Subgroups — C₇×#34483 #13211699

Order 1792.

2232 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	1	yes	maximal, characteristic
2	C₇×#2383	C₂	1	2	yes	maximal, complemented
3	C₇×#2377	C₂	1	2	yes	maximal, complemented
4	C₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2359	C₂	1	2	yes	maximal, complemented
8	C₇×#2354	C₂	1	2	yes	maximal, complemented
9	C₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2335	C₂	1	2	yes	maximal, complemented
14	C₇×#2334	C₂	1	2	yes	maximal, complemented
15	C₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2324	C₂	1	2	yes	maximal, complemented
18	C₇×#2318	C₂	1	2	yes	maximal, complemented
19	C₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2316	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#553	C₄	1	16	yes	complemented
25	C₂×C₇×#126	C₂²	1	2	yes	—
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic
27	C₂×C₇×#123	C₂²	1	2	yes	—
28	C₂×C₇×#121	C₂²	1	1	yes	characteristic
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₂×C₇×#121	C₂²	1	2	yes	—
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
37	C₂×C₇×#117	C₂²	1	1	yes	characteristic
38	C₂×C₇×#117	C₂²	1	1	yes	characteristic
39	C₂×C₇×#117	C₂²	1	2	yes	—
40	C₂×C₇×#117	C₂²	1	1	yes	characteristic
41	C₂×C₇×#117	C₂²	1	2	yes	—
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₇×#390	C₂²	1	1	yes	characteristic
46	C₇×#390	C₂²	1	1	yes	characteristic
47	C₇×#390	C₂²	1	1	yes	characteristic
48	C₇×#390	C₂²	1	1	yes	characteristic
49	C₇×#390	C₂²	1	2	yes	—
50	C₇×#390	C₂²	1	2	yes	—
51	C₇×#390	C₂²	1	2	yes	—
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	1	yes	characteristic
55	C₇×#389	C₂²	1	1	yes	characteristic
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
58	C₇×#389	C₂²	1	2	yes	—
59	C₇×#389	C₂²	1	1	yes	characteristic
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#389	C₂²	1	1	yes	characteristic
64	C₇×#389	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	1	yes	characteristic
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	1	yes	characteristic
68	C₇×#388	C₂²	1	1	yes	characteristic
69	C₇×#388	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#388	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#386	C₂²	1	2	yes	—
86	C₇×#386	C₂²	1	2	yes	—
87	C₇×#386	C₂²	1	2	yes	—
88	C₇×#386	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	—
90	C₇×#385	C₂²	1	2	yes	—
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#384	C₂²	1	2	yes	—
98	C₇×#383	C₂²	1	2	yes	—
99	C₇×#382	C₂²	1	1	yes	characteristic
100	C₇×#382	C₂²	1	2	yes	—
101	C₇×#381	C₂²	1	2	yes	—
102	C₇×#380	C₂²	1	2	yes	—
103	C₇×#380	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	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
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	C₂×C₇×#95	C₂²	1	2	yes	—
123	C₄³×C₇	C₂²	1	1	yes	characteristic
124	#34483	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₂²×C₇×D₄	C₂³	1	2	yes	—
127	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₇×D₄	C₂³	1	2	yes	—
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₇×#126	C₂×C₄	1	16	yes	complemented
137	C₇×#125	C₂×C₄	1	8	yes	complemented
138	C₇×#123	C₂×C₄	1	16	yes	complemented
139	C₇×#121	C₂×C₄	1	8	yes	—
140	C₇×#121	C₂×C₄	1	16	yes	complemented
141	C₇×#121	C₂×C₄	1	8	yes	complemented
142	C₄×C₇×D₄	—	4	4	no	—
143	C₄×C₇×D₄	—	4	2	no	—
144	C₄×C₇×D₄	—	4	2	no	—
145	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
146	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
147	C₄×C₇×D₄	C₂×C₄	1	8	yes	complemented
148	C₇×#117	—	4	2	no	—
149	C₇×#117	—	4	2	no	—
150	C₇×#117	—	4	4	no	—
151	C₇×#117	—	4	4	no	—
152	C₇×#117	—	4	2	no	—
153	C₇×#117	C₂×C₄	1	8	yes	complemented
154	C₂×C₇×C₄⋊C₄	—	4	2	no	—
155	C₂×C₇×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
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	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	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	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	1	yes	characteristic
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	1	yes	characteristic
226	C₇×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
232	C₇×#95	C₂³	1	1	yes	characteristic
233	C₇×#95	C₂³	1	1	yes	characteristic
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	C₂×#553	C₂×C₇	1	1	yes	characteristic
245	#2383	C₂×C₇	1	2	yes	complemented
246	#2377	C₂×C₇	1	2	yes	complemented
247	#2370	C₂×C₇	1	1	yes	characteristic, complemented
248	#2363	C₂×C₇	1	1	yes	characteristic, complemented
249	#2361	C₂×C₇	1	1	yes	characteristic, complemented
250	#2359	C₂×C₇	1	2	yes	complemented
251	#2354	C₂×C₇	1	2	yes	complemented
252	#2352	C₂×C₇	1	1	yes	characteristic, complemented
253	#2349	C₂×C₇	1	1	yes	characteristic, complemented
254	#2347	C₂×C₇	1	1	yes	characteristic, complemented
255	#2344	C₂×C₇	1	1	yes	characteristic, complemented
256	#2335	C₂×C₇	1	2	yes	complemented
257	#2334	C₂×C₇	1	2	yes	complemented
258	#2324	C₂×C₇	1	1	yes	characteristic, complemented
259	#2324	C₂×C₇	1	1	yes	characteristic, complemented
260	#2324	C₂×C₇	1	2	yes	complemented
261	#2318	C₂×C₇	1	2	yes	complemented
262	#2317	C₂×C₇	1	1	yes	characteristic, complemented
263	#2316	C₂×C₇	1	1	yes	characteristic, complemented
264	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
265	#2293	C₂×C₇	1	1	yes	characteristic, complemented
266	#2293	C₂×C₇	1	1	yes	characteristic, complemented
267	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₇	C₂⁴	1	2	yes	—
269	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂×C₇×D₄	—	4	2	no	—
273	C₂×C₇×D₄	—	4	2	no	—
274	C₂×C₇×D₄	—	4	1	no	—
275	C₂×C₇×D₄	—	4	1	no	—
276	C₂×C₇×D₄	—	4	2	no	—
277	C₂×C₇×D₄	—	4	2	no	—
278	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
279	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
280	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
281	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	4	2	no	—
287	C₂²×C₄×C₇	—	4	2	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	—	4	2	no	—
290	C₂²×C₄×C₇	—	4	2	no	—
291	C₂²×C₄×C₇	—	4	2	no	—
292	C₂²×C₄×C₇	—	4	2	no	—
293	C₂²×C₄×C₇	—	4	2	no	—
294	C₂²×C₄×C₇	—	4	2	no	—
295	C₂²×C₄×C₇	—	4	2	no	—
296	C₂²×C₄×C₇	—	4	2	no	—
297	C₂²×C₄×C₇	—	4	2	no	—
298	C₂²×C₄×C₇	—	4	2	no	—
299	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
300	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
301	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
302	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	2	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	2	no	—
327	C₇×C₄⋊C₄	—	2	2	no	—
328	C₇×C₄⋊C₄	—	4	2	no	—
329	C₇×C₄⋊C₄	—	4	1	no	—
330	C₇×C₄⋊C₄	—	4	1	no	—
331	C₇×C₄⋊C₄	—	4	2	no	—
332	C₇×C₄⋊C₄	—	4	2	no	—
333	C₇×C₄⋊C₄	—	4	2	no	—
334	C₇×C₄⋊C₄	—	4	2	no	—
335	C₇×C₄⋊C₄	—	4	1	no	—
336	C₇×C₄⋊C₄	—	4	1	no	—
337	C₇×C₄⋊C₄	—	4	2	no	—
338	C₇×C₄⋊C₄	—	4	2	no	—
339	C₇×C₄⋊C₄	—	4	1	no	—
340	C₇×C₄⋊C₄	—	4	1	no	—
341	C₇×C₄⋊C₄	—	4	2	no	—
342	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
343	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
344	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
345	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
346	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
347	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
348	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
349	C₇×C₂²⋊C₄	—	2	2	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	2	2	no	—
352	C₇×C₂²⋊C₄	—	4	2	no	—
353	C₇×C₂²⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	—	4	1	no	—
355	C₇×C₂²⋊C₄	—	4	2	no	—
356	C₇×C₂²⋊C₄	—	4	1	no	—
357	C₇×C₂²⋊C₄	—	4	1	no	—
358	C₇×C₂²⋊C₄	—	4	1	no	—
359	C₇×C₂²⋊C₄	—	4	1	no	—
360	C₇×C₂²⋊C₄	—	4	1	no	—
361	C₇×C₂²⋊C₄	—	4	2	no	—
362	C₇×C₂²⋊C₄	—	4	2	no	—
363	C₇×C₂²⋊C₄	—	4	2	no	—
364	C₇×C₂²⋊C₄	—	4	2	no	—
365	C₇×C₂²⋊C₄	—	4	2	no	—
366	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
367	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
368	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
369	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
370	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
371	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	2	4	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	2	no	—
377	C₄²×C₇	—	2	2	no	—
378	C₄²×C₇	—	4	2	no	—
379	C₄²×C₇	—	4	1	no	—
380	C₄²×C₇	—	4	2	no	—
381	C₄²×C₇	—	4	1	no	—
382	C₄²×C₇	—	4	1	no	—
383	C₄²×C₇	—	4	2	no	—
384	C₄²×C₇	—	4	2	no	—
385	C₄²×C₇	—	4	2	no	—
386	C₄²×C₇	C₂²×C₄	1	8	yes	—
387	C₄²×C₇	C₂²×C₄	1	4	yes	—
388	#553	C₄×C₇	1	16	yes	complemented
389	C₂×#126	C₂²×C₇	1	2	yes	—
390	C₂×#125	C₂²×C₇	1	1	yes	characteristic
391	C₂×#123	C₂²×C₇	1	2	yes	—
392	C₂×#121	C₂²×C₇	1	1	yes	characteristic
393	C₂×#121	C₂²×C₇	1	1	yes	characteristic
394	C₂×#121	C₂²×C₇	1	2	yes	—
395	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
399	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
401	C₂×#117	C₂²×C₇	1	1	yes	characteristic
402	C₂×#117	C₂²×C₇	1	1	yes	characteristic
403	C₂×#117	C₂²×C₇	1	1	yes	characteristic
404	C₂×#117	C₂²×C₇	1	2	yes	—
405	C₂×#117	C₂²×C₇	1	2	yes	—
406	C₂×#117	C₂²×C₇	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
409	#390	C₂²×C₇	1	2	yes	—
410	#390	C₂²×C₇	1	1	yes	characteristic
411	#390	C₂²×C₇	1	1	yes	characteristic
412	#390	C₂²×C₇	1	2	yes	—
413	#390	C₂²×C₇	1	2	yes	—
414	#390	C₂²×C₇	1	1	yes	characteristic
415	#390	C₂²×C₇	1	1	yes	characteristic
416	#389	C₂²×C₇	1	1	yes	characteristic
417	#389	C₂²×C₇	1	1	yes	characteristic
418	#389	C₂²×C₇	1	1	yes	characteristic
419	#389	C₂²×C₇	1	2	yes	—
420	#389	C₂²×C₇	1	1	yes	characteristic
421	#389	C₂²×C₇	1	2	yes	—
422	#389	C₂²×C₇	1	1	yes	characteristic
423	#389	C₂²×C₇	1	1	yes	characteristic
424	#389	C₂²×C₇	1	1	yes	characteristic
425	#389	C₂²×C₇	1	2	yes	—
426	#389	C₂²×C₇	1	1	yes	characteristic
427	#389	C₂²×C₇	1	1	yes	characteristic
428	#389	C₂²×C₇	1	1	yes	characteristic
429	#388	C₂²×C₇	1	1	yes	characteristic
430	#388	C₂²×C₇	1	2	yes	—
431	#388	C₂²×C₇	1	2	yes	—
432	#388	C₂²×C₇	1	2	yes	—
433	#388	C₂²×C₇	1	2	yes	—
434	#388	C₂²×C₇	1	2	yes	—
435	#388	C₂²×C₇	1	2	yes	—
436	#388	C₂²×C₇	1	1	yes	characteristic
437	#388	C₂²×C₇	1	2	yes	—
438	#388	C₂²×C₇	1	2	yes	—
439	#388	C₂²×C₇	1	1	yes	characteristic
440	#388	C₂²×C₇	1	1	yes	characteristic
441	#388	C₂²×C₇	1	2	yes	—
442	#387	C₂²×C₇	1	2	yes	—
443	#387	C₂²×C₇	1	2	yes	—
444	#387	C₂²×C₇	1	2	yes	—
445	#387	C₂²×C₇	1	2	yes	—
446	#387	C₂²×C₇	1	2	yes	—
447	#387	C₂²×C₇	1	2	yes	—
448	#387	C₂²×C₇	1	2	yes	—
449	#386	C₂²×C₇	1	2	yes	—
450	#386	C₂²×C₇	1	2	yes	—
451	#386	C₂²×C₇	1	2	yes	—
452	#386	C₂²×C₇	1	2	yes	—
453	#386	C₂²×C₇	1	2	yes	—
454	#385	C₂²×C₇	1	2	yes	—
455	#385	C₂²×C₇	1	2	yes	—
456	#385	C₂²×C₇	1	2	yes	—
457	#385	C₂²×C₇	1	2	yes	—
458	#385	C₂²×C₇	1	2	yes	—
459	#385	C₂²×C₇	1	2	yes	—
460	#385	C₂²×C₇	1	2	yes	—
461	#384	C₂²×C₇	1	2	yes	—
462	#383	C₂²×C₇	1	2	yes	—
463	#382	C₂²×C₇	1	1	yes	characteristic
464	#382	C₂²×C₇	1	2	yes	—
465	#381	C₂²×C₇	1	2	yes	—
466	#380	C₂²×C₇	1	2	yes	—
467	#380	C₂²×C₇	1	2	yes	—
468	#380	C₂²×C₇	1	1	yes	characteristic
469	#380	C₂²×C₇	1	1	yes	characteristic
470	#380	C₂²×C₇	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
473	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
480	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
485	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
486	C₂×#95	C₂²×C₇	1	2	yes	—
487	C₄³	C₂²×C₇	1	1	yes	characteristic
488	C₂³×C₇	—	2	1	no	—
489	C₂³×C₇	—	2	2	no	—
490	C₂³×C₇	—	2	1	no	—
491	C₂³×C₇	—	2	1	no	—
492	C₂³×C₇	—	2	1	no	—
493	C₂³×C₇	—	2	2	no	—
494	C₂³×C₇	—	2	1	no	—
495	C₂³×C₇	—	2	1	no	—
496	C₂³×C₇	—	2	2	no	—
497	C₂³×C₇	—	2	1	no	—
498	C₂³×C₇	—	2	1	no	—
499	C₂³×C₇	—	2	2	no	—
500	C₂³×C₇	—	2	2	no	—
501	C₂³×C₇	—	2	1	no	—
502	C₂³×C₇	—	2	1	no	—
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	1	no	—
505	C₂³×C₇	—	2	1	no	—
506	C₂³×C₇	C₂³×C₄	1	2	yes	—
507	C₂³×C₇	C₂³×C₄	1	4	yes	—
508	C₂³×C₇	C₂³×C₄	1	2	yes	—
509	C₂³×C₇	C₂⁵	1	1	yes	characteristic
510	C₇×D₄	—	2	8	no	—
511	C₇×D₄	—	4	8	no	—
512	C₇×D₄	—	4	4	no	—
513	C₇×D₄	—	4	8	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	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	2	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	2	no	—
528	C₂×C₄×C₇	—	2	2	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	8	no	—
531	C₂×C₄×C₇	—	2	8	no	—
532	C₂×C₄×C₇	—	2	1	no	—
533	C₂×C₄×C₇	—	2	1	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	2	1	no	—
537	C₂×C₄×C₇	—	2	1	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	2	1	no	—
540	C₂×C₄×C₇	—	2	1	no	—
541	C₂×C₄×C₇	—	2	2	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	2	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	1	no	—
550	C₂×C₄×C₇	—	2	1	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	2	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	2	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	2	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	—	4	8	no	—
566	C₂×C₄×C₇	—	4	8	no	—
567	C₂×C₄×C₇	—	8	4	no	—
568	C₂×C₄×C₇	—	8	4	no	—
569	C₂×C₄×C₇	—	8	4	no	—
570	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
571	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
572	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
574	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
577	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
579	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
580	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
581	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₇	1	2	yes	—
583	C₂²×D₄	C₂³×C₇	1	2	yes	—
584	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₇	1	2	yes	—
588	C₂³×C₄	C₂³×C₇	1	2	yes	—
589	C₂³×C₄	C₂³×C₇	1	2	yes	—
590	C₂³×C₄	C₂³×C₇	1	2	yes	—
591	C₂³×C₄	C₂³×C₇	1	2	yes	—
592	#126	C₂×C₄×C₇	1	16	yes	complemented
593	#125	C₂×C₄×C₇	1	8	yes	complemented
594	#123	C₂×C₄×C₇	1	16	yes	complemented
595	#121	C₂×C₄×C₇	1	8	yes	—
596	#121	C₂×C₄×C₇	1	16	yes	complemented
597	#121	C₂×C₄×C₇	1	8	yes	complemented
598	C₄×D₄	—	4	4	no	—
599	C₄×D₄	—	4	2	no	—
600	C₄×D₄	—	4	2	no	—
601	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
602	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
603	C₄×D₄	C₂×C₄×C₇	1	8	yes	complemented
604	#117	—	4	2	no	—
605	#117	—	4	2	no	—
606	#117	—	4	4	no	—
607	#117	—	4	4	no	—
608	#117	—	4	2	no	—
609	#117	C₂×C₄×C₇	1	8	yes	complemented
610	C₂×C₄⋊C₄	—	4	2	no	—
611	C₂×C₄⋊C₄	C₂×C₄×C₇	1	8	yes	complemented
612	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
668	C₂×C₄²	C₂³×C₇	1	2	yes	—
669	C₂×C₄²	C₂³×C₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₇	1	2	yes	—
674	C₂×C₄²	C₂³×C₇	1	2	yes	—
675	C₂×C₄²	C₂³×C₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
677	#95	C₂³×C₇	1	1	yes	characteristic
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	1	yes	characteristic
682	#95	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
688	#95	C₂³×C₇	1	1	yes	characteristic
689	#95	C₂³×C₇	1	1	yes	characteristic
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	C₂²×C₇	—	2	2	no	—
701	C₂²×C₇	—	2	2	no	—
702	C₂²×C₇	—	2	4	no	—
703	C₂²×C₇	—	2	2	no	—
704	C₂²×C₇	—	2	2	no	—
705	C₂²×C₇	—	2	4	no	—
706	C₂²×C₇	—	2	2	no	—
707	C₂²×C₇	—	2	4	no	—
708	C₂²×C₇	—	2	2	no	—
709	C₂²×C₇	—	4	1	no	—
710	C₂²×C₇	—	4	2	no	—
711	C₂²×C₇	—	4	1	no	—
712	C₂²×C₇	—	4	2	no	—
713	C₂²×C₇	—	4	1	no	—
714	C₂²×C₇	—	4	1	no	—
715	C₂²×C₇	—	4	1	no	—
716	C₂²×C₇	—	4	2	no	—
717	C₂²×C₇	—	4	1	no	—
718	C₂²×C₇	—	4	1	no	—
719	C₂²×C₇	—	4	1	no	—
720	C₂²×C₇	—	4	2	no	—
721	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
722	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
723	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
724	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
725	C₂²×C₇	#585	1	1	yes	characteristic
726	C₂²×C₇	#585	1	1	yes	characteristic
727	C₂²×C₇	#585	1	1	yes	characteristic
728	C₄×C₇	—	2	2	no	—
729	C₄×C₇	—	2	2	no	—
730	C₄×C₇	—	2	4	no	—
731	C₄×C₇	—	2	2	no	—
732	C₄×C₇	—	2	2	no	—
733	C₄×C₇	—	2	4	no	—
734	C₄×C₇	—	2	4	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	4	1	no	—
737	C₄×C₇	—	4	1	no	—
738	C₄×C₇	—	4	2	no	—
739	C₄×C₇	—	4	1	no	—
740	C₄×C₇	—	4	2	no	—
741	C₄×C₇	—	4	1	no	—
742	C₄×C₇	—	4	1	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	—	4	1	no	—
745	C₄×C₇	—	4	2	no	—
746	C₄×C₇	—	4	1	no	—
747	C₄×C₇	#520	1	4	yes	—
748	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
749	C₂⁴	C₂⁴×C₇	1	2	yes	—
750	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	1	no	—
756	C₂×D₄	—	4	1	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
760	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
761	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
762	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
781	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
782	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
783	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	1	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	1	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	1	no	—
818	C₄⋊C₄	—	4	1	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	2	no	—
821	C₄⋊C₄	—	4	2	no	—
822	C₄⋊C₄	—	4	2	no	—
823	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
824	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
825	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
826	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
827	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
828	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
829	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	4	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	1	no	—
835	C₂²⋊C₄	—	4	1	no	—
836	C₂²⋊C₄	—	4	1	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	1	no	—
847	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
848	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
849	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
850	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
851	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
852	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	4	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	4	2	no	—
860	C₄²	—	4	2	no	—
861	C₄²	—	4	2	no	—
862	C₄²	—	4	2	no	—
863	C₄²	—	4	1	no	—
864	C₄²	—	4	2	no	—
865	C₄²	—	4	1	no	—
866	C₄²	—	4	1	no	—
867	C₄²	C₂²×C₄×C₇	1	8	yes	—
868	C₄²	C₂²×C₄×C₇	1	4	yes	—
869	C₂×C₇	—	4	2	no	—
870	C₂×C₇	—	4	2	no	—
871	C₂×C₇	—	4	4	no	—
872	C₂×C₇	C₂×#520	1	1	yes	characteristic
873	C₂×C₇	#3428	1	1	yes	characteristic
874	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
875	C₂×C₇	#3546	1	1	yes	characteristic
876	C₂×C₇	#3551	1	1	yes	characteristic
877	C₂×C₇	#3559	1	1	yes	characteristic
878	C₂×C₇	#3565	1	1	yes	characteristic
879	C₂³	—	2	1	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	C₂³×C₄×C₇	1	2	yes	—
898	C₂³	C₂³×C₄×C₇	1	4	yes	—
899	C₂³	C₂³×C₄×C₇	1	2	yes	—
900	C₂³	C₂⁵×C₇	1	1	yes	characteristic
901	D₄	—	2	8	no	—
902	D₄	—	4	8	no	—
903	D₄	—	4	4	no	—
904	D₄	—	4	8	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	8	no	—
922	C₂×C₄	—	2	8	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	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	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	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	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	—	4	8	no	—
958	C₂×C₄	—	8	4	no	—
959	C₂×C₄	—	8	4	no	—
960	C₂×C₄	—	8	4	no	—
961	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
962	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
963	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
964	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
965	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
966	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
968	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
969	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
970	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
971	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
972	C₇	#34483	1	1	yes	characteristic, direct product factor, Sylow
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	4	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	4	1	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
995	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
996	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
997	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
998	C₂²	C₇×#585	1	1	yes	characteristic
999	C₂²	C₇×#585	1	1	yes	characteristic
1000	C₂²	C₇×#585	1	1	yes	characteristic
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	4	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	4	no	—
1007	C₄	—	2	4	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	C₇×#520	1	4	yes	—
1021	C₂	—	4	2	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	4	no	—
1024	C₂	C₂×C₇×#520	1	1	yes	characteristic
1025	C₂	C₇×#3428	1	1	yes	characteristic
1026	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1027	C₂	C₇×#3546	1	1	yes	characteristic
1028	C₂	C₇×#3551	1	1	yes	characteristic
1029	C₂	C₇×#3559	1	1	yes	characteristic
1030	C₂	C₇×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2383	C₂	semidirect
3. C₇×#2377	C₂	semidirect
4. C₇×#2370	C₂	semidirect
5. C₇×#2363	C₂	semidirect
6. C₇×#2361	C₂	semidirect
7. C₇×#2359	C₂	semidirect
8. C₇×#2354	C₂	semidirect
9. C₇×#2352	C₂	semidirect
10. C₇×#2349	C₂	semidirect
11. C₇×#2347	C₂	semidirect
12. C₇×#2344	C₂	semidirect
13. C₇×#2335	C₂	semidirect
14. C₇×#2334	C₂	semidirect
15. C₇×#2324	C₂	semidirect
16. C₇×#2324	C₂	semidirect
17. C₇×#2324	C₂	semidirect
18. C₇×#2318	C₂	semidirect
19. C₇×#2317	C₂	semidirect
20. C₇×#2316	C₂	semidirect
21. C₄×C₇×#125	C₂	semidirect
22. C₇×#2293	C₂	semidirect
23. C₇×#2293	C₂	semidirect
24. C₇×#553	C₄	semidirect
124. #34483	C₇	direct (N × H)
136. C₇×#126	C₂×C₄	semidirect
137. C₇×#125	C₂×C₄	semidirect
138. C₇×#123	C₂×C₄	semidirect
140. C₇×#121	C₂×C₄	semidirect
141. C₇×#121	C₂×C₄	semidirect
145. C₄×C₇×D₄	C₂×C₄	semidirect
146. C₄×C₇×D₄	C₂×C₄	semidirect
147. C₄×C₇×D₄	C₂×C₄	semidirect
153. C₇×#117	C₂×C₄	semidirect
155. C₂×C₇×C₄⋊C₄	C₂×C₄	semidirect
245. #2383	C₂×C₇	semidirect
246. #2377	C₂×C₇	semidirect
247. #2370	C₂×C₇	semidirect
248. #2363	C₂×C₇	semidirect
249. #2361	C₂×C₇	semidirect
250. #2359	C₂×C₇	semidirect
251. #2354	C₂×C₇	semidirect
252. #2352	C₂×C₇	semidirect
253. #2349	C₂×C₇	semidirect
254. #2347	C₂×C₇	semidirect
255. #2344	C₂×C₇	semidirect
256. #2335	C₂×C₇	semidirect
257. #2334	C₂×C₇	semidirect
258. #2324	C₂×C₇	semidirect
259. #2324	C₂×C₇	semidirect
260. #2324	C₂×C₇	semidirect
261. #2318	C₂×C₇	semidirect
262. #2317	C₂×C₇	semidirect
263. #2316	C₂×C₇	semidirect
264. C₄×#125	C₂×C₇	semidirect
265. #2293	C₂×C₇	semidirect
266. #2293	C₂×C₇	semidirect
388. #553	C₄×C₇	semidirect
592. #126	C₂×C₄×C₇	semidirect
593. #125	C₂×C₄×C₇	semidirect
594. #123	C₂×C₄×C₇	semidirect
596. #121	C₂×C₄×C₇	semidirect
597. #121	C₂×C₄×C₇	semidirect
601. C₄×D₄	C₂×C₄×C₇	semidirect
602. C₄×D₄	C₂×C₄×C₇	semidirect
603. C₄×D₄	C₂×C₄×C₇	semidirect
609. #117	C₂×C₄×C₇	semidirect
611. C₂×C₄⋊C₄	C₂×C₄×C₇	semidirect
972. C₇	#34483	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#553	2
C₇×#2383	2
C₇×#2377	2
C₇×#2370	2
C₇×#2363	2
C₇×#2361	2
C₇×#2359	2
C₇×#2354	2
C₇×#2352	2
C₇×#2349	2
C₇×#2347	2
C₇×#2344	2
C₇×#2335	2
C₇×#2334	2
C₇×#2324	2
C₇×#2318	2
C₇×#2317	2
C₇×#2316	2
C₄×C₇×#125	2
C₇×#2293	2
#34483	7

Subgroups — C7×#34483 #13211699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34483 #13211699