Subgroups — C₇×#35044 #13212260

Order 1792.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1106 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×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2648	C₂	1	2	yes	maximal, complemented
6	C₇×#2631	C₂	1	2	yes	maximal, complemented
7	C₇×#2597	C₂	1	2	yes	maximal, complemented
8	C₇×#2557	C₂	1	2	yes	maximal, complemented
9	C₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2459	C₂	1	2	yes	maximal, complemented
12	C₇×#2456	C₂	1	2	yes	maximal, complemented
13	C₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2439	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2428	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2337	C₂	1	2	yes	maximal, complemented
20	C₇×#2333	C₂	1	2	yes	maximal, complemented
21	C₄×C₇×#121	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×#127	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	2	yes	—
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#124	C₂²	1	2	yes	—
30	C₂×C₇×#123	C₂²	1	2	yes	—
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×#121	C₂²	1	1	yes	characteristic
33	C₂×C₇×#121	C₂²	1	2	yes	—
34	C₂×C₇×#121	C₂²	1	1	yes	characteristic
35	C₂×C₇×#121	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×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
41	C₂×C₇×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
44	C₇×#400	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×#397	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#394	C₂²	1	2	yes	—
51	C₇×#394	C₂²	1	2	yes	—
52	C₇×#394	C₂²	1	2	yes	—
53	C₇×#393	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#392	C₂²	1	2	yes	—
56	C₇×#392	C₂²	1	2	yes	—
57	C₇×#392	C₂²	1	2	yes	—
58	C₇×#392	C₂²	1	2	yes	—
59	C₇×#392	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	2	yes	—
63	C₇×#391	C₂²	1	1	yes	characteristic
64	C₇×#391	C₂²	1	2	yes	—
65	C₇×#391	C₂²	1	1	yes	characteristic
66	C₇×#390	C₂²	1	2	yes	—
67	C₇×#390	C₂²	1	1	yes	characteristic
68	C₇×#390	C₂²	1	1	yes	characteristic
69	C₇×#390	C₂²	1	2	yes	—
70	C₇×#390	C₂²	1	1	yes	characteristic
71	C₇×#390	C₂²	1	1	yes	characteristic
72	C₇×#390	C₂²	1	2	yes	—
73	C₇×#390	C₂²	1	1	yes	characteristic
74	C₇×#390	C₂²	1	1	yes	characteristic
75	C₇×#389	C₂²	1	1	yes	characteristic
76	C₇×#389	C₂²	1	1	yes	characteristic
77	C₇×#389	C₂²	1	1	yes	characteristic
78	C₇×#389	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
87	C₇×#388	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×#386	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×#386	C₂²	1	2	yes	—
98	C₇×#386	C₂²	1	2	yes	—
99	C₇×#386	C₂²	1	2	yes	—
100	C₇×#386	C₂²	1	2	yes	—
101	C₇×#386	C₂²	1	2	yes	—
102	C₇×#385	C₂²	1	2	yes	—
103	C₇×#385	C₂²	1	2	yes	—
104	C₇×#383	C₂²	1	2	yes	—
105	C₇×#382	C₂²	1	1	yes	characteristic
106	C₇×#381	C₂²	1	2	yes	—
107	C₇×#380	C₂²	1	1	yes	characteristic
108	C₇×#380	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	1	yes	characteristic
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	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	#35044	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	2	yes	—
129	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	2	yes	—
134	C₂²×C₇×D₄	C₂³	1	2	yes	—
135	C₂²×C₇×D₄	C₂³	1	2	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	2	yes	—
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₇	C₂³	1	2	yes	—
146	C₇×C₄⋊Q₈	—	4	2	no	—
147	C₇×#127	—	4	2	no	—
148	C₇×#124	—	2	8	no	—
149	C₇×#124	—	4	4	no	—
150	C₇×#124	—	4	2	no	—
151	C₇×#123	—	4	4	no	—
152	C₇×C₂²⋊Q₈	—	4	2	no	—
153	C₇×#121	—	2	4	no	—
154	C₇×#121	—	2	8	no	—
155	C₇×#121	—	4	2	no	—
156	C₇×#121	—	4	2	no	—
157	C₄×C₇×D₄	—	2	4	no	—
158	C₄×C₇×D₄	—	2	4	no	—
159	C₄×C₇×D₄	—	2	4	no	—
160	C₄×C₇×D₄	—	4	2	no	—
161	C₄×C₇×D₄	—	4	4	no	—
162	C₇×#117	—	4	2	no	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×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×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	—	4	2	no	—
206	C₂×C₄²×C₇	—	4	2	no	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	1	yes	characteristic
223	C₇×#95	C₂³	1	1	yes	characteristic
224	C₇×#95	C₂³	1	1	yes	characteristic
225	C₇×#95	C₂³	1	1	yes	characteristic
226	C₇×#95	C₂³	1	1	yes	characteristic
227	C₇×#95	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	#2863	C₂×C₇	1	1	yes	characteristic, complemented
246	#2858	C₂×C₇	1	1	yes	characteristic, complemented
247	#2854	C₂×C₇	1	1	yes	characteristic, complemented
248	#2850	C₂×C₇	1	1	yes	characteristic, complemented
249	#2648	C₂×C₇	1	2	yes	complemented
250	#2631	C₂×C₇	1	2	yes	complemented
251	#2597	C₂×C₇	1	2	yes	complemented
252	#2557	C₂×C₇	1	2	yes	complemented
253	#2513	C₂×C₇	1	1	yes	characteristic, complemented
254	#2492	C₂×C₇	1	1	yes	characteristic, complemented
255	#2459	C₂×C₇	1	2	yes	complemented
256	#2456	C₂×C₇	1	2	yes	complemented
257	#2447	C₂×C₇	1	1	yes	characteristic, complemented
258	#2439	C₂×C₇	1	1	yes	characteristic, complemented
259	#2431	C₂×C₇	1	1	yes	characteristic, complemented
260	#2428	C₂×C₇	1	1	yes	characteristic, complemented
261	#2414	C₂×C₇	1	1	yes	characteristic, complemented
262	#2407	C₂×C₇	1	1	yes	characteristic, complemented
263	#2337	C₂×C₇	1	2	yes	complemented
264	#2333	C₂×C₇	1	2	yes	complemented
265	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
266	#2297	C₂×C₇	1	1	yes	characteristic, complemented
267	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
268	C₂⁴×C₇	C₂⁴	1	2	yes	—
269	C₂⁴×C₇	C₂⁴	1	2	yes	—
270	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
272	C₇×#41	—	4	16	no	—
273	C₂×C₇×Q₈	—	2	2	no	—
274	C₂×C₇×Q₈	—	2	4	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×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	4	no	—
282	C₂×C₇×D₄	—	2	4	no	—
283	C₂×C₇×D₄	—	2	4	no	—
284	C₂×C₇×D₄	—	2	4	no	—
285	C₂×C₇×D₄	—	2	2	no	—
286	C₂×C₇×D₄	—	2	2	no	—
287	C₂×C₇×D₄	—	2	2	no	—
288	C₂×C₇×D₄	—	2	4	no	—
289	C₂×C₇×D₄	—	2	4	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	4	2	no	—
295	C₂×C₇×D₄	—	4	2	no	—
296	C₂×C₇×D₄	—	4	2	no	—
297	C₂×C₇×D₄	—	4	2	no	—
298	C₂×C₇×D₄	—	4	2	no	—
299	C₂×C₇×D₄	—	4	2	no	—
300	C₂×C₇×D₄	—	4	2	no	—
301	C₂×C₇×D₄	—	4	2	no	—
302	C₂×C₇×D₄	—	4	2	no	—
303	C₂×C₇×D₄	—	4	2	no	—
304	C₂×C₇×D₄	—	4	2	no	—
305	C₂×C₇×D₄	—	4	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	4	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	2	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	2	4	no	—
319	C₂²×C₄×C₇	—	4	1	no	—
320	C₂²×C₄×C₇	—	4	1	no	—
321	C₂²×C₄×C₇	—	4	1	no	—
322	C₂²×C₄×C₇	—	4	1	no	—
323	C₂²×C₄×C₇	—	4	1	no	—
324	C₂²×C₄×C₇	—	4	1	no	—
325	C₂²×C₄×C₇	—	4	2	no	—
326	C₂²×C₄×C₇	—	4	2	no	—
327	C₂²×C₄×C₇	—	4	2	no	—
328	C₂²×C₄×C₇	—	4	2	no	—
329	C₂²×C₄×C₇	#41	1	4	yes	—
330	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	4	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	4	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	4	2	no	—
360	C₇×C₄⋊C₄	—	4	2	no	—
361	C₇×C₄⋊C₄	—	4	2	no	—
362	C₇×C₄⋊C₄	—	4	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	4	no	—
369	C₇×C₂²⋊C₄	—	2	4	no	—
370	C₇×C₂²⋊C₄	—	2	4	no	—
371	C₇×C₂²⋊C₄	—	2	4	no	—
372	C₇×C₂²⋊C₄	—	2	4	no	—
373	C₇×C₂²⋊C₄	—	2	4	no	—
374	C₇×C₂²⋊C₄	—	2	4	no	—
375	C₇×C₂²⋊C₄	—	2	4	no	—
376	C₇×C₂²⋊C₄	—	4	2	no	—
377	C₇×C₂²⋊C₄	—	4	2	no	—
378	C₇×C₂²⋊C₄	—	4	2	no	—
379	C₇×C₂²⋊C₄	—	4	2	no	—
380	C₇×C₂²⋊C₄	—	4	2	no	—
381	C₇×C₂²⋊C₄	—	4	2	no	—
382	C₇×C₂²⋊C₄	—	4	2	no	—
383	C₇×C₂²⋊C₄	—	4	2	no	—
384	C₇×C₂²⋊C₄	—	4	2	no	—
385	C₇×C₂²⋊C₄	—	4	2	no	—
386	C₇×C₂²⋊C₄	—	4	2	no	—
387	C₇×C₂²⋊C₄	—	4	2	no	—
388	C₇×C₂²⋊C₄	—	4	2	no	—
389	C₇×C₂²⋊C₄	—	4	2	no	—
390	C₇×C₂²⋊C₄	#41	1	4	yes	complemented
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	—	4	1	no	—
399	C₄²×C₇	—	4	1	no	—
400	C₄²×C₇	—	4	1	no	—
401	C₄²×C₇	—	4	1	no	—
402	C₄²×C₇	—	4	1	no	—
403	C₄²×C₇	—	4	2	no	—
404	C₄²×C₇	—	4	2	no	—
405	C₄²×C₇	#41	1	4	yes	complemented
406	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
407	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
408	C₂×#127	C₂²×C₇	1	1	yes	characteristic
409	C₂×#124	C₂²×C₇	1	2	yes	—
410	C₂×#124	C₂²×C₇	1	1	yes	characteristic
411	C₂×#124	C₂²×C₇	1	2	yes	—
412	C₂×#123	C₂²×C₇	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
414	C₂×#121	C₂²×C₇	1	2	yes	—
415	C₂×#121	C₂²×C₇	1	1	yes	characteristic
416	C₂×#121	C₂²×C₇	1	1	yes	characteristic
417	C₂×#121	C₂²×C₇	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
423	C₂×#117	C₂²×C₇	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
425	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
426	#400	C₂²×C₇	1	2	yes	—
427	#397	C₂²×C₇	1	2	yes	—
428	#397	C₂²×C₇	1	2	yes	—
429	#397	C₂²×C₇	1	2	yes	—
430	#397	C₂²×C₇	1	2	yes	—
431	#396	C₂²×C₇	1	2	yes	—
432	#394	C₂²×C₇	1	2	yes	—
433	#394	C₂²×C₇	1	2	yes	—
434	#394	C₂²×C₇	1	2	yes	—
435	#393	C₂²×C₇	1	2	yes	—
436	#393	C₂²×C₇	1	2	yes	—
437	#392	C₂²×C₇	1	2	yes	—
438	#392	C₂²×C₇	1	2	yes	—
439	#392	C₂²×C₇	1	2	yes	—
440	#392	C₂²×C₇	1	2	yes	—
441	#392	C₂²×C₇	1	2	yes	—
442	#391	C₂²×C₇	1	2	yes	—
443	#391	C₂²×C₇	1	2	yes	—
444	#391	C₂²×C₇	1	1	yes	characteristic
445	#391	C₂²×C₇	1	1	yes	characteristic
446	#391	C₂²×C₇	1	1	yes	characteristic
447	#391	C₂²×C₇	1	1	yes	characteristic
448	#390	C₂²×C₇	1	2	yes	—
449	#390	C₂²×C₇	1	2	yes	—
450	#390	C₂²×C₇	1	1	yes	characteristic
451	#390	C₂²×C₇	1	2	yes	—
452	#390	C₂²×C₇	1	1	yes	characteristic
453	#390	C₂²×C₇	1	1	yes	characteristic
454	#390	C₂²×C₇	1	1	yes	characteristic
455	#390	C₂²×C₇	1	1	yes	characteristic
456	#390	C₂²×C₇	1	1	yes	characteristic
457	#389	C₂²×C₇	1	1	yes	characteristic
458	#389	C₂²×C₇	1	1	yes	characteristic
459	#389	C₂²×C₇	1	1	yes	characteristic
460	#389	C₂²×C₇	1	1	yes	characteristic
461	#388	C₂²×C₇	1	2	yes	—
462	#388	C₂²×C₇	1	2	yes	—
463	#388	C₂²×C₇	1	2	yes	—
464	#388	C₂²×C₇	1	2	yes	—
465	#388	C₂²×C₇	1	2	yes	—
466	#388	C₂²×C₇	1	2	yes	—
467	#388	C₂²×C₇	1	2	yes	—
468	#388	C₂²×C₇	1	2	yes	—
469	#388	C₂²×C₇	1	2	yes	—
470	#387	C₂²×C₇	1	2	yes	—
471	#387	C₂²×C₇	1	2	yes	—
472	#387	C₂²×C₇	1	2	yes	—
473	#387	C₂²×C₇	1	2	yes	—
474	#386	C₂²×C₇	1	2	yes	—
475	#386	C₂²×C₇	1	2	yes	—
476	#386	C₂²×C₇	1	2	yes	—
477	#386	C₂²×C₇	1	2	yes	—
478	#386	C₂²×C₇	1	2	yes	—
479	#386	C₂²×C₇	1	2	yes	—
480	#386	C₂²×C₇	1	2	yes	—
481	#386	C₂²×C₇	1	2	yes	—
482	#386	C₂²×C₇	1	2	yes	—
483	#386	C₂²×C₇	1	2	yes	—
484	#385	C₂²×C₇	1	2	yes	—
485	#385	C₂²×C₇	1	2	yes	—
486	#383	C₂²×C₇	1	2	yes	—
487	#382	C₂²×C₇	1	1	yes	characteristic
488	#381	C₂²×C₇	1	2	yes	—
489	#380	C₂²×C₇	1	1	yes	characteristic
490	#380	C₂²×C₇	1	1	yes	characteristic
491	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
493	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
494	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
496	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
501	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
502	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
503	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
504	C₄³	C₂²×C₇	1	1	yes	characteristic
505	C₂³×C₇	—	2	1	no	—
506	C₂³×C₇	—	2	1	no	—
507	C₂³×C₇	—	2	1	no	—
508	C₂³×C₇	—	2	1	no	—
509	C₂³×C₇	—	2	1	no	—
510	C₂³×C₇	—	2	1	no	—
511	C₂³×C₇	—	2	1	no	—
512	C₂³×C₇	—	2	1	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	1	no	—
516	C₂³×C₇	—	2	1	no	—
517	C₂³×C₇	—	2	2	no	—
518	C₂³×C₇	—	2	2	no	—
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	2	2	no	—
521	C₂³×C₇	—	2	2	no	—
522	C₂³×C₇	—	2	2	no	—
523	C₂³×C₇	—	2	2	no	—
524	C₂³×C₇	—	2	2	no	—
525	C₂³×C₇	—	2	2	no	—
526	C₂³×C₇	—	2	2	no	—
527	C₂³×C₇	—	2	2	no	—
528	C₂³×C₇	—	2	2	no	—
529	C₂³×C₇	—	2	2	no	—
530	C₂³×C₇	—	2	2	no	—
531	C₂³×C₇	C₂×#41	1	2	yes	—
532	C₂³×C₇	C₂×#41	1	2	yes	—
533	C₂³×C₇	C₂⁵	1	1	yes	characteristic
534	C₇×Q₈	—	4	4	no	—
535	C₇×Q₈	—	8	4	no	—
536	C₇×D₄	—	2	8	no	—
537	C₇×D₄	—	4	8	no	—
538	C₇×D₄	—	4	8	no	—
539	C₇×D₄	—	4	4	no	—
540	C₇×D₄	—	4	4	no	—
541	C₇×D₄	—	8	4	no	—
542	C₇×D₄	—	8	4	no	—
543	C₇×D₄	—	8	4	no	—
544	C₇×D₄	—	8	4	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	1	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	1	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	1	no	—
555	C₂×C₄×C₇	—	2	1	no	—
556	C₂×C₄×C₇	—	2	1	no	—
557	C₂×C₄×C₇	—	2	1	no	—
558	C₂×C₄×C₇	—	2	1	no	—
559	C₂×C₄×C₇	—	2	8	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	2	no	—
563	C₂×C₄×C₇	—	2	1	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	1	no	—
566	C₂×C₄×C₇	—	2	1	no	—
567	C₂×C₄×C₇	—	2	2	no	—
568	C₂×C₄×C₇	—	2	2	no	—
569	C₂×C₄×C₇	—	2	2	no	—
570	C₂×C₄×C₇	—	2	2	no	—
571	C₂×C₄×C₇	—	2	1	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	2	no	—
577	C₂×C₄×C₇	—	2	2	no	—
578	C₂×C₄×C₇	—	2	2	no	—
579	C₂×C₄×C₇	—	2	2	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	2	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	2	no	—
585	C₂×C₄×C₇	—	2	2	no	—
586	C₂×C₄×C₇	—	2	2	no	—
587	C₂×C₄×C₇	—	2	2	no	—
588	C₂×C₄×C₇	—	2	1	no	—
589	C₂×C₄×C₇	—	2	1	no	—
590	C₂×C₄×C₇	—	2	1	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	2	no	—
593	C₂×C₄×C₇	—	4	4	no	—
594	C₂×C₄×C₇	—	4	4	no	—
595	C₂×C₄×C₇	—	4	4	no	—
596	C₂×C₄×C₇	—	4	4	no	—
597	C₂×C₄×C₇	—	4	8	no	—
598	C₂×C₄×C₇	—	4	4	no	—
599	C₂×C₄×C₇	—	8	4	no	—
600	C₂×C₄×C₇	C₂×#41	1	2	yes	—
601	C₂×C₄×C₇	C₂×#41	1	2	yes	—
602	C₂×C₄×C₇	C₂×#41	1	2	yes	—
603	C₂×C₄×C₇	C₂×#41	1	2	yes	—
604	C₂×C₄×C₇	C₂×#41	1	2	yes	—
605	C₂×C₄×C₇	C₂×#41	1	2	yes	—
606	C₂×C₄×C₇	C₂×#41	1	2	yes	—
607	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
608	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
609	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
610	C₂×#41	—	2	4	no	—
611	C₂×#41	—	4	2	no	—
612	C₂×#41	—	4	2	no	—
613	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₇	1	2	yes	—
615	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₇	1	2	yes	—
619	C₂²×D₄	C₂³×C₇	1	2	yes	—
620	C₂²×D₄	C₂³×C₇	1	2	yes	—
621	C₂²×D₄	C₂³×C₇	1	2	yes	—
622	C₂²×D₄	C₂³×C₇	1	2	yes	—
623	C₂²×D₄	C₂³×C₇	1	2	yes	—
624	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₇	1	2	yes	—
629	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₇	1	2	yes	—
632	C₄⋊Q₈	—	4	2	no	—
633	#127	—	4	2	no	—
634	#124	—	2	8	no	—
635	#124	—	4	4	no	—
636	#124	—	4	2	no	—
637	#123	—	4	4	no	—
638	C₂²⋊Q₈	—	4	2	no	—
639	#121	—	2	4	no	—
640	#121	—	2	8	no	—
641	#121	—	4	2	no	—
642	#121	—	4	2	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	4	2	no	—
647	C₄×D₄	—	4	4	no	—
648	#117	—	4	2	no	—
649	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
691	C₂×C₄²	—	4	2	no	—
692	C₂×C₄²	—	4	2	no	—
693	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	2	yes	—
701	C₂×C₄²	C₂³×C₇	1	2	yes	—
702	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
708	#95	C₂³×C₇	1	1	yes	characteristic
709	#95	C₂³×C₇	1	1	yes	characteristic
710	#95	C₂³×C₇	1	1	yes	characteristic
711	#95	C₂³×C₇	1	1	yes	characteristic
712	#95	C₂³×C₇	1	1	yes	characteristic
713	#95	C₂³×C₇	1	1	yes	characteristic
714	#95	C₂³×C₇	1	2	yes	—
715	#95	C₂³×C₇	1	2	yes	—
716	#95	C₂³×C₇	1	2	yes	—
717	#95	C₂³×C₇	1	2	yes	—
718	#95	C₂³×C₇	1	2	yes	—
719	#95	C₂³×C₇	1	2	yes	—
720	#95	C₂³×C₇	1	2	yes	—
721	#95	C₂³×C₇	1	2	yes	—
722	#95	C₂³×C₇	1	2	yes	—
723	#95	C₂³×C₇	1	2	yes	—
724	#95	C₂³×C₇	1	2	yes	—
725	#95	C₂³×C₇	1	2	yes	—
726	#95	C₂³×C₇	1	2	yes	—
727	#95	C₂³×C₇	1	2	yes	—
728	#95	C₂³×C₇	1	2	yes	—
729	#95	C₂³×C₇	1	2	yes	—
730	#95	C₂³×C₇	1	2	yes	—
731	C₂²×C₇	—	2	2	no	—
732	C₂²×C₇	—	2	2	no	—
733	C₂²×C₇	—	2	2	no	—
734	C₂²×C₇	—	2	2	no	—
735	C₂²×C₇	—	2	2	no	—
736	C₂²×C₇	—	2	2	no	—
737	C₂²×C₇	—	4	1	no	—
738	C₂²×C₇	—	4	1	no	—
739	C₂²×C₇	—	4	1	no	—
740	C₂²×C₇	—	4	1	no	—
741	C₂²×C₇	—	4	1	no	—
742	C₂²×C₇	—	4	1	no	—
743	C₂²×C₇	—	4	1	no	—
744	C₂²×C₇	—	4	1	no	—
745	C₂²×C₇	—	4	2	no	—
746	C₂²×C₇	—	4	2	no	—
747	C₂²×C₇	—	4	2	no	—
748	C₂²×C₇	—	4	2	no	—
749	C₂²×C₇	—	4	2	no	—
750	C₂²×C₇	—	4	2	no	—
751	C₂²×C₇	—	4	2	no	—
752	C₂²×C₇	—	4	2	no	—
753	C₂²×C₇	—	4	2	no	—
754	C₂²×C₇	—	4	2	no	—
755	C₂²×C₇	—	4	2	no	—
756	C₂²×C₇	—	4	2	no	—
757	C₂²×C₇	—	4	2	no	—
758	C₂²×C₇	—	4	2	no	—
759	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
760	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
761	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
762	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂²×C₇	#585	1	1	yes	characteristic
766	C₄×C₇	—	2	2	no	—
767	C₄×C₇	—	2	2	no	—
768	C₄×C₇	—	2	2	no	—
769	C₄×C₇	—	2	2	no	—
770	C₄×C₇	—	2	2	no	—
771	C₄×C₇	—	2	2	no	—
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	4	1	no	—
774	C₄×C₇	—	4	2	no	—
775	C₄×C₇	—	4	1	no	—
776	C₄×C₇	—	4	2	no	—
777	C₄×C₇	—	4	1	no	—
778	C₄×C₇	—	4	1	no	—
779	C₄×C₇	—	4	2	no	—
780	C₄×C₇	—	4	2	no	—
781	C₄×C₇	—	4	2	no	—
782	C₄×C₇	—	4	1	no	—
783	C₄×C₇	—	4	2	no	—
784	C₄×C₇	#538	1	4	yes	—
785	C₂⁴	C₂⁴×C₇	1	2	yes	—
786	C₂⁴	C₂⁴×C₇	1	2	yes	—
787	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
788	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
789	#41	—	4	16	no	—
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	2	4	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	4	2	no	—
795	C₂×Q₈	—	4	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	4	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	4	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	4	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	4	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	1	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	1	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	1	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	C₇×#41	1	4	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	C₇×#41	1	4	yes	complemented
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	4	1	no	—
916	C₄²	—	4	1	no	—
917	C₄²	—	4	1	no	—
918	C₄²	—	4	1	no	—
919	C₄²	—	4	2	no	—
920	C₄²	—	4	2	no	—
921	C₄²	—	4	1	no	—
922	C₄²	C₇×#41	1	4	yes	complemented
923	C₂×C₇	—	4	2	no	—
924	C₂×C₇	—	4	2	no	—
925	C₂×C₇	—	8	2	no	—
926	C₂×C₇	—	8	2	no	—
927	C₂×C₇	#3444	1	1	yes	characteristic
928	C₂×C₇	C₂×#538	1	1	yes	characteristic
929	C₂×C₇	#3460	1	1	yes	characteristic
930	C₂×C₇	#3506	1	1	yes	characteristic
931	C₂×C₇	#3508	1	1	yes	characteristic
932	C₂×C₇	#3514	1	1	yes	characteristic
933	C₂×C₇	#3519	1	1	yes	characteristic
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	C₂×C₇×#41	1	2	yes	—
961	C₂³	C₂×C₇×#41	1	2	yes	—
962	C₂³	C₂⁵×C₇	1	1	yes	characteristic
963	Q₈	—	4	4	no	—
964	Q₈	—	8	4	no	—
965	D₄	—	2	8	no	—
966	D₄	—	4	8	no	—
967	D₄	—	4	8	no	—
968	D₄	—	4	4	no	—
969	D₄	—	4	4	no	—
970	D₄	—	8	4	no	—
971	D₄	—	8	4	no	—
972	D₄	—	8	4	no	—
973	D₄	—	8	4	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	8	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	4	4	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	8	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	8	4	no	—
1029	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1030	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1031	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1032	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1033	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1034	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1035	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1036	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1037	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1038	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1039	C₇	#35044	1	1	yes	characteristic, direct product factor, Sylow
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	2	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1069	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1070	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1071	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1072	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1073	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1074	C₂²	C₇×#585	1	1	yes	characteristic
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	2	no	—
1093	C₄	C₇×#538	1	4	yes	—
1094	C₂	—	4	2	no	—
1095	C₂	—	4	2	no	—
1096	C₂	—	8	2	no	—
1097	C₂	—	8	2	no	—
1098	C₂	C₇×#3444	1	1	yes	characteristic
1099	C₂	C₂×C₇×#538	1	1	yes	characteristic
1100	C₂	C₇×#3460	1	1	yes	characteristic
1101	C₂	C₇×#3506	1	1	yes	characteristic
1102	C₂	C₇×#3508	1	1	yes	characteristic
1103	C₂	C₇×#3514	1	1	yes	characteristic
1104	C₂	C₇×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
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×#2858	C₂	semidirect
3. C₇×#2854	C₂	semidirect
4. C₇×#2850	C₂	semidirect
5. C₇×#2648	C₂	semidirect
6. C₇×#2631	C₂	semidirect
7. C₇×#2597	C₂	semidirect
8. C₇×#2557	C₂	semidirect
9. C₇×#2513	C₂	semidirect
10. C₇×#2492	C₂	semidirect
11. C₇×#2459	C₂	semidirect
12. C₇×#2456	C₂	semidirect
13. C₇×#2447	C₂	semidirect
14. C₇×#2439	C₂	semidirect
15. C₇×#2431	C₂	semidirect
16. C₇×#2428	C₂	semidirect
17. C₇×#2414	C₂	semidirect
18. C₇×#2407	C₂	semidirect
19. C₇×#2337	C₂	semidirect
20. C₇×#2333	C₂	semidirect
21. C₄×C₇×#121	C₂	semidirect
22. C₇×#2297	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
123. #35044	C₇	direct (N × H)
245. #2863	C₂×C₇	semidirect
246. #2858	C₂×C₇	semidirect
247. #2854	C₂×C₇	semidirect
248. #2850	C₂×C₇	semidirect
249. #2648	C₂×C₇	semidirect
250. #2631	C₂×C₇	semidirect
251. #2597	C₂×C₇	semidirect
252. #2557	C₂×C₇	semidirect
253. #2513	C₂×C₇	semidirect
254. #2492	C₂×C₇	semidirect
255. #2459	C₂×C₇	semidirect
256. #2456	C₂×C₇	semidirect
257. #2447	C₂×C₇	semidirect
258. #2439	C₂×C₇	semidirect
259. #2431	C₂×C₇	semidirect
260. #2428	C₂×C₇	semidirect
261. #2414	C₂×C₇	semidirect
262. #2407	C₂×C₇	semidirect
263. #2337	C₂×C₇	semidirect
264. #2333	C₂×C₇	semidirect
265. C₄×#121	C₂×C₇	semidirect
266. #2297	C₂×C₇	semidirect
267. C₄²×D₄	C₂×C₇	semidirect
390. C₇×C₂²⋊C₄	#41	semidirect
405. C₄²×C₇	#41	semidirect
907. C₂²⋊C₄	C₇×#41	semidirect
922. C₄²	C₇×#41	semidirect
1039. C₇	#35044	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×#2858	2
C₇×#2854	2
C₇×#2850	2
C₇×#2648	2
C₇×#2631	2
C₇×#2597	2
C₇×#2557	2
C₇×#2513	2
C₇×#2492	2
C₇×#2459	2
C₇×#2456	2
C₇×#2447	2
C₇×#2439	2
C₇×#2431	2
C₇×#2428	2
C₇×#2414	2
C₇×#2407	2
C₇×#2337	2
C₇×#2333	2
C₄×C₇×#121	2
C₇×#2297	2
C₄²×C₇×D₄	2
#35044	7

Subgroups — C7×#35044 #13212260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35044 #13212260