Subgroups — C₇×#60562 #13237778

Order 1792.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3116	C₂	1	4	yes	maximal, complemented
4	C₇×#3113	C₂	1	2	yes	maximal, complemented
5	C₇×#3110	C₂	1	2	yes	maximal, complemented
6	C₇×#3107	C₂	1	4	yes	maximal, complemented
7	C₇×#3104	C₂	1	2	yes	maximal, complemented
8	C₇×#3101	C₂	1	2	yes	maximal, complemented
9	C₇×#3095	C₂	1	2	yes	maximal, complemented
10	C₇×#3079	C₂	1	2	yes	maximal, complemented
11	C₇×#3039	C₂	1	2	yes	maximal, complemented
12	C₇×#3007	C₂	1	2	yes	maximal
13	C₄×C₇×#137	C₂	1	4	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
16	C₂×C₇×#137	C₂²	1	4	yes	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	—	2	1	no	—
20	C₇×#533	—	2	1	no	—
21	C₇×#533	C₂²	1	2	yes	—
22	C₇×#533	C₂²	1	2	yes	—
23	C₇×#533	C₂²	1	2	yes	complemented
24	C₇×#533	C₂²	1	2	yes	complemented
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#125	—	2	1	no	—
28	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×C₇×#41	—	2	1	no	—
31	C₄×C₇×#41	—	2	1	no	—
32	C₄×C₇×#41	—	2	1	no	—
33	C₄×C₇×#41	—	2	1	no	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₄×C₇×#41	C₂²	1	2	yes	—
36	C₄×C₇×#41	C₂²	1	2	yes	—
37	C₄×C₇×#41	C₂²	1	2	yes	—
38	C₂×C₄×C₇×Q₈	—	2	1	no	—
39	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
42	C₂×C₄×C₇×D₄	—	2	1	no	—
43	C₂×C₄×C₇×D₄	—	2	1	no	—
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₇×#117	—	2	1	no	—
47	C₂×C₇×#117	—	2	1	no	—
48	C₂×C₇×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₇	—	2	1	no	—
50	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
51	C₇×#485	C₂²	1	8	yes	complemented
52	C₇×#484	C₂²	1	4	yes	—
53	C₇×#483	C₂²	1	4	yes	—
54	C₇×#477	C₂²	1	4	yes	complemented
55	C₇×#476	C₂²	1	4	yes	complemented
56	C₇×#475	C₂²	1	4	yes	complemented
57	C₇×#474	C₂²	1	4	yes	complemented
58	C₇×#462	C₂²	1	4	yes	complemented
59	C₇×#462	C₂²	1	4	yes	complemented
60	C₇×#461	C₂²	1	4	yes	complemented
61	C₇×#461	C₂²	1	4	yes	complemented
62	C₇×#452	C₂²	1	8	yes	—
63	C₇×#451	C₂²	1	4	yes	—
64	C₇×#450	C₂²	1	4	yes	—
65	C₇×#441	C₂²	1	8	yes	complemented
66	C₇×#440	C₂²	1	8	yes	complemented
67	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
68	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
69	C₇×#432	C₂²	1	2	yes	—
70	C₇×#432	C₂²	1	2	yes	complemented
71	C₇×#431	C₂²	1	2	yes	—
72	C₇×#431	C₂²	1	2	yes	complemented
73	C₇×#428	C₂²	1	4	yes	complemented
74	C₇×#423	C₂²	1	2	yes	complemented
75	C₇×#419	C₂²	1	4	yes	complemented
76	C₇×#417	C₂²	1	4	yes	—
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
79	#60562	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	8	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	—	2	1	no	—
83	C₂×C₇×#41	C₂³	1	2	yes	—
84	C₂×C₇×#41	C₂³	1	2	yes	—
85	C₂²×C₇×Q₈	—	2	1	no	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	C₂³	1	2	yes	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	—	2	1	no	—
93	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
96	C₇×#137	—	2	16	no	—
97	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
98	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
99	C₂×C₇×M₁₆	C₂³	1	4	yes	—
100	C₇×C₄⋊Q₈	—	2	1	no	—
101	C₇×C₄⋊Q₈	—	2	1	no	—
102	C₇×C₄⋊Q₈	—	2	1	no	—
103	C₇×C₄⋊Q₈	—	2	1	no	—
104	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₇×#125	—	2	2	no	—
109	C₇×#125	—	2	2	no	—
110	C₇×#125	—	2	2	no	—
111	C₇×#125	—	2	2	no	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	2	no	—
114	C₇×C₂²⋊Q₈	—	2	2	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	2	no	—
117	C₇×C₂²⋊Q₈	—	2	2	no	—
118	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₄×C₇×Q₈	—	2	2	no	—
121	C₄×C₇×Q₈	—	2	2	no	—
122	C₄×C₇×Q₈	—	2	2	no	—
123	C₄×C₇×Q₈	—	2	2	no	—
124	C₄×C₇×Q₈	—	2	1	no	—
125	C₄×C₇×Q₈	—	2	1	no	—
126	C₄×C₇×Q₈	—	2	1	no	—
127	C₄×C₇×Q₈	—	2	1	no	—
128	C₄×C₇×Q₈	—	2	2	no	—
129	C₄×C₇×Q₈	—	2	2	no	—
130	C₄×C₇×Q₈	C₂³	1	2	yes	—
131	C₄×C₇×Q₈	C₂³	1	2	yes	—
132	C₄×C₇×Q₈	C₂³	1	2	yes	—
133	C₄×C₇×Q₈	C₂³	1	2	yes	—
134	C₄×C₇×Q₈	C₂³	1	4	yes	—
135	C₄×C₇×Q₈	C₂³	1	4	yes	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	2	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	—	2	2	no	—
144	C₄×C₇×D₄	—	2	1	no	—
145	C₄×C₇×D₄	—	2	1	no	—
146	C₄×C₇×D₄	—	2	1	no	—
147	C₄×C₇×D₄	—	2	1	no	—
148	C₄×C₇×D₄	C₂³	1	2	yes	—
149	C₄×C₇×D₄	C₂³	1	2	yes	—
150	C₄×C₇×D₄	C₂³	1	2	yes	—
151	C₄×C₇×D₄	C₂³	1	2	yes	—
152	C₇×#117	—	2	2	no	—
153	C₇×#117	—	2	2	no	—
154	C₇×#117	—	2	2	no	—
155	C₇×#117	—	2	2	no	—
156	C₇×#117	—	2	1	no	—
157	C₇×#117	—	2	1	no	—
158	C₇×#117	—	2	2	no	—
159	C₇×#117	—	2	2	no	—
160	C₇×#117	—	2	2	no	—
161	C₇×#117	—	2	2	no	—
162	C₇×#117	C₂³	1	2	yes	—
163	C₇×#117	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	—	2	1	no	—
165	C₂×C₇×C₄⋊C₄	—	2	1	no	—
166	C₂×C₇×C₄⋊C₄	—	2	1	no	—
167	C₂×C₇×C₄⋊C₄	—	2	1	no	—
168	C₂×C₇×C₄⋊C₄	—	2	1	no	—
169	C₂×C₇×C₄⋊C₄	—	2	2	no	—
170	C₂×C₇×C₄⋊C₄	—	2	2	no	—
171	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
175	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₄²×C₇	—	2	1	no	—
179	C₂×C₄²×C₇	—	2	1	no	—
180	C₂×C₄²×C₇	—	2	1	no	—
181	C₂×C₄²×C₇	—	2	2	no	—
182	C₂×C₄²×C₇	—	2	2	no	—
183	C₂×C₄²×C₇	—	2	2	no	—
184	C₂×C₄²×C₇	—	2	2	no	—
185	C₂×C₄²×C₇	—	2	2	no	—
186	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₇×#107	C₂³	1	8	yes	—
199	C₇×#106	C₂³	1	8	yes	—
200	C₇×C₄⋊C₈	C₂³	1	4	yes	—
201	C₇×C₄⋊C₈	C₂³	1	4	yes	—
202	C₇×#103	C₂³	1	8	yes	—
203	C₇×#103	C₂³	1	8	yes	—
204	C₇×#103	C₂³	1	8	yes	—
205	C₇×#102	C₂³	1	8	yes	—
206	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₇×#97	C₂³	1	4	yes	—
209	C₄×C₇×C₈	C₂³	1	4	yes	—
210	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
211	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
212	#3116	C₂×C₇	1	4	yes	complemented
213	#3113	C₂×C₇	1	2	yes	complemented
214	#3110	C₂×C₇	1	2	yes	complemented
215	#3107	C₂×C₇	1	4	yes	complemented
216	#3104	C₂×C₇	1	2	yes	complemented
217	#3101	C₂×C₇	1	2	yes	complemented
218	#3095	C₂×C₇	1	2	yes	complemented
219	#3079	C₂×C₇	1	2	yes	complemented
220	#3039	C₂×C₇	1	2	yes	complemented
221	#3007	C₂×C₇	1	2	yes	—
222	C₄×#137	C₂×C₇	1	4	yes	complemented
223	#2920	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂⁴×C₇	—	2	1	no	—
225	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
226	C₇×#41	—	2	8	no	—
227	C₇×#41	—	2	8	no	—
228	C₇×#41	—	2	4	no	—
229	C₇×#41	—	2	4	no	—
230	C₇×#41	—	2	4	no	—
231	C₇×#41	#41	1	8	yes	—
232	C₂×C₇×Q₈	—	2	4	no	—
233	C₂×C₇×Q₈	—	2	1	no	—
234	C₂×C₇×Q₈	—	2	2	no	—
235	C₂×C₇×Q₈	—	2	2	no	—
236	C₂×C₇×Q₈	—	2	2	no	—
237	C₂×C₇×Q₈	—	2	8	no	—
238	C₂×C₇×Q₈	—	4	4	no	—
239	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
240	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
241	C₂×C₇×D₄	—	2	8	no	—
242	C₂×C₇×D₄	—	2	2	no	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	4	no	—
245	C₂×C₇×D₄	—	2	1	no	—
246	C₂×C₇×D₄	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇	—	2	8	no	—
248	C₂²×C₄×C₇	—	2	1	no	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	—	2	2	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	4	no	—
253	C₂²×C₄×C₇	—	2	1	no	—
254	C₂²×C₄×C₇	—	2	1	no	—
255	C₂²×C₄×C₇	—	2	2	no	—
256	C₂²×C₄×C₇	—	2	2	no	—
257	C₂²×C₄×C₇	—	2	2	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	2	no	—
261	C₂²×C₄×C₇	—	4	2	no	—
262	C₂²×C₄×C₇	—	4	4	no	—
263	C₂²×C₄×C₇	—	4	4	no	—
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₇×Q₁₆	—	2	16	no	—
283	C₇×SD₁₆	—	2	16	no	—
284	C₇×M₁₆	—	2	8	no	—
285	C₂×C₇×C₈	C₂⁴	1	8	yes	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	2	no	—
289	C₇×C₄⋊C₄	—	2	2	no	—
290	C₇×C₄⋊C₄	—	2	2	no	—
291	C₇×C₄⋊C₄	—	2	2	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	2	no	—
294	C₇×C₄⋊C₄	—	2	2	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	4	no	—
297	C₇×C₄⋊C₄	—	2	4	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	4	no	—
300	C₇×C₄⋊C₄	—	2	1	no	—
301	C₇×C₄⋊C₄	—	2	1	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	2	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	2	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	2	no	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	—	2	2	no	—
316	C₄²×C₇	—	2	2	no	—
317	C₄²×C₇	—	2	2	no	—
318	C₄²×C₇	—	2	2	no	—
319	C₄²×C₇	—	2	4	no	—
320	C₄²×C₇	—	2	2	no	—
321	C₄²×C₇	—	2	4	no	—
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₇	C₂⁴	1	1	yes	characteristic
336	C₄²×C₇	C₂⁴	1	1	yes	characteristic
337	C₄²×C₇	C₂⁴	1	1	yes	characteristic
338	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
339	C₂×#137	C₂²×C₇	1	4	yes	—
340	#533	—	2	1	no	—
341	#533	—	2	1	no	—
342	#533	—	2	1	no	—
343	#533	—	2	1	no	—
344	#533	C₂²×C₇	1	2	yes	—
345	#533	C₂²×C₇	1	2	yes	—
346	#533	C₂²×C₇	1	2	yes	complemented
347	#533	C₂²×C₇	1	2	yes	complemented
348	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
349	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₂×#125	—	2	1	no	—
351	C₂×C₂²⋊Q₈	—	2	1	no	—
352	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
353	C₄×#41	—	2	1	no	—
354	C₄×#41	—	2	1	no	—
355	C₄×#41	—	2	1	no	—
356	C₄×#41	—	2	1	no	—
357	C₄×#41	C₂²×C₇	1	2	yes	—
358	C₄×#41	C₂²×C₇	1	2	yes	—
359	C₄×#41	C₂²×C₇	1	2	yes	—
360	C₄×#41	C₂²×C₇	1	2	yes	—
361	C₂×C₄×Q₈	—	2	1	no	—
362	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
365	C₂×C₄×D₄	—	2	1	no	—
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
369	C₂×#117	—	2	1	no	—
370	C₂×#117	—	2	1	no	—
371	C₂×#117	C₂²×C₇	1	1	yes	characteristic
372	C₂²×C₄²	—	2	1	no	—
373	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
374	#485	C₂²×C₇	1	8	yes	complemented
375	#484	C₂²×C₇	1	4	yes	—
376	#483	C₂²×C₇	1	4	yes	—
377	#477	C₂²×C₇	1	4	yes	complemented
378	#476	C₂²×C₇	1	4	yes	complemented
379	#475	C₂²×C₇	1	4	yes	complemented
380	#474	C₂²×C₇	1	4	yes	complemented
381	#462	C₂²×C₇	1	4	yes	complemented
382	#462	C₂²×C₇	1	4	yes	complemented
383	#461	C₂²×C₇	1	4	yes	complemented
384	#461	C₂²×C₇	1	4	yes	complemented
385	#452	C₂²×C₇	1	8	yes	—
386	#451	C₂²×C₇	1	4	yes	—
387	#450	C₂²×C₇	1	4	yes	—
388	#441	C₂²×C₇	1	8	yes	complemented
389	#440	C₂²×C₇	1	8	yes	complemented
390	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
391	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
392	#432	C₂²×C₇	1	2	yes	—
393	#432	C₂²×C₇	1	2	yes	complemented
394	#431	C₂²×C₇	1	2	yes	—
395	#431	C₂²×C₇	1	2	yes	complemented
396	#428	C₂²×C₇	1	4	yes	complemented
397	#423	C₂²×C₇	1	2	yes	complemented
398	#419	C₂²×C₇	1	4	yes	complemented
399	#417	C₂²×C₇	1	4	yes	—
400	#407	C₂²×C₇	1	2	yes	—
401	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
402	C₂³×C₇	—	2	4	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	2	2	no	—
405	C₂³×C₇	—	2	2	no	—
406	C₂³×C₇	—	4	1	no	—
407	C₂³×C₇	—	4	2	no	—
408	C₂³×C₇	—	4	2	no	—
409	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
410	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
412	C₇×Q₈	—	2	4	no	—
413	C₇×Q₈	—	2	2	no	—
414	C₇×Q₈	—	2	8	no	—
415	C₇×Q₈	—	4	4	no	—
416	C₇×Q₈	—	4	4	no	—
417	C₇×Q₈	—	4	4	no	—
418	C₇×Q₈	C₂×#41	1	4	yes	—
419	C₇×D₄	—	2	8	no	—
420	C₇×D₄	—	2	4	no	—
421	C₇×D₄	—	2	8	no	—
422	C₇×D₄	—	2	2	no	—
423	C₇×D₄	C₂×#41	1	4	yes	—
424	C₂×C₄×C₇	—	2	4	no	—
425	C₂×C₄×C₇	—	2	8	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	8	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	4	no	—
444	C₂×C₄×C₇	—	2	4	no	—
445	C₂×C₄×C₇	—	4	1	no	—
446	C₂×C₄×C₇	—	4	1	no	—
447	C₂×C₄×C₇	—	4	1	no	—
448	C₂×C₄×C₇	—	4	4	no	—
449	C₂×C₄×C₇	—	4	2	no	—
450	C₂×C₄×C₇	—	4	4	no	—
451	C₂×C₄×C₇	—	4	4	no	—
452	C₂×C₄×C₇	—	4	2	no	—
453	C₂×C₄×C₇	—	4	4	no	—
454	C₂×C₄×C₇	—	4	4	no	—
455	C₂×C₄×C₇	—	4	4	no	—
456	C₂×C₄×C₇	#137	1	4	yes	complemented
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂×#41	1	4	yes	—
469	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
470	C₇×C₈	—	2	8	no	—
471	C₂×#41	—	2	8	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	C₂³×C₇	1	2	yes	—
475	C₂×#41	C₂³×C₇	1	2	yes	—
476	C₂²×Q₈	—	2	1	no	—
477	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₇	1	2	yes	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
485	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
487	#137	—	2	16	no	—
488	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
489	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
490	C₂×M₁₆	C₂³×C₇	1	4	yes	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	—	2	1	no	—
493	C₄⋊Q₈	—	2	1	no	—
494	C₄⋊Q₈	—	2	1	no	—
495	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
498	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
499	#125	—	2	2	no	—
500	#125	—	2	2	no	—
501	#125	—	2	2	no	—
502	#125	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
510	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
511	C₄×Q₈	—	2	2	no	—
512	C₄×Q₈	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	C₂³×C₇	1	2	yes	—
522	C₄×Q₈	C₂³×C₇	1	2	yes	—
523	C₄×Q₈	C₂³×C₇	1	2	yes	—
524	C₄×Q₈	C₂³×C₇	1	2	yes	—
525	C₄×Q₈	C₂³×C₇	1	4	yes	—
526	C₄×Q₈	C₂³×C₇	1	4	yes	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	C₂³×C₇	1	2	yes	—
540	C₄×D₄	C₂³×C₇	1	2	yes	—
541	C₄×D₄	C₂³×C₇	1	2	yes	—
542	C₄×D₄	C₂³×C₇	1	2	yes	—
543	#117	—	2	2	no	—
544	#117	—	2	2	no	—
545	#117	—	2	2	no	—
546	#117	—	2	2	no	—
547	#117	—	2	1	no	—
548	#117	—	2	1	no	—
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	C₂³×C₇	1	2	yes	—
554	#117	C₂³×C₇	1	2	yes	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	2	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₂²⋊C₄	—	2	2	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	2	no	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	—	2	2	no	—
574	C₂×C₄²	—	2	2	no	—
575	C₂×C₄²	—	2	2	no	—
576	C₂×C₄²	—	2	2	no	—
577	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
578	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
579	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
580	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
581	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
582	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
586	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
589	#107	C₂³×C₇	1	8	yes	—
590	#106	C₂³×C₇	1	8	yes	—
591	C₄⋊C₈	C₂³×C₇	1	4	yes	—
592	C₄⋊C₈	C₂³×C₇	1	4	yes	—
593	#103	C₂³×C₇	1	8	yes	—
594	#103	C₂³×C₇	1	8	yes	—
595	#103	C₂³×C₇	1	8	yes	—
596	#102	C₂³×C₇	1	8	yes	—
597	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
598	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
599	#97	C₂³×C₇	1	4	yes	—
600	C₄×C₈	C₂³×C₇	1	4	yes	—
601	C₂²×C₇	—	2	1	no	—
602	C₂²×C₇	—	2	1	no	—
603	C₂²×C₇	—	2	1	no	—
604	C₂²×C₇	—	2	1	no	—
605	C₂²×C₇	—	2	1	no	—
606	C₂²×C₇	—	2	4	no	—
607	C₂²×C₇	—	2	1	no	—
608	C₂²×C₇	—	2	1	no	—
609	C₂²×C₇	—	4	4	no	—
610	C₂²×C₇	—	4	8	no	—
611	C₂²×C₇	—	4	2	no	—
612	C₂²×C₇	—	4	2	no	—
613	C₂²×C₇	#525	1	2	yes	—
614	C₂²×C₇	C₂×#137	1	2	yes	—
615	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₇	—	2	1	no	—
617	C₄×C₇	—	2	4	no	—
618	C₄×C₇	—	2	1	no	—
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	2	1	no	—
621	C₄×C₇	—	2	1	no	—
622	C₄×C₇	—	2	1	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	4	4	no	—
625	C₄×C₇	—	4	2	no	—
626	C₄×C₇	—	4	2	no	—
627	C₄×C₇	—	4	4	no	—
628	C₄×C₇	#525	1	2	yes	—
629	C₄×C₇	C₂×#137	1	2	yes	—
630	C₄×C₇	C₂×#137	1	2	yes	—
631	C₄×C₇	#575	1	2	yes	—
632	C₄×C₇	C₂²×#41	1	2	yes	—
633	C₂⁴	—	2	1	no	—
634	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
635	#41	—	2	8	no	—
636	#41	—	2	8	no	—
637	#41	—	2	4	no	—
638	#41	—	2	4	no	—
639	#41	—	2	4	no	—
640	#41	C₇×#41	1	8	yes	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	8	no	—
647	C₂×Q₈	—	4	4	no	—
648	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
649	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	C₂⁴×C₇	1	2	yes	—
656	C₂²×C₄	—	2	8	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	4	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
678	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
679	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
680	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
681	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
682	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
683	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
684	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
685	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
686	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
687	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
691	Q₁₆	—	2	16	no	—
692	SD₁₆	—	2	16	no	—
693	M₁₆	—	2	8	no	—
694	C₂×C₈	C₂⁴×C₇	1	8	yes	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
713	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
714	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	2	4	no	—
731	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
732	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
733	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
734	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
735	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
736	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
737	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
738	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
739	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
740	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
741	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
742	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
743	C₄²	C₂⁴×C₇	1	1	yes	characteristic
744	C₄²	C₂⁴×C₇	1	1	yes	characteristic
745	C₄²	C₂⁴×C₇	1	1	yes	characteristic
746	C₄²	C₂⁴×C₇	1	1	yes	characteristic
747	C₂×C₇	—	2	2	no	—
748	C₂×C₇	—	2	2	no	—
749	C₂×C₇	—	4	1	no	—
750	C₂×C₇	—	4	4	no	—
751	C₂×C₇	C₂×#525	1	1	yes	characteristic
752	C₂×C₇	C₂²×#137	1	1	yes	characteristic
753	C₂×C₇	C₂×#575	1	1	yes	characteristic
754	C₂³	—	2	4	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
762	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
763	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
764	Q₈	—	2	4	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	8	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	4	no	—
769	Q₈	—	4	4	no	—
770	Q₈	C₂×C₇×#41	1	4	yes	—
771	D₄	—	2	8	no	—
772	D₄	—	2	4	no	—
773	D₄	—	2	8	no	—
774	D₄	—	2	2	no	—
775	D₄	C₂×C₇×#41	1	4	yes	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	8	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	8	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	C₇×#137	1	4	yes	complemented
809	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
810	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
811	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
813	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
815	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
816	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
817	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
818	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
820	C₂×C₄	C₂×C₇×#41	1	4	yes	—
821	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
822	C₈	—	2	8	no	—
823	C₇	#60562	1	1	yes	characteristic, direct product factor, Sylow
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	8	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	C₇×#525	1	2	yes	—
837	C₂²	C₂×C₇×#137	1	2	yes	—
838	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	4	no	—
851	C₄	C₇×#525	1	2	yes	—
852	C₄	C₂×C₇×#137	1	2	yes	—
853	C₄	C₂×C₇×#137	1	2	yes	—
854	C₄	C₇×#575	1	2	yes	—
855	C₄	C₂²×C₇×#41	1	2	yes	—
856	C₂	—	2	2	no	—
857	C₂	—	2	2	no	—
858	C₂	—	4	1	no	—
859	C₂	—	4	4	no	—
860	C₂	C₂×C₇×#525	1	1	yes	characteristic
861	C₂	C₂²×C₇×#137	1	1	yes	characteristic
862	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
prime radical	C₂²×C₇×#41	C₂²
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. C₂×C₇×#533	C₂	semidirect
3. C₇×#3116	C₂	semidirect
4. C₇×#3113	C₂	semidirect
5. C₇×#3110	C₂	semidirect
6. C₇×#3107	C₂	semidirect
7. C₇×#3104	C₂	semidirect
8. C₇×#3101	C₂	semidirect
9. C₇×#3095	C₂	semidirect
10. C₇×#3079	C₂	semidirect
11. C₇×#3039	C₂	semidirect
13. C₄×C₇×#137	C₂	semidirect
14. C₇×#2920	C₂	semidirect
23. C₇×#533	C₂²	semidirect
24. C₇×#533	C₂²	semidirect
25. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₄×C₇×Q₈	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
54. C₇×#477	C₂²	semidirect
55. C₇×#476	C₂²	semidirect
56. C₇×#475	C₂²	semidirect
57. C₇×#474	C₂²	semidirect
58. C₇×#462	C₂²	semidirect
59. C₇×#462	C₂²	semidirect
60. C₇×#461	C₂²	semidirect
61. C₇×#461	C₂²	semidirect
65. C₇×#441	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₄×C₇×Q₁₆	C₂²	semidirect
68. C₄×C₇×SD₁₆	C₂²	semidirect
70. C₇×#432	C₂²	semidirect
72. C₇×#431	C₂²	semidirect
73. C₇×#428	C₂²	semidirect
74. C₇×#423	C₂²	semidirect
75. C₇×#419	C₂²	semidirect
78. C₄×C₇×M₁₆	C₂²	semidirect
79. #60562	C₇	direct (N × H)
210. C₂×#533	C₂×C₇	semidirect
212. #3116	C₂×C₇	semidirect
213. #3113	C₂×C₇	semidirect
214. #3110	C₂×C₇	semidirect
215. #3107	C₂×C₇	semidirect
216. #3104	C₂×C₇	semidirect
217. #3101	C₂×C₇	semidirect
218. #3095	C₂×C₇	semidirect
219. #3079	C₂×C₇	semidirect
220. #3039	C₂×C₇	semidirect
222. C₄×#137	C₂×C₇	semidirect
223. #2920	C₂×C₇	semidirect
346. #533	C₂²×C₇	semidirect
347. #533	C₂²×C₇	semidirect
348. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
349. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
364. C₂×C₄×Q₈	C₂²×C₇	semidirect
374. #485	C₂²×C₇	semidirect
377. #477	C₂²×C₇	semidirect
378. #476	C₂²×C₇	semidirect
379. #475	C₂²×C₇	semidirect
380. #474	C₂²×C₇	semidirect
381. #462	C₂²×C₇	semidirect
382. #462	C₂²×C₇	semidirect
383. #461	C₂²×C₇	semidirect
384. #461	C₂²×C₇	semidirect
388. #441	C₂²×C₇	semidirect
389. #440	C₂²×C₇	semidirect
390. C₄×Q₁₆	C₂²×C₇	semidirect
391. C₄×SD₁₆	C₂²×C₇	semidirect
393. #432	C₂²×C₇	semidirect
395. #431	C₂²×C₇	semidirect
396. #428	C₂²×C₇	semidirect
397. #423	C₂²×C₇	semidirect
398. #419	C₂²×C₇	semidirect
401. C₄×M₁₆	C₂²×C₇	semidirect
456. C₂×C₄×C₇	#137	semidirect
808. C₂×C₄	C₇×#137	semidirect
823. C₇	#60562	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×#533	2
C₂×C₄×C₇×#41	2
C₇×#3116	2
C₇×#3113	2
C₇×#3110	2
C₇×#3107	2
C₇×#3104	2
C₇×#3101	2
C₇×#3095	2
C₇×#3079	2
C₇×#3039	2
C₇×#3007	2
C₄×C₇×#137	2
C₇×#2920	2
#60562	7

Subgroups — C7×#60562 #13237778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60562 #13237778