Subgroups — C₇×#62020 #13239236

Order 1792.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3561	C₂	1	1	yes	maximal, characteristic
2	C₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3398	C₂	1	2	yes	maximal, complemented
4	C₇×#3377	C₂	1	2	yes	maximal, complemented
5	C₇×#3313	C₂	1	2	yes	maximal, complemented
6	C₇×#3312	C₂	1	2	yes	maximal, complemented
7	C₇×#3296	C₂	1	2	yes	maximal, complemented
8	C₇×D₄×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₇×#3266	C₂	1	2	yes	maximal, complemented
11	C₇×#3258	C₂	1	2	yes	maximal, complemented
12	C₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3223	C₂	1	2	yes	maximal, complemented
14	C₇×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3121	C₂	1	2	yes	maximal, complemented
16	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3044	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#137	C₂²	1	2	yes	—
21	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×Q₁₆	C₂²	1	2	yes	complemented
23	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
24	C₇×#563	—	2	1	no	—
25	C₇×#562	—	2	1	no	—
26	C₇×#557	—	2	1	no	—
27	C₇×#557	C₂²	1	1	yes	characteristic, complemented
28	C₇×#557	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	—	2	1	no	—
30	C₇×#556	C₂²	1	2	yes	—
31	C₇×#556	C₂²	1	1	yes	characteristic, complemented
32	C₇×#552	—	2	2	no	—
33	C₇×#552	C₂²	1	2	yes	—
34	C₇×#551	—	2	2	no	—
35	C₇×D₄×Q₈	C₂²	1	2	yes	—
36	C₇×D₄×Q₈	C₂²	1	2	yes	—
37	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#546	C₂²	1	2	yes	—
40	C₇×#543	—	2	1	no	—
41	C₇×#542	—	2	2	no	—
42	C₇×#542	C₂²	1	2	yes	—
43	C₇×#541	—	2	2	no	—
44	C₇×#541	C₂²	1	2	yes	complemented
45	C₇×#538	—	2	1	no	—
46	C₇×#536	C₂²	1	2	yes	—
47	C₇×#533	—	2	1	no	—
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#529	—	2	1	no	—
51	C₇×#529	C₂²	1	1	yes	characteristic
52	C₂×C₇×#124	C₂²	1	1	yes	characteristic
53	C₇×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
55	C₇×#497	C₂²	1	2	yes	—
56	C₇×#497	C₂²	1	2	yes	—
57	C₇×#494	C₂²	1	2	yes	complemented
58	C₇×#491	C₂²	1	2	yes	complemented
59	C₇×#489	C₂²	1	2	yes	—
60	C₇×#488	C₂²	1	2	yes	—
61	C₇×#485	C₂²	1	2	yes	complemented
62	C₇×#483	C₂²	1	2	yes	—
63	C₇×#482	C₂²	1	2	yes	—
64	C₇×#479	C₂²	1	2	yes	complemented
65	C₇×#478	C₂²	1	2	yes	—
66	C₇×#477	C₂²	1	2	yes	complemented
67	C₇×#477	C₂²	1	2	yes	complemented
68	C₇×#475	C₂²	1	1	yes	characteristic, complemented
69	C₇×#475	C₂²	1	1	yes	characteristic, complemented
70	C₇×#470	C₂²	1	2	yes	complemented
71	C₇×#468	C₂²	1	2	yes	—
72	C₇×#467	C₂²	1	2	yes	—
73	C₇×#467	C₂²	1	2	yes	—
74	C₇×#467	C₂²	1	2	yes	complemented
75	C₇×#465	C₂²	1	2	yes	—
76	C₇×#464	C₂²	1	2	yes	—
77	C₇×#464	C₂²	1	2	yes	—
78	C₇×#464	C₂²	1	2	yes	—
79	C₇×#464	C₂²	1	2	yes	—
80	C₇×#464	C₂²	1	2	yes	—
81	C₇×#464	C₂²	1	2	yes	—
82	C₇×#464	C₂²	1	2	yes	—
83	C₇×#464	C₂²	1	2	yes	—
84	C₇×#462	C₂²	1	1	yes	characteristic, complemented
85	C₇×#462	C₂²	1	2	yes	complemented
86	C₇×#462	C₂²	1	2	yes	complemented
87	C₇×#462	C₂²	1	2	yes	complemented
88	C₇×#462	C₂²	1	2	yes	complemented
89	C₇×#462	C₂²	1	1	yes	characteristic, complemented
90	C₇×#462	C₂²	1	2	yes	complemented
91	C₇×#461	C₂²	1	2	yes	—
92	C₇×#452	C₂²	1	2	yes	—
93	C₇×#452	C₂²	1	2	yes	—
94	C₇×#451	C₂²	1	2	yes	—
95	C₇×#451	C₂²	1	2	yes	—
96	C₇×#451	C₂²	1	2	yes	complemented
97	C₇×#451	C₂²	1	2	yes	complemented
98	C₇×#451	C₂²	1	2	yes	complemented
99	C₇×#450	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#441	C₂²	1	2	yes	complemented
103	C₇×#441	C₂²	1	2	yes	complemented
104	C₇×#441	C₂²	1	2	yes	complemented
105	C₇×#440	C₂²	1	2	yes	—
106	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
108	C₇×#435	C₂²	1	2	yes	—
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×C₈×D₄	C₂²	1	2	yes	—
111	C₇×#433	C₂²	1	2	yes	complemented
112	C₇×#432	C₂²	1	1	yes	characteristic
113	C₇×#424	C₂²	1	2	yes	complemented
114	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₇×#419	C₂²	1	2	yes	complemented
116	C₇×#416	C₂²	1	2	yes	—
117	C₂×C₇×#103	C₂²	1	1	yes	characteristic
118	C₂×C₇×#102	C₂²	1	1	yes	characteristic
119	#62020	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	C₂³	1	2	yes	—
121	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
122	C₂²×C₇×Q₈	C₂³	1	2	yes	—
123	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
124	C₂²×C₇×Q₈	C₂³	1	2	yes	—
125	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₇×#137	—	4	4	no	—
127	C₂×C₇×Q₁₆	—	4	2	no	—
128	C₂×C₇×Q₁₆	—	4	4	no	—
129	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
130	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
135	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
136	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
137	C₂×C₇×SD₁₆	—	4	2	no	—
138	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
142	C₂×C₇×M₁₆	C₂³	1	2	yes	—
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₂²×C₇×C₈	C₂³	1	2	yes	—
146	C₇×C₄⋊Q₈	—	2	1	no	—
147	C₇×C₄⋊Q₈	—	2	1	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	—	2	2	no	—
150	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₇×#126	—	2	2	no	—
157	C₇×#126	—	2	2	no	—
158	C₇×#126	—	2	2	no	—
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	—	2	2	no	—
162	C₇×#126	—	2	2	no	—
163	C₇×#126	D₄	1	2	yes	—
164	C₇×#125	—	2	1	no	—
165	C₇×#125	—	2	2	no	—
166	C₇×#125	—	2	2	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	2	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	1	no	—
171	C₇×#125	—	2	1	no	—
172	C₇×#125	D₄	1	1	yes	characteristic
173	C₇×#125	C₂³	1	2	yes	—
174	C₇×#124	—	2	1	no	—
175	C₇×#124	—	2	2	no	—
176	C₇×#124	—	2	2	no	—
177	C₇×#124	—	2	1	no	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	D₄	1	1	yes	characteristic
180	C₇×#124	C₂³	1	2	yes	—
181	C₇×#124	C₂³	1	2	yes	—
182	C₇×#124	C₂³	1	2	yes	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×#123	—	2	2	no	—
187	C₇×#123	—	2	2	no	—
188	C₇×#123	D₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	1	no	—
191	C₇×C₂²⋊Q₈	—	2	1	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₇×#121	—	2	2	no	—
208	C₇×#121	—	2	2	no	—
209	C₇×#121	D₄	1	1	yes	characteristic
210	C₇×#121	C₂³	1	2	yes	—
211	C₇×#120	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	2	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	1	no	—
220	C₄×C₇×Q₈	—	2	1	no	—
221	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
225	C₄×C₇×Q₈	C₂³	1	2	yes	—
226	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×Q₈	C₂³	1	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	2	yes	—
230	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×D₄	—	2	2	no	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	2	no	—
234	C₄×C₇×D₄	—	2	2	no	—
235	C₄×C₇×D₄	C₂³	1	2	yes	—
236	C₄×C₇×D₄	C₂³	1	2	yes	—
237	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
238	C₇×#117	—	2	1	no	—
239	C₇×#117	—	2	1	no	—
240	C₇×#117	—	2	2	no	—
241	C₇×#117	—	2	2	no	—
242	C₇×#117	—	2	2	no	—
243	C₇×#117	—	2	2	no	—
244	C₇×#117	C₂³	1	2	yes	—
245	C₇×#117	C₂³	1	2	yes	—
246	C₂×C₇×C₄⋊C₄	—	2	1	no	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²×C₇	—	2	1	no	—
252	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
253	C₇×#107	C₂³	1	2	yes	—
254	C₇×#107	C₂³	1	2	yes	—
255	C₇×#106	C₂³	1	2	yes	—
256	C₇×#106	C₂³	1	2	yes	—
257	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₈	C₂³	1	2	yes	—
260	C₇×C₄⋊C₈	C₂³	1	2	yes	—
261	C₇×C₄⋊C₈	C₂³	1	2	yes	—
262	C₇×C₄⋊C₈	C₂³	1	2	yes	—
263	C₇×#103	C₂³	1	2	yes	—
264	C₇×#103	C₂³	1	2	yes	—
265	C₇×#103	C₂³	1	2	yes	—
266	C₇×#103	C₂³	1	2	yes	—
267	C₇×#103	C₂³	1	2	yes	—
268	C₇×#103	C₂³	1	2	yes	—
269	C₇×#103	C₂³	1	2	yes	—
270	C₇×#103	C₂³	1	2	yes	—
271	C₇×#103	C₂³	1	2	yes	—
272	C₇×#103	C₂³	1	2	yes	—
273	C₇×#103	C₂³	1	2	yes	—
274	C₇×#103	C₂³	1	2	yes	—
275	C₇×#102	C₂³	1	2	yes	—
276	C₇×#102	C₂³	1	2	yes	—
277	C₇×#102	C₂³	1	2	yes	—
278	C₇×#102	C₂³	1	2	yes	—
279	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₇×#97	C₂³	1	2	yes	—
283	C₇×#97	C₂³	1	2	yes	—
284	C₄×C₇×C₈	C₂³	1	2	yes	—
285	#3561	C₂×C₇	1	1	yes	characteristic
286	#3523	C₂×C₇	1	1	yes	characteristic, complemented
287	#3398	C₂×C₇	1	2	yes	complemented
288	#3377	C₂×C₇	1	2	yes	complemented
289	#3313	C₂×C₇	1	2	yes	complemented
290	#3312	C₂×C₇	1	2	yes	complemented
291	#3296	C₂×C₇	1	2	yes	complemented
292	D₄×Q₁₆	C₂×C₇	1	2	yes	complemented
293	#3270	C₂×C₇	1	2	yes	complemented
294	#3266	C₂×C₇	1	2	yes	complemented
295	#3258	C₂×C₇	1	2	yes	complemented
296	#3249	C₂×C₇	1	1	yes	characteristic, complemented
297	#3223	C₂×C₇	1	2	yes	complemented
298	#3215	C₂×C₇	1	1	yes	characteristic, complemented
299	#3121	C₂×C₇	1	2	yes	complemented
300	#3113	C₂×C₇	1	1	yes	characteristic, complemented
301	#3044	C₂×C₇	1	2	yes	complemented
302	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
303	#2992	C₂×C₇	1	1	yes	characteristic, complemented
304	C₂⁴×C₇	—	2	1	no	—
305	C₇×#41	—	4	2	no	—
306	C₇×#41	—	4	2	no	—
307	C₂×C₇×Q₈	—	2	1	no	—
308	C₂×C₇×Q₈	—	2	2	no	—
309	C₂×C₇×Q₈	—	2	1	no	—
310	C₂×C₇×Q₈	—	2	1	no	—
311	C₂×C₇×Q₈	—	2	2	no	—
312	C₂×C₇×Q₈	—	2	1	no	—
313	C₂×C₇×Q₈	—	2	2	no	—
314	C₂×C₇×Q₈	—	2	4	no	—
315	C₂×C₇×Q₈	—	4	1	no	—
316	C₂×C₇×Q₈	—	4	2	no	—
317	C₂×C₇×Q₈	—	4	1	no	—
318	C₂×C₇×Q₈	—	4	2	no	—
319	C₂×C₇×Q₈	—	4	1	no	—
320	C₂×C₇×Q₈	—	4	2	no	—
321	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
322	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
323	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
324	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
326	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×C₇×D₄	—	2	2	no	—
328	C₂×C₇×D₄	—	2	2	no	—
329	C₂×C₇×D₄	—	2	1	no	—
330	C₂×C₇×D₄	—	4	1	no	—
331	C₂×C₇×D₄	—	4	1	no	—
332	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
333	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
334	C₂×C₇×D₄	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₇	—	2	1	no	—
336	C₂²×C₄×C₇	—	2	1	no	—
337	C₂²×C₄×C₇	—	2	2	no	—
338	C₂²×C₄×C₇	—	2	1	no	—
339	C₂²×C₄×C₇	—	2	2	no	—
340	C₂²×C₄×C₇	—	2	2	no	—
341	C₂²×C₄×C₇	—	2	2	no	—
342	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
346	C₇×Q₁₆	—	2	4	no	—
347	C₇×Q₁₆	—	2	4	no	—
348	C₇×Q₁₆	—	4	2	no	—
349	C₇×Q₁₆	—	4	2	no	—
350	C₇×Q₁₆	—	4	2	no	—
351	C₇×Q₁₆	—	4	2	no	—
352	C₇×Q₁₆	—	4	2	no	—
353	C₇×Q₁₆	—	4	2	no	—
354	C₇×SD₁₆	—	2	4	no	—
355	C₇×SD₁₆	—	4	2	no	—
356	C₇×SD₁₆	—	4	2	no	—
357	C₇×SD₁₆	—	4	2	no	—
358	C₇×M₁₆	—	4	2	no	—
359	C₂×C₇×C₈	—	4	1	no	—
360	C₂×C₇×C₈	—	4	1	no	—
361	C₂×C₇×C₈	—	4	2	no	—
362	C₂×C₇×C₈	C₂⁴	1	2	yes	—
363	C₂×C₇×C₈	C₂⁴	1	2	yes	—
364	C₂×C₇×C₈	C₂⁴	1	2	yes	—
365	C₂×C₇×C₈	C₂⁴	1	2	yes	—
366	C₇×C₄⋊C₄	—	2	1	no	—
367	C₇×C₄⋊C₄	—	2	1	no	—
368	C₇×C₄⋊C₄	—	2	1	no	—
369	C₇×C₄⋊C₄	—	2	1	no	—
370	C₇×C₄⋊C₄	—	2	1	no	—
371	C₇×C₄⋊C₄	—	2	2	no	—
372	C₇×C₄⋊C₄	—	2	2	no	—
373	C₇×C₄⋊C₄	—	2	2	no	—
374	C₇×C₄⋊C₄	—	2	2	no	—
375	C₇×C₄⋊C₄	—	2	1	no	—
376	C₇×C₄⋊C₄	—	2	1	no	—
377	C₇×C₄⋊C₄	—	2	2	no	—
378	C₇×C₄⋊C₄	—	2	1	no	—
379	C₇×C₄⋊C₄	—	2	1	no	—
380	C₇×C₄⋊C₄	—	2	2	no	—
381	C₇×C₄⋊C₄	—	2	1	no	—
382	C₇×C₄⋊C₄	—	2	2	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	2	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₇×C₂²⋊C₄	—	2	2	no	—
404	C₇×C₂²⋊C₄	—	2	2	no	—
405	C₇×C₂²⋊C₄	—	2	2	no	—
406	C₇×C₂²⋊C₄	—	2	2	no	—
407	C₇×C₂²⋊C₄	—	2	2	no	—
408	C₇×C₂²⋊C₄	—	2	2	no	—
409	C₇×C₂²⋊C₄	—	2	2	no	—
410	C₇×C₂²⋊C₄	—	2	2	no	—
411	C₇×C₂²⋊C₄	—	2	2	no	—
412	C₇×C₂²⋊C₄	—	2	2	no	—
413	C₇×C₂²⋊C₄	—	2	2	no	—
414	C₇×C₂²⋊C₄	—	2	2	no	—
415	C₇×C₂²⋊C₄	—	2	2	no	—
416	C₇×C₂²⋊C₄	—	2	2	no	—
417	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
418	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
421	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₄²×C₇	—	2	1	no	—
423	C₄²×C₇	—	2	1	no	—
424	C₄²×C₇	—	2	1	no	—
425	C₄²×C₇	—	2	1	no	—
426	C₄²×C₇	—	2	2	no	—
427	C₄²×C₇	—	2	2	no	—
428	C₄²×C₇	—	2	2	no	—
429	C₄²×C₇	—	2	2	no	—
430	C₄²×C₇	—	2	2	no	—
431	C₄²×C₇	—	2	2	no	—
432	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₇	C₂⁴	1	2	yes	—
435	C₄²×C₇	C₂⁴	1	1	yes	characteristic
436	C₄²×C₇	C₂⁴	1	1	yes	characteristic
437	C₂×#137	C₂²×C₇	1	2	yes	—
438	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
439	C₂²×Q₁₆	C₂²×C₇	1	2	yes	complemented
440	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
441	#563	—	2	1	no	—
442	#562	—	2	1	no	—
443	#557	—	2	1	no	—
444	#557	C₂²×C₇	1	1	yes	characteristic, complemented
445	#557	C₂²×C₇	1	1	yes	characteristic, complemented
446	#556	—	2	1	no	—
447	#556	C₂²×C₇	1	2	yes	—
448	#556	C₂²×C₇	1	1	yes	characteristic, complemented
449	#552	—	2	2	no	—
450	#552	C₂²×C₇	1	2	yes	—
451	#551	—	2	2	no	—
452	D₄×Q₈	C₂²×C₇	1	2	yes	—
453	D₄×Q₈	C₂²×C₇	1	2	yes	—
454	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
455	#548	C₂²×C₇	1	2	yes	—
456	#546	C₂²×C₇	1	2	yes	—
457	#543	—	2	1	no	—
458	#542	—	2	2	no	—
459	#542	C₂²×C₇	1	2	yes	—
460	#541	—	2	2	no	—
461	#541	C₂²×C₇	1	2	yes	complemented
462	#538	—	2	1	no	—
463	#536	C₂²×C₇	1	2	yes	—
464	#533	—	2	1	no	—
465	#533	C₂²×C₇	1	1	yes	characteristic
466	#533	C₂²×C₇	1	1	yes	characteristic
467	#529	—	2	1	no	—
468	#529	C₂²×C₇	1	1	yes	characteristic
469	C₂×#124	C₂²×C₇	1	1	yes	characteristic
470	#519	C₂²×C₇	1	2	yes	complemented
471	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
472	#497	C₂²×C₇	1	2	yes	—
473	#497	C₂²×C₇	1	2	yes	—
474	#494	C₂²×C₇	1	2	yes	complemented
475	#491	C₂²×C₇	1	2	yes	complemented
476	#489	C₂²×C₇	1	2	yes	—
477	#488	C₂²×C₇	1	2	yes	—
478	#485	C₂²×C₇	1	2	yes	complemented
479	#483	C₂²×C₇	1	2	yes	—
480	#482	C₂²×C₇	1	2	yes	—
481	#479	C₂²×C₇	1	2	yes	complemented
482	#478	C₂²×C₇	1	2	yes	—
483	#477	C₂²×C₇	1	2	yes	complemented
484	#477	C₂²×C₇	1	2	yes	complemented
485	#475	C₂²×C₇	1	1	yes	characteristic, complemented
486	#475	C₂²×C₇	1	1	yes	characteristic, complemented
487	#470	C₂²×C₇	1	2	yes	complemented
488	#468	C₂²×C₇	1	2	yes	—
489	#467	C₂²×C₇	1	2	yes	—
490	#467	C₂²×C₇	1	2	yes	—
491	#467	C₂²×C₇	1	2	yes	complemented
492	#465	C₂²×C₇	1	2	yes	—
493	#464	C₂²×C₇	1	2	yes	—
494	#464	C₂²×C₇	1	2	yes	—
495	#464	C₂²×C₇	1	2	yes	—
496	#464	C₂²×C₇	1	2	yes	—
497	#464	C₂²×C₇	1	2	yes	—
498	#464	C₂²×C₇	1	2	yes	—
499	#464	C₂²×C₇	1	2	yes	—
500	#464	C₂²×C₇	1	2	yes	—
501	#462	C₂²×C₇	1	1	yes	characteristic, complemented
502	#462	C₂²×C₇	1	1	yes	characteristic, complemented
503	#462	C₂²×C₇	1	2	yes	complemented
504	#462	C₂²×C₇	1	2	yes	complemented
505	#462	C₂²×C₇	1	2	yes	complemented
506	#462	C₂²×C₇	1	2	yes	complemented
507	#462	C₂²×C₇	1	2	yes	complemented
508	#461	C₂²×C₇	1	2	yes	—
509	#452	C₂²×C₇	1	2	yes	—
510	#452	C₂²×C₇	1	2	yes	—
511	#451	C₂²×C₇	1	2	yes	—
512	#451	C₂²×C₇	1	2	yes	—
513	#451	C₂²×C₇	1	2	yes	complemented
514	#451	C₂²×C₇	1	2	yes	complemented
515	#451	C₂²×C₇	1	2	yes	complemented
516	#450	C₂²×C₇	1	2	yes	—
517	#448	C₂²×C₇	1	2	yes	—
518	#446	C₂²×C₇	1	2	yes	complemented
519	#441	C₂²×C₇	1	2	yes	complemented
520	#441	C₂²×C₇	1	2	yes	complemented
521	#441	C₂²×C₇	1	2	yes	complemented
522	#440	C₂²×C₇	1	2	yes	—
523	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
524	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
525	#435	C₂²×C₇	1	2	yes	—
526	#435	C₂²×C₇	1	2	yes	complemented
527	C₈×D₄	C₂²×C₇	1	2	yes	—
528	#433	C₂²×C₇	1	2	yes	complemented
529	#432	C₂²×C₇	1	1	yes	characteristic
530	#424	C₂²×C₇	1	2	yes	complemented
531	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
532	#419	C₂²×C₇	1	2	yes	complemented
533	#416	C₂²×C₇	1	2	yes	—
534	C₂×#103	C₂²×C₇	1	1	yes	characteristic
535	C₂×#102	C₂²×C₇	1	1	yes	characteristic
536	C₂³×C₇	—	2	2	no	—
537	C₂³×C₇	—	4	2	no	—
538	C₂³×C₇	—	8	1	no	—
539	C₂³×C₇	—	8	1	no	—
540	C₂³×C₇	C₂²×D₄	1	2	yes	—
541	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
542	C₇×Q₈	—	2	1	no	—
543	C₇×Q₈	—	2	1	no	—
544	C₇×Q₈	—	2	2	no	—
545	C₇×Q₈	—	2	2	no	—
546	C₇×Q₈	—	2	2	no	—
547	C₇×Q₈	—	2	2	no	—
548	C₇×Q₈	—	2	1	no	—
549	C₇×Q₈	—	2	2	no	—
550	C₇×Q₈	—	2	2	no	—
551	C₇×Q₈	—	4	1	no	—
552	C₇×Q₈	—	4	4	no	—
553	C₇×Q₈	—	4	2	no	—
554	C₇×Q₈	—	4	2	no	—
555	C₇×Q₈	—	8	1	no	—
556	C₇×Q₈	—	8	2	no	—
557	C₇×Q₈	—	8	1	no	—
558	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
559	C₇×D₄	—	2	4	no	—
560	C₇×D₄	—	2	2	no	—
561	C₇×D₄	—	2	2	no	—
562	C₇×D₄	—	4	1	no	—
563	C₇×D₄	—	8	1	no	—
564	C₇×D₄	—	8	2	no	—
565	C₇×D₄	—	8	2	no	—
566	C₂×C₄×C₇	—	2	2	no	—
567	C₂×C₄×C₇	—	2	1	no	—
568	C₂×C₄×C₇	—	2	1	no	—
569	C₂×C₄×C₇	—	2	2	no	—
570	C₂×C₄×C₇	—	2	1	no	—
571	C₂×C₄×C₇	—	2	2	no	—
572	C₂×C₄×C₇	—	2	1	no	—
573	C₂×C₄×C₇	—	2	2	no	—
574	C₂×C₄×C₇	—	2	2	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	1	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	—	4	1	no	—
581	C₂×C₄×C₇	—	4	2	no	—
582	C₂×C₄×C₇	—	4	4	no	—
583	C₂×C₄×C₇	—	4	2	no	—
584	C₂×C₄×C₇	—	8	2	no	—
585	C₂×C₄×C₇	—	8	2	no	—
586	C₂×C₄×C₇	—	8	2	no	—
587	C₂×C₄×C₇	—	8	1	no	—
588	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
589	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
593	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
594	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
595	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
597	C₇×C₈	—	2	2	no	—
598	C₇×C₈	—	2	2	no	—
599	C₇×C₈	—	2	2	no	—
600	C₇×C₈	—	2	2	no	—
601	C₂×#41	C₂³×C₇	1	2	yes	—
602	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
603	C₂²×Q₈	C₂³×C₇	1	2	yes	—
604	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
605	C₂²×Q₈	C₂³×C₇	1	2	yes	—
606	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
607	#137	—	4	4	no	—
608	C₂×Q₁₆	—	4	2	no	—
609	C₂×Q₁₆	—	4	4	no	—
610	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
611	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
612	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
613	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
615	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
616	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
617	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
618	C₂×SD₁₆	—	4	2	no	—
619	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
623	C₂×M₁₆	C₂³×C₇	1	2	yes	—
624	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₇	1	2	yes	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	1	no	—
629	C₄⋊Q₈	—	2	2	no	—
630	C₄⋊Q₈	—	2	2	no	—
631	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
635	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
636	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	C₇×D₄	1	2	yes	—
645	#125	—	2	1	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	C₇×D₄	1	1	yes	characteristic
654	#125	C₂³×C₇	1	2	yes	—
655	#124	—	2	1	no	—
656	#124	—	2	2	no	—
657	#124	—	2	2	no	—
658	#124	—	2	1	no	—
659	#124	—	2	1	no	—
660	#124	C₇×D₄	1	1	yes	characteristic
661	#124	C₂³×C₇	1	2	yes	—
662	#124	C₂³×C₇	1	2	yes	—
663	#124	C₂³×C₇	1	2	yes	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	C₇×D₄	1	2	yes	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
683	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
684	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
685	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	C₇×D₄	1	1	yes	characteristic
691	#121	C₂³×C₇	1	2	yes	—
692	#120	—	2	2	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	2	no	—
695	C₄×Q₈	—	2	2	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	—	2	1	no	—
699	C₄×Q₈	—	2	1	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
705	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
706	C₄×Q₈	C₂³×C₇	1	2	yes	—
707	C₄×Q₈	C₂³×C₇	1	2	yes	—
708	C₄×Q₈	C₂³×C₇	1	2	yes	—
709	C₄×Q₈	C₂³×C₇	1	2	yes	—
710	C₄×Q₈	C₂³×C₇	1	2	yes	—
711	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	C₂³×C₇	1	2	yes	—
717	C₄×D₄	C₂³×C₇	1	2	yes	—
718	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
719	#117	—	2	1	no	—
720	#117	—	2	1	no	—
721	#117	—	2	2	no	—
722	#117	—	2	2	no	—
723	#117	—	2	2	no	—
724	#117	—	2	2	no	—
725	#117	C₂³×C₇	1	2	yes	—
726	#117	C₂³×C₇	1	2	yes	—
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	—	2	1	no	—
730	C₂×C₂²⋊C₄	—	2	1	no	—
731	C₂×C₂²⋊C₄	—	2	2	no	—
732	C₂×C₄²	—	2	1	no	—
733	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
734	#107	C₂³×C₇	1	2	yes	—
735	#107	C₂³×C₇	1	2	yes	—
736	#106	C₂³×C₇	1	2	yes	—
737	#106	C₂³×C₇	1	2	yes	—
738	C₄⋊C₈	C₂³×C₇	1	2	yes	—
739	C₄⋊C₈	C₂³×C₇	1	2	yes	—
740	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
741	C₄⋊C₈	C₂³×C₇	1	2	yes	—
742	C₄⋊C₈	C₂³×C₇	1	2	yes	—
743	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
744	#103	C₂³×C₇	1	2	yes	—
745	#103	C₂³×C₇	1	2	yes	—
746	#103	C₂³×C₇	1	2	yes	—
747	#103	C₂³×C₇	1	2	yes	—
748	#103	C₂³×C₇	1	2	yes	—
749	#103	C₂³×C₇	1	2	yes	—
750	#103	C₂³×C₇	1	2	yes	—
751	#103	C₂³×C₇	1	2	yes	—
752	#103	C₂³×C₇	1	2	yes	—
753	#103	C₂³×C₇	1	2	yes	—
754	#103	C₂³×C₇	1	2	yes	—
755	#103	C₂³×C₇	1	2	yes	—
756	#102	C₂³×C₇	1	2	yes	—
757	#102	C₂³×C₇	1	2	yes	—
758	#102	C₂³×C₇	1	2	yes	—
759	#102	C₂³×C₇	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
763	#97	C₂³×C₇	1	2	yes	—
764	#97	C₂³×C₇	1	2	yes	—
765	C₄×C₈	C₂³×C₇	1	2	yes	—
766	C₂²×C₇	—	2	1	no	—
767	C₂²×C₇	—	2	1	no	—
768	C₂²×C₇	—	2	2	no	—
769	C₂²×C₇	—	2	2	no	—
770	C₂²×C₇	—	2	2	no	—
771	C₂²×C₇	—	4	2	no	—
772	C₂²×C₇	—	4	2	no	—
773	C₂²×C₇	—	4	2	no	—
774	C₂²×C₇	—	16	2	no	—
775	C₂²×C₇	#578	1	2	yes	—
776	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
777	C₄×C₇	—	2	1	no	—
778	C₄×C₇	—	2	1	no	—
779	C₄×C₇	—	2	2	no	—
780	C₄×C₇	—	2	2	no	—
781	C₄×C₇	—	2	1	no	—
782	C₄×C₇	—	2	2	no	—
783	C₄×C₇	—	2	1	no	—
784	C₄×C₇	—	2	1	no	—
785	C₄×C₇	—	2	2	no	—
786	C₄×C₇	—	4	2	no	—
787	C₄×C₇	—	4	2	no	—
788	C₄×C₇	—	4	1	no	—
789	C₄×C₇	—	4	2	no	—
790	C₄×C₇	—	4	2	no	—
791	C₄×C₇	—	4	2	no	—
792	C₄×C₇	—	4	1	no	—
793	C₄×C₇	—	4	1	no	—
794	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
795	C₄×C₇	#585	1	1	yes	characteristic
796	C₂⁴	—	2	1	no	—
797	#41	—	4	2	no	—
798	#41	—	4	2	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	2	4	no	—
807	C₂×Q₈	—	4	1	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	1	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	—	4	1	no	—
812	C₂×Q₈	—	4	2	no	—
813	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
814	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
815	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
816	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
817	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
818	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	4	1	no	—
823	C₂×D₄	—	4	1	no	—
824	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
825	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
826	C₂×D₄	C₂⁴×C₇	1	2	yes	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
835	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
838	Q₁₆	—	2	4	no	—
839	Q₁₆	—	2	4	no	—
840	Q₁₆	—	4	2	no	—
841	Q₁₆	—	4	2	no	—
842	Q₁₆	—	4	2	no	—
843	Q₁₆	—	4	2	no	—
844	Q₁₆	—	4	2	no	—
845	Q₁₆	—	4	2	no	—
846	SD₁₆	—	2	4	no	—
847	SD₁₆	—	4	2	no	—
848	SD₁₆	—	4	2	no	—
849	SD₁₆	—	4	2	no	—
850	M₁₆	—	4	2	no	—
851	C₂×C₈	—	4	1	no	—
852	C₂×C₈	—	4	1	no	—
853	C₂×C₈	—	4	2	no	—
854	C₂×C₈	C₂⁴×C₇	1	2	yes	—
855	C₂×C₈	C₂⁴×C₇	1	2	yes	—
856	C₂×C₈	C₂⁴×C₇	1	2	yes	—
857	C₂×C₈	C₂⁴×C₇	1	2	yes	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
886	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
887	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
888	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
889	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
890	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
891	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
892	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
893	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
894	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
910	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
911	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
912	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
913	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
914	C₄²	—	2	1	no	—
915	C₄²	—	2	1	no	—
916	C₄²	—	2	1	no	—
917	C₄²	—	2	1	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	2	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	2	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
925	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
926	C₄²	C₂⁴×C₇	1	2	yes	—
927	C₄²	C₂⁴×C₇	1	1	yes	characteristic
928	C₄²	C₂⁴×C₇	1	1	yes	characteristic
929	C₂×C₇	—	2	2	no	—
930	C₂×C₇	—	4	2	no	—
931	C₂×C₇	—	8	2	no	—
932	C₂×C₇	#3488	1	1	yes	characteristic
933	C₂×C₇	C₂×#578	1	1	yes	characteristic
934	C₂×C₇	#3586	1	1	yes	characteristic
935	C₂³	—	2	2	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	8	1	no	—
938	C₂³	—	8	1	no	—
939	C₂³	C₂²×C₇×D₄	1	2	yes	—
940	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
941	Q₈	—	2	1	no	—
942	Q₈	—	2	1	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	1	no	—
948	Q₈	—	2	2	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	4	1	no	—
951	Q₈	—	4	4	no	—
952	Q₈	—	4	2	no	—
953	Q₈	—	4	2	no	—
954	Q₈	—	8	1	no	—
955	Q₈	—	8	2	no	—
956	Q₈	—	8	1	no	—
957	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
958	D₄	—	2	4	no	—
959	D₄	—	2	2	no	—
960	D₄	—	2	2	no	—
961	D₄	—	4	1	no	—
962	D₄	—	8	1	no	—
963	D₄	—	8	2	no	—
964	D₄	—	8	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	8	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	1	no	—
987	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
988	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
989	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
990	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
991	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
992	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
993	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
994	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
996	C₈	—	2	2	no	—
997	C₈	—	2	2	no	—
998	C₈	—	2	2	no	—
999	C₈	—	2	2	no	—
1000	C₇	#62020	1	1	yes	characteristic, direct product factor, Sylow
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	16	2	no	—
1010	C₂²	C₇×#578	1	2	yes	—
1011	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₄	C₇×#585	1	1	yes	characteristic
1031	C₂	—	2	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₇×#3488	1	1	yes	characteristic
1035	C₂	C₂×C₇×#578	1	1	yes	characteristic
1036	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3561	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3523	C₂	semidirect
3. C₇×#3398	C₂	semidirect
4. C₇×#3377	C₂	semidirect
5. C₇×#3313	C₂	semidirect
6. C₇×#3312	C₂	semidirect
7. C₇×#3296	C₂	semidirect
8. C₇×D₄×Q₁₆	C₂	semidirect
9. C₇×#3270	C₂	semidirect
10. C₇×#3266	C₂	semidirect
11. C₇×#3258	C₂	semidirect
12. C₇×#3249	C₂	semidirect
13. C₇×#3223	C₂	semidirect
14. C₇×#3215	C₂	semidirect
15. C₇×#3121	C₂	semidirect
16. C₇×#3113	C₂	semidirect
17. C₇×#3044	C₂	semidirect
18. C₂×C₇×#464	C₂	semidirect
19. C₇×#2992	C₂	semidirect
22. C₂²×C₇×Q₁₆	C₂²	semidirect
27. C₇×#557	C₂²	semidirect
28. C₇×#557	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
44. C₇×#541	C₂²	semidirect
53. C₇×#519	C₂²	semidirect
57. C₇×#494	C₂²	semidirect
58. C₇×#491	C₂²	semidirect
61. C₇×#485	C₂²	semidirect
64. C₇×#479	C₂²	semidirect
66. C₇×#477	C₂²	semidirect
67. C₇×#477	C₂²	semidirect
68. C₇×#475	C₂²	semidirect
69. C₇×#475	C₂²	semidirect
70. C₇×#470	C₂²	semidirect
74. C₇×#467	C₂²	semidirect
84. C₇×#462	C₂²	semidirect
85. C₇×#462	C₂²	semidirect
86. C₇×#462	C₂²	semidirect
87. C₇×#462	C₂²	semidirect
88. C₇×#462	C₂²	semidirect
89. C₇×#462	C₂²	semidirect
90. C₇×#462	C₂²	semidirect
96. C₇×#451	C₂²	semidirect
97. C₇×#451	C₂²	semidirect
98. C₇×#451	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#441	C₂²	semidirect
103. C₇×#441	C₂²	semidirect
104. C₇×#441	C₂²	semidirect
106. C₄×C₇×Q₁₆	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
111. C₇×#433	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
115. C₇×#419	C₂²	semidirect
119. #62020	C₇	direct (N × H)
286. #3523	C₂×C₇	semidirect
287. #3398	C₂×C₇	semidirect
288. #3377	C₂×C₇	semidirect
289. #3313	C₂×C₇	semidirect
290. #3312	C₂×C₇	semidirect
291. #3296	C₂×C₇	semidirect
292. D₄×Q₁₆	C₂×C₇	semidirect
293. #3270	C₂×C₇	semidirect
294. #3266	C₂×C₇	semidirect
295. #3258	C₂×C₇	semidirect
296. #3249	C₂×C₇	semidirect
297. #3223	C₂×C₇	semidirect
298. #3215	C₂×C₇	semidirect
299. #3121	C₂×C₇	semidirect
300. #3113	C₂×C₇	semidirect
301. #3044	C₂×C₇	semidirect
302. C₂×#464	C₂×C₇	semidirect
303. #2992	C₂×C₇	semidirect
439. C₂²×Q₁₆	C₂²×C₇	semidirect
444. #557	C₂²×C₇	semidirect
445. #557	C₂²×C₇	semidirect
448. #556	C₂²×C₇	semidirect
454. D₄×Q₈	C₂²×C₇	semidirect
461. #541	C₂²×C₇	semidirect
470. #519	C₂²×C₇	semidirect
474. #494	C₂²×C₇	semidirect
475. #491	C₂²×C₇	semidirect
478. #485	C₂²×C₇	semidirect
481. #479	C₂²×C₇	semidirect
483. #477	C₂²×C₇	semidirect
484. #477	C₂²×C₇	semidirect
485. #475	C₂²×C₇	semidirect
486. #475	C₂²×C₇	semidirect
487. #470	C₂²×C₇	semidirect
491. #467	C₂²×C₇	semidirect
501. #462	C₂²×C₇	semidirect
502. #462	C₂²×C₇	semidirect
503. #462	C₂²×C₇	semidirect
504. #462	C₂²×C₇	semidirect
505. #462	C₂²×C₇	semidirect
506. #462	C₂²×C₇	semidirect
507. #462	C₂²×C₇	semidirect
513. #451	C₂²×C₇	semidirect
514. #451	C₂²×C₇	semidirect
515. #451	C₂²×C₇	semidirect
518. #446	C₂²×C₇	semidirect
519. #441	C₂²×C₇	semidirect
520. #441	C₂²×C₇	semidirect
521. #441	C₂²×C₇	semidirect
523. C₄×Q₁₆	C₂²×C₇	semidirect
526. #435	C₂²×C₇	semidirect
528. #433	C₂²×C₇	semidirect
530. #424	C₂²×C₇	semidirect
532. #419	C₂²×C₇	semidirect
1000. C₇	#62020	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×#3561	2
C₇×#3523	2
C₇×#3398	2
C₇×#3377	2
C₇×#3313	2
C₇×#3312	2
C₇×#3296	2
C₇×D₄×Q₁₆	2
C₇×#3270	2
C₇×#3266	2
C₇×#3258	2
C₇×#3249	2
C₇×#3223	2
C₇×#3215	2
C₇×#3121	2
C₇×#3113	2
C₇×#3044	2
C₂×C₇×#464	2
C₇×#2992	2
#62020	7

Subgroups — C7×#62020 #13239236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62020 #13239236