Subgroups — C₇×#36748 #13213964

Order 1792.

1858 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2848	C₂	1	2	yes	maximal
2	C₇×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2790	C₂	1	2	yes	maximal, complemented
4	C₇×#2788	C₂	1	2	yes	maximal, complemented
5	C₇×#2768	C₂	1	2	yes	maximal, complemented
6	C₇×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2729	C₂	1	2	yes	maximal, complemented
9	C₇×#2720	C₂	1	2	yes	maximal, complemented
10	C₇×#2704	C₂	1	2	yes	maximal, complemented
11	C₇×#2677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2626	C₂	1	1	yes	maximal, characteristic
13	C₇×#2626	C₂	1	1	yes	maximal, characteristic
14	C₇×#2569	C₂	1	2	yes	maximal, complemented
15	C₇×#2549	C₂	1	2	yes	maximal, complemented
16	C₇×#2442	C₂	1	2	yes	maximal, complemented
17	C₇×#2440	C₂	1	2	yes	maximal, complemented
18	C₇×#2312	C₂	1	2	yes	maximal
19	C₂×C₇×#385	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₇×#125	C₂²	1	2	yes	complemented
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₇×#400	C₂²	1	2	yes	complemented
32	C₇×#400	C₂²	1	2	yes	complemented
33	C₇×#400	C₂²	1	2	yes	complemented
34	C₇×#400	C₂²	1	2	yes	complemented
35	C₇×#399	C₂²	1	1	yes	characteristic
36	C₇×#399	C₂²	1	1	yes	characteristic
37	C₇×#399	C₂²	1	1	yes	characteristic
38	C₇×#399	C₂²	1	1	yes	characteristic
39	C₇×#398	C₂²	1	2	yes	complemented
40	C₇×#398	C₂²	1	2	yes	complemented
41	C₇×#398	C₂²	1	2	yes	complemented
42	C₇×#398	C₂²	1	2	yes	complemented
43	C₇×#398	C₂²	1	2	yes	complemented
44	C₇×#398	C₂²	1	2	yes	complemented
45	C₇×#398	C₂²	1	2	yes	complemented
46	C₇×#398	C₂²	1	2	yes	complemented
47	C₇×#396	C₂²	1	2	yes	—
48	C₇×#396	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#396	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	complemented
52	C₇×#395	C₂²	1	2	yes	complemented
53	C₇×#395	C₂²	1	2	yes	complemented
54	C₇×#395	C₂²	1	2	yes	complemented
55	C₇×#393	C₂²	1	1	yes	characteristic
56	C₇×#393	C₂²	1	1	yes	characteristic
57	C₇×#393	C₂²	1	1	yes	characteristic
58	C₇×#393	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	2	yes	complemented
60	C₇×#391	C₂²	1	2	yes	complemented
61	C₇×#389	C₂²	1	2	yes	complemented
62	C₇×#389	C₂²	1	2	yes	complemented
63	C₇×#389	C₂²	1	2	yes	complemented
64	C₇×#389	C₂²	1	2	yes	complemented
65	C₇×#389	C₂²	1	2	yes	complemented
66	C₇×#389	C₂²	1	2	yes	complemented
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	complemented
76	C₇×#387	C₂²	1	2	yes	complemented
77	C₇×#387	C₂²	1	2	yes	complemented
78	C₇×#387	C₂²	1	2	yes	complemented
79	C₇×#385	C₂²	1	1	yes	characteristic
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	1	yes	characteristic
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	—
86	C₇×#385	C₂²	1	2	yes	—
87	C₇×#385	C₂²	1	2	yes	—
88	C₇×#385	C₂²	1	2	yes	—
89	C₇×#385	C₂²	1	1	yes	characteristic
90	C₇×#385	C₂²	1	1	yes	characteristic
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#384	C₂²	1	2	yes	complemented
94	C₇×#382	C₂²	1	2	yes	complemented
95	C₇×#380	C₂²	1	2	yes	—
96	C₇×#380	C₂²	1	1	yes	characteristic
97	C₇×#380	C₂²	1	2	yes	—
98	C₇×#380	C₂²	1	2	yes	—
99	C₇×#380	C₂²	1	2	yes	—
100	C₇×#380	C₂²	1	2	yes	—
101	C₇×#380	C₂²	1	1	yes	characteristic
102	C₇×#379	C₂²	1	2	yes	—
103	C₇×#379	C₂²	1	2	yes	—
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₇×#95	C₂²	1	2	yes	—
107	#36748	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	2	yes	—
110	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	—	4	4	no	—
113	C₂³×C₄×C₇	—	4	2	no	—
114	C₂³×C₄×C₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇	C₂³	1	2	yes	—
121	C₇×C₄⋊Q₈	—	4	4	no	—
122	C₇×#125	—	4	4	no	—
123	C₇×C₂²⋊Q₈	—	4	4	no	—
124	C₇×C₂²⋊Q₈	—	4	2	no	—
125	C₇×C₂²⋊Q₈	—	4	2	no	—
126	C₇×C₂²⋊Q₈	—	4	4	no	—
127	C₇×C₂²⋊Q₈	—	4	4	no	—
128	C₂×C₇×C₄⋊C₄	—	4	4	no	—
129	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
157	C₂×C₇×C₂²⋊C₄	Q₈	1	8	yes	complemented
158	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₇	C₂³	1	2	yes	—
181	C₇×#95	C₂³	1	2	yes	—
182	C₇×#95	C₂³	1	2	yes	—
183	C₇×#95	C₂³	1	2	yes	—
184	C₇×#95	C₂³	1	2	yes	—
185	C₇×#95	C₂³	1	2	yes	—
186	C₇×#95	C₂³	1	2	yes	—
187	C₇×#95	C₂³	1	2	yes	—
188	C₇×#95	C₂³	1	2	yes	—
189	C₇×#95	C₂³	1	1	yes	characteristic
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	1	yes	characteristic
199	C₇×#95	C₂³	1	1	yes	characteristic
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	1	yes	characteristic
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	#2848	C₂×C₇	1	2	yes	—
208	#2807	C₂×C₇	1	1	yes	characteristic, complemented
209	#2790	C₂×C₇	1	2	yes	complemented
210	#2788	C₂×C₇	1	2	yes	complemented
211	#2768	C₂×C₇	1	2	yes	complemented
212	#2763	C₂×C₇	1	1	yes	characteristic, complemented
213	#2742	C₂×C₇	1	1	yes	characteristic, complemented
214	#2729	C₂×C₇	1	2	yes	complemented
215	#2720	C₂×C₇	1	2	yes	complemented
216	#2704	C₂×C₇	1	2	yes	complemented
217	#2677	C₂×C₇	1	1	yes	characteristic, complemented
218	#2626	C₂×C₇	1	1	yes	characteristic
219	#2626	C₂×C₇	1	1	yes	characteristic
220	#2569	C₂×C₇	1	2	yes	complemented
221	#2549	C₂×C₇	1	2	yes	complemented
222	#2442	C₂×C₇	1	2	yes	complemented
223	#2440	C₂×C₇	1	2	yes	complemented
224	#2312	C₂×C₇	1	2	yes	—
225	C₂×#385	C₂×C₇	1	1	yes	characteristic
226	C₂⁴×C₇	—	2	2	no	—
227	C₂⁴×C₇	—	2	2	no	—
228	C₂⁴×C₇	—	4	2	no	—
229	C₂⁴×C₇	—	4	2	no	—
230	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
231	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₇×Q₈	—	2	4	no	—
235	C₂×C₇×Q₈	—	4	2	no	—
236	C₂×C₇×Q₈	—	4	2	no	—
237	C₂×C₇×Q₈	—	4	1	no	—
238	C₂×C₇×Q₈	—	4	1	no	—
239	C₂×C₇×Q₈	—	4	2	no	—
240	C₂×C₇×Q₈	—	4	2	no	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	4	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	4	2	no	—
248	C₂²×C₄×C₇	—	4	1	no	—
249	C₂²×C₄×C₇	—	4	2	no	—
250	C₂²×C₄×C₇	—	4	2	no	—
251	C₂²×C₄×C₇	—	4	2	no	—
252	C₂²×C₄×C₇	—	4	2	no	—
253	C₂²×C₄×C₇	—	4	1	no	—
254	C₂²×C₄×C₇	—	4	2	no	—
255	C₂²×C₄×C₇	—	4	2	no	—
256	C₂²×C₄×C₇	—	4	2	no	—
257	C₂²×C₄×C₇	—	4	16	no	—
258	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	4	2	no	—
281	C₇×C₄⋊C₄	—	4	2	no	—
282	C₇×C₄⋊C₄	—	4	2	no	—
283	C₇×C₄⋊C₄	—	4	2	no	—
284	C₇×C₄⋊C₄	—	4	2	no	—
285	C₇×C₄⋊C₄	—	4	2	no	—
286	C₇×C₄⋊C₄	—	4	2	no	—
287	C₇×C₄⋊C₄	—	4	2	no	—
288	C₇×C₄⋊C₄	—	4	2	no	—
289	C₇×C₄⋊C₄	—	4	2	no	—
290	C₇×C₄⋊C₄	—	4	2	no	—
291	C₇×C₄⋊C₄	—	4	1	no	—
292	C₇×C₄⋊C₄	—	4	2	no	—
293	C₇×C₄⋊C₄	—	4	2	no	—
294	C₇×C₄⋊C₄	—	4	2	no	—
295	C₇×C₄⋊C₄	—	4	1	no	—
296	C₇×C₄⋊C₄	—	4	2	no	—
297	C₇×C₄⋊C₄	—	4	2	no	—
298	C₇×C₄⋊C₄	—	4	2	no	—
299	C₇×C₄⋊C₄	—	4	2	no	—
300	C₇×C₄⋊C₄	—	4	2	no	—
301	C₇×C₄⋊C₄	—	4	2	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	4	no	—
306	C₇×C₂²⋊C₄	—	4	1	no	—
307	C₇×C₂²⋊C₄	—	4	1	no	—
308	C₇×C₂²⋊C₄	—	4	1	no	—
309	C₇×C₂²⋊C₄	—	4	1	no	—
310	C₇×C₂²⋊C₄	—	4	2	no	—
311	C₇×C₂²⋊C₄	—	4	2	no	—
312	C₇×C₂²⋊C₄	—	4	2	no	—
313	C₇×C₂²⋊C₄	—	4	2	no	—
314	C₇×C₂²⋊C₄	—	4	2	no	—
315	C₇×C₂²⋊C₄	—	4	2	no	—
316	C₇×C₂²⋊C₄	—	4	2	no	—
317	C₇×C₂²⋊C₄	—	4	2	no	—
318	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
319	C₇×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
320	C₇×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
321	C₄²×C₇	—	4	2	no	—
322	C₄²×C₇	—	4	2	no	—
323	C₄²×C₇	—	4	2	no	—
324	C₄²×C₇	—	4	2	no	—
325	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
327	C₂×#125	C₂²×C₇	1	2	yes	complemented
328	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
329	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
332	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
334	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
336	#400	C₂²×C₇	1	2	yes	complemented
337	#400	C₂²×C₇	1	2	yes	complemented
338	#400	C₂²×C₇	1	2	yes	complemented
339	#400	C₂²×C₇	1	2	yes	complemented
340	#399	C₂²×C₇	1	1	yes	characteristic
341	#399	C₂²×C₇	1	1	yes	characteristic
342	#399	C₂²×C₇	1	1	yes	characteristic
343	#399	C₂²×C₇	1	1	yes	characteristic
344	#398	C₂²×C₇	1	2	yes	complemented
345	#398	C₂²×C₇	1	2	yes	complemented
346	#398	C₂²×C₇	1	2	yes	complemented
347	#398	C₂²×C₇	1	2	yes	complemented
348	#398	C₂²×C₇	1	2	yes	complemented
349	#398	C₂²×C₇	1	2	yes	complemented
350	#398	C₂²×C₇	1	2	yes	complemented
351	#398	C₂²×C₇	1	2	yes	complemented
352	#396	C₂²×C₇	1	2	yes	—
353	#396	C₂²×C₇	1	2	yes	—
354	#396	C₂²×C₇	1	2	yes	—
355	#396	C₂²×C₇	1	2	yes	—
356	#395	C₂²×C₇	1	2	yes	complemented
357	#395	C₂²×C₇	1	2	yes	complemented
358	#395	C₂²×C₇	1	2	yes	complemented
359	#395	C₂²×C₇	1	2	yes	complemented
360	#393	C₂²×C₇	1	1	yes	characteristic
361	#393	C₂²×C₇	1	1	yes	characteristic
362	#393	C₂²×C₇	1	1	yes	characteristic
363	#393	C₂²×C₇	1	1	yes	characteristic
364	#391	C₂²×C₇	1	2	yes	complemented
365	#391	C₂²×C₇	1	2	yes	complemented
366	#389	C₂²×C₇	1	2	yes	complemented
367	#389	C₂²×C₇	1	2	yes	complemented
368	#389	C₂²×C₇	1	2	yes	complemented
369	#389	C₂²×C₇	1	2	yes	complemented
370	#389	C₂²×C₇	1	2	yes	complemented
371	#389	C₂²×C₇	1	2	yes	complemented
372	#388	C₂²×C₇	1	2	yes	—
373	#388	C₂²×C₇	1	2	yes	—
374	#388	C₂²×C₇	1	2	yes	—
375	#388	C₂²×C₇	1	2	yes	—
376	#388	C₂²×C₇	1	2	yes	—
377	#388	C₂²×C₇	1	2	yes	—
378	#388	C₂²×C₇	1	2	yes	—
379	#388	C₂²×C₇	1	2	yes	—
380	#387	C₂²×C₇	1	2	yes	complemented
381	#387	C₂²×C₇	1	2	yes	complemented
382	#387	C₂²×C₇	1	2	yes	complemented
383	#387	C₂²×C₇	1	2	yes	complemented
384	#385	C₂²×C₇	1	2	yes	—
385	#385	C₂²×C₇	1	2	yes	—
386	#385	C₂²×C₇	1	2	yes	—
387	#385	C₂²×C₇	1	2	yes	—
388	#385	C₂²×C₇	1	2	yes	—
389	#385	C₂²×C₇	1	2	yes	—
390	#385	C₂²×C₇	1	2	yes	—
391	#385	C₂²×C₇	1	2	yes	—
392	#385	C₂²×C₇	1	1	yes	characteristic
393	#385	C₂²×C₇	1	1	yes	characteristic
394	#385	C₂²×C₇	1	2	yes	—
395	#385	C₂²×C₇	1	2	yes	—
396	#385	C₂²×C₇	1	1	yes	characteristic
397	#385	C₂²×C₇	1	1	yes	characteristic
398	#384	C₂²×C₇	1	2	yes	complemented
399	#382	C₂²×C₇	1	2	yes	complemented
400	#380	C₂²×C₇	1	2	yes	—
401	#380	C₂²×C₇	1	2	yes	—
402	#380	C₂²×C₇	1	1	yes	characteristic
403	#380	C₂²×C₇	1	2	yes	—
404	#380	C₂²×C₇	1	2	yes	—
405	#380	C₂²×C₇	1	2	yes	—
406	#380	C₂²×C₇	1	1	yes	characteristic
407	#379	C₂²×C₇	1	2	yes	—
408	#379	C₂²×C₇	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
411	C₂×#95	C₂²×C₇	1	2	yes	—
412	C₂³×C₇	—	2	2	no	—
413	C₂³×C₇	—	2	2	no	—
414	C₂³×C₇	—	2	8	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	1	no	—
418	C₂³×C₇	—	2	1	no	—
419	C₂³×C₇	—	2	1	no	—
420	C₂³×C₇	—	2	1	no	—
421	C₂³×C₇	—	2	2	no	—
422	C₂³×C₇	—	2	2	no	—
423	C₂³×C₇	—	4	8	no	—
424	C₂³×C₇	—	4	4	no	—
425	C₂³×C₇	—	4	4	no	—
426	C₂³×C₇	—	4	8	no	—
427	C₂³×C₇	C₂²×Q₈	1	2	yes	—
428	C₂³×C₇	C₂²×Q₈	1	2	yes	—
429	C₂³×C₇	C₂²×Q₈	1	2	yes	—
430	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
431	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
432	C₂³×C₇	C₂⁵	1	1	yes	characteristic
433	C₇×Q₈	—	8	4	no	—
434	C₇×Q₈	—	8	2	no	—
435	C₇×Q₈	—	8	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	1	no	—
451	C₂×C₄×C₇	—	2	1	no	—
452	C₂×C₄×C₇	—	2	1	no	—
453	C₂×C₄×C₇	—	2	1	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	2	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	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	2	no	—
468	C₂×C₄×C₇	—	2	2	no	—
469	C₂×C₄×C₇	—	2	2	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	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	2	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	4	8	no	—
478	C₂×C₄×C₇	—	4	4	no	—
479	C₂×C₄×C₇	—	4	8	no	—
480	C₂×C₄×C₇	—	4	8	no	—
481	C₂×C₄×C₇	—	4	4	no	—
482	C₂×C₄×C₇	—	8	2	no	—
483	C₂×C₄×C₇	—	8	2	no	—
484	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
485	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
486	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
487	C₂⁵	C₂³×C₇	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₇	1	2	yes	—
489	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
491	C₂³×C₄	—	4	4	no	—
492	C₂³×C₄	—	4	2	no	—
493	C₂³×C₄	C₂³×C₇	1	2	yes	—
494	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
495	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₇	1	2	yes	—
498	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₇	1	2	yes	—
500	C₄⋊Q₈	—	4	4	no	—
501	#125	—	4	4	no	—
502	C₂²⋊Q₈	—	4	4	no	—
503	C₂²⋊Q₈	—	4	2	no	—
504	C₂²⋊Q₈	—	4	2	no	—
505	C₂²⋊Q₈	—	4	4	no	—
506	C₂²⋊Q₈	—	4	4	no	—
507	C₂×C₄⋊C₄	—	4	4	no	—
508	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
535	C₂×C₂²⋊C₄	—	4	2	no	—
536	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	complemented
537	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
556	C₂×C₄²	C₂³×C₇	1	2	yes	—
557	C₂×C₄²	C₂³×C₇	1	2	yes	—
558	C₂×C₄²	C₂³×C₇	1	2	yes	—
559	C₂×C₄²	C₂³×C₇	1	2	yes	—
560	#95	C₂³×C₇	1	2	yes	—
561	#95	C₂³×C₇	1	2	yes	—
562	#95	C₂³×C₇	1	2	yes	—
563	#95	C₂³×C₇	1	2	yes	—
564	#95	C₂³×C₇	1	2	yes	—
565	#95	C₂³×C₇	1	2	yes	—
566	#95	C₂³×C₇	1	2	yes	—
567	#95	C₂³×C₇	1	2	yes	—
568	#95	C₂³×C₇	1	1	yes	characteristic
569	#95	C₂³×C₇	1	2	yes	—
570	#95	C₂³×C₇	1	2	yes	—
571	#95	C₂³×C₇	1	2	yes	—
572	#95	C₂³×C₇	1	2	yes	—
573	#95	C₂³×C₇	1	2	yes	—
574	#95	C₂³×C₇	1	2	yes	—
575	#95	C₂³×C₇	1	2	yes	—
576	#95	C₂³×C₇	1	2	yes	—
577	#95	C₂³×C₇	1	1	yes	characteristic
578	#95	C₂³×C₇	1	1	yes	characteristic
579	#95	C₂³×C₇	1	2	yes	—
580	#95	C₂³×C₇	1	2	yes	—
581	#95	C₂³×C₇	1	1	yes	characteristic
582	#95	C₂³×C₇	1	2	yes	—
583	#95	C₂³×C₇	1	2	yes	—
584	#95	C₂³×C₇	1	2	yes	—
585	#95	C₂³×C₇	1	2	yes	—
586	C₂²×C₇	—	2	4	no	—
587	C₂²×C₇	—	2	2	no	—
588	C₂²×C₇	—	2	2	no	—
589	C₂²×C₇	—	2	4	no	—
590	C₂²×C₇	—	2	2	no	—
591	C₂²×C₇	—	2	2	no	—
592	C₂²×C₇	—	2	4	no	—
593	C₂²×C₇	—	2	4	no	—
594	C₂²×C₇	—	4	16	no	—
595	C₂²×C₇	—	4	1	no	—
596	C₂²×C₇	—	4	1	no	—
597	C₂²×C₇	—	4	1	no	—
598	C₂²×C₇	—	4	1	no	—
599	C₂²×C₇	—	4	2	no	—
600	C₂²×C₇	—	4	2	no	—
601	C₂²×C₇	#544	1	4	yes	—
602	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
603	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
605	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
606	C₂²×C₇	#585	1	2	yes	—
607	C₄×C₇	—	2	4	no	—
608	C₄×C₇	—	2	4	no	—
609	C₄×C₇	—	2	4	no	—
610	C₄×C₇	—	4	2	no	—
611	C₄×C₇	—	4	1	no	—
612	C₄×C₇	—	4	1	no	—
613	C₄×C₇	—	4	2	no	—
614	C₄×C₇	—	4	2	no	—
615	C₄×C₇	—	4	2	no	—
616	C₄×C₇	—	4	1	no	—
617	C₄×C₇	—	4	1	no	—
618	C₄×C₇	—	4	2	no	—
619	C₄×C₇	—	4	2	no	—
620	C₄×C₇	—	4	2	no	—
621	C₄×C₇	—	4	2	no	—
622	C₄×C₇	—	4	2	no	—
623	C₂⁴	—	2	2	no	—
624	C₂⁴	—	2	2	no	—
625	C₂⁴	—	4	2	no	—
626	C₂⁴	—	4	2	no	—
627	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
628	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
629	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
630	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
631	C₂×Q₈	—	2	4	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	—	4	1	no	—
635	C₂×Q₈	—	4	1	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	16	no	—
655	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
656	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	4	1	no	—
704	C₂²⋊C₄	—	4	1	no	—
705	C₂²⋊C₄	—	4	1	no	—
706	C₂²⋊C₄	—	4	1	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
716	C₂²⋊C₄	C₂×C₇×Q₈	1	4	yes	—
717	C₂²⋊C₄	C₂×C₇×Q₈	1	8	yes	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	2	no	—
722	C₂×C₇	—	2	4	no	—
723	C₂×C₇	—	4	2	no	—
724	C₂×C₇	—	4	2	no	—
725	C₂×C₇	C₂×#544	1	1	yes	characteristic
726	C₂×C₇	#3501	1	2	yes	—
727	C₂×C₇	#3532	1	1	yes	characteristic
728	C₂×C₇	#3533	1	1	yes	characteristic
729	C₂×C₇	#3541	1	2	yes	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	8	no	—
741	C₂³	—	4	8	no	—
742	C₂³	—	4	4	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	8	no	—
745	C₂³	C₂²×C₇×Q₈	1	2	yes	—
746	C₂³	C₂²×C₇×Q₈	1	2	yes	—
747	C₂³	C₂²×C₇×Q₈	1	2	yes	—
748	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
749	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
750	C₂³	C₂⁵×C₇	1	1	yes	characteristic
751	Q₈	—	8	4	no	—
752	Q₈	—	8	2	no	—
753	Q₈	—	8	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	4	8	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	4	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
803	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
804	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
805	C₇	#36748	1	1	yes	characteristic, direct product factor, Sylow
806	C₂²	—	2	4	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	16	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	C₇×#544	1	4	yes	—
822	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
823	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
825	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
826	C₂²	C₇×#585	1	2	yes	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₂	—	2	4	no	—
844	C₂	—	4	2	no	—
845	C₂	—	4	2	no	—
846	C₂	C₂×C₇×#544	1	1	yes	characteristic
847	C₂	C₇×#3501	1	2	yes	—
848	C₂	C₇×#3532	1	1	yes	characteristic
849	C₂	C₇×#3533	1	1	yes	characteristic
850	C₂	C₇×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	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
2. C₇×#2807	C₂	semidirect
3. C₇×#2790	C₂	semidirect
4. C₇×#2788	C₂	semidirect
5. C₇×#2768	C₂	semidirect
6. C₇×#2763	C₂	semidirect
7. C₇×#2742	C₂	semidirect
8. C₇×#2729	C₂	semidirect
9. C₇×#2720	C₂	semidirect
10. C₇×#2704	C₂	semidirect
11. C₇×#2677	C₂	semidirect
14. C₇×#2569	C₂	semidirect
15. C₇×#2549	C₂	semidirect
16. C₇×#2442	C₂	semidirect
17. C₇×#2440	C₂	semidirect
21. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₇×#125	C₂²	semidirect
31. C₇×#400	C₂²	semidirect
32. C₇×#400	C₂²	semidirect
33. C₇×#400	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
40. C₇×#398	C₂²	semidirect
41. C₇×#398	C₂²	semidirect
42. C₇×#398	C₂²	semidirect
43. C₇×#398	C₂²	semidirect
44. C₇×#398	C₂²	semidirect
45. C₇×#398	C₂²	semidirect
46. C₇×#398	C₂²	semidirect
51. C₇×#395	C₂²	semidirect
52. C₇×#395	C₂²	semidirect
53. C₇×#395	C₂²	semidirect
54. C₇×#395	C₂²	semidirect
59. C₇×#391	C₂²	semidirect
60. C₇×#391	C₂²	semidirect
61. C₇×#389	C₂²	semidirect
62. C₇×#389	C₂²	semidirect
63. C₇×#389	C₂²	semidirect
64. C₇×#389	C₂²	semidirect
65. C₇×#389	C₂²	semidirect
66. C₇×#389	C₂²	semidirect
75. C₇×#387	C₂²	semidirect
76. C₇×#387	C₂²	semidirect
77. C₇×#387	C₂²	semidirect
78. C₇×#387	C₂²	semidirect
93. C₇×#384	C₂²	semidirect
94. C₇×#382	C₂²	semidirect
107. #36748	C₇	direct (N × H)
157. C₂×C₇×C₂²⋊C₄	Q₈	semidirect
208. #2807	C₂×C₇	semidirect
209. #2790	C₂×C₇	semidirect
210. #2788	C₂×C₇	semidirect
211. #2768	C₂×C₇	semidirect
212. #2763	C₂×C₇	semidirect
213. #2742	C₂×C₇	semidirect
214. #2729	C₂×C₇	semidirect
215. #2720	C₂×C₇	semidirect
216. #2704	C₂×C₇	semidirect
217. #2677	C₂×C₇	semidirect
220. #2569	C₂×C₇	semidirect
221. #2549	C₂×C₇	semidirect
222. #2442	C₂×C₇	semidirect
223. #2440	C₂×C₇	semidirect
326. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
327. C₂×#125	C₂²×C₇	semidirect
336. #400	C₂²×C₇	semidirect
337. #400	C₂²×C₇	semidirect
338. #400	C₂²×C₇	semidirect
339. #400	C₂²×C₇	semidirect
344. #398	C₂²×C₇	semidirect
345. #398	C₂²×C₇	semidirect
346. #398	C₂²×C₇	semidirect
347. #398	C₂²×C₇	semidirect
348. #398	C₂²×C₇	semidirect
349. #398	C₂²×C₇	semidirect
350. #398	C₂²×C₇	semidirect
351. #398	C₂²×C₇	semidirect
356. #395	C₂²×C₇	semidirect
357. #395	C₂²×C₇	semidirect
358. #395	C₂²×C₇	semidirect
359. #395	C₂²×C₇	semidirect
364. #391	C₂²×C₇	semidirect
365. #391	C₂²×C₇	semidirect
366. #389	C₂²×C₇	semidirect
367. #389	C₂²×C₇	semidirect
368. #389	C₂²×C₇	semidirect
369. #389	C₂²×C₇	semidirect
370. #389	C₂²×C₇	semidirect
371. #389	C₂²×C₇	semidirect
380. #387	C₂²×C₇	semidirect
381. #387	C₂²×C₇	semidirect
382. #387	C₂²×C₇	semidirect
383. #387	C₂²×C₇	semidirect
398. #384	C₂²×C₇	semidirect
399. #382	C₂²×C₇	semidirect
536. C₂×C₂²⋊C₄	C₇×Q₈	semidirect
805. C₇	#36748	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×#2848	2
C₇×#2807	2
C₇×#2790	2
C₇×#2788	2
C₇×#2768	2
C₇×#2763	2
C₇×#2742	2
C₇×#2729	2
C₇×#2720	2
C₇×#2704	2
C₇×#2677	2
C₇×#2626	2
C₇×#2569	2
C₇×#2549	2
C₇×#2442	2
C₇×#2440	2
C₇×#2312	2
C₂×C₇×#385	2
#36748	7

Subgroups — C7×#36748 #13213964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36748 #13213964