes	complemented
277	#3162	C₂×C₇	1	1	yes	characteristic, complemented
278	#3091	C₂×C₇	1	2	yes	complemented
279	#3091	C₂×C₇	1	2	yes	complemented
280	#3076	C₂×C₇	1	2	yes	complemented
281	#3054	C₂×C₇	1	1	yes	characteristic, complemented
282	#3050	C₂×C₇	1	1	yes	characteristic, complemented
283	#2943	C₂×C₇	1	1	yes	characteristic, complemented
284	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
285	#2911	C₂×C₇	1	1	yes	characteristic, complemented
286	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
287	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
289	C₇×#41	—	2	4	no	—
290	C₇×#41	—	2	4	no	—
291	C₇×#41	—	4	8	no	—
292	C₂×C₇×Q₈	—	2	2	no	—
293	C₂×C₇×Q₈	—	2	2	no	—
294	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	2	no	—
297	C₂×C₇×D₄	—	2	2	no	—
298	C₂×C₇×D₄	—	2	2	no	—
299	C₂×C₇×D₄	—	2	2	no	—
300	C₂×C₇×D₄	—	4	2	no	—
301	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
302	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
303	C₂×C₇×D₄	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₇×Q₁₆	—	2	2	no	—
327	C₇×SD₁₆	—	2	4	no	—
328	C₇×D₈	—	2	2	no	—
329	C₇×M₁₆	—	2	4	no	—
330	C₇×M₁₆	—	2	4	no	—
331	C₂×C₇×C₈	—	2	2	no	—
332	C₂×C₇×C₈	—	2	2	no	—
333	C₂×C₇×C₈	—	2	2	no	—
334	C₂×C₇×C₈	—	2	2	no	—
335	C₂×C₇×C₈	—	2	2	no	—
336	C₂×C₇×C₈	—	2	2	no	—
337	C₂×C₇×C₈	—	2	2	no	—
338	C₂×C₇×C₈	#41	1	4	yes	complemented
339	C₂×C₇×C₈	C₂⁴	1	2	yes	—
340	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₇×C₈	C₂⁴	1	2	yes	—
342	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
343	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	2	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₄²×C₇	—	2	2	no	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	2	no	—
396	C₄²×C₇	—	2	2	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	C₂×D₄	1	2	yes	—
400	C₄²×C₇	C₂⁴	1	2	yes	—
401	C₂×#135	C₂²×C₇	1	1	yes	characteristic
402	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
403	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
404	#556	C₂²×C₇	1	2	yes	—
405	#555	C₂²×C₇	1	2	yes	—
406	#554	C₂²×C₇	1	2	yes	—
407	#553	C₂²×C₇	1	2	yes	—
408	#553	C₂²×C₇	1	2	yes	—
409	#552	—	2	2	no	—
410	#552	C₂²×C₇	1	2	yes	—
411	#552	C₂²×C₇	1	2	yes	—
412	#551	—	2	2	no	—
413	#551	—	2	2	no	—
414	#547	C₂²×C₇	1	2	yes	—
415	#546	—	2	2	no	—
416	#533	C₂²×C₇	1	2	yes	—
417	#529	—	2	2	no	—
418	#529	—	2	2	no	—
419	#529	—	2	2	no	—
420	#525	C₂²×C₇	1	2	yes	—
421	#525	C₂²×C₇	1	2	yes	—
422	C₄×#41	—	2	2	no	—
423	C₄×#41	C₂²×C₇	1	2	yes	—
424	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
425	C₂×#117	C₂²×C₇	1	2	yes	—
426	C₂×#117	C₂²×C₇	1	2	yes	—
427	#501	C₂²×C₇	1	2	yes	complemented
428	#501	C₂²×C₇	1	2	yes	complemented
429	#501	C₂²×C₇	1	2	yes	complemented
430	#501	C₂²×C₇	1	2	yes	complemented
431	#485	C₂²×C₇	1	2	yes	complemented
432	#485	C₂²×C₇	1	2	yes	complemented
433	#485	C₂²×C₇	1	2	yes	complemented
434	#485	C₂²×C₇	1	2	yes	complemented
435	#484	C₂²×C₇	1	2	yes	complemented
436	#484	C₂²×C₇	1	2	yes	complemented
437	#483	C₂²×C₇	1	2	yes	complemented
438	#483	C₂²×C₇	1	2	yes	complemented
439	#482	C₂²×C₇	1	2	yes	complemented
440	#482	C₂²×C₇	1	2	yes	complemented
441	#482	C₂²×C₇	1	2	yes	complemented
442	#482	C₂²×C₇	1	2	yes	complemented
443	#481	C₂²×C₇	1	2	yes	complemented
444	#481	C₂²×C₇	1	2	yes	complemented
445	#480	C₂²×C₇	1	2	yes	complemented
446	#480	C₂²×C₇	1	2	yes	complemented
447	#479	C₂²×C₇	1	2	yes	complemented
448	#479	C₂²×C₇	1	2	yes	complemented
449	#478	C₂²×C₇	1	2	yes	complemented
450	#478	C₂²×C₇	1	2	yes	complemented
451	#477	C₂²×C₇	1	2	yes	complemented
452	#476	C₂²×C₇	1	2	yes	complemented
453	#475	C₂²×C₇	1	2	yes	complemented
454	#474	C₂²×C₇	1	2	yes	complemented
455	#470	C₂²×C₇	1	2	yes	complemented
456	#469	C₂²×C₇	1	2	yes	complemented
457	#468	C₂²×C₇	1	2	yes	complemented
458	#468	C₂²×C₇	1	2	yes	complemented
459	#467	C₂²×C₇	1	1	yes	characteristic, complemented
460	#467	C₂²×C₇	1	1	yes	characteristic, complemented
461	#466	C₂²×C₇	1	1	yes	characteristic, complemented
462	#466	C₂²×C₇	1	1	yes	characteristic, complemented
463	#465	C₂²×C₇	1	2	yes	complemented
464	#465	C₂²×C₇	1	2	yes	complemented
465	#442	C₂²×C₇	1	2	yes	complemented
466	#441	C₂²×C₇	1	2	yes	complemented
467	#440	C₂²×C₇	1	2	yes	complemented
468	#440	C₂²×C₇	1	2	yes	complemented
469	#435	C₂²×C₇	1	2	yes	—
470	#435	C₂²×C₇	1	2	yes	—
471	#435	C₂²×C₇	1	2	yes	—
472	#435	C₂²×C₇	1	2	yes	—
473	#428	C₂²×C₇	1	2	yes	complemented
474	#428	C₂²×C₇	1	2	yes	complemented
475	#428	C₂²×C₇	1	2	yes	complemented
476	#428	C₂²×C₇	1	2	yes	complemented
477	#427	C₂²×C₇	1	2	yes	—
478	#427	C₂²×C₇	1	2	yes	—
479	#427	C₂²×C₇	1	2	yes	—
480	#427	C₂²×C₇	1	1	yes	characteristic
481	#427	C₂²×C₇	1	1	yes	characteristic
482	#427	C₂²×C₇	1	1	yes	characteristic
483	#427	C₂²×C₇	1	2	yes	complemented
484	#427	C₂²×C₇	1	1	yes	characteristic, complemented
485	#427	C₂²×C₇	1	1	yes	characteristic, complemented
486	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
487	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
488	C₂×#106	C₂²×C₇	1	2	yes	complemented
489	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
490	#416	C₂²×C₇	1	2	yes	—
491	#416	C₂²×C₇	1	2	yes	—
492	#416	C₂²×C₇	1	2	yes	—
493	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
494	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
495	C₂×#97	C₂²×C₇	1	1	yes	characteristic
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	2	no	—
498	C₂³×C₇	—	2	2	no	—
499	C₂³×C₇	—	2	2	no	—
500	C₂³×C₇	—	4	1	no	—
501	C₂³×C₇	—	4	1	no	—
502	C₂³×C₇	—	4	1	no	—
503	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
504	C₂³×C₇	C₂²×D₄	1	2	yes	—
505	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
506	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
507	C₇×Q₈	—	2	2	no	—
508	C₇×Q₈	—	2	2	no	—
509	C₇×Q₈	—	4	4	no	—
510	C₇×Q₈	—	8	2	no	—
511	C₇×D₄	—	2	4	no	—
512	C₇×D₄	—	2	2	no	—
513	C₇×D₄	—	2	2	no	—
514	C₇×D₄	—	4	2	no	—
515	C₇×D₄	—	4	4	no	—
516	C₇×D₄	—	4	4	no	—
517	C₇×D₄	—	4	4	no	—
518	C₇×D₄	—	8	2	no	—
519	C₇×D₄	—	8	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	4	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	4	1	no	—
539	C₂×C₄×C₇	—	4	1	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	—	4	4	no	—
542	C₂×C₄×C₇	—	4	4	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	8	2	no	—
545	C₂×C₄×C₇	—	8	2	no	—
546	C₂×C₄×C₇	—	8	2	no	—
547	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₇	C₂×#41	1	2	yes	—
554	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
555	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
556	C₇×C₈	—	2	1	no	—
557	C₇×C₈	—	2	1	no	—
558	C₇×C₈	—	2	2	no	—
559	C₇×C₈	—	2	2	no	—
560	C₇×C₈	C₂×#41	1	2	yes	—
561	C₇×C₈	C₂×#41	1	2	yes	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	C₂³×C₇	1	2	yes	—
564	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
567	#135	—	2	4	no	—
568	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
569	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
570	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
571	C₂×M₁₆	—	2	4	no	—
572	C₂×M₁₆	C₂³×C₇	1	2	yes	—
573	C₂×M₁₆	C₂³×C₇	1	2	yes	—
574	C₂²×C₈	—	2	4	no	—
575	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
576	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
577	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
578	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
579	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
580	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
581	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#125	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	—	2	2	no	—
594	#125	C₂³×C₇	1	2	yes	—
595	#125	C₂³×C₇	1	2	yes	—
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
614	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
615	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	C₂³×C₇	1	2	yes	—
620	#121	C₂³×C₇	1	2	yes	—
621	#121	C₂³×C₇	1	2	yes	—
622	#121	C₂³×C₇	1	2	yes	—
623	#120	—	2	2	no	—
624	#120	—	2	2	no	—
625	C₄×Q₈	—	2	2	no	—
626	C₄×Q₈	—	2	2	no	—
627	C₄×Q₈	—	2	2	no	—
628	C₄×Q₈	C₂³×C₇	1	2	yes	—
629	C₄×Q₈	C₂³×C₇	1	2	yes	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	C₇×D₄	1	2	yes	—
640	C₄×D₄	C₇×D₄	1	2	yes	—
641	C₄×D₄	C₂³×C₇	1	2	yes	—
642	C₄×D₄	C₂³×C₇	1	2	yes	—
643	C₄×D₄	C₂³×C₇	1	2	yes	—
644	C₄×D₄	C₂³×C₇	1	2	yes	—
645	#117	—	2	2	no	—
646	#117	—	2	2	no	—
647	#117	—	2	2	no	—
648	#117	—	2	2	no	—
649	#117	—	2	2	no	—
650	#117	—	2	2	no	—
651	#117	—	2	2	no	—
652	#117	—	2	2	no	—
653	#117	C₂³×C₇	1	2	yes	—
654	#117	C₂³×C₇	1	2	yes	—
655	#117	C₂³×C₇	1	2	yes	—
656	#117	C₂³×C₇	1	2	yes	—
657	#117	C₂³×C₇	1	2	yes	—
658	#117	C₂³×C₇	1	2	yes	—
659	#117	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
669	C₂×C₄²	—	2	2	no	—
670	C₂×C₄²	—	2	2	no	—
671	C₂×C₄²	—	2	2	no	—
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	#107	C₂³×C₇	1	1	yes	characteristic
674	#107	C₂³×C₇	1	1	yes	characteristic
675	#107	C₂³×C₇	1	1	yes	characteristic
676	#107	C₂³×C₇	1	1	yes	characteristic
677	#107	C₂³×C₇	1	2	yes	—
678	#107	C₂³×C₇	1	2	yes	—
679	#107	C₂³×C₇	1	1	yes	characteristic
680	#107	C₂³×C₇	1	1	yes	characteristic
681	#107	C₂³×C₇	1	2	yes	—
682	#107	C₂³×C₇	1	2	yes	—
683	#107	C₂³×C₇	1	2	yes	—
684	#107	C₂³×C₇	1	2	yes	—
685	#106	C₂³×C₇	1	2	yes	—
686	#106	C₂³×C₇	1	2	yes	—
687	#106	C₂³×C₇	1	2	yes	—
688	#106	C₂³×C₇	1	2	yes	—
689	#106	C₂³×C₇	1	2	yes	—
690	#106	C₂³×C₇	1	2	yes	—
691	#106	C₂³×C₇	1	2	yes	—
692	#106	C₂³×C₇	1	2	yes	—
693	#106	C₂³×C₇	1	2	yes	—
694	C₄⋊C₈	C₂³×C₇	1	2	yes	—
695	C₄⋊C₈	C₂³×C₇	1	2	yes	—
696	#103	C₂³×C₇	1	2	yes	—
697	#103	C₂³×C₇	1	2	yes	—
698	#103	C₂³×C₇	1	2	yes	—
699	#103	C₂³×C₇	1	2	yes	—
700	#103	C₂³×C₇	1	2	yes	—
701	#103	C₂³×C₇	1	2	yes	—
702	#102	C₂³×C₇	1	2	yes	—
703	#102	C₂³×C₇	1	2	yes	—
704	#102	C₂³×C₇	1	2	yes	—
705	#102	C₂³×C₇	1	2	yes	—
706	#102	C₂³×C₇	1	2	yes	—
707	#102	C₂³×C₇	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
712	#97	C₂³×C₇	1	2	yes	—
713	#97	C₂³×C₇	1	2	yes	—
714	C₂²×C₇	—	2	1	no	—
715	C₂²×C₇	—	2	1	no	—
716	C₂²×C₇	—	2	1	no	—
717	C₂²×C₇	—	2	1	no	—
718	C₂²×C₇	—	2	2	no	—
719	C₂²×C₇	—	2	1	no	—
720	C₂²×C₇	—	2	1	no	—
721	C₂²×C₇	—	2	2	no	—
722	C₂²×C₇	—	2	2	no	—
723	C₂²×C₇	—	2	1	no	—
724	C₂²×C₇	—	4	4	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	4	2	no	—
727	C₂²×C₇	—	4	2	no	—
728	C₂²×C₇	—	8	2	no	—
729	C₂²×C₇	#547	1	2	yes	—
730	C₂²×C₇	#575	1	2	yes	—
731	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	—	2	1	no	—
734	C₄×C₇	—	2	1	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	2	2	no	—
737	C₄×C₇	—	4	2	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	#547	1	2	yes	—
745	C₄×C₇	C₂²×#41	1	1	yes	characteristic
746	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
747	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
748	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
749	#41	—	2	4	no	—
750	#41	—	2	4	no	—
751	#41	—	4	8	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
762	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
763	C₂×D₄	C₂⁴×C₇	1	2	yes	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
776	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
777	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
778	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
779	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
780	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
781	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
786	Q₁₆	—	2	2	no	—
787	SD₁₆	—	2	4	no	—
788	D₈	—	2	2	no	—
789	M₁₆	—	2	4	no	—
790	M₁₆	—	2	4	no	—
791	C₂×C₈	—	2	2	no	—
792	C₂×C₈	—	2	2	no	—
793	C₂×C₈	—	2	2	no	—
794	C₂×C₈	—	2	2	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	2	2	no	—
798	C₂×C₈	C₇×#41	1	4	yes	complemented
799	C₂×C₈	C₂⁴×C₇	1	2	yes	—
800	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₇	1	2	yes	—
802	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
803	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
804	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
822	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
847	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
848	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
849	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	C₂×C₇×D₄	1	2	yes	—
860	C₄²	C₂⁴×C₇	1	2	yes	—
861	C₂×C₇	—	2	2	no	—
862	C₂×C₇	—	2	2	no	—
863	C₂×C₇	—	4	1	no	—
864	C₂×C₇	—	4	2	no	—
865	C₂×C₇	—	8	2	no	—
866	C₂×C₇	C₂×#547	1	1	yes	characteristic
867	C₂×C₇	C₂×#575	1	1	yes	characteristic
868	C₂×C₇	#3584	1	1	yes	characteristic
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	1	no	—
874	C₂³	—	4	1	no	—
875	C₂³	—	4	1	no	—
876	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
877	C₂³	C₂²×C₇×D₄	1	2	yes	—
878	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
879	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
880	Q₈	—	2	2	no	—
881	Q₈	—	2	2	no	—
882	Q₈	—	4	4	no	—
883	Q₈	—	8	2	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	4	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	8	2	no	—
892	D₄	—	8	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
921	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
922	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
923	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
924	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂×C₇×#41	1	2	yes	—
927	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
928	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
929	C₈	—	2	1	no	—
930	C₈	—	2	1	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	C₂×C₇×#41	1	2	yes	—
934	C₈	C₂×C₇×#41	1	2	yes	—
935	C₇	#61243	1	1	yes	characteristic, direct product factor, Sylow
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	4	4	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	8	2	no	—
951	C₂²	C₇×#547	1	2	yes	—
952	C₂²	C₇×#575	1	2	yes	—
953	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	C₇×#547	1	2	yes	—
967	C₄	C₂²×C₇×#41	1	1	yes	characteristic
968	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
969	C₂	—	2	2	no	—
970	C₂	—	2	2	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	2	no	—
974	C₂	C₂×C₇×#547	1	1	yes	characteristic
975	C₂	C₂×C₇×#575	1	1	yes	characteristic
976	C₂	C₇×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₇×#3350	C₂	semidirect
3. C₇×#3349	C₂	semidirect
4. C₇×#3348	C₂	semidirect
5. C₇×#3347	C₂	semidirect
6. C₇×#3346	C₂	semidirect
7. C₇×#3345	C₂	semidirect
8. C₇×#3344	C₂	semidirect
9. C₇×#3343	C₂	semidirect
10. C₇×#3162	C₂	semidirect
11. C₇×#3091	C₂	semidirect
12. C₇×#3091	C₂	semidirect
13. C₇×#3076	C₂	semidirect
14. C₇×#3054	C₂	semidirect
15. C₇×#3050	C₂	semidirect
16. C₇×#2943	C₂	semidirect
17. C₂×C₇×#435	C₂	semidirect
18. C₇×#2911	C₂	semidirect
19. C₂×C₇×#427	C₂	semidirect
46. C₇×#501	C₂²	semidirect
47. C₇×#501	C₂²	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#501	C₂²	semidirect
50. C₇×#485	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
52. C₇×#485	C₂²	semidirect
53. C₇×#485	C₂²	semidirect
54. C₇×#484	C₂²	semidirect
55. C₇×#484	C₂²	semidirect
56. C₇×#483	C₂²	semidirect
57. C₇×#483	C₂²	semidirect
58. C₇×#482	C₂²	semidirect
59. C₇×#482	C₂²	semidirect
60. C₇×#482	C₂²	semidirect
61. C₇×#482	C₂²	semidirect
62. C₇×#481	C₂²	semidirect
63. C₇×#481	C₂²	semidirect
64. C₇×#480	C₂²	semidirect
65. C₇×#480	C₂²	semidirect
66. C₇×#479	C₂²	semidirect
67. C₇×#479	C₂²	semidirect
68. C₇×#478	C₂²	semidirect
69. C₇×#478	C₂²	semidirect
70. C₇×#477	C₂²	semidirect
71. C₇×#476	C₂²	semidirect
72. C₇×#475	C₂²	semidirect
73. C₇×#474	C₂²	semidirect
74. C₇×#470	C₂²	semidirect
75. C₇×#469	C₂²	semidirect
76. C₇×#468	C₂²	semidirect
77. C₇×#468	C₂²	semidirect
78. C₇×#467	C₂²	semidirect
79. C₇×#467	C₂²	semidirect
80. C₇×#466	C₂²	semidirect
81. C₇×#466	C₂²	semidirect
82. C₇×#465	C₂²	semidirect
83. C₇×#465	C₂²	semidirect
84. C₇×#442	C₂²	semidirect
85. C₇×#441	C₂²	semidirect
86. C₇×#440	C₂²	semidirect
87. C₇×#440	C₂²	semidirect
92. C₇×#428	C₂²	semidirect
93. C₇×#428	C₂²	semidirect
94. C₇×#428	C₂²	semidirect
95. C₇×#428	C₂²	semidirect
102. C₇×#427	C₂²	semidirect
103. C₇×#427	C₂²	semidirect
104. C₇×#427	C₂²	semidirect
105. C₂×C₇×#107	C₂²	semidirect
106. C₂×C₇×#107	C₂²	semidirect
107. C₂×C₇×#106	C₂²	semidirect
115. #61243	C₇	direct (N × H)
268. #3475	C₂×C₇	semidirect
269. #3350	C₂×C₇	semidirect
270. #3349	C₂×C₇	semidirect
271. #3348	C₂×C₇	semidirect
272. #3347	C₂×C₇	semidirect
273. #3346	C₂×C₇	semidirect
274. #3345	C₂×C₇	semidirect
275. #3344	C₂×C₇	semidirect
276. #3343	C₂×C₇	semidirect
277. #3162	C₂×C₇	semidirect
278. #3091	C₂×C₇	semidirect
279. #3091	C₂×C₇	semidirect
280. #3076	C₂×C₇	semidirect
281. #3054	C₂×C₇	semidirect
282. #3050	C₂×C₇	semidirect
283. #2943	C₂×C₇	semidirect
284. C₂×#435	C₂×C₇	semidirect
285. #2911	C₂×C₇	semidirect
286. C₂×#427	C₂×C₇	semidirect
338. C₂×C₇×C₈	#41	semidirect
427. #501	C₂²×C₇	semidirect
428. #501	C₂²×C₇	semidirect
429. #501	C₂²×C₇	semidirect
430. #501	C₂²×C₇	semidirect
431. #485	C₂²×C₇	semidirect
432. #485	C₂²×C₇	semidirect
433. #485	C₂²×C₇	semidirect
434. #485	C₂²×C₇	semidirect
435. #484	C₂²×C₇	semidirect
436. #484	C₂²×C₇	semidirect
437. #483	C₂²×C₇	semidirect
438. #483	C₂²×C₇	semidirect
439. #482	C₂²×C₇	semidirect
440. #482	C₂²×C₇	semidirect
441. #482	C₂²×C₇	semidirect
442. #482	C₂²×C₇	semidirect
443. #481	C₂²×C₇	semidirect
444. #481	C₂²×C₇	semidirect
445. #480	C₂²×C₇	semidirect
446. #480	C₂²×C₇	semidirect
447. #479	C₂²×C₇	semidirect
448. #479	C₂²×C₇	semidirect
449. #478	C₂²×C₇	semidirect
450. #478	C₂²×C₇	semidirect
451. #477	C₂²×C₇	semidirect
452. #476	C₂²×C₇	semidirect
453. #475	C₂²×C₇	semidirect
454. #474	C₂²×C₇	semidirect
455. #470	C₂²×C₇	semidirect
456. #469	C₂²×C₇	semidirect
457. #468	C₂²×C₇	semidirect
458. #468	C₂²×C₇	semidirect
459. #467	C₂²×C₇	semidirect
460. #467	C₂²×C₇	semidirect
461. #466	C₂²×C₇	semidirect
462. #466	C₂²×C₇	semidirect
463. #465	C₂²×C₇	semidirect
464. #465	C₂²×C₇	semidirect
465. #442	C₂²×C₇	semidirect
466. #441	C₂²×C₇	semidirect
467. #440	C₂²×C₇	semidirect
468. #440	C₂²×C₇	semidirect
473. #428	C₂²×C₇	semidirect
474. #428	C₂²×C₇	semidirect
475. #428	C₂²×C₇	semidirect
476. #428	C₂²×C₇	semidirect
483. #427	C₂²×C₇	semidirect
484. #427	C₂²×C₇	semidirect
485. #427	C₂²×C₇	semidirect
486. C₂×#107	C₂²×C₇	semidirect
487. C₂×#107	C₂²×C₇	semidirect
488. C₂×#106	C₂²×C₇	semidirect
798. C₂×C₈	C₇×#41	semidirect
935. C₇	#61243	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
C₇×#3350	2
C₇×#3349	2
C₇×#3348	2
C₇×#3347	2
C₇×#3346	2
C₇×#3345	2
C₇×#3344	2
C₇×#3343	2
C₇×#3162	2
C₇×#3091	2
C₇×#3076	2
C₇×#3054	2
C₇×#3050	2
C₇×#2943	2
C₂×C₇×#435	2
C₇×#2911	2
C₂×C₇×#427	2
#61243	7

Subgroups — C7×#61243 #13238459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61243 #13238459