Subgroups — C₇×#35036 #13212252

Order 1792.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1038 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×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2649	C₂	1	2	yes	maximal, complemented
6	C₇×#2630	C₂	1	2	yes	maximal, complemented
7	C₇×#2587	C₂	1	2	yes	maximal, complemented
8	C₇×#2578	C₂	1	2	yes	maximal, complemented
9	C₇×#2518	C₂	1	2	yes	maximal, complemented
10	C₇×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2467	C₂	1	2	yes	maximal, complemented
13	C₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2415	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2407	C₂	1	1	yes	maximal, characteristic
19	C₇×#2335	C₂	1	2	yes	maximal, complemented
20	C₇×#2334	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#126	C₂²	1	2	yes	—
27	C₂×C₇×#125	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#123	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×C₇×#121	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	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	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#400	C₂²	1	2	yes	—
43	C₇×#399	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	2	yes	—
45	C₇×#397	C₂²	1	2	yes	—
46	C₇×#397	C₂²	1	2	yes	—
47	C₇×#397	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×#394	C₂²	1	2	yes	—
52	C₇×#394	C₂²	1	2	yes	—
53	C₇×#394	C₂²	1	2	yes	—
54	C₇×#394	C₂²	1	2	yes	—
55	C₇×#394	C₂²	1	2	yes	—
56	C₇×#392	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	1	yes	characteristic
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×#390	C₂²	1	1	yes	characteristic
64	C₇×#390	C₂²	1	2	yes	—
65	C₇×#390	C₂²	1	1	yes	characteristic
66	C₇×#390	C₂²	1	1	yes	characteristic
67	C₇×#390	C₂²	1	1	yes	characteristic
68	C₇×#389	C₂²	1	2	yes	—
69	C₇×#389	C₂²	1	1	yes	characteristic
70	C₇×#389	C₂²	1	2	yes	—
71	C₇×#389	C₂²	1	1	yes	characteristic
72	C₇×#389	C₂²	1	1	yes	characteristic
73	C₇×#389	C₂²	1	2	yes	—
74	C₇×#389	C₂²	1	2	yes	—
75	C₇×#389	C₂²	1	1	yes	characteristic
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#388	C₂²	1	2	yes	—
78	C₇×#388	C₂²	1	2	yes	—
79	C₇×#388	C₂²	1	2	yes	—
80	C₇×#388	C₂²	1	2	yes	—
81	C₇×#388	C₂²	1	2	yes	—
82	C₇×#388	C₂²	1	2	yes	—
83	C₇×#388	C₂²	1	2	yes	—
84	C₇×#388	C₂²	1	2	yes	—
85	C₇×#388	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×#387	C₂²	1	2	yes	—
91	C₇×#387	C₂²	1	2	yes	—
92	C₇×#387	C₂²	1	2	yes	—
93	C₇×#386	C₂²	1	2	yes	—
94	C₇×#386	C₂²	1	2	yes	—
95	C₇×#386	C₂²	1	2	yes	—
96	C₇×#386	C₂²	1	2	yes	—
97	C₇×#385	C₂²	1	2	yes	—
98	C₇×#385	C₂²	1	2	yes	—
99	C₇×#385	C₂²	1	2	yes	—
100	C₇×#385	C₂²	1	2	yes	—
101	C₇×#384	C₂²	1	1	yes	characteristic
102	C₇×#383	C₂²	1	2	yes	—
103	C₇×#382	C₂²	1	2	yes	—
104	C₇×#380	C₂²	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
120	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#35036	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂×C₇×#41	—	2	4	no	—
125	C₂×C₇×#41	—	4	2	no	—
126	C₂×C₇×#41	—	4	2	no	—
127	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
129	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₇×D₄	C₂³	1	2	yes	—
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₇×C₄⋊Q₈	—	4	2	no	—
141	C₇×#126	—	2	8	no	—
142	C₇×#125	—	4	2	no	—
143	C₇×#124	—	4	2	no	—
144	C₇×#123	—	2	8	no	—
145	C₇×C₂²⋊Q₈	—	2	4	no	—
146	C₇×C₂²⋊Q₈	—	4	2	no	—
147	C₇×C₂²⋊Q₈	—	4	2	no	—
148	C₇×#121	—	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	—	2	4	no	—
153	C₇×#117	—	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	1	yes	characteristic
176	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₂²⋊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	2	yes	—
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	—	4	2	no	—
200	C₂×C₄²×C₇	—	4	2	no	—
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	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
242	#2863	C₂×C₇	1	1	yes	characteristic, complemented
243	#2861	C₂×C₇	1	1	yes	characteristic, complemented
244	#2857	C₂×C₇	1	1	yes	characteristic, complemented
245	#2854	C₂×C₇	1	1	yes	characteristic, complemented
246	#2649	C₂×C₇	1	2	yes	complemented
247	#2630	C₂×C₇	1	2	yes	complemented
248	#2587	C₂×C₇	1	2	yes	complemented
249	#2578	C₂×C₇	1	2	yes	complemented
250	#2518	C₂×C₇	1	2	yes	complemented
251	#2512	C₂×C₇	1	1	yes	characteristic, complemented
252	#2489	C₂×C₇	1	1	yes	characteristic, complemented
253	#2467	C₂×C₇	1	2	yes	complemented
254	#2446	C₂×C₇	1	1	yes	characteristic, complemented
255	#2441	C₂×C₇	1	1	yes	characteristic, complemented
256	#2432	C₂×C₇	1	1	yes	characteristic, complemented
257	#2426	C₂×C₇	1	1	yes	characteristic, complemented
258	#2415	C₂×C₇	1	1	yes	characteristic, complemented
259	#2407	C₂×C₇	1	1	yes	characteristic
260	#2335	C₂×C₇	1	2	yes	complemented
261	#2334	C₂×C₇	1	2	yes	complemented
262	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
263	#2297	C₂×C₇	1	1	yes	characteristic, complemented
264	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
265	C₂⁴×C₇	C₂⁴	1	2	yes	—
266	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
268	C₇×#41	—	4	16	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	2	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×D₄	—	2	2	no	—
276	C₂×C₇×D₄	—	2	2	no	—
277	C₂×C₇×D₄	—	2	4	no	—
278	C₂×C₇×D₄	—	2	4	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	4	2	no	—
284	C₂×C₇×D₄	—	4	2	no	—
285	C₂×C₇×D₄	—	4	2	no	—
286	C₂×C₇×D₄	—	4	2	no	—
287	C₂²×C₄×C₇	—	2	2	no	—
288	C₂²×C₄×C₇	—	2	2	no	—
289	C₂²×C₄×C₇	—	2	2	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	4	no	—
294	C₂²×C₄×C₇	—	2	2	no	—
295	C₂²×C₄×C₇	—	2	2	no	—
296	C₂²×C₄×C₇	—	2	2	no	—
297	C₂²×C₄×C₇	—	2	2	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	1	no	—
303	C₂²×C₄×C₇	—	4	1	no	—
304	C₂²×C₄×C₇	—	4	2	no	—
305	C₂²×C₄×C₇	—	4	2	no	—
306	C₂²×C₄×C₇	#41	1	4	yes	—
307	C₂²×C₄×C₇	#41	1	4	yes	complemented
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	2	no	—
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	4	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	2	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	—	4	2	no	—
341	C₇×C₄⋊C₄	—	4	2	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	#41	1	4	yes	complemented
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	2	no	—
352	C₇×C₂²⋊C₄	—	2	4	no	—
353	C₇×C₂²⋊C₄	—	2	4	no	—
354	C₇×C₂²⋊C₄	—	2	2	no	—
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	4	no	—
359	C₇×C₂²⋊C₄	—	2	4	no	—
360	C₇×C₂²⋊C₄	—	2	4	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	4	no	—
363	C₇×C₂²⋊C₄	—	2	4	no	—
364	C₇×C₂²⋊C₄	—	4	2	no	—
365	C₇×C₂²⋊C₄	—	4	2	no	—
366	C₇×C₂²⋊C₄	—	4	2	no	—
367	C₇×C₂²⋊C₄	—	4	2	no	—
368	C₇×C₂²⋊C₄	—	4	2	no	—
369	C₇×C₂²⋊C₄	—	4	2	no	—
370	C₇×C₂²⋊C₄	—	4	2	no	—
371	C₇×C₂²⋊C₄	—	4	2	no	—
372	C₇×C₂²⋊C₄	—	4	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	2	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	4	no	—
377	C₄²×C₇	—	2	2	no	—
378	C₄²×C₇	—	2	2	no	—
379	C₄²×C₇	—	2	2	no	—
380	C₄²×C₇	—	2	2	no	—
381	C₄²×C₇	—	2	2	no	—
382	C₄²×C₇	—	4	1	no	—
383	C₄²×C₇	—	4	1	no	—
384	C₄²×C₇	—	4	1	no	—
385	C₄²×C₇	—	4	1	no	—
386	C₄²×C₇	—	4	1	no	—
387	C₄²×C₇	—	4	2	no	—
388	C₄²×C₇	—	4	2	no	—
389	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
391	C₂×#126	C₂²×C₇	1	2	yes	—
392	C₂×#125	C₂²×C₇	1	1	yes	characteristic
393	C₂×#124	C₂²×C₇	1	1	yes	characteristic
394	C₂×#123	C₂²×C₇	1	2	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
398	C₂×#121	C₂²×C₇	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
403	C₂×#117	C₂²×C₇	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
405	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
406	#400	C₂²×C₇	1	2	yes	—
407	#400	C₂²×C₇	1	2	yes	—
408	#399	C₂²×C₇	1	2	yes	—
409	#398	C₂²×C₇	1	2	yes	—
410	#397	C₂²×C₇	1	2	yes	—
411	#397	C₂²×C₇	1	2	yes	—
412	#397	C₂²×C₇	1	2	yes	—
413	#396	C₂²×C₇	1	2	yes	—
414	#396	C₂²×C₇	1	2	yes	—
415	#396	C₂²×C₇	1	2	yes	—
416	#394	C₂²×C₇	1	2	yes	—
417	#394	C₂²×C₇	1	2	yes	—
418	#394	C₂²×C₇	1	2	yes	—
419	#394	C₂²×C₇	1	2	yes	—
420	#394	C₂²×C₇	1	2	yes	—
421	#392	C₂²×C₇	1	2	yes	—
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	1	yes	characteristic
427	#391	C₂²×C₇	1	1	yes	characteristic
428	#390	C₂²×C₇	1	2	yes	—
429	#390	C₂²×C₇	1	1	yes	characteristic
430	#390	C₂²×C₇	1	1	yes	characteristic
431	#390	C₂²×C₇	1	1	yes	characteristic
432	#390	C₂²×C₇	1	1	yes	characteristic
433	#389	C₂²×C₇	1	2	yes	—
434	#389	C₂²×C₇	1	2	yes	—
435	#389	C₂²×C₇	1	2	yes	—
436	#389	C₂²×C₇	1	2	yes	—
437	#389	C₂²×C₇	1	1	yes	characteristic
438	#389	C₂²×C₇	1	1	yes	characteristic
439	#389	C₂²×C₇	1	1	yes	characteristic
440	#389	C₂²×C₇	1	1	yes	characteristic
441	#388	C₂²×C₇	1	2	yes	—
442	#388	C₂²×C₇	1	2	yes	—
443	#388	C₂²×C₇	1	2	yes	—
444	#388	C₂²×C₇	1	2	yes	—
445	#388	C₂²×C₇	1	2	yes	—
446	#388	C₂²×C₇	1	2	yes	—
447	#388	C₂²×C₇	1	2	yes	—
448	#388	C₂²×C₇	1	2	yes	—
449	#388	C₂²×C₇	1	2	yes	—
450	#388	C₂²×C₇	1	2	yes	—
451	#387	C₂²×C₇	1	2	yes	—
452	#387	C₂²×C₇	1	2	yes	—
453	#387	C₂²×C₇	1	2	yes	—
454	#387	C₂²×C₇	1	2	yes	—
455	#387	C₂²×C₇	1	2	yes	—
456	#387	C₂²×C₇	1	2	yes	—
457	#387	C₂²×C₇	1	2	yes	—
458	#386	C₂²×C₇	1	2	yes	—
459	#386	C₂²×C₇	1	2	yes	—
460	#386	C₂²×C₇	1	2	yes	—
461	#386	C₂²×C₇	1	2	yes	—
462	#385	C₂²×C₇	1	2	yes	—
463	#385	C₂²×C₇	1	2	yes	—
464	#385	C₂²×C₇	1	2	yes	—
465	#385	C₂²×C₇	1	2	yes	—
466	#384	C₂²×C₇	1	1	yes	characteristic
467	#383	C₂²×C₇	1	2	yes	—
468	#382	C₂²×C₇	1	2	yes	—
469	#380	C₂²×C₇	1	2	yes	—
470	#380	C₂²×C₇	1	2	yes	—
471	#380	C₂²×C₇	1	1	yes	characteristic
472	#380	C₂²×C₇	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
475	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
476	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
478	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
479	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
484	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
485	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
487	C₄³	C₂²×C₇	1	1	yes	characteristic
488	C₂³×C₇	—	2	1	no	—
489	C₂³×C₇	—	2	1	no	—
490	C₂³×C₇	—	2	1	no	—
491	C₂³×C₇	—	2	1	no	—
492	C₂³×C₇	—	2	1	no	—
493	C₂³×C₇	—	2	1	no	—
494	C₂³×C₇	—	2	1	no	—
495	C₂³×C₇	—	2	1	no	—
496	C₂³×C₇	—	2	1	no	—
497	C₂³×C₇	—	2	1	no	—
498	C₂³×C₇	—	2	1	no	—
499	C₂³×C₇	—	2	1	no	—
500	C₂³×C₇	—	2	2	no	—
501	C₂³×C₇	—	2	2	no	—
502	C₂³×C₇	—	2	2	no	—
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	2	no	—
505	C₂³×C₇	—	2	2	no	—
506	C₂³×C₇	—	2	2	no	—
507	C₂³×C₇	C₂×#41	1	2	yes	—
508	C₂³×C₇	C₂×#41	1	2	yes	—
509	C₂³×C₇	C₂⁵	1	1	yes	characteristic
510	C₇×Q₈	—	4	4	no	—
511	C₇×Q₈	—	4	4	no	—
512	C₇×D₄	—	2	8	no	—
513	C₇×D₄	—	4	8	no	—
514	C₇×D₄	—	4	4	no	—
515	C₇×D₄	—	8	4	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	1	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	1	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	8	no	—
531	C₂×C₄×C₇	—	2	1	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	1	no	—
541	C₂×C₄×C₇	—	2	1	no	—
542	C₂×C₄×C₇	—	2	2	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	1	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	1	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	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	—	2	2	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	1	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	2	no	—
561	C₂×C₄×C₇	—	2	1	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	2	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	2	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	4	4	no	—
568	C₂×C₄×C₇	—	4	4	no	—
569	C₂×C₄×C₇	—	4	4	no	—
570	C₂×C₄×C₇	—	4	4	no	—
571	C₂×C₄×C₇	—	4	8	no	—
572	C₂×C₄×C₇	—	4	4	no	—
573	C₂×C₄×C₇	C₂×#41	1	2	yes	—
574	C₂×C₄×C₇	C₂×#41	1	2	yes	—
575	C₂×C₄×C₇	C₂×#41	1	2	yes	—
576	C₂×C₄×C₇	C₂×#41	1	2	yes	—
577	C₂×C₄×C₇	C₂×#41	1	2	yes	—
578	C₂×C₄×C₇	C₂×#41	1	2	yes	—
579	C₂×C₄×C₇	C₂×#41	1	2	yes	—
580	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
581	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
582	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
583	C₂×#41	—	2	4	no	—
584	C₂×#41	—	4	2	no	—
585	C₂×#41	—	4	2	no	—
586	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
587	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
590	C₂²×D₄	C₂³×C₇	1	2	yes	—
591	C₂²×D₄	C₂³×C₇	1	2	yes	—
592	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇	1	2	yes	—
598	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
599	C₄⋊Q₈	—	4	2	no	—
600	#126	—	2	8	no	—
601	#125	—	4	2	no	—
602	#124	—	4	2	no	—
603	#123	—	2	8	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₂²⋊Q₈	—	4	2	no	—
606	C₂²⋊Q₈	—	4	2	no	—
607	#121	—	4	2	no	—
608	C₄×Q₈	—	4	2	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	2	4	no	—
612	#117	—	4	2	no	—
613	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄²	—	4	2	no	—
659	C₂×C₄²	—	4	2	no	—
660	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₇	1	2	yes	—
666	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
676	#95	C₂³×C₇	1	1	yes	characteristic
677	#95	C₂³×C₇	1	1	yes	characteristic
678	#95	C₂³×C₇	1	1	yes	characteristic
679	#95	C₂³×C₇	1	1	yes	characteristic
680	#95	C₂³×C₇	1	1	yes	characteristic
681	#95	C₂³×C₇	1	1	yes	characteristic
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	#95	C₂³×C₇	1	2	yes	—
691	#95	C₂³×C₇	1	2	yes	—
692	#95	C₂³×C₇	1	2	yes	—
693	#95	C₂³×C₇	1	2	yes	—
694	#95	C₂³×C₇	1	2	yes	—
695	#95	C₂³×C₇	1	2	yes	—
696	#95	C₂³×C₇	1	2	yes	—
697	#95	C₂³×C₇	1	2	yes	—
698	#95	C₂³×C₇	1	2	yes	—
699	#95	C₂³×C₇	1	2	yes	—
700	#95	C₂³×C₇	1	2	yes	—
701	C₂²×C₇	—	2	2	no	—
702	C₂²×C₇	—	2	2	no	—
703	C₂²×C₇	—	2	2	no	—
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	2	no	—
706	C₂²×C₇	—	2	2	no	—
707	C₂²×C₇	—	4	1	no	—
708	C₂²×C₇	—	4	1	no	—
709	C₂²×C₇	—	4	1	no	—
710	C₂²×C₇	—	4	1	no	—
711	C₂²×C₇	—	4	1	no	—
712	C₂²×C₇	—	4	1	no	—
713	C₂²×C₇	—	4	1	no	—
714	C₂²×C₇	—	4	1	no	—
715	C₂²×C₇	—	4	2	no	—
716	C₂²×C₇	—	4	2	no	—
717	C₂²×C₇	—	4	2	no	—
718	C₂²×C₇	—	4	2	no	—
719	C₂²×C₇	—	4	2	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	—	4	2	no	—
722	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
723	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
724	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
725	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
728	C₂²×C₇	#585	1	1	yes	characteristic
729	C₄×C₇	—	2	2	no	—
730	C₄×C₇	—	2	2	no	—
731	C₄×C₇	—	2	2	no	—
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	—	2	2	no	—
734	C₄×C₇	—	2	2	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	4	2	no	—
737	C₄×C₇	—	4	1	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	2	no	—
740	C₄×C₇	—	4	1	no	—
741	C₄×C₇	—	4	1	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	1	no	—
744	C₄×C₇	—	4	2	no	—
745	C₄×C₇	—	4	1	no	—
746	C₄×C₇	—	4	2	no	—
747	C₄×C₇	—	4	2	no	—
748	C₄×C₇	#538	1	4	yes	—
749	C₂⁴	C₂⁴×C₇	1	2	yes	—
750	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
751	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
752	#41	—	4	16	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	2	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	—	4	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	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	1	no	—
784	C₂²×C₄	—	4	1	no	—
785	C₂²×C₄	—	4	1	no	—
786	C₂²×C₄	—	4	1	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	C₇×#41	1	4	yes	—
791	C₂²×C₄	C₇×#41	1	4	yes	complemented
792	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	4	no	—
817	C₄⋊C₄	—	2	4	no	—
818	C₄⋊C₄	—	2	4	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	C₇×#41	1	4	yes	complemented
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	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	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	4	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	4	1	no	—
867	C₄²	—	4	1	no	—
868	C₄²	—	4	1	no	—
869	C₄²	—	4	1	no	—
870	C₄²	—	4	2	no	—
871	C₄²	—	4	2	no	—
872	C₄²	—	4	1	no	—
873	C₂×C₇	—	4	2	no	—
874	C₂×C₇	—	4	2	no	—
875	C₂×C₇	—	8	2	no	—
876	C₂×C₇	#3444	1	1	yes	characteristic
877	C₂×C₇	C₂×#538	1	1	yes	characteristic
878	C₂×C₇	#3461	1	1	yes	characteristic
879	C₂×C₇	#3505	1	1	yes	characteristic
880	C₂×C₇	#3511	1	1	yes	characteristic
881	C₂×C₇	#3517	1	1	yes	characteristic
882	C₂×C₇	#3520	1	1	yes	characteristic
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	C₂×C₇×#41	1	2	yes	—
903	C₂³	C₂×C₇×#41	1	2	yes	—
904	C₂³	C₂⁵×C₇	1	1	yes	characteristic
905	Q₈	—	4	4	no	—
906	Q₈	—	4	4	no	—
907	D₄	—	2	8	no	—
908	D₄	—	4	8	no	—
909	D₄	—	4	4	no	—
910	D₄	—	8	4	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	8	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	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	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	4	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	8	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	C₂×C₇×#41	1	2	yes	—
969	C₂×C₄	C₂×C₇×#41	1	2	yes	—
970	C₂×C₄	C₂×C₇×#41	1	2	yes	—
971	C₂×C₄	C₂×C₇×#41	1	2	yes	—
972	C₂×C₄	C₂×C₇×#41	1	2	yes	—
973	C₂×C₄	C₂×C₇×#41	1	2	yes	—
974	C₂×C₄	C₂×C₇×#41	1	2	yes	—
975	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
976	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
977	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
978	C₇	#35036	1	1	yes	characteristic, direct product factor, Sylow
979	C₂²	—	2	2	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1001	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1002	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1003	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1004	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1005	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1006	C₂²	C₇×#585	1	1	yes	characteristic
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	C₇×#538	1	4	yes	—
1027	C₂	—	4	2	no	—
1028	C₂	—	4	2	no	—
1029	C₂	—	8	2	no	—
1030	C₂	C₇×#3444	1	1	yes	characteristic
1031	C₂	C₂×C₇×#538	1	1	yes	characteristic
1032	C₂	C₇×#3461	1	1	yes	characteristic
1033	C₂	C₇×#3505	1	1	yes	characteristic
1034	C₂	C₇×#3511	1	1	yes	characteristic
1035	C₂	C₇×#3517	1	1	yes	characteristic
1036	C₂	C₇×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2407	C₂
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×#2861	C₂	semidirect
3. C₇×#2857	C₂	semidirect
4. C₇×#2854	C₂	semidirect
5. C₇×#2649	C₂	semidirect
6. C₇×#2630	C₂	semidirect
7. C₇×#2587	C₂	semidirect
8. C₇×#2578	C₂	semidirect
9. C₇×#2518	C₂	semidirect
10. C₇×#2512	C₂	semidirect
11. C₇×#2489	C₂	semidirect
12. C₇×#2467	C₂	semidirect
13. C₇×#2446	C₂	semidirect
14. C₇×#2441	C₂	semidirect
15. C₇×#2432	C₂	semidirect
16. C₇×#2426	C₂	semidirect
17. C₇×#2415	C₂	semidirect
19. C₇×#2335	C₂	semidirect
20. C₇×#2334	C₂	semidirect
21. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
22. C₇×#2297	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
123. #35036	C₇	direct (N × H)
242. #2863	C₂×C₇	semidirect
243. #2861	C₂×C₇	semidirect
244. #2857	C₂×C₇	semidirect
245. #2854	C₂×C₇	semidirect
246. #2649	C₂×C₇	semidirect
247. #2630	C₂×C₇	semidirect
248. #2587	C₂×C₇	semidirect
249. #2578	C₂×C₇	semidirect
250. #2518	C₂×C₇	semidirect
251. #2512	C₂×C₇	semidirect
252. #2489	C₂×C₇	semidirect
253. #2467	C₂×C₇	semidirect
254. #2446	C₂×C₇	semidirect
255. #2441	C₂×C₇	semidirect
256. #2432	C₂×C₇	semidirect
257. #2426	C₂×C₇	semidirect
258. #2415	C₂×C₇	semidirect
260. #2335	C₂×C₇	semidirect
261. #2334	C₂×C₇	semidirect
262. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
263. #2297	C₂×C₇	semidirect
264. C₄²×D₄	C₂×C₇	semidirect
307. C₂²×C₄×C₇	#41	semidirect
349. C₇×C₄⋊C₄	#41	semidirect
791. C₂²×C₄	C₇×#41	semidirect
833. C₄⋊C₄	C₇×#41	semidirect
978. C₇	#35036	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×#2861	2
C₇×#2857	2
C₇×#2854	2
C₇×#2649	2
C₇×#2630	2
C₇×#2587	2
C₇×#2578	2
C₇×#2518	2
C₇×#2512	2
C₇×#2489	2
C₇×#2467	2
C₇×#2446	2
C₇×#2441	2
C₇×#2432	2
C₇×#2426	2
C₇×#2415	2
C₇×#2407	2
C₇×#2335	2
C₇×#2334	2
C₄×C₇×C₂²⋊Q₈	2
C₇×#2297	2
C₄²×C₇×D₄	2
#35036	7

Subgroups — C7×#35036 #13212252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35036 #13212252