Subgroups — C₇×#35016 #13212232

Order 1792.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2666	C₂	1	2	yes	maximal, complemented
6	C₇×#2665	C₂	1	2	yes	maximal, complemented
7	C₇×#2586	C₂	1	2	yes	maximal, complemented
8	C₇×#2574	C₂	1	2	yes	maximal, complemented
9	C₇×#2511	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2505	C₂	1	2	yes	maximal, complemented
11	C₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2450	C₂	1	2	yes	maximal
13	C₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2434	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2417	C₂	1	1	yes	maximal, characteristic
18	C₇×#2409	C₂	1	1	yes	maximal, characteristic
19	C₇×#2329	C₂	1	2	yes	maximal, complemented
20	C₇×#2318	C₂	1	2	yes	maximal
21	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
24	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#400	C₂²	1	2	yes	—
43	C₇×#400	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#398	C₂²	1	2	yes	—
48	C₇×#396	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#395	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	—
52	C₇×#395	C₂²	1	2	yes	—
53	C₇×#395	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#393	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	1	yes	characteristic
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	2	yes	—
59	C₇×#391	C₂²	1	2	yes	—
60	C₇×#391	C₂²	1	1	yes	characteristic
61	C₇×#391	C₂²	1	1	yes	characteristic
62	C₇×#391	C₂²	1	1	yes	characteristic
63	C₇×#391	C₂²	1	1	yes	characteristic
64	C₇×#391	C₂²	1	1	yes	characteristic
65	C₇×#391	C₂²	1	2	yes	—
66	C₇×#391	C₂²	1	2	yes	—
67	C₇×#391	C₂²	1	2	yes	—
68	C₇×#391	C₂²	1	1	yes	characteristic
69	C₇×#391	C₂²	1	1	yes	characteristic
70	C₇×#391	C₂²	1	1	yes	characteristic
71	C₇×#389	C₂²	1	2	yes	—
72	C₇×#389	C₂²	1	1	yes	characteristic
73	C₇×#389	C₂²	1	1	yes	characteristic
74	C₇×#389	C₂²	1	2	yes	—
75	C₇×#389	C₂²	1	1	yes	characteristic
76	C₇×#389	C₂²	1	2	yes	—
77	C₇×#389	C₂²	1	1	yes	characteristic
78	C₇×#388	C₂²	1	2	yes	—
79	C₇×#388	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	—
91	C₇×#386	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#384	C₂²	1	1	yes	characteristic
99	C₇×#383	C₂²	1	2	yes	—
100	C₇×#382	C₂²	1	2	yes	—
101	C₇×#382	C₂²	1	2	yes	—
102	C₇×#381	C₂²	1	2	yes	—
103	C₇×#380	C₂²	1	1	yes	characteristic
104	C₇×#380	C₂²	1	2	yes	—
105	C₇×#380	C₂²	1	1	yes	characteristic
106	C₇×#380	C₂²	1	2	yes	—
107	C₇×#380	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₇×#95	C₂²	1	2	yes	—
121	C₂×C₇×#95	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#35016	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	—	2	4	no	—
125	C₂²×C₇×Q₈	—	4	2	no	—
126	C₂²×C₇×Q₈	—	4	2	no	—
127	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₇×Q₈	C₂³	1	2	yes	—
131	C₂²×C₇×Q₈	C₂³	1	2	yes	—
132	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₇×C₄⋊Q₈	—	4	2	no	—
142	C₇×C₄⋊Q₈	—	4	2	no	—
143	C₇×C₄⋊Q₈	—	4	2	no	—
144	C₇×C₂²⋊Q₈	—	2	4	no	—
145	C₇×C₂²⋊Q₈	—	2	8	no	—
146	C₇×C₂²⋊Q₈	—	4	2	no	—
147	C₇×C₂²⋊Q₈	—	4	2	no	—
148	C₇×C₂²⋊Q₈	—	4	2	no	—
149	C₄×C₇×Q₈	—	4	2	no	—
150	C₄×C₇×D₄	—	2	4	no	—
151	C₄×C₇×D₄	—	2	4	no	—
152	C₄×C₇×D₄	Q₈	1	8	yes	complemented
153	C₂×C₇×C₄⋊C₄	—	4	2	no	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	—	4	2	no	—
192	C₂×C₄²×C₇	—	4	2	no	—
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	C₇×#95	C₂³	1	1	yes	characteristic
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	1	yes	characteristic
219	C₇×#95	C₂³	1	1	yes	characteristic
220	C₇×#95	C₂³	1	1	yes	characteristic
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	C₇×#95	C₂³	1	2	yes	—
241	#2863	C₂×C₇	1	1	yes	characteristic, complemented
242	#2862	C₂×C₇	1	1	yes	characteristic, complemented
243	#2857	C₂×C₇	1	1	yes	characteristic, complemented
244	#2855	C₂×C₇	1	1	yes	characteristic, complemented
245	#2666	C₂×C₇	1	2	yes	complemented
246	#2665	C₂×C₇	1	2	yes	complemented
247	#2586	C₂×C₇	1	2	yes	complemented
248	#2574	C₂×C₇	1	2	yes	complemented
249	#2511	C₂×C₇	1	1	yes	characteristic, complemented
250	#2505	C₂×C₇	1	2	yes	complemented
251	#2492	C₂×C₇	1	1	yes	characteristic, complemented
252	#2450	C₂×C₇	1	2	yes	—
253	#2446	C₂×C₇	1	1	yes	characteristic, complemented
254	#2440	C₂×C₇	1	1	yes	characteristic, complemented
255	#2434	C₂×C₇	1	1	yes	characteristic, complemented
256	#2429	C₂×C₇	1	1	yes	characteristic, complemented
257	#2417	C₂×C₇	1	1	yes	characteristic
258	#2409	C₂×C₇	1	1	yes	characteristic
259	#2329	C₂×C₇	1	2	yes	complemented
260	#2318	C₂×C₇	1	2	yes	—
261	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
262	C₂×#391	C₂×C₇	1	1	yes	characteristic, complemented
263	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
264	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	4	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	4	no	—
271	C₂×C₇×Q₈	—	2	2	no	—
272	C₂×C₇×Q₈	—	2	2	no	—
273	C₂×C₇×Q₈	—	2	2	no	—
274	C₂×C₇×Q₈	—	2	2	no	—
275	C₂×C₇×Q₈	—	2	2	no	—
276	C₂×C₇×Q₈	—	2	2	no	—
277	C₂×C₇×Q₈	—	4	2	no	—
278	C₂×C₇×Q₈	—	4	2	no	—
279	C₂×C₇×Q₈	—	4	2	no	—
280	C₂×C₇×Q₈	—	4	2	no	—
281	C₂×C₇×Q₈	—	4	16	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	2	no	—
288	C₂²×C₄×C₇	—	2	4	no	—
289	C₂²×C₄×C₇	—	2	4	no	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	2	2	no	—
292	C₂²×C₄×C₇	—	2	2	no	—
293	C₂²×C₄×C₇	—	2	2	no	—
294	C₂²×C₄×C₇	—	2	2	no	—
295	C₂²×C₄×C₇	—	2	2	no	—
296	C₂²×C₄×C₇	—	4	1	no	—
297	C₂²×C₄×C₇	—	4	1	no	—
298	C₂²×C₄×C₇	—	4	1	no	—
299	C₂²×C₄×C₇	—	4	1	no	—
300	C₂²×C₄×C₇	—	4	1	no	—
301	C₂²×C₄×C₇	—	4	1	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	—	4	2	no	—
305	C₂²×C₄×C₇	—	4	2	no	—
306	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
307	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	complemented
308	C₂²×C₄×C₇	#41	1	4	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	2	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	4	no	—
334	C₇×C₄⋊C₄	—	2	4	no	—
335	C₇×C₄⋊C₄	—	2	4	no	—
336	C₇×C₄⋊C₄	—	2	4	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	4	no	—
342	C₇×C₄⋊C₄	—	4	2	no	—
343	C₇×C₄⋊C₄	—	4	2	no	—
344	C₇×C₄⋊C₄	—	4	2	no	—
345	C₇×C₄⋊C₄	—	4	2	no	—
346	C₇×C₄⋊C₄	—	4	2	no	—
347	C₇×C₄⋊C₄	—	4	2	no	—
348	C₇×C₄⋊C₄	—	4	2	no	—
349	C₇×C₄⋊C₄	—	4	2	no	—
350	C₇×C₄⋊C₄	—	4	2	no	—
351	C₇×C₄⋊C₄	—	4	2	no	—
352	C₇×C₄⋊C₄	—	4	2	no	—
353	C₇×C₄⋊C₄	—	4	2	no	—
354	C₇×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	4	no	—
357	C₇×C₂²⋊C₄	—	2	4	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	4	2	no	—
361	C₇×C₂²⋊C₄	—	4	2	no	—
362	C₇×C₂²⋊C₄	—	4	2	no	—
363	C₇×C₂²⋊C₄	—	4	2	no	—
364	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
365	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	complemented
366	C₇×C₂²⋊C₄	#41	1	4	yes	—
367	C₄²×C₇	—	2	2	no	—
368	C₄²×C₇	—	2	2	no	—
369	C₄²×C₇	—	2	2	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	4	1	no	—
375	C₄²×C₇	—	4	1	no	—
376	C₄²×C₇	—	4	1	no	—
377	C₄²×C₇	—	4	1	no	—
378	C₄²×C₇	—	4	2	no	—
379	C₄²×C₇	—	4	1	no	—
380	C₄²×C₇	—	4	2	no	—
381	C₄²×C₇	C₂×Q₈	1	4	yes	complemented
382	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
383	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
384	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
385	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
386	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
388	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
389	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
398	#400	C₂²×C₇	1	2	yes	—
399	#400	C₂²×C₇	1	2	yes	—
400	#400	C₂²×C₇	1	2	yes	—
401	#400	C₂²×C₇	1	2	yes	—
402	#398	C₂²×C₇	1	2	yes	—
403	#398	C₂²×C₇	1	2	yes	—
404	#398	C₂²×C₇	1	2	yes	—
405	#398	C₂²×C₇	1	2	yes	—
406	#396	C₂²×C₇	1	2	yes	—
407	#396	C₂²×C₇	1	2	yes	—
408	#395	C₂²×C₇	1	2	yes	—
409	#395	C₂²×C₇	1	2	yes	—
410	#395	C₂²×C₇	1	2	yes	—
411	#395	C₂²×C₇	1	2	yes	—
412	#393	C₂²×C₇	1	2	yes	—
413	#393	C₂²×C₇	1	2	yes	—
414	#391	C₂²×C₇	1	2	yes	—
415	#391	C₂²×C₇	1	2	yes	—
416	#391	C₂²×C₇	1	2	yes	—
417	#391	C₂²×C₇	1	2	yes	—
418	#391	C₂²×C₇	1	1	yes	characteristic
419	#391	C₂²×C₇	1	1	yes	characteristic
420	#391	C₂²×C₇	1	1	yes	characteristic
421	#391	C₂²×C₇	1	1	yes	characteristic
422	#391	C₂²×C₇	1	1	yes	characteristic
423	#391	C₂²×C₇	1	1	yes	characteristic
424	#391	C₂²×C₇	1	1	yes	characteristic
425	#391	C₂²×C₇	1	1	yes	characteristic
426	#391	C₂²×C₇	1	2	yes	—
427	#391	C₂²×C₇	1	1	yes	characteristic
428	#391	C₂²×C₇	1	1	yes	characteristic
429	#389	C₂²×C₇	1	2	yes	—
430	#389	C₂²×C₇	1	2	yes	—
431	#389	C₂²×C₇	1	2	yes	—
432	#389	C₂²×C₇	1	1	yes	characteristic
433	#389	C₂²×C₇	1	1	yes	characteristic
434	#389	C₂²×C₇	1	1	yes	characteristic
435	#389	C₂²×C₇	1	1	yes	characteristic
436	#388	C₂²×C₇	1	2	yes	—
437	#388	C₂²×C₇	1	2	yes	—
438	#387	C₂²×C₇	1	2	yes	—
439	#387	C₂²×C₇	1	2	yes	—
440	#387	C₂²×C₇	1	2	yes	—
441	#387	C₂²×C₇	1	2	yes	—
442	#387	C₂²×C₇	1	2	yes	—
443	#387	C₂²×C₇	1	2	yes	—
444	#387	C₂²×C₇	1	2	yes	—
445	#387	C₂²×C₇	1	2	yes	—
446	#387	C₂²×C₇	1	2	yes	—
447	#387	C₂²×C₇	1	2	yes	—
448	#386	C₂²×C₇	1	2	yes	—
449	#386	C₂²×C₇	1	2	yes	—
450	#385	C₂²×C₇	1	2	yes	—
451	#385	C₂²×C₇	1	2	yes	—
452	#385	C₂²×C₇	1	2	yes	—
453	#385	C₂²×C₇	1	2	yes	—
454	#385	C₂²×C₇	1	2	yes	—
455	#385	C₂²×C₇	1	2	yes	—
456	#384	C₂²×C₇	1	1	yes	characteristic
457	#383	C₂²×C₇	1	2	yes	—
458	#382	C₂²×C₇	1	2	yes	—
459	#382	C₂²×C₇	1	2	yes	—
460	#381	C₂²×C₇	1	2	yes	—
461	#380	C₂²×C₇	1	2	yes	—
462	#380	C₂²×C₇	1	2	yes	—
463	#380	C₂²×C₇	1	2	yes	—
464	#380	C₂²×C₇	1	1	yes	characteristic
465	#380	C₂²×C₇	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
471	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
473	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
475	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
476	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
478	C₂×#95	C₂²×C₇	1	2	yes	—
479	C₂×#95	C₂²×C₇	1	2	yes	—
480	C₄³	C₂²×C₇	1	1	yes	characteristic
481	C₂³×C₇	—	2	1	no	—
482	C₂³×C₇	—	2	1	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	—	2	1	no	—
486	C₂³×C₇	—	2	1	no	—
487	C₂³×C₇	—	2	1	no	—
488	C₂³×C₇	—	2	1	no	—
489	C₂³×C₇	—	2	1	no	—
490	C₂³×C₇	—	2	1	no	—
491	C₂³×C₇	C₂²×Q₈	1	2	yes	—
492	C₂³×C₇	C₂²×Q₈	1	2	yes	—
493	C₂³×C₇	C₂×#41	1	2	yes	—
494	C₂³×C₇	C₂×#41	1	2	yes	—
495	C₂³×C₇	C₂⁵	1	1	yes	characteristic
496	C₇×Q₈	—	4	8	no	—
497	C₇×Q₈	—	4	4	no	—
498	C₇×Q₈	—	4	4	no	—
499	C₇×Q₈	—	4	4	no	—
500	C₇×Q₈	—	8	4	no	—
501	C₇×D₄	—	2	8	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	1	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	8	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	1	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	2	no	—
553	C₂×C₄×C₇	—	2	2	no	—
554	C₂×C₄×C₇	—	4	4	no	—
555	C₂×C₄×C₇	—	4	4	no	—
556	C₂×C₄×C₇	—	4	4	no	—
557	C₂×C₄×C₇	—	4	4	no	—
558	C₂×C₄×C₇	—	4	8	no	—
559	C₂×C₄×C₇	—	4	4	no	—
560	C₂×C₄×C₇	—	8	4	no	—
561	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
562	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
563	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
564	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
565	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
566	C₂×C₄×C₇	C₂×#41	1	2	yes	—
567	C₂×C₄×C₇	C₂×#41	1	2	yes	—
568	C₂×C₄×C₇	C₂×#41	1	2	yes	—
569	C₂×C₄×C₇	C₂×#41	1	2	yes	—
570	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
571	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
573	C₂²×Q₈	—	2	4	no	—
574	C₂²×Q₈	—	4	2	no	—
575	C₂²×Q₈	—	4	2	no	—
576	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
577	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
579	C₂²×Q₈	C₂³×C₇	1	2	yes	—
580	C₂²×Q₈	C₂³×C₇	1	2	yes	—
581	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₇	1	2	yes	—
587	C₂³×C₄	C₂³×C₇	1	2	yes	—
588	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
590	C₄⋊Q₈	—	4	2	no	—
591	C₄⋊Q₈	—	4	2	no	—
592	C₄⋊Q₈	—	4	2	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	—	2	8	no	—
595	C₂²⋊Q₈	—	4	2	no	—
596	C₂²⋊Q₈	—	4	2	no	—
597	C₂²⋊Q₈	—	4	2	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₄×D₄	—	2	4	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	C₇×Q₈	1	8	yes	complemented
602	C₂×C₄⋊C₄	—	4	2	no	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₄²	—	4	2	no	—
641	C₂×C₄²	—	4	2	no	—
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇	1	2	yes	—
650	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	2	yes	—
653	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
657	#95	C₂³×C₇	1	2	yes	—
658	#95	C₂³×C₇	1	2	yes	—
659	#95	C₂³×C₇	1	2	yes	—
660	#95	C₂³×C₇	1	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	2	yes	—
663	#95	C₂³×C₇	1	2	yes	—
664	#95	C₂³×C₇	1	2	yes	—
665	#95	C₂³×C₇	1	1	yes	characteristic
666	#95	C₂³×C₇	1	1	yes	characteristic
667	#95	C₂³×C₇	1	1	yes	characteristic
668	#95	C₂³×C₇	1	1	yes	characteristic
669	#95	C₂³×C₇	1	1	yes	characteristic
670	#95	C₂³×C₇	1	1	yes	characteristic
671	#95	C₂³×C₇	1	2	yes	—
672	#95	C₂³×C₇	1	2	yes	—
673	#95	C₂³×C₇	1	2	yes	—
674	#95	C₂³×C₇	1	2	yes	—
675	#95	C₂³×C₇	1	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	2	yes	—
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	2	yes	—
684	#95	C₂³×C₇	1	2	yes	—
685	#95	C₂³×C₇	1	2	yes	—
686	#95	C₂³×C₇	1	2	yes	—
687	#95	C₂³×C₇	1	2	yes	—
688	#95	C₂³×C₇	1	2	yes	—
689	#95	C₂³×C₇	1	2	yes	—
690	C₂²×C₇	—	2	2	no	—
691	C₂²×C₇	—	2	2	no	—
692	C₂²×C₇	—	2	2	no	—
693	C₂²×C₇	—	2	2	no	—
694	C₂²×C₇	—	2	2	no	—
695	C₂²×C₇	—	2	2	no	—
696	C₂²×C₇	—	2	2	no	—
697	C₂²×C₇	—	2	2	no	—
698	C₂²×C₇	—	2	2	no	—
699	C₂²×C₇	—	4	1	no	—
700	C₂²×C₇	—	4	1	no	—
701	C₂²×C₇	—	4	1	no	—
702	C₂²×C₇	—	4	1	no	—
703	C₂²×C₇	#533	1	4	yes	—
704	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
705	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
706	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
707	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
709	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂²×C₇	#585	1	1	yes	characteristic
711	C₄×C₇	—	2	2	no	—
712	C₄×C₇	—	2	2	no	—
713	C₄×C₇	—	2	2	no	—
714	C₄×C₇	—	2	2	no	—
715	C₄×C₇	—	2	2	no	—
716	C₄×C₇	—	2	2	no	—
717	C₄×C₇	—	2	2	no	—
718	C₄×C₇	—	2	2	no	—
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	4	1	no	—
721	C₄×C₇	—	4	2	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	2	no	—
724	C₄×C₇	—	4	1	no	—
725	C₄×C₇	—	4	2	no	—
726	C₄×C₇	—	4	2	no	—
727	C₄×C₇	—	4	2	no	—
728	C₄×C₇	—	4	2	no	—
729	C₄×C₇	—	4	2	no	—
730	C₄×C₇	—	4	1	no	—
731	C₄×C₇	#538	1	4	yes	—
732	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
733	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	4	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	4	no	—
739	C₂×Q₈	—	2	2	no	—
740	C₂×Q₈	—	2	2	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	4	2	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	—	4	16	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
775	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	complemented
776	C₂²×C₄	C₇×#41	1	4	yes	—
777	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
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	4	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	2	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	C₂×C₇×Q₈	1	4	yes	complemented
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
833	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	complemented
834	C₂²⋊C₄	C₇×#41	1	4	yes	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	1	no	—
845	C₄²	—	4	1	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₄²	—	4	1	no	—
849	C₄²	C₂×C₇×Q₈	1	4	yes	complemented
850	C₂×C₇	—	2	4	no	—
851	C₂×C₇	—	4	2	no	—
852	C₂×C₇	C₂×#533	1	1	yes	characteristic
853	C₂×C₇	C₂×#538	1	1	yes	characteristic
854	C₂×C₇	#3461	1	1	yes	characteristic
855	C₂×C₇	#3501	1	1	yes	characteristic
856	C₂×C₇	#3503	1	1	yes	characteristic
857	C₂×C₇	#3514	1	1	yes	characteristic
858	C₂×C₇	#3520	1	1	yes	characteristic
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	C₂²×C₇×Q₈	1	2	yes	—
870	C₂³	C₂²×C₇×Q₈	1	2	yes	—
871	C₂³	C₂×C₇×#41	1	2	yes	—
872	C₂³	C₂×C₇×#41	1	2	yes	—
873	C₂³	C₂⁵×C₇	1	1	yes	characteristic
874	Q₈	—	4	8	no	—
875	Q₈	—	4	4	no	—
876	Q₈	—	4	4	no	—
877	Q₈	—	4	4	no	—
878	Q₈	—	8	4	no	—
879	D₄	—	2	8	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	8	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	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	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	8	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	8	4	no	—
939	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
940	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
941	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
942	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
943	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
944	C₂×C₄	C₂×C₇×#41	1	2	yes	—
945	C₂×C₄	C₂×C₇×#41	1	2	yes	—
946	C₂×C₄	C₂×C₇×#41	1	2	yes	—
947	C₂×C₄	C₂×C₇×#41	1	2	yes	—
948	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
949	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
950	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
951	C₇	#35016	1	1	yes	characteristic, direct product factor, Sylow
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	4	1	no	—
965	C₂²	C₇×#533	1	4	yes	—
966	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
967	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
968	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
969	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
970	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
971	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
972	C₂²	C₇×#585	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	1	no	—
992	C₄	—	4	2	no	—
993	C₄	C₇×#538	1	4	yes	—
994	C₂	—	2	4	no	—
995	C₂	—	4	2	no	—
996	C₂	C₂×C₇×#533	1	1	yes	characteristic
997	C₂	C₂×C₇×#538	1	1	yes	characteristic
998	C₂	C₇×#3461	1	1	yes	characteristic
999	C₂	C₇×#3501	1	1	yes	characteristic
1000	C₂	C₇×#3503	1	1	yes	characteristic
1001	C₂	C₇×#3514	1	1	yes	characteristic
1002	C₂	C₇×#3520	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₇×#2863	C₂	semidirect
2. C₇×#2862	C₂	semidirect
3. C₇×#2857	C₂	semidirect
4. C₇×#2855	C₂	semidirect
5. C₇×#2666	C₂	semidirect
6. C₇×#2665	C₂	semidirect
7. C₇×#2586	C₂	semidirect
8. C₇×#2574	C₂	semidirect
9. C₇×#2511	C₂	semidirect
10. C₇×#2505	C₂	semidirect
11. C₇×#2492	C₂	semidirect
13. C₇×#2446	C₂	semidirect
14. C₇×#2440	C₂	semidirect
15. C₇×#2434	C₂	semidirect
16. C₇×#2429	C₂	semidirect
19. C₇×#2329	C₂	semidirect
21. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₇×#391	C₂	semidirect
123. #35016	C₇	direct (N × H)
152. C₄×C₇×D₄	Q₈	semidirect
241. #2863	C₂×C₇	semidirect
242. #2862	C₂×C₇	semidirect
243. #2857	C₂×C₇	semidirect
244. #2855	C₂×C₇	semidirect
245. #2666	C₂×C₇	semidirect
246. #2665	C₂×C₇	semidirect
247. #2586	C₂×C₇	semidirect
248. #2574	C₂×C₇	semidirect
249. #2511	C₂×C₇	semidirect
250. #2505	C₂×C₇	semidirect
251. #2492	C₂×C₇	semidirect
253. #2446	C₂×C₇	semidirect
254. #2440	C₂×C₇	semidirect
255. #2434	C₂×C₇	semidirect
256. #2429	C₂×C₇	semidirect
259. #2329	C₂×C₇	semidirect
261. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
262. C₂×#391	C₂×C₇	semidirect
307. C₂²×C₄×C₇	C₂×Q₈	semidirect
354. C₇×C₄⋊C₄	C₂×Q₈	semidirect
365. C₇×C₂²⋊C₄	C₂×Q₈	semidirect
381. C₄²×C₇	C₂×Q₈	semidirect
601. C₄×D₄	C₇×Q₈	semidirect
775. C₂²×C₄	C₂×C₇×Q₈	semidirect
822. C₄⋊C₄	C₂×C₇×Q₈	semidirect
833. C₂²⋊C₄	C₂×C₇×Q₈	semidirect
849. C₄²	C₂×C₇×Q₈	semidirect
951. C₇	#35016	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×#2863	2
C₇×#2862	2
C₇×#2857	2
C₇×#2855	2
C₇×#2666	2
C₇×#2665	2
C₇×#2586	2
C₇×#2574	2
C₇×#2511	2
C₇×#2505	2
C₇×#2492	2
C₇×#2450	2
C₇×#2446	2
C₇×#2440	2
C₇×#2434	2
C₇×#2429	2
C₇×#2417	2
C₇×#2409	2
C₇×#2329	2
C₇×#2318	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#391	2
C₄²×C₇×D₄	2
#35016	7

Subgroups — C7×#35016 #13212232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35016 #13212232