Subgroups — C₇×#34997 #13212213

Order 1792.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2849	C₂	1	2	yes	maximal, complemented
2	C₇×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2847	C₂	1	1	yes	maximal, characteristic
4	C₇×#2646	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2643	C₂	1	2	yes	maximal, complemented
6	C₇×#2639	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2510	C₂	1	2	yes	maximal, complemented
8	C₇×#2505	C₂	1	2	yes	maximal, complemented
9	C₇×#2493	C₂	1	2	yes	maximal, complemented
10	C₇×#2488	C₂	1	2	yes	maximal, complemented
11	C₇×#2450	C₂	1	2	yes	maximal, complemented
12	C₇×#2444	C₂	1	2	yes	maximal, complemented
13	C₇×#2425	C₂	1	2	yes	maximal, complemented
14	C₇×#2419	C₂	1	2	yes	maximal, complemented
15	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2325	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×C₇×#120	C₂	1	2	yes	maximal, complemented
19	C₂²×C₇×#95	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
23	C₂×C₇×#123	C₂²	1	2	yes	—
24	C₂×C₇×#123	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#121	C₂²	1	1	yes	characteristic
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#120	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
35	C₇×#401	C₂²	1	2	yes	complemented
36	C₇×#400	C₂²	1	2	yes	complemented
37	C₇×#400	C₂²	1	2	yes	complemented
38	C₇×#400	C₂²	1	2	yes	complemented
39	C₇×#400	C₂²	1	2	yes	complemented
40	C₇×#400	C₂²	1	2	yes	complemented
41	C₇×#400	C₂²	1	2	yes	complemented
42	C₇×#398	C₂²	1	2	yes	complemented
43	C₇×#398	C₂²	1	2	yes	complemented
44	C₇×#397	C₂²	1	2	yes	complemented
45	C₇×#397	C₂²	1	2	yes	complemented
46	C₇×#397	C₂²	1	2	yes	complemented
47	C₇×#397	C₂²	1	2	yes	complemented
48	C₇×#396	C₂²	1	2	yes	complemented
49	C₇×#394	C₂²	1	2	yes	complemented
50	C₇×#393	C₂²	1	2	yes	complemented
51	C₇×#391	C₂²	1	2	yes	complemented
52	C₇×#389	C₂²	1	2	yes	complemented
53	C₇×#388	C₂²	1	2	yes	complemented
54	C₇×#388	C₂²	1	2	yes	complemented
55	C₇×#388	C₂²	1	2	yes	complemented
56	C₇×#387	C₂²	1	2	yes	complemented
57	C₇×#387	C₂²	1	2	yes	complemented
58	C₇×#387	C₂²	1	2	yes	complemented
59	C₇×#387	C₂²	1	2	yes	complemented
60	C₇×#387	C₂²	1	2	yes	complemented
61	C₇×#386	C₂²	1	2	yes	—
62	C₇×#386	C₂²	1	2	yes	—
63	C₇×#386	C₂²	1	2	yes	—
64	C₇×#386	C₂²	1	2	yes	—
65	C₇×#386	C₂²	1	2	yes	—
66	C₇×#386	C₂²	1	2	yes	—
67	C₇×#386	C₂²	1	2	yes	—
68	C₇×#386	C₂²	1	2	yes	—
69	C₇×#386	C₂²	1	2	yes	—
70	C₇×#386	C₂²	1	2	yes	—
71	C₇×#386	C₂²	1	2	yes	complemented
72	C₇×#385	C₂²	1	2	yes	—
73	C₇×#385	C₂²	1	2	yes	—
74	C₇×#385	C₂²	1	2	yes	—
75	C₇×#385	C₂²	1	2	yes	—
76	C₇×#385	C₂²	1	2	yes	—
77	C₇×#385	C₂²	1	2	yes	—
78	C₇×#385	C₂²	1	2	yes	—
79	C₇×#385	C₂²	1	2	yes	—
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	complemented
83	C₇×#383	C₂²	1	2	yes	complemented
84	C₇×#382	C₂²	1	2	yes	complemented
85	C₇×#381	C₂²	1	2	yes	—
86	C₇×#381	C₂²	1	2	yes	—
87	C₇×#381	C₂²	1	2	yes	complemented
88	C₇×#380	C₂²	1	1	yes	characteristic
89	C₇×#380	C₂²	1	1	yes	characteristic
90	C₇×#380	C₂²	1	1	yes	characteristic
91	C₇×#380	C₂²	1	1	yes	characteristic
92	C₇×#380	C₂²	1	1	yes	characteristic
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₇×#380	C₂²	1	2	yes	complemented
95	C₇×#379	C₂²	1	2	yes	—
96	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂×C₇×#95	C₂²	1	1	yes	characteristic
100	C₂×C₇×#95	C₂²	1	1	yes	characteristic
101	C₂×C₇×#95	C₂²	1	2	yes	—
102	C₂×C₇×#95	C₂²	1	2	yes	—
103	C₂×C₇×#95	C₂²	1	2	yes	—
104	C₂×C₇×#95	C₂²	1	2	yes	—
105	C₂×C₇×#95	C₂²	1	1	yes	characteristic
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	#34997	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	2	yes	—
112	C₂²×C₇×D₄	C₂³	1	2	yes	—
113	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇	—	2	4	no	—
115	C₂³×C₄×C₇	—	2	4	no	—
116	C₂³×C₄×C₇	—	2	4	no	—
117	C₂³×C₄×C₇	—	4	2	no	—
118	C₂³×C₄×C₇	—	4	2	no	—
119	C₂³×C₄×C₇	—	4	2	no	—
120	C₂³×C₄×C₇	—	4	2	no	—
121	C₂³×C₄×C₇	—	4	2	no	—
122	C₂³×C₄×C₇	—	4	2	no	—
123	C₂³×C₄×C₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₇×#123	—	4	4	no	—
139	C₇×#123	—	4	4	no	—
140	C₇×C₂²⋊Q₈	—	2	4	no	—
141	C₇×C₂²⋊Q₈	—	4	2	no	—
142	C₇×C₂²⋊Q₈	—	4	2	no	—
143	C₇×#121	—	2	4	no	—
144	C₇×#121	—	4	2	no	—
145	C₇×#121	—	4	2	no	—
146	C₇×#120	—	2	8	no	—
147	C₄×C₇×D₄	—	2	8	no	—
148	C₄×C₇×D₄	—	4	4	no	—
149	C₄×C₇×D₄	—	4	4	no	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₇	C₂³	1	2	yes	—
187	C₂×C₄²×C₇	C₂³	1	2	yes	—
188	C₇×#95	C₂³	1	2	yes	—
189	C₇×#95	C₂³	1	2	yes	—
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	2	yes	—
214	C₇×#95	C₂³	1	2	yes	—
215	C₇×#95	C₂³	1	2	yes	—
216	#2849	C₂×C₇	1	2	yes	complemented
217	#2848	C₂×C₇	1	1	yes	characteristic, complemented
218	#2847	C₂×C₇	1	1	yes	characteristic
219	#2646	C₂×C₇	1	1	yes	characteristic, complemented
220	#2643	C₂×C₇	1	2	yes	complemented
221	#2639	C₂×C₇	1	1	yes	characteristic, complemented
222	#2510	C₂×C₇	1	2	yes	complemented
223	#2505	C₂×C₇	1	2	yes	complemented
224	#2493	C₂×C₇	1	2	yes	complemented
225	#2488	C₂×C₇	1	2	yes	complemented
226	#2450	C₂×C₇	1	2	yes	complemented
227	#2444	C₂×C₇	1	2	yes	complemented
228	#2425	C₂×C₇	1	2	yes	complemented
229	#2419	C₂×C₇	1	2	yes	complemented
230	#2329	C₂×C₇	1	1	yes	characteristic, complemented
231	#2325	C₂×C₇	1	1	yes	characteristic, complemented
232	#2318	C₂×C₇	1	2	yes	complemented
233	C₄×#120	C₂×C₇	1	2	yes	complemented
234	C₂²×#95	C₂×C₇	1	1	yes	characteristic, complemented
235	C₂⁴×C₇	—	2	2	no	—
236	C₂⁴×C₇	—	2	2	no	—
237	C₂⁴×C₇	—	2	2	no	—
238	C₂⁴×C₇	—	2	2	no	—
239	C₂⁴×C₇	—	2	2	no	—
240	C₂⁴×C₇	—	2	2	no	—
241	C₂⁴×C₇	#41	1	4	yes	—
242	C₂⁴×C₇	C₂⁴	1	2	yes	—
243	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₇×Q₈	—	2	2	no	—
247	C₂×C₇×Q₈	—	4	1	no	—
248	C₂×C₇×Q₈	—	4	1	no	—
249	C₂×C₇×D₄	—	2	4	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	4	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	2	4	no	—
256	C₂×C₇×D₄	—	2	4	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	2	2	no	—
259	C₂×C₇×D₄	—	4	1	no	—
260	C₂×C₇×D₄	—	4	1	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	2	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	4	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	4	no	—
274	C₂²×C₄×C₇	—	2	4	no	—
275	C₂²×C₄×C₇	—	2	4	no	—
276	C₂²×C₄×C₇	—	2	4	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	4	no	—
282	C₂²×C₄×C₇	—	4	1	no	—
283	C₂²×C₄×C₇	—	4	1	no	—
284	C₂²×C₄×C₇	—	4	2	no	—
285	C₂²×C₄×C₇	—	4	2	no	—
286	C₂²×C₄×C₇	—	4	1	no	—
287	C₂²×C₄×C₇	—	4	1	no	—
288	C₂²×C₄×C₇	—	4	1	no	—
289	C₂²×C₄×C₇	—	4	1	no	—
290	C₂²×C₄×C₇	—	4	1	no	—
291	C₂²×C₄×C₇	—	4	1	no	—
292	C₂²×C₄×C₇	—	4	1	no	—
293	C₂²×C₄×C₇	—	4	1	no	—
294	C₂²×C₄×C₇	—	4	1	no	—
295	C₂²×C₄×C₇	—	4	1	no	—
296	C₂²×C₄×C₇	—	4	1	no	—
297	C₂²×C₄×C₇	—	4	1	no	—
298	C₂²×C₄×C₇	—	4	2	no	—
299	C₂²×C₄×C₇	—	4	2	no	—
300	C₂²×C₄×C₇	—	4	1	no	—
301	C₂²×C₄×C₇	—	4	1	no	—
302	C₂²×C₄×C₇	—	4	2	no	—
303	C₂²×C₄×C₇	—	4	2	no	—
304	C₂²×C₄×C₇	—	4	16	no	—
305	C₂²×C₄×C₇	—	4	16	no	—
306	C₂²×C₄×C₇	—	4	16	no	—
307	C₂²×C₄×C₇	#41	1	4	yes	—
308	C₂²×C₄×C₇	#41	1	4	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
324	C₇×C₄⋊C₄	—	2	4	no	—
325	C₇×C₄⋊C₄	—	2	2	no	—
326	C₇×C₄⋊C₄	—	2	2	no	—
327	C₇×C₄⋊C₄	—	2	4	no	—
328	C₇×C₄⋊C₄	—	4	2	no	—
329	C₇×C₄⋊C₄	—	4	2	no	—
330	C₇×C₄⋊C₄	—	4	1	no	—
331	C₇×C₄⋊C₄	—	4	1	no	—
332	C₇×C₄⋊C₄	—	4	1	no	—
333	C₇×C₄⋊C₄	—	4	1	no	—
334	C₇×C₄⋊C₄	—	4	2	no	—
335	C₇×C₄⋊C₄	—	4	2	no	—
336	C₇×C₄⋊C₄	—	4	2	no	—
337	C₇×C₄⋊C₄	—	4	2	no	—
338	C₇×C₄⋊C₄	—	4	2	no	—
339	C₇×C₄⋊C₄	—	4	2	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	4	2	no	—
352	C₇×C₂²⋊C₄	—	4	2	no	—
353	C₇×C₂²⋊C₄	—	4	2	no	—
354	C₇×C₂²⋊C₄	—	4	2	no	—
355	C₇×C₂²⋊C₄	—	4	2	no	—
356	C₇×C₂²⋊C₄	—	4	2	no	—
357	C₇×C₂²⋊C₄	—	4	2	no	—
358	C₇×C₂²⋊C₄	—	4	2	no	—
359	C₄²×C₇	—	2	4	no	—
360	C₄²×C₇	—	4	2	no	—
361	C₄²×C₇	—	4	2	no	—
362	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
364	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
365	C₂×#123	C₂²×C₇	1	2	yes	—
366	C₂×#123	C₂²×C₇	1	2	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×#121	C₂²×C₇	1	1	yes	characteristic
371	C₂×#121	C₂²×C₇	1	1	yes	characteristic
372	C₂×#121	C₂²×C₇	1	1	yes	characteristic
373	C₂×#120	C₂²×C₇	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
377	#401	C₂²×C₇	1	2	yes	complemented
378	#400	C₂²×C₇	1	2	yes	complemented
379	#400	C₂²×C₇	1	2	yes	complemented
380	#400	C₂²×C₇	1	2	yes	complemented
381	#400	C₂²×C₇	1	2	yes	complemented
382	#400	C₂²×C₇	1	2	yes	complemented
383	#400	C₂²×C₇	1	2	yes	complemented
384	#398	C₂²×C₇	1	2	yes	complemented
385	#398	C₂²×C₇	1	2	yes	complemented
386	#397	C₂²×C₇	1	2	yes	complemented
387	#397	C₂²×C₇	1	2	yes	complemented
388	#397	C₂²×C₇	1	2	yes	complemented
389	#397	C₂²×C₇	1	2	yes	complemented
390	#396	C₂²×C₇	1	2	yes	complemented
391	#394	C₂²×C₇	1	2	yes	complemented
392	#393	C₂²×C₇	1	2	yes	complemented
393	#391	C₂²×C₇	1	2	yes	complemented
394	#389	C₂²×C₇	1	2	yes	complemented
395	#388	C₂²×C₇	1	2	yes	complemented
396	#388	C₂²×C₇	1	2	yes	complemented
397	#388	C₂²×C₇	1	2	yes	complemented
398	#387	C₂²×C₇	1	2	yes	complemented
399	#387	C₂²×C₇	1	2	yes	complemented
400	#387	C₂²×C₇	1	2	yes	complemented
401	#387	C₂²×C₇	1	2	yes	complemented
402	#387	C₂²×C₇	1	2	yes	complemented
403	#386	C₂²×C₇	1	2	yes	—
404	#386	C₂²×C₇	1	2	yes	—
405	#386	C₂²×C₇	1	2	yes	—
406	#386	C₂²×C₇	1	2	yes	—
407	#386	C₂²×C₇	1	2	yes	—
408	#386	C₂²×C₇	1	2	yes	—
409	#386	C₂²×C₇	1	2	yes	—
410	#386	C₂²×C₇	1	2	yes	—
411	#386	C₂²×C₇	1	2	yes	—
412	#386	C₂²×C₇	1	2	yes	—
413	#386	C₂²×C₇	1	2	yes	complemented
414	#385	C₂²×C₇	1	2	yes	—
415	#385	C₂²×C₇	1	2	yes	—
416	#385	C₂²×C₇	1	2	yes	—
417	#385	C₂²×C₇	1	2	yes	—
418	#385	C₂²×C₇	1	2	yes	—
419	#385	C₂²×C₇	1	2	yes	—
420	#385	C₂²×C₇	1	2	yes	—
421	#385	C₂²×C₇	1	2	yes	—
422	#385	C₂²×C₇	1	2	yes	—
423	#385	C₂²×C₇	1	2	yes	—
424	#385	C₂²×C₇	1	2	yes	complemented
425	#383	C₂²×C₇	1	2	yes	complemented
426	#382	C₂²×C₇	1	2	yes	complemented
427	#381	C₂²×C₇	1	2	yes	—
428	#381	C₂²×C₇	1	2	yes	—
429	#381	C₂²×C₇	1	2	yes	complemented
430	#380	C₂²×C₇	1	1	yes	characteristic
431	#380	C₂²×C₇	1	1	yes	characteristic
432	#380	C₂²×C₇	1	1	yes	characteristic
433	#380	C₂²×C₇	1	1	yes	characteristic
434	#380	C₂²×C₇	1	1	yes	characteristic
435	#380	C₂²×C₇	1	1	yes	characteristic
436	#380	C₂²×C₇	1	2	yes	complemented
437	#379	C₂²×C₇	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
441	C₂×#95	C₂²×C₇	1	1	yes	characteristic
442	C₂×#95	C₂²×C₇	1	1	yes	characteristic
443	C₂×#95	C₂²×C₇	1	1	yes	characteristic
444	C₂×#95	C₂²×C₇	1	1	yes	characteristic
445	C₂×#95	C₂²×C₇	1	2	yes	—
446	C₂×#95	C₂²×C₇	1	2	yes	—
447	C₂×#95	C₂²×C₇	1	2	yes	—
448	C₂×#95	C₂²×C₇	1	2	yes	—
449	C₂³×C₇	—	2	8	no	—
450	C₂³×C₇	—	2	8	no	—
451	C₂³×C₇	—	2	8	no	—
452	C₂³×C₇	—	2	8	no	—
453	C₂³×C₇	—	2	8	no	—
454	C₂³×C₇	—	2	8	no	—
455	C₂³×C₇	—	2	8	no	—
456	C₂³×C₇	—	2	1	no	—
457	C₂³×C₇	—	2	1	no	—
458	C₂³×C₇	—	2	1	no	—
459	C₂³×C₇	—	2	1	no	—
460	C₂³×C₇	—	2	1	no	—
461	C₂³×C₇	—	2	1	no	—
462	C₂³×C₇	—	2	1	no	—
463	C₂³×C₇	—	2	1	no	—
464	C₂³×C₇	—	2	1	no	—
465	C₂³×C₇	—	2	1	no	—
466	C₂³×C₇	—	2	1	no	—
467	C₂³×C₇	—	2	1	no	—
468	C₂³×C₇	—	2	2	no	—
469	C₂³×C₇	—	2	2	no	—
470	C₂³×C₇	—	2	2	no	—
471	C₂³×C₇	—	2	2	no	—
472	C₂³×C₇	—	2	2	no	—
473	C₂³×C₇	—	2	2	no	—
474	C₂³×C₇	—	2	2	no	—
475	C₂³×C₇	C₂×#41	1	2	yes	—
476	C₂³×C₇	C₂×#41	1	2	yes	—
477	C₂³×C₇	C₂×#41	1	2	yes	—
478	C₂³×C₇	C₂×#41	1	2	yes	—
479	C₂³×C₇	C₂×#41	1	2	yes	—
480	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
481	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
482	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
483	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
484	C₂³×C₇	C₂⁵	1	1	yes	characteristic
485	C₇×Q₈	—	8	2	no	—
486	C₇×D₄	—	4	8	no	—
487	C₇×D₄	—	4	8	no	—
488	C₇×D₄	—	4	8	no	—
489	C₇×D₄	—	8	2	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	1	no	—
493	C₂×C₄×C₇	—	2	1	no	—
494	C₂×C₄×C₇	—	2	1	no	—
495	C₂×C₄×C₇	—	2	1	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	2	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	2	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	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	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	2	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	2	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	2	no	—
527	C₂×C₄×C₇	—	2	1	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	2	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	4	4	no	—
533	C₂×C₄×C₇	—	4	4	no	—
534	C₂×C₄×C₇	—	4	8	no	—
535	C₂×C₄×C₇	—	4	8	no	—
536	C₂×C₄×C₇	—	4	4	no	—
537	C₂×C₄×C₇	—	4	4	no	—
538	C₂×C₄×C₇	—	4	4	no	—
539	C₂×C₄×C₇	—	4	4	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	—	4	4	no	—
542	C₂×C₄×C₇	—	4	8	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	4	4	no	—
545	C₂×C₄×C₇	—	4	8	no	—
546	C₂×C₄×C₇	—	8	4	no	—
547	C₂×C₄×C₇	C₂×#41	1	4	yes	—
548	C₂×C₄×C₇	C₂×#41	1	2	yes	—
549	C₂×C₄×C₇	C₂×#41	1	2	yes	—
550	C₂⁵	C₂³×C₇	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₇	1	2	yes	—
553	C₂²×D₄	C₂³×C₇	1	2	yes	—
554	C₂²×D₄	C₂³×C₇	1	2	yes	—
555	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
556	C₂³×C₄	—	2	4	no	—
557	C₂³×C₄	—	2	4	no	—
558	C₂³×C₄	—	2	4	no	—
559	C₂³×C₄	—	4	2	no	—
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	—	4	2	no	—
562	C₂³×C₄	—	4	2	no	—
563	C₂³×C₄	—	4	2	no	—
564	C₂³×C₄	—	4	2	no	—
565	C₂³×C₄	C₂³×C₇	1	2	yes	—
566	C₂³×C₄	C₂³×C₇	1	2	yes	—
567	C₂³×C₄	C₂³×C₇	1	2	yes	—
568	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
572	C₂³×C₄	C₂³×C₇	1	2	yes	—
573	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
580	#123	—	4	4	no	—
581	#123	—	4	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	4	2	no	—
584	C₂²⋊Q₈	—	4	2	no	—
585	#121	—	2	4	no	—
586	#121	—	4	2	no	—
587	#121	—	4	2	no	—
588	#120	—	2	8	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	4	4	no	—
591	C₄×D₄	—	4	4	no	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₇	1	2	yes	—
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	2	yes	—
638	#95	C₂³×C₇	1	2	yes	—
639	#95	C₂³×C₇	1	2	yes	—
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
642	#95	C₂³×C₇	1	2	yes	—
643	#95	C₂³×C₇	1	2	yes	—
644	#95	C₂³×C₇	1	2	yes	—
645	#95	C₂³×C₇	1	2	yes	—
646	#95	C₂³×C₇	1	2	yes	—
647	#95	C₂³×C₇	1	2	yes	—
648	#95	C₂³×C₇	1	2	yes	—
649	#95	C₂³×C₇	1	2	yes	—
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	#95	C₂³×C₇	1	2	yes	—
653	#95	C₂³×C₇	1	2	yes	—
654	#95	C₂³×C₇	1	2	yes	—
655	#95	C₂³×C₇	1	2	yes	—
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	2	yes	—
658	C₂²×C₇	—	2	32	no	—
659	C₂²×C₇	—	2	2	no	—
660	C₂²×C₇	—	2	2	no	—
661	C₂²×C₇	—	2	2	no	—
662	C₂²×C₇	—	2	2	no	—
663	C₂²×C₇	—	2	2	no	—
664	C₂²×C₇	—	2	2	no	—
665	C₂²×C₇	—	2	2	no	—
666	C₂²×C₇	—	2	2	no	—
667	C₂²×C₇	—	2	2	no	—
668	C₂²×C₇	—	2	2	no	—
669	C₂²×C₇	—	2	2	no	—
670	C₂²×C₇	—	2	2	no	—
671	C₂²×C₇	—	2	2	no	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	2	2	no	—
675	C₂²×C₇	—	2	2	no	—
676	C₂²×C₇	—	2	2	no	—
677	C₂²×C₇	—	4	2	no	—
678	C₂²×C₇	—	4	2	no	—
679	C₂²×C₇	—	4	2	no	—
680	C₂²×C₇	—	4	2	no	—
681	C₂²×C₇	—	4	2	no	—
682	C₂²×C₇	—	4	2	no	—
683	C₂²×C₇	—	4	2	no	—
684	C₂²×C₇	#529	1	4	yes	—
685	C₂²×C₇	#538	1	4	yes	—
686	C₂²×C₇	#539	1	4	yes	—
687	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
688	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
694	C₄×C₇	—	2	4	no	—
695	C₄×C₇	—	2	2	no	—
696	C₄×C₇	—	2	2	no	—
697	C₄×C₇	—	4	2	no	—
698	C₄×C₇	—	4	2	no	—
699	C₄×C₇	—	4	2	no	—
700	C₄×C₇	—	4	2	no	—
701	C₄×C₇	—	4	2	no	—
702	C₄×C₇	—	4	1	no	—
703	C₄×C₇	—	4	1	no	—
704	C₄×C₇	—	4	2	no	—
705	C₄×C₇	—	4	2	no	—
706	C₄×C₇	—	4	2	no	—
707	C₄×C₇	—	4	2	no	—
708	C₄×C₇	—	4	2	no	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	—	2	2	no	—
711	C₂⁴	—	2	2	no	—
712	C₂⁴	—	2	2	no	—
713	C₂⁴	—	2	2	no	—
714	C₂⁴	—	2	2	no	—
715	C₂⁴	C₇×#41	1	4	yes	—
716	C₂⁴	C₂⁴×C₇	1	2	yes	—
717	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
718	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	4	1	no	—
722	C₂×Q₈	—	4	1	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	4	1	no	—
734	C₂×D₄	—	4	1	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	4	1	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	1	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	1	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	16	no	—
779	C₂²×C₄	—	4	16	no	—
780	C₂²×C₄	—	4	16	no	—
781	C₂²×C₄	C₇×#41	1	4	yes	—
782	C₂²×C₄	C₇×#41	1	4	yes	—
783	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	—	4	1	no	—
806	C₄⋊C₄	—	4	1	no	—
807	C₄⋊C₄	—	4	1	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	4	2	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₄²	—	2	4	no	—
834	C₄²	—	4	2	no	—
835	C₄²	—	4	2	no	—
836	C₂×C₇	—	2	4	no	—
837	C₂×C₇	—	2	4	no	—
838	C₂×C₇	—	2	4	no	—
839	C₂×C₇	—	8	2	no	—
840	C₂×C₇	C₂×#529	1	1	yes	characteristic
841	C₂×C₇	C₂×#538	1	1	yes	characteristic
842	C₂×C₇	C₂×#539	1	1	yes	characteristic
843	C₂×C₇	#3490	1	1	yes	characteristic
844	C₂×C₇	#3490	1	1	yes	characteristic
845	C₂×C₇	#3492	1	1	yes	characteristic
846	C₂×C₇	#3492	1	1	yes	characteristic
847	C₂³	—	2	8	no	—
848	C₂³	—	2	8	no	—
849	C₂³	—	2	8	no	—
850	C₂³	—	2	8	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	8	no	—
864	C₂³	—	2	8	no	—
865	C₂³	—	2	8	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	C₂×C₇×#41	1	2	yes	—
874	C₂³	C₂×C₇×#41	1	2	yes	—
875	C₂³	C₂×C₇×#41	1	2	yes	—
876	C₂³	C₂×C₇×#41	1	2	yes	—
877	C₂³	C₂×C₇×#41	1	2	yes	—
878	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
879	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
880	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
881	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
882	C₂³	C₂⁵×C₇	1	1	yes	characteristic
883	Q₈	—	8	2	no	—
884	D₄	—	4	8	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	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	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	8	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	8	no	—
944	C₂×C₄	—	8	4	no	—
945	C₂×C₄	C₂×C₇×#41	1	4	yes	—
946	C₂×C₄	C₂×C₇×#41	1	2	yes	—
947	C₂×C₄	C₂×C₇×#41	1	2	yes	—
948	C₇	#34997	1	1	yes	characteristic, direct product factor, Sylow
949	C₂²	—	2	32	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	2	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	2	2	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	2	no	—
963	C₂²	—	2	2	no	—
964	C₂²	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	2	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	C₇×#529	1	4	yes	—
976	C₂²	C₇×#538	1	4	yes	—
977	C₂²	C₇×#539	1	4	yes	—
978	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
979	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
980	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
981	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
983	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
984	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
985	C₄	—	2	4	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	—	4	2	no	—
999	C₄	—	4	2	no	—
1000	C₂	—	2	4	no	—
1001	C₂	—	2	4	no	—
1002	C₂	—	2	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂×C₇×#529	1	1	yes	characteristic
1005	C₂	C₂×C₇×#538	1	1	yes	characteristic
1006	C₂	C₂×C₇×#539	1	1	yes	characteristic
1007	C₂	C₇×#3490	1	1	yes	characteristic
1008	C₂	C₇×#3490	1	1	yes	characteristic
1009	C₂	C₇×#3492	1	1	yes	characteristic
1010	C₂	C₇×#3492	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2847	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×#2849	C₂	semidirect
2. C₇×#2848	C₂	semidirect
4. C₇×#2646	C₂	semidirect
5. C₇×#2643	C₂	semidirect
6. C₇×#2639	C₂	semidirect
7. C₇×#2510	C₂	semidirect
8. C₇×#2505	C₂	semidirect
9. C₇×#2493	C₂	semidirect
10. C₇×#2488	C₂	semidirect
11. C₇×#2450	C₂	semidirect
12. C₇×#2444	C₂	semidirect
13. C₇×#2425	C₂	semidirect
14. C₇×#2419	C₂	semidirect
15. C₇×#2329	C₂	semidirect
16. C₇×#2325	C₂	semidirect
17. C₇×#2318	C₂	semidirect
18. C₄×C₇×#120	C₂	semidirect
19. C₂²×C₇×#95	C₂	semidirect
35. C₇×#401	C₂²	semidirect
36. C₇×#400	C₂²	semidirect
37. C₇×#400	C₂²	semidirect
38. C₇×#400	C₂²	semidirect
39. C₇×#400	C₂²	semidirect
40. C₇×#400	C₂²	semidirect
41. C₇×#400	C₂²	semidirect
42. C₇×#398	C₂²	semidirect
43. C₇×#398	C₂²	semidirect
44. C₇×#397	C₂²	semidirect
45. C₇×#397	C₂²	semidirect
46. C₇×#397	C₂²	semidirect
47. C₇×#397	C₂²	semidirect
48. C₇×#396	C₂²	semidirect
49. C₇×#394	C₂²	semidirect
50. C₇×#393	C₂²	semidirect
51. C₇×#391	C₂²	semidirect
52. C₇×#389	C₂²	semidirect
53. C₇×#388	C₂²	semidirect
54. C₇×#388	C₂²	semidirect
55. C₇×#388	C₂²	semidirect
56. C₇×#387	C₂²	semidirect
57. C₇×#387	C₂²	semidirect
58. C₇×#387	C₂²	semidirect
59. C₇×#387	C₂²	semidirect
60. C₇×#387	C₂²	semidirect
71. C₇×#386	C₂²	semidirect
82. C₇×#385	C₂²	semidirect
83. C₇×#383	C₂²	semidirect
84. C₇×#382	C₂²	semidirect
87. C₇×#381	C₂²	semidirect
94. C₇×#380	C₂²	semidirect
107. #34997	C₇	direct (N × H)
216. #2849	C₂×C₇	semidirect
217. #2848	C₂×C₇	semidirect
219. #2646	C₂×C₇	semidirect
220. #2643	C₂×C₇	semidirect
221. #2639	C₂×C₇	semidirect
222. #2510	C₂×C₇	semidirect
223. #2505	C₂×C₇	semidirect
224. #2493	C₂×C₇	semidirect
225. #2488	C₂×C₇	semidirect
226. #2450	C₂×C₇	semidirect
227. #2444	C₂×C₇	semidirect
228. #2425	C₂×C₇	semidirect
229. #2419	C₂×C₇	semidirect
230. #2329	C₂×C₇	semidirect
231. #2325	C₂×C₇	semidirect
232. #2318	C₂×C₇	semidirect
233. C₄×#120	C₂×C₇	semidirect
234. C₂²×#95	C₂×C₇	semidirect
377. #401	C₂²×C₇	semidirect
378. #400	C₂²×C₇	semidirect
379. #400	C₂²×C₇	semidirect
380. #400	C₂²×C₇	semidirect
381. #400	C₂²×C₇	semidirect
382. #400	C₂²×C₇	semidirect
383. #400	C₂²×C₇	semidirect
384. #398	C₂²×C₇	semidirect
385. #398	C₂²×C₇	semidirect
386. #397	C₂²×C₇	semidirect
387. #397	C₂²×C₇	semidirect
388. #397	C₂²×C₇	semidirect
389. #397	C₂²×C₇	semidirect
390. #396	C₂²×C₇	semidirect
391. #394	C₂²×C₇	semidirect
392. #393	C₂²×C₇	semidirect
393. #391	C₂²×C₇	semidirect
394. #389	C₂²×C₇	semidirect
395. #388	C₂²×C₇	semidirect
396. #388	C₂²×C₇	semidirect
397. #388	C₂²×C₇	semidirect
398. #387	C₂²×C₇	semidirect
399. #387	C₂²×C₇	semidirect
400. #387	C₂²×C₇	semidirect
401. #387	C₂²×C₇	semidirect
402. #387	C₂²×C₇	semidirect
413. #386	C₂²×C₇	semidirect
424. #385	C₂²×C₇	semidirect
425. #383	C₂²×C₇	semidirect
426. #382	C₂²×C₇	semidirect
429. #381	C₂²×C₇	semidirect
436. #380	C₂²×C₇	semidirect
948. C₇	#34997	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×#2849	2
C₇×#2848	2
C₇×#2847	2
C₇×#2646	2
C₇×#2643	2
C₇×#2639	2
C₇×#2510	2
C₇×#2505	2
C₇×#2493	2
C₇×#2488	2
C₇×#2450	2
C₇×#2444	2
C₇×#2425	2
C₇×#2419	2
C₇×#2329	2
C₇×#2325	2
C₇×#2318	2
C₄×C₇×#120	2
C₂²×C₇×#95	2
#34997	7

Subgroups — C7×#34997 #13212213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34997 #13212213