Subgroups — C₇×#60546 #13237762

Order 1792.

2172 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3117	C₂	1	2	yes	maximal, complemented
4	C₇×#3116	C₂	1	2	yes	maximal, complemented
5	C₇×#3115	C₂	1	2	yes	maximal, complemented
6	C₇×#3114	C₂	1	2	yes	maximal, complemented
7	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3111	C₂	1	4	yes	maximal, complemented
10	C₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3091	C₂	1	2	yes	maximal, complemented
13	C₇×#3076	C₂	1	2	yes	maximal, complemented
14	C₇×#3035	C₂	1	2	yes	maximal, complemented
15	C₇×#3002	C₂	1	2	yes	maximal, complemented
16	C₇×#2943	C₂	1	4	yes	maximal, complemented
17	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂×C₇×#135	C₂²	1	4	yes	—
20	C₇×#533	C₂²	1	1	yes	characteristic
21	C₇×#533	C₂²	1	1	yes	characteristic, complemented
22	C₇×#533	C₂²	1	1	yes	characteristic, complemented
23	C₇×#532	C₂²	1	1	yes	characteristic
24	C₇×#532	C₂²	1	1	yes	characteristic, complemented
25	C₇×#532	C₂²	1	1	yes	characteristic, complemented
26	C₇×#529	—	2	1	no	—
27	C₇×#529	—	2	1	no	—
28	C₇×#529	—	2	1	no	—
29	C₇×#529	—	2	1	no	—
30	C₇×#529	C₂²	1	2	yes	—
31	C₇×#529	C₂²	1	2	yes	complemented
32	C₇×#525	—	2	1	no	—
33	C₇×#525	—	2	1	no	—
34	C₇×#525	C₂²	1	2	yes	—
35	C₄×C₇×#41	—	2	1	no	—
36	C₄×C₇×#41	—	2	1	no	—
37	C₄×C₇×#41	—	2	1	no	—
38	C₄×C₇×#41	—	2	1	no	—
39	C₄×C₇×#41	—	2	1	no	—
40	C₄×C₇×#41	—	2	1	no	—
41	C₄×C₇×#41	C₂²	1	2	yes	—
42	C₄×C₇×#41	C₂²	1	2	yes	—
43	C₄×C₇×#41	C₂²	1	2	yes	—
44	C₄×C₇×#41	C₂²	1	2	yes	—
45	C₄×C₇×#41	C₂²	1	2	yes	complemented
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	—	2	1	no	—
49	C₂×C₄×C₇×D₄	—	2	1	no	—
50	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₇×#117	—	2	1	no	—
53	C₂×C₇×#117	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₇	—	2	1	no	—
55	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
56	C₇×#485	C₂²	1	4	yes	complemented
57	C₇×#484	C₂²	1	2	yes	—
58	C₇×#483	C₂²	1	2	yes	—
59	C₇×#482	C₂²	1	4	yes	complemented
60	C₇×#481	C₂²	1	2	yes	—
61	C₇×#480	C₂²	1	2	yes	—
62	C₇×#479	C₂²	1	4	yes	complemented
63	C₇×#478	C₂²	1	4	yes	complemented
64	C₇×#477	C₂²	1	2	yes	complemented
65	C₇×#476	C₂²	1	2	yes	complemented
66	C₇×#475	C₂²	1	2	yes	complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#464	C₂²	1	4	yes	complemented
69	C₇×#463	C₂²	1	4	yes	complemented
70	C₇×#462	C₂²	1	2	yes	complemented
71	C₇×#461	C₂²	1	2	yes	complemented
72	C₇×#460	C₂²	1	2	yes	complemented
73	C₇×#459	C₂²	1	2	yes	complemented
74	C₇×#452	C₂²	1	4	yes	—
75	C₇×#451	C₂²	1	2	yes	—
76	C₇×#450	C₂²	1	2	yes	—
77	C₇×#449	C₂²	1	4	yes	—
78	C₇×#448	C₂²	1	2	yes	—
79	C₇×#447	C₂²	1	2	yes	—
80	C₇×#442	C₂²	1	4	yes	complemented
81	C₇×#442	C₂²	1	4	yes	complemented
82	C₇×#441	C₂²	1	4	yes	complemented
83	C₇×#441	C₂²	1	4	yes	complemented
84	C₇×#440	C₂²	1	4	yes	complemented
85	C₇×#440	C₂²	1	4	yes	complemented
86	C₇×#440	C₂²	1	4	yes	complemented
87	C₇×#440	C₂²	1	4	yes	complemented
88	C₇×#432	C₂²	1	1	yes	characteristic
89	C₇×#432	C₂²	1	1	yes	characteristic
90	C₇×#432	C₂²	1	2	yes	—
91	C₇×#432	C₂²	1	2	yes	complemented
92	C₇×#432	C₂²	1	2	yes	complemented
93	C₇×#427	C₂²	1	4	yes	complemented
94	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
95	C₇×#416	C₂²	1	4	yes	—
96	C₇×#416	C₂²	1	4	yes	complemented
97	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
98	C₂×C₇×#97	C₂²	1	2	yes	complemented
99	#60546	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×C₇×#41	—	2	8	no	—
101	C₂×C₇×#41	—	2	1	no	—
102	C₂×C₇×#41	—	2	1	no	—
103	C₂×C₇×#41	—	2	1	no	—
104	C₂×C₇×#41	—	2	1	no	—
105	C₂×C₇×#41	C₂³	1	2	yes	—
106	C₂×C₇×#41	C₂³	1	2	yes	—
107	C₂×C₇×#41	C₂³	1	2	yes	—
108	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×D₄	—	2	1	no	—
110	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	—	2	1	no	—
112	C₂³×C₄×C₇	—	2	1	no	—
113	C₂³×C₄×C₇	—	2	1	no	—
114	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
115	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₇×#135	—	2	16	no	—
118	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
119	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₇×D₈	C₂³	1	4	yes	—
122	C₂²×C₇×C₈	C₂³	1	4	yes	—
123	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₇×#127	C₂³	1	1	yes	characteristic
127	C₇×#126	—	2	2	no	—
128	C₇×#126	—	2	2	no	—
129	C₇×#125	—	2	1	no	—
130	C₇×#125	—	2	1	no	—
131	C₇×#125	C₂³	1	2	yes	—
132	C₇×#124	—	2	1	no	—
133	C₇×#124	—	2	1	no	—
134	C₇×#124	C₂³	1	2	yes	—
135	C₇×#123	—	2	2	no	—
136	C₇×#123	—	2	2	no	—
137	C₇×#123	—	2	2	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	1	no	—
140	C₇×C₂²⋊Q₈	—	2	1	no	—
141	C₇×C₂²⋊Q₈	—	2	1	no	—
142	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₇×#121	—	2	1	no	—
145	C₇×#121	—	2	1	no	—
146	C₇×#121	—	2	1	no	—
147	C₇×#121	—	2	1	no	—
148	C₇×#121	C₂³	1	2	yes	—
149	C₇×#121	C₂³	1	2	yes	—
150	C₇×#120	—	2	2	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×Q₈	—	2	1	no	—
156	C₄×C₇×Q₈	—	2	1	no	—
157	C₄×C₇×Q₈	—	2	1	no	—
158	C₄×C₇×Q₈	—	2	1	no	—
159	C₄×C₇×Q₈	C₂³	1	2	yes	—
160	C₄×C₇×Q₈	C₂³	1	2	yes	—
161	C₄×C₇×Q₈	C₂³	1	2	yes	—
162	C₄×C₇×Q₈	C₂³	1	2	yes	—
163	C₄×C₇×Q₈	C₂³	1	2	yes	—
164	C₄×C₇×Q₈	C₂³	1	2	yes	—
165	C₄×C₇×D₄	—	2	2	no	—
166	C₄×C₇×D₄	—	2	2	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	—	2	2	no	—
171	C₄×C₇×D₄	—	2	2	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	2	no	—
174	C₄×C₇×D₄	—	2	2	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	2	no	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	1	no	—
180	C₄×C₇×D₄	—	2	1	no	—
181	C₄×C₇×D₄	—	2	1	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	—	2	1	no	—
184	C₄×C₇×D₄	—	2	1	no	—
185	C₄×C₇×D₄	—	2	1	no	—
186	C₄×C₇×D₄	—	2	1	no	—
187	C₄×C₇×D₄	C₂³	1	2	yes	—
188	C₄×C₇×D₄	C₂³	1	2	yes	—
189	C₄×C₇×D₄	C₂³	1	2	yes	—
190	C₄×C₇×D₄	C₂³	1	2	yes	—
191	C₄×C₇×D₄	C₂³	1	2	yes	—
192	C₄×C₇×D₄	C₂³	1	2	yes	—
193	C₇×#117	—	2	1	no	—
194	C₇×#117	—	2	1	no	—
195	C₇×#117	—	2	1	no	—
196	C₇×#117	—	2	1	no	—
197	C₇×#117	—	2	2	no	—
198	C₇×#117	—	2	2	no	—
199	C₇×#117	—	2	2	no	—
200	C₇×#117	—	2	2	no	—
201	C₇×#117	—	2	2	no	—
202	C₇×#117	—	2	2	no	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	C₂³	1	2	yes	—
205	C₇×#117	C₂³	1	2	yes	—
206	C₇×#117	C₂³	1	2	yes	—
207	C₂×C₇×C₄⋊C₄	—	2	1	no	—
208	C₂×C₇×C₄⋊C₄	—	2	1	no	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
213	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
214	C₂×C₄²×C₇	—	2	1	no	—
215	C₂×C₄²×C₇	—	2	1	no	—
216	C₂×C₄²×C₇	—	2	1	no	—
217	C₂×C₄²×C₇	—	2	2	no	—
218	C₂×C₄²×C₇	—	2	2	no	—
219	C₂×C₄²×C₇	—	2	2	no	—
220	C₂×C₄²×C₇	—	2	2	no	—
221	C₂×C₄²×C₇	—	2	2	no	—
222	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₇×#107	C₂³	1	4	yes	—
235	C₇×#107	C₂³	1	4	yes	—
236	C₇×#106	C₂³	1	4	yes	—
237	C₇×#106	C₂³	1	4	yes	—
238	C₇×C₄⋊C₈	C₂³	1	2	yes	—
239	C₇×C₄⋊C₈	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	4	yes	—
241	C₇×#103	C₂³	1	4	yes	—
242	C₇×#103	C₂³	1	4	yes	—
243	C₇×#103	C₂³	1	4	yes	—
244	C₇×#103	C₂³	1	4	yes	—
245	C₇×#102	C₂³	1	4	yes	—
246	C₇×#102	C₂³	1	4	yes	—
247	C₇×#102	C₂³	1	4	yes	—
248	C₇×#102	C₂³	1	4	yes	—
249	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
252	C₇×#97	C₂³	1	2	yes	—
253	C₇×#97	C₂³	1	4	yes	—
254	C₇×#97	C₂³	1	2	yes	—
255	#3444	C₂×C₇	1	1	yes	characteristic, complemented
256	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
257	#3117	C₂×C₇	1	2	yes	complemented
258	#3116	C₂×C₇	1	2	yes	complemented
259	#3115	C₂×C₇	1	2	yes	complemented
260	#3114	C₂×C₇	1	2	yes	complemented
261	#3113	C₂×C₇	1	1	yes	characteristic, complemented
262	#3112	C₂×C₇	1	1	yes	characteristic, complemented
263	#3111	C₂×C₇	1	4	yes	complemented
264	#3110	C₂×C₇	1	1	yes	characteristic, complemented
265	#3109	C₂×C₇	1	1	yes	characteristic, complemented
266	#3091	C₂×C₇	1	2	yes	complemented
267	#3076	C₂×C₇	1	2	yes	complemented
268	#3035	C₂×C₇	1	2	yes	complemented
269	#3002	C₂×C₇	1	2	yes	complemented
270	#2943	C₂×C₇	1	4	yes	complemented
271	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
272	C₂⁴×C₇	—	2	1	no	—
273	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
274	C₇×#41	—	2	8	no	—
275	C₇×#41	—	2	8	no	—
276	C₇×#41	—	2	4	no	—
277	C₇×#41	—	2	4	no	—
278	C₇×#41	—	2	4	no	—
279	C₇×#41	—	2	8	no	—
280	C₇×#41	—	4	4	no	—
281	C₇×#41	—	4	4	no	—
282	C₇×#41	#41	1	8	yes	complemented
283	C₂×C₇×Q₈	—	2	4	no	—
284	C₂×C₇×Q₈	—	2	1	no	—
285	C₂×C₇×Q₈	—	2	1	no	—
286	C₂×C₇×Q₈	—	2	1	no	—
287	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
288	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
289	C₂×C₇×D₄	—	2	8	no	—
290	C₂×C₇×D₄	—	2	2	no	—
291	C₂×C₇×D₄	—	2	2	no	—
292	C₂×C₇×D₄	—	2	4	no	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	2	2	no	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	—	2	1	no	—
297	C₂×C₇×D₄	—	2	1	no	—
298	C₂×C₇×D₄	—	2	1	no	—
299	C₂×C₇×D₄	C₂⁴	1	2	yes	—
300	C₂×C₇×D₄	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	—	2	8	no	—
302	C₂²×C₄×C₇	—	2	1	no	—
303	C₂²×C₄×C₇	—	2	2	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	4	no	—
306	C₂²×C₄×C₇	—	2	1	no	—
307	C₂²×C₄×C₇	—	2	1	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	2	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	4	2	no	—
316	C₂²×C₄×C₇	—	4	2	no	—
317	C₂²×C₄×C₇	—	4	4	no	—
318	C₂²×C₄×C₇	—	4	4	no	—
319	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
337	C₇×Q₁₆	—	2	8	no	—
338	C₇×SD₁₆	—	2	8	no	—
339	C₇×SD₁₆	—	2	8	no	—
340	C₇×D₈	—	2	8	no	—
341	C₂×C₇×C₈	—	2	8	no	—
342	C₂×C₇×C₈	C₂⁴	1	4	yes	—
343	C₂×C₇×C₈	C₂⁴	1	4	yes	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	1	no	—
349	C₇×C₄⋊C₄	—	2	1	no	—
350	C₇×C₄⋊C₄	—	2	1	no	—
351	C₇×C₄⋊C₄	—	2	1	no	—
352	C₇×C₄⋊C₄	—	2	1	no	—
353	C₇×C₄⋊C₄	—	2	1	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
362	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	2	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₄²×C₇	—	2	2	no	—
380	C₄²×C₇	—	2	2	no	—
381	C₄²×C₇	—	2	2	no	—
382	C₄²×C₇	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	—	2	2	no	—
388	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₇	C₂⁴	1	1	yes	characteristic
401	C₄²×C₇	C₂⁴	1	1	yes	characteristic
402	C₄²×C₇	C₂⁴	1	1	yes	characteristic
403	C₄²×C₇	C₂⁴	1	1	yes	characteristic
404	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
405	C₂×#135	C₂²×C₇	1	4	yes	—
406	#533	C₂²×C₇	1	1	yes	characteristic
407	#533	C₂²×C₇	1	1	yes	characteristic, complemented
408	#533	C₂²×C₇	1	1	yes	characteristic, complemented
409	#532	C₂²×C₇	1	1	yes	characteristic
410	#532	C₂²×C₇	1	1	yes	characteristic, complemented
411	#532	C₂²×C₇	1	1	yes	characteristic, complemented
412	#529	—	2	1	no	—
413	#529	—	2	1	no	—
414	#529	—	2	1	no	—
415	#529	—	2	1	no	—
416	#529	C₂²×C₇	1	2	yes	—
417	#529	C₂²×C₇	1	2	yes	complemented
418	#525	—	2	1	no	—
419	#525	—	2	1	no	—
420	#525	C₂²×C₇	1	2	yes	—
421	C₄×#41	—	2	1	no	—
422	C₄×#41	—	2	1	no	—
423	C₄×#41	—	2	1	no	—
424	C₄×#41	—	2	1	no	—
425	C₄×#41	—	2	1	no	—
426	C₄×#41	—	2	1	no	—
427	C₄×#41	C₂²×C₇	1	2	yes	—
428	C₄×#41	C₂²×C₇	1	2	yes	—
429	C₄×#41	C₂²×C₇	1	2	yes	—
430	C₄×#41	C₂²×C₇	1	2	yes	—
431	C₄×#41	C₂²×C₇	1	2	yes	complemented
432	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
434	C₂×C₄×D₄	—	2	1	no	—
435	C₂×C₄×D₄	—	2	1	no	—
436	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
438	C₂×#117	—	2	1	no	—
439	C₂×#117	C₂²×C₇	1	1	yes	characteristic
440	C₂²×C₄²	—	2	1	no	—
441	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
442	#485	C₂²×C₇	1	4	yes	complemented
443	#484	C₂²×C₇	1	2	yes	—
444	#483	C₂²×C₇	1	2	yes	—
445	#482	C₂²×C₇	1	4	yes	complemented
446	#481	C₂²×C₇	1	2	yes	—
447	#480	C₂²×C₇	1	2	yes	—
448	#479	C₂²×C₇	1	4	yes	complemented
449	#478	C₂²×C₇	1	4	yes	complemented
450	#477	C₂²×C₇	1	2	yes	complemented
451	#476	C₂²×C₇	1	2	yes	complemented
452	#475	C₂²×C₇	1	2	yes	complemented
453	#474	C₂²×C₇	1	2	yes	complemented
454	#464	C₂²×C₇	1	4	yes	complemented
455	#463	C₂²×C₇	1	4	yes	complemented
456	#462	C₂²×C₇	1	2	yes	complemented
457	#461	C₂²×C₇	1	2	yes	complemented
458	#460	C₂²×C₇	1	2	yes	complemented
459	#459	C₂²×C₇	1	2	yes	complemented
460	#452	C₂²×C₇	1	4	yes	—
461	#451	C₂²×C₇	1	2	yes	—
462	#450	C₂²×C₇	1	2	yes	—
463	#449	C₂²×C₇	1	4	yes	—
464	#448	C₂²×C₇	1	2	yes	—
465	#447	C₂²×C₇	1	2	yes	—
466	#442	C₂²×C₇	1	4	yes	complemented
467	#442	C₂²×C₇	1	4	yes	complemented
468	#441	C₂²×C₇	1	4	yes	complemented
469	#441	C₂²×C₇	1	4	yes	complemented
470	#440	C₂²×C₇	1	4	yes	complemented
471	#440	C₂²×C₇	1	4	yes	complemented
472	#440	C₂²×C₇	1	4	yes	complemented
473	#440	C₂²×C₇	1	4	yes	complemented
474	#432	C₂²×C₇	1	1	yes	characteristic
475	#432	C₂²×C₇	1	1	yes	characteristic
476	#432	C₂²×C₇	1	2	yes	—
477	#432	C₂²×C₇	1	2	yes	complemented
478	#432	C₂²×C₇	1	2	yes	complemented
479	#427	C₂²×C₇	1	4	yes	complemented
480	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
481	#416	C₂²×C₇	1	4	yes	—
482	#416	C₂²×C₇	1	4	yes	complemented
483	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
484	C₂×#97	C₂²×C₇	1	2	yes	complemented
485	C₂³×C₇	—	2	4	no	—
486	C₂³×C₇	—	2	2	no	—
487	C₂³×C₇	—	2	2	no	—
488	C₂³×C₇	—	2	2	no	—
489	C₂³×C₇	—	2	2	no	—
490	C₂³×C₇	—	4	1	no	—
491	C₂³×C₇	—	4	2	no	—
492	C₂³×C₇	—	4	2	no	—
493	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
494	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
495	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
496	C₇×Q₈	—	2	4	no	—
497	C₇×Q₈	—	2	2	no	—
498	C₇×Q₈	—	2	4	no	—
499	C₇×Q₈	—	4	2	no	—
500	C₇×Q₈	—	4	2	no	—
501	C₇×Q₈	C₂×#41	1	4	yes	—
502	C₇×D₄	—	2	8	no	—
503	C₇×D₄	—	2	4	no	—
504	C₇×D₄	—	2	8	no	—
505	C₇×D₄	—	2	2	no	—
506	C₇×D₄	—	2	4	no	—
507	C₇×D₄	—	4	2	no	—
508	C₇×D₄	—	4	4	no	—
509	C₇×D₄	—	4	4	no	—
510	C₇×D₄	—	4	4	no	—
511	C₇×D₄	—	4	2	no	—
512	C₇×D₄	C₂×#41	1	4	yes	—
513	C₂×C₄×C₇	—	2	4	no	—
514	C₂×C₄×C₇	—	2	8	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	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	8	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	2	no	—
528	C₂×C₄×C₇	—	2	2	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	1	no	—
533	C₂×C₄×C₇	—	4	1	no	—
534	C₂×C₄×C₇	—	4	1	no	—
535	C₂×C₄×C₇	—	4	1	no	—
536	C₂×C₄×C₇	—	4	1	no	—
537	C₂×C₄×C₇	—	4	1	no	—
538	C₂×C₄×C₇	—	4	1	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	4	no	—
543	C₂×C₄×C₇	—	4	4	no	—
544	C₂×C₄×C₇	—	4	2	no	—
545	C₂×C₄×C₇	—	4	2	no	—
546	C₂×C₄×C₇	—	4	4	no	—
547	C₂×C₄×C₇	—	4	4	no	—
548	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₇	C₂×#41	1	4	yes	—
560	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
561	C₇×C₈	—	2	4	no	—
562	C₇×C₈	—	2	4	no	—
563	C₂×#41	—	2	8	no	—
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	C₂³×C₇	1	2	yes	—
569	C₂×#41	C₂³×C₇	1	2	yes	—
570	C₂×#41	C₂³×C₇	1	2	yes	—
571	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	—	2	1	no	—
576	C₂³×C₄	—	2	1	no	—
577	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
578	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
580	#135	—	2	16	no	—
581	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
584	C₂×D₈	C₂³×C₇	1	4	yes	—
585	C₂²×C₈	C₂³×C₇	1	4	yes	—
586	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
587	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
588	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
589	#127	C₂³×C₇	1	1	yes	characteristic
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	1	no	—
593	#125	—	2	1	no	—
594	#125	C₂³×C₇	1	2	yes	—
595	#124	—	2	1	no	—
596	#124	—	2	1	no	—
597	#124	C₂³×C₇	1	2	yes	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	1	no	—
605	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
606	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	C₂³×C₇	1	2	yes	—
612	#121	C₂³×C₇	1	2	yes	—
613	#120	—	2	2	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	—	2	1	no	—
620	C₄×Q₈	—	2	1	no	—
621	C₄×Q₈	—	2	1	no	—
622	C₄×Q₈	C₂³×C₇	1	2	yes	—
623	C₄×Q₈	C₂³×C₇	1	2	yes	—
624	C₄×Q₈	C₂³×C₇	1	2	yes	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×Q₈	C₂³×C₇	1	2	yes	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	C₂³×C₇	1	2	yes	—
651	C₄×D₄	C₂³×C₇	1	2	yes	—
652	C₄×D₄	C₂³×C₇	1	2	yes	—
653	C₄×D₄	C₂³×C₇	1	2	yes	—
654	C₄×D₄	C₂³×C₇	1	2	yes	—
655	C₄×D₄	C₂³×C₇	1	2	yes	—
656	#117	—	2	1	no	—
657	#117	—	2	1	no	—
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	—	2	2	no	—
667	#117	C₂³×C₇	1	2	yes	—
668	#117	C₂³×C₇	1	2	yes	—
669	#117	C₂³×C₇	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	2	no	—
681	C₂×C₄²	—	2	2	no	—
682	C₂×C₄²	—	2	2	no	—
683	C₂×C₄²	—	2	2	no	—
684	C₂×C₄²	—	2	2	no	—
685	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
686	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
687	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
688	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
689	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
697	#107	C₂³×C₇	1	4	yes	—
698	#107	C₂³×C₇	1	4	yes	—
699	#106	C₂³×C₇	1	4	yes	—
700	#106	C₂³×C₇	1	4	yes	—
701	C₄⋊C₈	C₂³×C₇	1	2	yes	—
702	C₄⋊C₈	C₂³×C₇	1	2	yes	—
703	C₄⋊C₈	C₂³×C₇	1	4	yes	—
704	#103	C₂³×C₇	1	4	yes	—
705	#103	C₂³×C₇	1	4	yes	—
706	#103	C₂³×C₇	1	4	yes	—
707	#103	C₂³×C₇	1	4	yes	—
708	#102	C₂³×C₇	1	4	yes	—
709	#102	C₂³×C₇	1	4	yes	—
710	#102	C₂³×C₇	1	4	yes	—
711	#102	C₂³×C₇	1	4	yes	—
712	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
715	#97	C₂³×C₇	1	2	yes	—
716	#97	C₂³×C₇	1	4	yes	—
717	#97	C₂³×C₇	1	2	yes	—
718	C₂²×C₇	—	2	1	no	—
719	C₂²×C₇	—	2	1	no	—
720	C₂²×C₇	—	2	1	no	—
721	C₂²×C₇	—	2	1	no	—
722	C₂²×C₇	—	2	1	no	—
723	C₂²×C₇	—	2	4	no	—
724	C₂²×C₇	—	2	1	no	—
725	C₂²×C₇	—	2	1	no	—
726	C₂²×C₇	—	4	4	no	—
727	C₂²×C₇	—	4	8	no	—
728	C₂²×C₇	—	4	2	no	—
729	C₂²×C₇	—	4	2	no	—
730	C₂²×C₇	—	4	2	no	—
731	C₂²×C₇	—	4	2	no	—
732	C₂²×C₇	—	4	2	no	—
733	C₂²×C₇	#525	1	2	yes	—
734	C₂²×C₇	#575	1	2	yes	—
735	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
736	C₄×C₇	—	2	1	no	—
737	C₄×C₇	—	2	4	no	—
738	C₄×C₇	—	2	1	no	—
739	C₄×C₇	—	2	1	no	—
740	C₄×C₇	—	2	1	no	—
741	C₄×C₇	—	2	1	no	—
742	C₄×C₇	—	2	1	no	—
743	C₄×C₇	—	2	1	no	—
744	C₄×C₇	—	2	1	no	—
745	C₄×C₇	—	2	1	no	—
746	C₄×C₇	—	4	2	no	—
747	C₄×C₇	—	4	2	no	—
748	C₄×C₇	—	4	2	no	—
749	C₄×C₇	—	4	2	no	—
750	C₄×C₇	—	4	2	no	—
751	C₄×C₇	#525	1	2	yes	—
752	C₄×C₇	#575	1	2	yes	—
753	C₄×C₇	C₂²×#41	1	2	yes	—
754	C₂⁴	—	2	1	no	—
755	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
756	#41	—	2	8	no	—
757	#41	—	2	8	no	—
758	#41	—	2	4	no	—
759	#41	—	2	4	no	—
760	#41	—	2	4	no	—
761	#41	—	2	8	no	—
762	#41	—	4	4	no	—
763	#41	—	4	4	no	—
764	#41	C₇×#41	1	8	yes	complemented
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	—	2	1	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
771	C₂×D₄	—	2	8	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	C₂⁴×C₇	1	2	yes	—
782	C₂×D₄	C₂⁴×C₇	1	2	yes	—
783	C₂²×C₄	—	2	8	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	4	no	—
800	C₂²×C₄	—	4	4	no	—
801	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
802	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
803	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
804	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
805	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
806	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
807	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
808	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
809	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
810	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
812	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
813	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
814	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
815	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
819	Q₁₆	—	2	8	no	—
820	SD₁₆	—	2	8	no	—
821	SD₁₆	—	2	8	no	—
822	D₈	—	2	8	no	—
823	C₂×C₈	—	2	8	no	—
824	C₂×C₈	C₂⁴×C₇	1	4	yes	—
825	C₂×C₈	C₂⁴×C₇	1	4	yes	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
871	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
872	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
873	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
874	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
875	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
876	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
877	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
878	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
879	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
880	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
881	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
882	C₄²	C₂⁴×C₇	1	1	yes	characteristic
883	C₄²	C₂⁴×C₇	1	1	yes	characteristic
884	C₄²	C₂⁴×C₇	1	1	yes	characteristic
885	C₄²	C₂⁴×C₇	1	1	yes	characteristic
886	C₂×C₇	—	2	2	no	—
887	C₂×C₇	—	2	2	no	—
888	C₂×C₇	—	4	1	no	—
889	C₂×C₇	—	4	4	no	—
890	C₂×C₇	—	8	2	no	—
891	C₂×C₇	C₂×#525	1	1	yes	characteristic
892	C₂×C₇	C₂×#575	1	1	yes	characteristic
893	C₂×C₇	C₂×#575	1	1	yes	characteristic
894	C₂³	—	2	4	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	2	no	—
901	C₂³	—	4	2	no	—
902	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
903	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
904	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
905	Q₈	—	2	4	no	—
906	Q₈	—	2	2	no	—
907	Q₈	—	2	4	no	—
908	Q₈	—	4	2	no	—
909	Q₈	—	4	2	no	—
910	Q₈	C₂×C₇×#41	1	4	yes	—
911	D₄	—	2	8	no	—
912	D₄	—	2	4	no	—
913	D₄	—	2	8	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	4	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	4	no	—
918	D₄	—	4	4	no	—
919	D₄	—	4	4	no	—
920	D₄	—	4	2	no	—
921	D₄	C₂×C₇×#41	1	4	yes	—
922	C₂×C₄	—	2	4	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	8	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	1	no	—
944	C₂×C₄	—	4	1	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	4	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	2	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
958	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
959	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
960	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
961	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
962	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
963	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
964	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
965	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
966	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
967	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
968	C₂×C₄	C₂×C₇×#41	1	4	yes	—
969	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
970	C₈	—	2	4	no	—
971	C₈	—	2	4	no	—
972	C₇	#60546	1	1	yes	characteristic, direct product factor, Sylow
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	4	4	no	—
982	C₂²	—	4	8	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	C₇×#525	1	2	yes	—
989	C₂²	C₇×#575	1	2	yes	—
990	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	4	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	C₇×#525	1	2	yes	—
1007	C₄	C₇×#575	1	2	yes	—
1008	C₄	C₂²×C₇×#41	1	2	yes	—
1009	C₂	—	2	2	no	—
1010	C₂	—	2	2	no	—
1011	C₂	—	4	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₂×C₇×#525	1	1	yes	characteristic
1015	C₂	C₂×C₇×#575	1	1	yes	characteristic
1016	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₇×#3117	C₂	semidirect
4. C₇×#3116	C₂	semidirect
5. C₇×#3115	C₂	semidirect
6. C₇×#3114	C₂	semidirect
7. C₇×#3113	C₂	semidirect
8. C₇×#3112	C₂	semidirect
9. C₇×#3111	C₂	semidirect
10. C₇×#3110	C₂	semidirect
11. C₇×#3109	C₂	semidirect
12. C₇×#3091	C₂	semidirect
13. C₇×#3076	C₂	semidirect
14. C₇×#3035	C₂	semidirect
15. C₇×#3002	C₂	semidirect
16. C₇×#2943	C₂	semidirect
17. C₂×C₇×#432	C₂	semidirect
21. C₇×#533	C₂²	semidirect
22. C₇×#533	C₂²	semidirect
24. C₇×#532	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
31. C₇×#529	C₂²	semidirect
45. C₄×C₇×#41	C₂²	semidirect
56. C₇×#485	C₂²	semidirect
59. C₇×#482	C₂²	semidirect
62. C₇×#479	C₂²	semidirect
63. C₇×#478	C₂²	semidirect
64. C₇×#477	C₂²	semidirect
65. C₇×#476	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#464	C₂²	semidirect
69. C₇×#463	C₂²	semidirect
70. C₇×#462	C₂²	semidirect
71. C₇×#461	C₂²	semidirect
72. C₇×#460	C₂²	semidirect
73. C₇×#459	C₂²	semidirect
80. C₇×#442	C₂²	semidirect
81. C₇×#442	C₂²	semidirect
82. C₇×#441	C₂²	semidirect
83. C₇×#441	C₂²	semidirect
84. C₇×#440	C₂²	semidirect
85. C₇×#440	C₂²	semidirect
86. C₇×#440	C₂²	semidirect
87. C₇×#440	C₂²	semidirect
91. C₇×#432	C₂²	semidirect
92. C₇×#432	C₂²	semidirect
93. C₇×#427	C₂²	semidirect
94. C₂×C₇×C₄⋊C₈	C₂²	semidirect
96. C₇×#416	C₂²	semidirect
98. C₂×C₇×#97	C₂²	semidirect
99. #60546	C₇	direct (N × H)
255. #3444	C₂×C₇	semidirect
256. C₂×C₄×#41	C₂×C₇	semidirect
257. #3117	C₂×C₇	semidirect
258. #3116	C₂×C₇	semidirect
259. #3115	C₂×C₇	semidirect
260. #3114	C₂×C₇	semidirect
261. #3113	C₂×C₇	semidirect
262. #3112	C₂×C₇	semidirect
263. #3111	C₂×C₇	semidirect
264. #3110	C₂×C₇	semidirect
265. #3109	C₂×C₇	semidirect
266. #3091	C₂×C₇	semidirect
267. #3076	C₂×C₇	semidirect
268. #3035	C₂×C₇	semidirect
269. #3002	C₂×C₇	semidirect
270. #2943	C₂×C₇	semidirect
271. C₂×#432	C₂×C₇	semidirect
282. C₇×#41	#41	semidirect
407. #533	C₂²×C₇	semidirect
408. #533	C₂²×C₇	semidirect
410. #532	C₂²×C₇	semidirect
411. #532	C₂²×C₇	semidirect
417. #529	C₂²×C₇	semidirect
431. C₄×#41	C₂²×C₇	semidirect
442. #485	C₂²×C₇	semidirect
445. #482	C₂²×C₇	semidirect
448. #479	C₂²×C₇	semidirect
449. #478	C₂²×C₇	semidirect
450. #477	C₂²×C₇	semidirect
451. #476	C₂²×C₇	semidirect
452. #475	C₂²×C₇	semidirect
453. #474	C₂²×C₇	semidirect
454. #464	C₂²×C₇	semidirect
455. #463	C₂²×C₇	semidirect
456. #462	C₂²×C₇	semidirect
457. #461	C₂²×C₇	semidirect
458. #460	C₂²×C₇	semidirect
459. #459	C₂²×C₇	semidirect
466. #442	C₂²×C₇	semidirect
467. #442	C₂²×C₇	semidirect
468. #441	C₂²×C₇	semidirect
469. #441	C₂²×C₇	semidirect
470. #440	C₂²×C₇	semidirect
471. #440	C₂²×C₇	semidirect
472. #440	C₂²×C₇	semidirect
473. #440	C₂²×C₇	semidirect
477. #432	C₂²×C₇	semidirect
478. #432	C₂²×C₇	semidirect
479. #427	C₂²×C₇	semidirect
480. C₂×C₄⋊C₈	C₂²×C₇	semidirect
482. #416	C₂²×C₇	semidirect
484. C₂×#97	C₂²×C₇	semidirect
764. #41	C₇×#41	semidirect
972. C₇	#60546	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×#3444	2
C₂×C₄×C₇×#41	2
C₇×#3117	2
C₇×#3116	2
C₇×#3115	2
C₇×#3114	2
C₇×#3113	2
C₇×#3112	2
C₇×#3111	2
C₇×#3110	2
C₇×#3109	2
C₇×#3091	2
C₇×#3076	2
C₇×#3035	2
C₇×#3002	2
C₇×#2943	2
C₂×C₇×#432	2
#60546	7

Subgroups — C7×#60546 #13237762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60546 #13237762