Subgroups — C₇×#61165 #13238381

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3328	C₂	1	2	yes	maximal, complemented
4	C₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₇×#3313	C₂	1	4	yes	maximal, complemented
6	C₇×#3311	C₂	1	4	yes	maximal, complemented
7	C₇×#3304	C₂	1	2	yes	maximal, complemented
8	C₇×#3302	C₂	1	2	yes	maximal, complemented
9	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3093	C₂	1	2	yes	maximal, complemented
11	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3056	C₂	1	2	yes	maximal, complemented
13	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×C₇×#41	C₂²	1	2	yes	—
19	C₂×C₇×#137	C₂²	1	1	yes	characteristic
20	C₂×C₇×#137	C₂²	1	2	yes	complemented
21	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
22	C₇×#556	—	2	1	no	—
23	C₇×#556	—	2	2	no	—
24	C₇×#556	—	2	1	no	—
25	C₇×#556	C₂²	1	2	yes	—
26	C₇×#556	C₂²	1	2	yes	complemented
27	C₇×#556	C₂²	1	4	yes	complemented
28	C₇×#550	C₂²	1	1	yes	characteristic
29	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
30	C₇×#548	C₂²	1	2	yes	—
31	C₇×#547	—	2	1	no	—
32	C₇×#547	C₂²	1	1	yes	characteristic
33	C₇×#546	—	2	2	no	—
34	C₇×#546	C₂²	1	2	yes	—
35	C₇×D₄²	—	2	1	no	—
36	C₇×D₄²	C₂²	1	1	yes	characteristic
37	C₇×#532	—	2	1	no	—
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#126	—	2	2	no	—
41	C₂×C₇×#124	—	2	1	no	—
42	C₇×#525	—	2	2	no	—
43	C₇×#525	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×Q₈	—	2	1	no	—
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×C₇×D₄	—	2	1	no	—
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₇×#117	C₂²	1	2	yes	complemented
51	C₇×#489	C₂²	1	4	yes	complemented
52	C₇×#487	C₂²	1	2	yes	complemented
53	C₇×#486	C₂²	1	2	yes	complemented
54	C₇×#485	C₂²	1	4	yes	complemented
55	C₇×#485	C₂²	1	4	yes	complemented
56	C₇×#482	C₂²	1	4	yes	complemented
57	C₇×#482	C₂²	1	4	yes	complemented
58	C₇×#477	C₂²	1	2	yes	complemented
59	C₇×#476	C₂²	1	2	yes	complemented
60	C₇×#475	C₂²	1	2	yes	complemented
61	C₇×#474	C₂²	1	2	yes	complemented
62	C₇×#470	C₂²	1	4	yes	complemented
63	C₇×#468	C₂²	1	4	yes	complemented
64	C₇×#467	C₂²	1	4	yes	complemented
65	C₇×#465	C₂²	1	4	yes	complemented
66	C₇×#464	C₂²	1	4	yes	complemented
67	C₇×#462	C₂²	1	2	yes	complemented
68	C₇×#460	C₂²	1	2	yes	complemented
69	C₇×#452	C₂²	1	4	yes	complemented
70	C₇×#452	C₂²	1	4	yes	complemented
71	C₇×#451	C₂²	1	4	yes	complemented
72	C₇×#450	C₂²	1	4	yes	complemented
73	C₇×#441	C₂²	1	2	yes	complemented
74	C₇×#440	C₂²	1	2	yes	complemented
75	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
77	C₇×#436	C₂²	1	2	yes	—
78	C₇×#435	C₂²	1	4	yes	complemented
79	C₇×C₈×D₄	C₂²	1	2	yes	complemented
80	C₇×#428	C₂²	1	1	yes	characteristic, complemented
81	C₇×#428	C₂²	1	2	yes	complemented
82	C₇×#423	C₂²	1	1	yes	characteristic, complemented
83	C₇×#419	C₂²	1	1	yes	characteristic, complemented
84	C₇×#419	C₂²	1	4	yes	complemented
85	C₇×#418	C₂²	1	4	yes	complemented
86	C₇×#417	C₂²	1	1	yes	characteristic
87	C₇×#417	C₂²	1	2	yes	—
88	C₇×#417	C₂²	1	2	yes	complemented
89	C₇×#417	C₂²	1	2	yes	complemented
90	C₇×#417	C₂²	1	2	yes	complemented
91	C₇×#416	C₂²	1	4	yes	complemented
92	C₇×#416	C₂²	1	4	yes	complemented
93	C₇×#407	C₂²	1	2	yes	complemented
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	#61165	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	—	2	2	no	—
98	C₂×C₇×#41	—	2	8	no	—
99	C₂×C₇×#41	—	4	4	no	—
100	C₂×C₇×#41	C₂³	1	2	yes	—
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂×C₇×#41	C₂³	1	2	yes	—
103	C₂×C₇×#41	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	—	2	1	no	—
105	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×Q₈	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	—	2	2	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂³×C₄×C₇	—	2	2	no	—
112	C₂³×C₄×C₇	C₂³	1	2	yes	—
113	C₇×#137	—	2	4	no	—
114	C₇×#137	—	4	4	no	—
115	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
117	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₇×M₁₆	—	4	4	no	—
120	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₇×M₁₆	C₂³	1	2	yes	—
123	C₂×C₇×M₁₆	C₂³	1	4	yes	—
124	C₂²×C₇×C₈	C₂³	1	4	yes	—
125	C₇×C₄⋊Q₈	—	2	1	no	—
126	C₇×C₄⋊Q₈	—	2	1	no	—
127	C₇×C₄⋊Q₈	—	2	1	no	—
128	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×#127	—	2	1	no	—
132	C₇×#127	C₂³	1	1	yes	characteristic
133	C₇×#126	—	2	4	no	—
134	C₇×#126	—	2	4	no	—
135	C₇×#126	—	2	4	no	—
136	C₇×#126	—	2	4	no	—
137	C₇×#124	—	2	2	no	—
138	C₇×#124	—	2	2	no	—
139	C₇×#124	—	2	4	no	—
140	C₇×#124	—	2	2	no	—
141	C₇×#124	C₂³	1	2	yes	—
142	C₇×#123	—	2	2	no	—
143	C₇×#123	—	2	2	no	—
144	C₇×#123	—	2	2	no	—
145	C₇×C₂²⋊Q₈	—	2	2	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₇×C₂²⋊Q₈	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₇×#121	—	2	2	no	—
154	C₇×#121	—	2	1	no	—
155	C₇×#121	—	2	1	no	—
156	C₇×#121	—	2	1	no	—
157	C₇×#121	—	2	1	no	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	2	no	—
160	C₇×#121	C₂³	1	2	yes	—
161	C₇×#121	C₂³	1	2	yes	—
162	C₇×#120	—	2	2	no	—
163	C₇×#120	—	2	2	no	—
164	C₇×#120	—	2	2	no	—
165	C₄×C₇×Q₈	—	2	2	no	—
166	C₄×C₇×Q₈	—	2	2	no	—
167	C₄×C₇×Q₈	—	2	4	no	—
168	C₄×C₇×Q₈	—	2	1	no	—
169	C₄×C₇×Q₈	—	2	1	no	—
170	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
171	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
172	C₄×C₇×Q₈	C₂³	1	2	yes	—
173	C₄×C₇×Q₈	C₂³	1	2	yes	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	1	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	1	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	1	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	D₄	1	1	yes	characteristic
184	C₄×C₇×D₄	D₄	1	2	yes	—
185	C₄×C₇×D₄	D₄	1	1	yes	characteristic
186	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
187	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
188	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
189	C₄×C₇×D₄	C₂³	1	2	yes	—
190	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
191	C₇×#117	—	2	2	no	—
192	C₇×#117	—	2	2	no	—
193	C₇×#117	—	2	1	no	—
194	C₇×#117	C₂³	1	4	yes	—
195	C₇×#117	C₂³	1	4	yes	—
196	C₇×#117	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₄⋊C₄	—	2	2	no	—
198	C₂×C₇×C₄⋊C₄	—	2	1	no	—
199	C₂×C₇×C₄⋊C₄	—	2	1	no	—
200	C₂×C₇×C₄⋊C₄	—	2	1	no	—
201	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
208	C₂×C₄²×C₇	—	2	2	no	—
209	C₂×C₄²×C₇	—	2	1	no	—
210	C₂×C₄²×C₇	—	2	1	no	—
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₇×#107	C₂³	1	4	yes	—
213	C₇×#107	C₂³	1	2	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	2	yes	—
216	C₇×C₄⋊C₈	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×#103	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	2	yes	—
221	C₇×#103	C₂³	1	4	yes	—
222	C₇×#103	C₂³	1	4	yes	—
223	C₇×#103	C₂³	1	4	yes	—
224	C₇×#103	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	4	yes	—
227	C₇×#102	C₂³	1	4	yes	—
228	C₇×#102	C₂³	1	4	yes	—
229	C₇×#102	C₂³	1	2	yes	—
230	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₇×#97	C₂³	1	2	yes	—
233	C₄×C₇×C₈	C₂³	1	2	yes	—
234	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
235	D₄×#41	C₂×C₇	1	1	yes	characteristic
236	#3328	C₂×C₇	1	2	yes	complemented
237	#3324	C₂×C₇	1	2	yes	complemented
238	#3313	C₂×C₇	1	4	yes	complemented
239	#3311	C₂×C₇	1	4	yes	complemented
240	#3304	C₂×C₇	1	2	yes	complemented
241	#3302	C₂×C₇	1	2	yes	complemented
242	#3141	C₂×C₇	1	1	yes	characteristic, complemented
243	#3093	C₂×C₇	1	2	yes	complemented
244	#3079	C₂×C₇	1	1	yes	characteristic, complemented
245	#3056	C₂×C₇	1	2	yes	complemented
246	#3037	C₂×C₇	1	1	yes	characteristic, complemented
247	#3007	C₂×C₇	1	2	yes	complemented
248	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
249	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
250	#2896	C₂×C₇	1	2	yes	complemented
251	C₂⁴×C₇	—	2	2	no	—
252	C₂⁴×C₇	C₂×D₄	1	2	yes	—
253	C₇×#41	—	2	2	no	—
254	C₇×#41	—	2	4	no	—
255	C₇×#41	—	2	4	no	—
256	C₇×#41	—	2	4	no	—
257	C₇×#41	—	2	4	no	—
258	C₇×#41	—	4	8	no	—
259	C₇×#41	—	4	2	no	—
260	C₇×#41	—	4	2	no	—
261	C₇×#41	—	4	8	no	—
262	C₇×#41	#41	1	4	yes	—
263	C₂×C₇×Q₈	—	2	1	no	—
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	4	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	4	2	no	—
271	C₂×C₇×Q₈	—	4	4	no	—
272	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
273	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
274	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×D₄	—	2	1	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	2	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	1	no	—
283	C₂×C₇×D₄	—	2	2	no	—
284	C₂×C₇×D₄	—	2	1	no	—
285	C₂×C₇×D₄	—	4	2	no	—
286	C₂×C₇×D₄	—	4	2	no	—
287	C₂×C₇×D₄	—	4	8	no	—
288	C₂×C₇×D₄	—	4	4	no	—
289	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
291	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
292	C₂×C₇×D₄	C₂⁴	1	2	yes	—
293	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	—	2	1	no	—
295	C₂²×C₄×C₇	—	2	4	no	—
296	C₂²×C₄×C₇	—	2	4	no	—
297	C₂²×C₄×C₇	—	2	1	no	—
298	C₂²×C₄×C₇	—	2	1	no	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	1	no	—
302	C₂²×C₄×C₇	—	2	2	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	1	no	—
306	C₂²×C₄×C₇	—	4	8	no	—
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₇×Q₁₆	—	2	4	no	—
316	C₇×Q₁₆	—	4	4	no	—
317	C₇×SD₁₆	—	2	4	no	—
318	C₇×SD₁₆	—	4	4	no	—
319	C₇×M₁₆	—	2	2	no	—
320	C₇×M₁₆	—	2	2	no	—
321	C₇×M₁₆	—	2	4	no	—
322	C₇×M₁₆	—	4	4	no	—
323	C₂×C₇×C₈	—	4	4	no	—
324	C₂×C₇×C₈	C₂⁴	1	2	yes	—
325	C₂×C₇×C₈	C₂⁴	1	2	yes	—
326	C₂×C₇×C₈	C₂⁴	1	4	yes	—
327	C₇×C₄⋊C₄	—	2	1	no	—
328	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	4	no	—
330	C₇×C₄⋊C₄	—	2	4	no	—
331	C₇×C₄⋊C₄	—	2	2	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	2	no	—
335	C₇×C₄⋊C₄	—	2	1	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	1	no	—
339	C₇×C₄⋊C₄	—	2	1	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
342	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
343	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
344	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
346	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
347	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₇×C₂²⋊C₄	—	2	4	no	—
353	C₇×C₂²⋊C₄	—	2	1	no	—
354	C₇×C₂²⋊C₄	—	2	2	no	—
355	C₇×C₂²⋊C₄	—	2	2	no	—
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	1	no	—
358	C₇×C₂²⋊C₄	—	2	1	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	2	no	—
361	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
362	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
363	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₄²×C₇	—	2	1	no	—
366	C₄²×C₇	—	2	4	no	—
367	C₄²×C₇	—	2	4	no	—
368	C₄²×C₇	—	2	1	no	—
369	C₄²×C₇	—	2	1	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₇	C₂⁴	1	1	yes	characteristic
375	C₄²×C₇	C₂⁴	1	1	yes	characteristic
376	C₂²×#41	C₂²×C₇	1	2	yes	—
377	C₂×#137	C₂²×C₇	1	1	yes	characteristic
378	C₂×#137	C₂²×C₇	1	2	yes	complemented
379	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
380	#556	—	2	1	no	—
381	#556	—	2	2	no	—
382	#556	—	2	1	no	—
383	#556	C₂²×C₇	1	2	yes	—
384	#556	C₂²×C₇	1	2	yes	complemented
385	#556	C₂²×C₇	1	4	yes	complemented
386	#550	C₂²×C₇	1	1	yes	characteristic
387	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
388	#548	C₂²×C₇	1	2	yes	—
389	#547	—	2	1	no	—
390	#547	C₂²×C₇	1	1	yes	characteristic
391	#546	—	2	2	no	—
392	#546	C₂²×C₇	1	2	yes	—
393	D₄²	—	2	1	no	—
394	D₄²	C₂²×C₇	1	1	yes	characteristic
395	#532	—	2	1	no	—
396	#532	C₂²×C₇	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
398	C₂×#126	—	2	2	no	—
399	C₂×#124	—	2	1	no	—
400	#525	—	2	2	no	—
401	#525	C₂²×C₇	1	2	yes	—
402	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
403	C₄×#41	C₂²×C₇	1	1	yes	characteristic
404	C₂×C₄×Q₈	—	2	1	no	—
405	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
406	C₂×C₄×D₄	—	2	1	no	—
407	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
408	C₂×#117	C₂²×C₇	1	2	yes	complemented
409	#489	C₂²×C₇	1	4	yes	complemented
410	#487	C₂²×C₇	1	2	yes	complemented
411	#486	C₂²×C₇	1	2	yes	complemented
412	#485	C₂²×C₇	1	4	yes	complemented
413	#485	C₂²×C₇	1	4	yes	complemented
414	#482	C₂²×C₇	1	4	yes	complemented
415	#482	C₂²×C₇	1	4	yes	complemented
416	#477	C₂²×C₇	1	2	yes	complemented
417	#476	C₂²×C₇	1	2	yes	complemented
418	#475	C₂²×C₇	1	2	yes	complemented
419	#474	C₂²×C₇	1	2	yes	complemented
420	#470	C₂²×C₇	1	4	yes	complemented
421	#468	C₂²×C₇	1	4	yes	complemented
422	#467	C₂²×C₇	1	4	yes	complemented
423	#465	C₂²×C₇	1	4	yes	complemented
424	#464	C₂²×C₇	1	4	yes	complemented
425	#462	C₂²×C₇	1	2	yes	complemented
426	#460	C₂²×C₇	1	2	yes	complemented
427	#452	C₂²×C₇	1	4	yes	complemented
428	#452	C₂²×C₇	1	4	yes	complemented
429	#451	C₂²×C₇	1	4	yes	complemented
430	#450	C₂²×C₇	1	4	yes	complemented
431	#441	C₂²×C₇	1	2	yes	complemented
432	#440	C₂²×C₇	1	2	yes	complemented
433	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
434	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
435	#436	C₂²×C₇	1	2	yes	—
436	#435	C₂²×C₇	1	4	yes	complemented
437	C₈×D₄	C₂²×C₇	1	2	yes	complemented
438	#428	C₂²×C₇	1	2	yes	complemented
439	#428	C₂²×C₇	1	1	yes	characteristic, complemented
440	#423	C₂²×C₇	1	1	yes	characteristic, complemented
441	#419	C₂²×C₇	1	4	yes	complemented
442	#419	C₂²×C₇	1	1	yes	characteristic, complemented
443	#418	C₂²×C₇	1	4	yes	complemented
444	#417	C₂²×C₇	1	2	yes	—
445	#417	C₂²×C₇	1	1	yes	characteristic
446	#417	C₂²×C₇	1	2	yes	complemented
447	#417	C₂²×C₇	1	2	yes	complemented
448	#417	C₂²×C₇	1	2	yes	complemented
449	#416	C₂²×C₇	1	4	yes	complemented
450	#416	C₂²×C₇	1	4	yes	complemented
451	#407	C₂²×C₇	1	2	yes	complemented
452	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
453	C₂³×C₇	—	2	1	no	—
454	C₂³×C₇	—	2	4	no	—
455	C₂³×C₇	—	2	2	no	—
456	C₂³×C₇	—	4	2	no	—
457	C₂³×C₇	—	4	2	no	—
458	C₂³×C₇	—	4	4	no	—
459	C₂³×C₇	—	4	4	no	—
460	C₂³×C₇	—	8	2	no	—
461	C₂³×C₇	C₂²×D₄	1	2	yes	—
462	C₂³×C₇	C₂²×D₄	1	2	yes	—
463	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
464	C₇×Q₈	—	2	1	no	—
465	C₇×Q₈	—	2	2	no	—
466	C₇×Q₈	—	2	2	no	—
467	C₇×Q₈	—	2	2	no	—
468	C₇×Q₈	—	2	2	no	—
469	C₇×Q₈	—	4	4	no	—
470	C₇×Q₈	—	4	4	no	—
471	C₇×Q₈	—	4	2	no	—
472	C₇×Q₈	—	4	4	no	—
473	C₇×Q₈	C₂×#41	1	2	yes	—
474	C₇×D₄	—	2	4	no	—
475	C₇×D₄	—	2	2	no	—
476	C₇×D₄	—	2	2	no	—
477	C₇×D₄	—	2	2	no	—
478	C₇×D₄	—	2	1	no	—
479	C₇×D₄	—	2	2	no	—
480	C₇×D₄	—	4	2	no	—
481	C₇×D₄	—	4	4	no	—
482	C₇×D₄	—	4	4	no	—
483	C₇×D₄	—	4	4	no	—
484	C₇×D₄	—	4	4	no	—
485	C₇×D₄	—	4	4	no	—
486	C₇×D₄	—	4	2	no	—
487	C₇×D₄	—	8	1	no	—
488	C₇×D₄	—	8	2	no	—
489	C₇×D₄	C₂×#41	1	2	yes	—
490	C₂×C₄×C₇	—	2	4	no	—
491	C₂×C₄×C₇	—	2	1	no	—
492	C₂×C₄×C₇	—	2	4	no	—
493	C₂×C₄×C₇	—	2	4	no	—
494	C₂×C₄×C₇	—	2	4	no	—
495	C₂×C₄×C₇	—	2	2	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	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	4	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	4	1	no	—
507	C₂×C₄×C₇	—	4	4	no	—
508	C₂×C₄×C₇	—	4	4	no	—
509	C₂×C₄×C₇	—	4	4	no	—
510	C₂×C₄×C₇	—	4	2	no	—
511	C₂×C₄×C₇	—	4	4	no	—
512	C₂×C₄×C₇	—	4	2	no	—
513	C₂×C₄×C₇	—	4	4	no	—
514	C₂×C₄×C₇	—	4	2	no	—
515	C₂×C₄×C₇	—	8	1	no	—
516	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇	C₂×#41	1	2	yes	—
524	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
526	C₇×C₈	—	2	2	no	—
527	C₇×C₈	—	2	2	no	—
528	C₇×C₈	—	2	4	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	2	8	no	—
532	C₂×#41	—	4	4	no	—
533	C₂×#41	C₂³×C₇	1	2	yes	—
534	C₂×#41	C₂³×C₇	1	2	yes	—
535	C₂×#41	C₂³×C₇	1	2	yes	—
536	C₂×#41	C₂³×C₇	1	1	yes	characteristic
537	C₂²×Q₈	—	2	1	no	—
538	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₇	1	2	yes	—
540	C₂²×D₄	—	2	2	no	—
541	C₂²×D₄	—	2	1	no	—
542	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₇	1	2	yes	—
544	C₂³×C₄	—	2	2	no	—
545	C₂³×C₄	C₂³×C₇	1	2	yes	—
546	#137	—	2	4	no	—
547	#137	—	4	4	no	—
548	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
549	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
552	C₂×M₁₆	—	4	4	no	—
553	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
554	C₂×M₁₆	C₂³×C₇	1	2	yes	—
555	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
556	C₂×M₁₆	C₂³×C₇	1	4	yes	—
557	C₂²×C₈	C₂³×C₇	1	4	yes	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
562	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
564	#127	—	2	1	no	—
565	#127	C₂³×C₇	1	1	yes	characteristic
566	#126	—	2	4	no	—
567	#126	—	2	4	no	—
568	#126	—	2	4	no	—
569	#126	—	2	4	no	—
570	#124	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	4	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₇	1	2	yes	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
584	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₇	1	2	yes	—
594	#121	C₂³×C₇	1	2	yes	—
595	#120	—	2	2	no	—
596	#120	—	2	2	no	—
597	#120	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	4	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	C₂³×C₇	1	2	yes	—
604	C₄×Q₈	C₂³×C₇	1	2	yes	—
605	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	C₇×D₄	1	1	yes	characteristic
617	C₄×D₄	C₇×D₄	1	2	yes	—
618	C₄×D₄	C₇×D₄	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₇	1	2	yes	—
623	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₇	1	4	yes	—
628	#117	C₂³×C₇	1	4	yes	—
629	#117	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	2	no	—
640	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
645	#107	C₂³×C₇	1	2	yes	—
646	#107	C₂³×C₇	1	4	yes	—
647	#106	C₂³×C₇	1	2	yes	—
648	#106	C₂³×C₇	1	4	yes	—
649	C₄⋊C₈	C₂³×C₇	1	2	yes	—
650	C₄⋊C₈	C₂³×C₇	1	2	yes	—
651	#103	C₂³×C₇	1	2	yes	—
652	#103	C₂³×C₇	1	4	yes	—
653	#103	C₂³×C₇	1	4	yes	—
654	#103	C₂³×C₇	1	4	yes	—
655	#103	C₂³×C₇	1	4	yes	—
656	#103	C₂³×C₇	1	2	yes	—
657	#103	C₂³×C₇	1	2	yes	—
658	#102	C₂³×C₇	1	2	yes	—
659	#102	C₂³×C₇	1	4	yes	—
660	#102	C₂³×C₇	1	4	yes	—
661	#102	C₂³×C₇	1	4	yes	—
662	#102	C₂³×C₇	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
665	#97	C₂³×C₇	1	2	yes	—
666	C₄×C₈	C₂³×C₇	1	2	yes	—
667	C₂²×C₇	—	2	1	no	—
668	C₂²×C₇	—	2	1	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	—	4	1	no	—
677	C₂²×C₇	—	4	1	no	—
678	C₂²×C₇	—	4	2	no	—
679	C₂²×C₇	—	4	2	no	—
680	C₂²×C₇	—	4	2	no	—
681	C₂²×C₇	—	8	4	no	—
682	C₂²×C₇	—	8	8	no	—
683	C₂²×C₇	#546	1	2	yes	—
684	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
685	C₄×C₇	—	2	1	no	—
686	C₄×C₇	—	2	1	no	—
687	C₄×C₇	—	2	2	no	—
688	C₄×C₇	—	2	2	no	—
689	C₄×C₇	—	2	2	no	—
690	C₄×C₇	—	2	1	no	—
691	C₄×C₇	—	4	2	no	—
692	C₄×C₇	—	4	1	no	—
693	C₄×C₇	—	4	2	no	—
694	C₄×C₇	—	4	2	no	—
695	C₄×C₇	—	4	1	no	—
696	C₄×C₇	—	4	4	no	—
697	C₄×C₇	#546	1	2	yes	—
698	C₄×C₇	#575	1	2	yes	—
699	C₄×C₇	C₂²×#41	1	1	yes	characteristic
700	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂⁴	—	2	2	no	—
702	C₂⁴	C₂×C₇×D₄	1	2	yes	—
703	#41	—	2	2	no	—
704	#41	—	2	4	no	—
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	4	8	no	—
709	#41	—	4	2	no	—
710	#41	—	4	2	no	—
711	#41	—	4	8	no	—
712	#41	C₇×#41	1	4	yes	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	4	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×Q₈	—	4	4	no	—
722	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
723	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	4	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	8	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
740	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
741	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
742	C₂×D₄	C₂⁴×C₇	1	2	yes	—
743	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	4	8	no	—
757	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
758	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
759	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
760	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
761	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
765	Q₁₆	—	2	4	no	—
766	Q₁₆	—	4	4	no	—
767	SD₁₆	—	2	4	no	—
768	SD₁₆	—	4	4	no	—
769	M₁₆	—	2	2	no	—
770	M₁₆	—	2	2	no	—
771	M₁₆	—	2	4	no	—
772	M₁₆	—	4	4	no	—
773	C₂×C₈	—	4	4	no	—
774	C₂×C₈	C₂⁴×C₇	1	2	yes	—
775	C₂×C₈	C₂⁴×C₇	1	2	yes	—
776	C₂×C₈	C₂⁴×C₇	1	4	yes	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
792	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
793	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
796	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
797	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
812	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
813	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
814	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	4	no	—
817	C₄²	—	2	4	no	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	1	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
823	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
824	C₄²	C₂⁴×C₇	1	1	yes	characteristic
825	C₄²	C₂⁴×C₇	1	1	yes	characteristic
826	C₂×C₇	—	2	2	no	—
827	C₂×C₇	—	4	2	no	—
828	C₂×C₇	—	4	2	no	—
829	C₂×C₇	—	4	2	no	—
830	C₂×C₇	—	8	2	no	—
831	C₂×C₇	C₂×#546	1	1	yes	characteristic
832	C₂×C₇	C₂×#575	1	1	yes	characteristic
833	C₂×C₇	#3586	1	1	yes	characteristic
834	C₂³	—	2	1	no	—
835	C₂³	—	2	4	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	4	2	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	4	4	no	—
841	C₂³	—	8	2	no	—
842	C₂³	C₂²×C₇×D₄	1	2	yes	—
843	C₂³	C₂²×C₇×D₄	1	2	yes	—
844	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
845	Q₈	—	2	1	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	4	4	no	—
851	Q₈	—	4	4	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	4	4	no	—
854	Q₈	C₂×C₇×#41	1	2	yes	—
855	D₄	—	2	4	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	1	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	2	no	—
868	D₄	—	8	1	no	—
869	D₄	—	8	2	no	—
870	D₄	C₂×C₇×#41	1	2	yes	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	4	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	8	1	no	—
897	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
899	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
900	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
901	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
902	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
903	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
904	C₂×C₄	C₂×C₇×#41	1	2	yes	—
905	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
906	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₈	—	2	4	no	—
910	C₇	#61165	1	1	yes	characteristic, direct product factor, Sylow
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	8	no	—
927	C₂²	C₇×#546	1	2	yes	—
928	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	4	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	C₇×#546	1	2	yes	—
942	C₄	C₇×#575	1	2	yes	—
943	C₄	C₂²×C₇×#41	1	1	yes	characteristic
944	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂	—	2	2	no	—
946	C₂	—	4	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₂×C₇×#546	1	1	yes	characteristic
951	C₂	C₂×C₇×#575	1	1	yes	characteristic
952	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×D₄×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#556	C₂	semidirect
3. C₇×#3328	C₂	semidirect
4. C₇×#3324	C₂	semidirect
5. C₇×#3313	C₂	semidirect
6. C₇×#3311	C₂	semidirect
7. C₇×#3304	C₂	semidirect
8. C₇×#3302	C₂	semidirect
9. C₇×#3141	C₂	semidirect
10. C₇×#3093	C₂	semidirect
11. C₇×#3079	C₂	semidirect
12. C₇×#3056	C₂	semidirect
13. C₇×#3037	C₂	semidirect
14. C₇×#3007	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₇×#2896	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
21. C₂²×C₇×M₁₆	C₂²	semidirect
26. C₇×#556	C₂²	semidirect
27. C₇×#556	C₂²	semidirect
39. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₄×C₇×Q₈	C₂²	semidirect
50. C₂×C₇×#117	C₂²	semidirect
51. C₇×#489	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#485	C₂²	semidirect
55. C₇×#485	C₂²	semidirect
56. C₇×#482	C₂²	semidirect
57. C₇×#482	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
62. C₇×#470	C₂²	semidirect
63. C₇×#468	C₂²	semidirect
64. C₇×#467	C₂²	semidirect
65. C₇×#465	C₂²	semidirect
66. C₇×#464	C₂²	semidirect
67. C₇×#462	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#452	C₂²	semidirect
70. C₇×#452	C₂²	semidirect
71. C₇×#451	C₂²	semidirect
72. C₇×#450	C₂²	semidirect
73. C₇×#441	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₄×C₇×Q₁₆	C₂²	semidirect
76. C₄×C₇×SD₁₆	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
79. C₇×C₈×D₄	C₂²	semidirect
80. C₇×#428	C₂²	semidirect
81. C₇×#428	C₂²	semidirect
82. C₇×#423	C₂²	semidirect
83. C₇×#419	C₂²	semidirect
84. C₇×#419	C₂²	semidirect
85. C₇×#418	C₂²	semidirect
88. C₇×#417	C₂²	semidirect
89. C₇×#417	C₂²	semidirect
90. C₇×#417	C₂²	semidirect
91. C₇×#416	C₂²	semidirect
92. C₇×#416	C₂²	semidirect
93. C₇×#407	C₂²	semidirect
94. C₄×C₇×M₁₆	C₂²	semidirect
95. #61165	C₇	direct (N × H)
234. C₂×#556	C₂×C₇	semidirect
236. #3328	C₂×C₇	semidirect
237. #3324	C₂×C₇	semidirect
238. #3313	C₂×C₇	semidirect
239. #3311	C₂×C₇	semidirect
240. #3304	C₂×C₇	semidirect
241. #3302	C₂×C₇	semidirect
242. #3141	C₂×C₇	semidirect
243. #3093	C₂×C₇	semidirect
244. #3079	C₂×C₇	semidirect
245. #3056	C₂×C₇	semidirect
246. #3037	C₂×C₇	semidirect
247. #3007	C₂×C₇	semidirect
248. C₄×#137	C₂×C₇	semidirect
249. D₄×M₁₆	C₂×C₇	semidirect
250. #2896	C₂×C₇	semidirect
378. C₂×#137	C₂²×C₇	semidirect
379. C₂²×M₁₆	C₂²×C₇	semidirect
384. #556	C₂²×C₇	semidirect
385. #556	C₂²×C₇	semidirect
397. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
402. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
405. C₂×C₄×Q₈	C₂²×C₇	semidirect
408. C₂×#117	C₂²×C₇	semidirect
409. #489	C₂²×C₇	semidirect
410. #487	C₂²×C₇	semidirect
411. #486	C₂²×C₇	semidirect
412. #485	C₂²×C₇	semidirect
413. #485	C₂²×C₇	semidirect
414. #482	C₂²×C₇	semidirect
415. #482	C₂²×C₇	semidirect
416. #477	C₂²×C₇	semidirect
417. #476	C₂²×C₇	semidirect
418. #475	C₂²×C₇	semidirect
419. #474	C₂²×C₇	semidirect
420. #470	C₂²×C₇	semidirect
421. #468	C₂²×C₇	semidirect
422. #467	C₂²×C₇	semidirect
423. #465	C₂²×C₇	semidirect
424. #464	C₂²×C₇	semidirect
425. #462	C₂²×C₇	semidirect
426. #460	C₂²×C₇	semidirect
427. #452	C₂²×C₇	semidirect
428. #452	C₂²×C₇	semidirect
429. #451	C₂²×C₇	semidirect
430. #450	C₂²×C₇	semidirect
431. #441	C₂²×C₇	semidirect
432. #440	C₂²×C₇	semidirect
433. C₄×Q₁₆	C₂²×C₇	semidirect
434. C₄×SD₁₆	C₂²×C₇	semidirect
436. #435	C₂²×C₇	semidirect
437. C₈×D₄	C₂²×C₇	semidirect
438. #428	C₂²×C₇	semidirect
439. #428	C₂²×C₇	semidirect
440. #423	C₂²×C₇	semidirect
441. #419	C₂²×C₇	semidirect
442. #419	C₂²×C₇	semidirect
443. #418	C₂²×C₇	semidirect
446. #417	C₂²×C₇	semidirect
447. #417	C₂²×C₇	semidirect
448. #417	C₂²×C₇	semidirect
449. #416	C₂²×C₇	semidirect
450. #416	C₂²×C₇	semidirect
451. #407	C₂²×C₇	semidirect
452. C₄×M₁₆	C₂²×C₇	semidirect
910. C₇	#61165	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×#556	2
C₇×D₄×#41	2
C₇×#3328	2
C₇×#3324	2
C₇×#3313	2
C₇×#3311	2
C₇×#3304	2
C₇×#3302	2
C₇×#3141	2
C₇×#3093	2
C₇×#3079	2
C₇×#3056	2
C₇×#3037	2
C₇×#3007	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₇×#2896	2
#61165	7

Subgroups — C7×#61165 #13238381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61165 #13238381