Subgroups — C₇×#60560 #13237776

Order 1792.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 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
2	C₂²×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3117	C₂	1	4	yes	maximal, complemented
4	C₇×#3113	C₂	1	2	yes	maximal, complemented
5	C₇×#3112	C₂	1	2	yes	maximal, complemented
6	C₇×#3108	C₂	1	4	yes	maximal, complemented
7	C₇×#3104	C₂	1	2	yes	maximal, complemented
8	C₇×#3103	C₂	1	2	yes	maximal, complemented
9	C₇×#3092	C₂	1	2	yes	maximal, complemented
10	C₇×#3078	C₂	1	2	yes	maximal, complemented
11	C₇×#3037	C₂	1	2	yes	maximal, complemented
12	C₇×#3004	C₂	1	2	yes	maximal, complemented
13	C₄×C₇×#137	C₂	1	4	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×#137	C₂²	1	4	yes	—
17	C₇×#533	C₂²	1	1	yes	characteristic
18	C₇×#533	C₂²	1	1	yes	characteristic
19	C₇×#533	C₂²	1	1	yes	characteristic
20	C₇×#532	C₂²	1	1	yes	characteristic
21	C₇×#532	C₂²	1	1	yes	characteristic
22	C₇×#532	C₂²	1	1	yes	characteristic
23	C₇×#529	—	2	1	no	—
24	C₇×#529	—	2	1	no	—
25	C₇×#529	—	2	1	no	—
26	C₇×#529	—	2	1	no	—
27	C₇×#529	C₂²	1	2	yes	—
28	C₇×#529	C₂²	1	2	yes	—
29	C₇×#525	—	2	1	no	—
30	C₇×#525	—	2	1	no	—
31	C₇×#525	C₂²	1	2	yes	—
32	C₄×C₇×#41	—	2	1	no	—
33	C₄×C₇×#41	—	2	1	no	—
34	C₄×C₇×#41	C₂²	1	2	yes	—
35	C₂×C₄×C₇×Q₈	—	2	1	no	—
36	C₂×C₄×C₇×Q₈	—	2	1	no	—
37	C₂×C₄×C₇×Q₈	—	2	1	no	—
38	C₂×C₄×C₇×Q₈	—	2	1	no	—
39	C₂×C₄×C₇×Q₈	—	2	1	no	—
40	C₂×C₄×C₇×Q₈	—	2	1	no	—
41	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
42	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
43	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
44	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
45	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
46	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
47	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
48	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₇	—	2	1	no	—
50	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
51	C₇×#484	C₂²	1	4	yes	—
52	C₇×#483	C₂²	1	4	yes	—
53	C₇×#481	C₂²	1	4	yes	—
54	C₇×#480	C₂²	1	4	yes	—
55	C₇×#479	C₂²	1	8	yes	complemented
56	C₇×#477	C₂²	1	4	yes	complemented
57	C₇×#475	C₂²	1	4	yes	complemented
58	C₇×#464	C₂²	1	8	yes	complemented
59	C₇×#462	C₂²	1	4	yes	complemented
60	C₇×#460	C₂²	1	4	yes	complemented
61	C₇×#451	C₂²	1	4	yes	—
62	C₇×#451	C₂²	1	4	yes	—
63	C₇×#448	C₂²	1	4	yes	—
64	C₇×#448	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	—
71	C₇×#431	C₂²	1	2	yes	—
72	C₇×#431	C₂²	1	2	yes	—
73	C₇×#428	C₂²	1	4	yes	—
74	C₇×#423	C₂²	1	2	yes	—
75	C₇×#419	C₂²	1	4	yes	—
76	C₇×#417	C₂²	1	4	yes	—
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	—
79	#60560	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	C₂³	1	2	yes	—
83	C₂²×C₇×Q₈	—	2	8	no	—
84	C₂²×C₇×Q₈	—	2	1	no	—
85	C₂²×C₇×Q₈	—	2	1	no	—
86	C₂²×C₇×Q₈	—	2	1	no	—
87	C₂²×C₇×Q₈	C₂³	1	2	yes	—
88	C₂²×C₇×Q₈	C₂³	1	2	yes	—
89	C₂²×C₇×Q₈	C₂³	1	2	yes	—
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₇×#137	—	2	16	no	—
96	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
97	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
98	C₂×C₇×M₁₆	C₂³	1	4	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₇×#127	C₂³	1	1	yes	characteristic
103	C₇×#126	—	2	2	no	—
104	C₇×#126	—	2	2	no	—
105	C₇×#125	—	2	1	no	—
106	C₇×#125	—	2	1	no	—
107	C₇×#125	C₂³	1	2	yes	—
108	C₇×#124	—	2	1	no	—
109	C₇×#124	—	2	1	no	—
110	C₇×#124	C₂³	1	2	yes	—
111	C₇×#123	—	2	2	no	—
112	C₇×#123	—	2	2	no	—
113	C₇×#123	—	2	2	no	—
114	C₇×C₂²⋊Q₈	—	2	1	no	—
115	C₇×C₂²⋊Q₈	—	2	1	no	—
116	C₇×C₂²⋊Q₈	—	2	1	no	—
117	C₇×C₂²⋊Q₈	—	2	1	no	—
118	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
120	C₇×#121	—	2	1	no	—
121	C₇×#121	—	2	1	no	—
122	C₇×#121	—	2	1	no	—
123	C₇×#121	—	2	1	no	—
124	C₇×#121	C₂³	1	2	yes	—
125	C₇×#121	C₂³	1	2	yes	—
126	C₇×#120	—	2	2	no	—
127	C₄×C₇×Q₈	—	2	2	no	—
128	C₄×C₇×Q₈	—	2	2	no	—
129	C₄×C₇×Q₈	—	2	2	no	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	—	2	2	no	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	—	2	2	no	—
135	C₄×C₇×Q₈	—	2	2	no	—
136	C₄×C₇×Q₈	—	2	2	no	—
137	C₄×C₇×Q₈	—	2	2	no	—
138	C₄×C₇×Q₈	—	2	2	no	—
139	C₄×C₇×Q₈	—	2	1	no	—
140	C₄×C₇×Q₈	—	2	1	no	—
141	C₄×C₇×Q₈	—	2	1	no	—
142	C₄×C₇×Q₈	—	2	1	no	—
143	C₄×C₇×Q₈	C₂³	1	4	yes	—
144	C₄×C₇×Q₈	C₂³	1	4	yes	—
145	C₄×C₇×Q₈	C₂³	1	4	yes	—
146	C₄×C₇×Q₈	C₂³	1	4	yes	—
147	C₄×C₇×Q₈	C₂³	1	2	yes	—
148	C₄×C₇×Q₈	C₂³	1	2	yes	—
149	C₄×C₇×D₄	—	2	2	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	2	no	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	1	no	—
156	C₄×C₇×D₄	—	2	1	no	—
157	C₄×C₇×D₄	—	2	1	no	—
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	C₂³	1	2	yes	—
160	C₄×C₇×D₄	C₂³	1	2	yes	—
161	C₇×#117	—	2	1	no	—
162	C₇×#117	—	2	1	no	—
163	C₇×#117	—	2	2	no	—
164	C₇×#117	—	2	2	no	—
165	C₇×#117	—	2	2	no	—
166	C₇×#117	C₂³	1	2	yes	—
167	C₂×C₇×C₄⋊C₄	—	2	2	no	—
168	C₂×C₇×C₄⋊C₄	—	2	2	no	—
169	C₂×C₇×C₄⋊C₄	—	2	2	no	—
170	C₂×C₇×C₄⋊C₄	—	2	2	no	—
171	C₂×C₇×C₄⋊C₄	—	2	2	no	—
172	C₂×C₇×C₄⋊C₄	—	2	2	no	—
173	C₂×C₇×C₄⋊C₄	—	2	1	no	—
174	C₂×C₇×C₄⋊C₄	—	2	1	no	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₇	—	2	2	no	—
180	C₂×C₄²×C₇	—	2	2	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	#3444	C₂×C₇	1	1	yes	characteristic
211	C₂²×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
212	#3117	C₂×C₇	1	4	yes	complemented
213	#3113	C₂×C₇	1	2	yes	complemented
214	#3112	C₂×C₇	1	2	yes	complemented
215	#3108	C₂×C₇	1	4	yes	complemented
216	#3104	C₂×C₇	1	2	yes	complemented
217	#3103	C₂×C₇	1	2	yes	complemented
218	#3092	C₂×C₇	1	2	yes	complemented
219	#3078	C₂×C₇	1	2	yes	complemented
220	#3037	C₂×C₇	1	2	yes	complemented
221	#3004	C₂×C₇	1	2	yes	complemented
222	C₄×#137	C₂×C₇	1	4	yes	complemented
223	#2920	C₂×C₇	1	1	yes	characteristic, complemented
224	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
225	C₇×#41	—	2	8	no	—
226	C₇×#41	—	4	4	no	—
227	C₇×#41	—	4	4	no	—
228	C₂×C₇×Q₈	—	2	8	no	—
229	C₂×C₇×Q₈	—	2	8	no	—
230	C₂×C₇×Q₈	—	2	8	no	—
231	C₂×C₇×Q₈	—	2	8	no	—
232	C₂×C₇×Q₈	—	2	8	no	—
233	C₂×C₇×Q₈	—	2	2	no	—
234	C₂×C₇×Q₈	—	2	2	no	—
235	C₂×C₇×Q₈	—	2	2	no	—
236	C₂×C₇×Q₈	—	2	1	no	—
237	C₂×C₇×Q₈	—	2	1	no	—
238	C₂×C₇×Q₈	—	2	4	no	—
239	C₂×C₇×Q₈	#41	1	8	yes	complemented
240	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
241	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
242	C₂×C₇×D₄	—	2	2	no	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	2	no	—
245	C₂×C₇×D₄	—	2	1	no	—
246	C₂×C₇×D₄	—	2	1	no	—
247	C₂×C₇×D₄	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₇	—	2	8	no	—
249	C₂²×C₄×C₇	—	2	2	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	4	no	—
254	C₂²×C₄×C₇	—	2	2	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	—	4	2	no	—
261	C₂²×C₄×C₇	—	4	4	no	—
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₇×Q₁₆	—	2	16	no	—
281	C₇×SD₁₆	—	2	16	no	—
282	C₇×M₁₆	—	2	8	no	—
283	C₂×C₇×C₈	C₂⁴	1	8	yes	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	2	4	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	1	no	—
292	C₇×C₄⋊C₄	—	2	1	no	—
293	C₇×C₄⋊C₄	—	2	1	no	—
294	C₇×C₄⋊C₄	—	2	1	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	2	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	C₄²×C₇	—	2	4	no	—
314	C₄²×C₇	—	2	4	no	—
315	C₄²×C₇	—	2	4	no	—
316	C₄²×C₇	—	2	2	no	—
317	C₄²×C₇	—	2	2	no	—
318	C₄²×C₇	—	2	4	no	—
319	C₄²×C₇	—	2	2	no	—
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
333	C₄²×C₇	C₂⁴	1	1	yes	characteristic
334	C₄²×C₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₇	C₂⁴	1	1	yes	characteristic
336	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
337	C₂×#137	C₂²×C₇	1	4	yes	—
338	#533	C₂²×C₇	1	1	yes	characteristic
339	#533	C₂²×C₇	1	1	yes	characteristic
340	#533	C₂²×C₇	1	1	yes	characteristic
341	#532	C₂²×C₇	1	1	yes	characteristic
342	#532	C₂²×C₇	1	1	yes	characteristic
343	#532	C₂²×C₇	1	1	yes	characteristic
344	#529	—	2	1	no	—
345	#529	—	2	1	no	—
346	#529	—	2	1	no	—
347	#529	—	2	1	no	—
348	#529	C₂²×C₇	1	2	yes	—
349	#529	C₂²×C₇	1	2	yes	—
350	#525	—	2	1	no	—
351	#525	—	2	1	no	—
352	#525	C₂²×C₇	1	2	yes	—
353	C₄×#41	—	2	1	no	—
354	C₄×#41	—	2	1	no	—
355	C₄×#41	C₂²×C₇	1	2	yes	—
356	C₂×C₄×Q₈	—	2	1	no	—
357	C₂×C₄×Q₈	—	2	1	no	—
358	C₂×C₄×Q₈	—	2	1	no	—
359	C₂×C₄×Q₈	—	2	1	no	—
360	C₂×C₄×Q₈	—	2	1	no	—
361	C₂×C₄×Q₈	—	2	1	no	—
362	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
363	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
365	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
368	C₂²×C₄⋊C₄	—	2	1	no	—
369	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
370	C₂²×C₄²	—	2	1	no	—
371	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
372	#484	C₂²×C₇	1	4	yes	—
373	#483	C₂²×C₇	1	4	yes	—
374	#481	C₂²×C₇	1	4	yes	—
375	#480	C₂²×C₇	1	4	yes	—
376	#479	C₂²×C₇	1	8	yes	complemented
377	#477	C₂²×C₇	1	4	yes	complemented
378	#475	C₂²×C₇	1	4	yes	complemented
379	#464	C₂²×C₇	1	8	yes	complemented
380	#462	C₂²×C₇	1	4	yes	complemented
381	#460	C₂²×C₇	1	4	yes	complemented
382	#451	C₂²×C₇	1	4	yes	—
383	#451	C₂²×C₇	1	4	yes	—
384	#448	C₂²×C₇	1	4	yes	—
385	#448	C₂²×C₇	1	4	yes	—
386	#441	C₂²×C₇	1	8	yes	complemented
387	#440	C₂²×C₇	1	8	yes	complemented
388	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
389	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
390	#432	C₂²×C₇	1	2	yes	—
391	#432	C₂²×C₇	1	2	yes	—
392	#431	C₂²×C₇	1	2	yes	—
393	#431	C₂²×C₇	1	2	yes	—
394	#428	C₂²×C₇	1	4	yes	—
395	#423	C₂²×C₇	1	2	yes	—
396	#419	C₂²×C₇	1	4	yes	—
397	#417	C₂²×C₇	1	4	yes	—
398	#407	C₂²×C₇	1	2	yes	—
399	C₄×M₁₆	C₂²×C₇	1	2	yes	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	2	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
405	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₇×Q₈	—	2	8	no	—
408	C₇×Q₈	—	2	8	no	—
409	C₇×Q₈	—	2	8	no	—
410	C₇×Q₈	—	2	4	no	—
411	C₇×Q₈	—	2	4	no	—
412	C₇×Q₈	—	4	2	no	—
413	C₇×Q₈	—	4	2	no	—
414	C₇×Q₈	C₂×#41	1	8	yes	—
415	C₇×D₄	—	2	4	no	—
416	C₇×D₄	—	4	2	no	—
417	C₇×D₄	—	4	4	no	—
418	C₇×D₄	—	4	4	no	—
419	C₇×D₄	—	4	4	no	—
420	C₇×D₄	—	4	2	no	—
421	C₂×C₄×C₇	—	2	8	no	—
422	C₂×C₄×C₇	—	2	8	no	—
423	C₂×C₄×C₇	—	2	8	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	4	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	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	4	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	—	4	1	no	—
442	C₂×C₄×C₇	—	4	1	no	—
443	C₂×C₄×C₇	—	4	1	no	—
444	C₂×C₄×C₇	—	4	1	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	4	4	no	—
447	C₂×C₄×C₇	—	4	4	no	—
448	C₂×C₄×C₇	—	4	4	no	—
449	C₂×C₄×C₇	—	4	4	no	—
450	C₂×C₄×C₇	—	4	4	no	—
451	C₂×C₄×C₇	#137	1	4	yes	complemented
452	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	4	yes	—
464	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
465	C₇×C₈	—	2	8	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	C₂³×C₇	1	2	yes	—
469	C₂²×Q₈	—	2	8	no	—
470	C₂²×Q₈	—	2	1	no	—
471	C₂²×Q₈	—	2	1	no	—
472	C₂²×Q₈	—	2	1	no	—
473	C₂²×Q₈	C₂³×C₇	1	2	yes	—
474	C₂²×Q₈	C₂³×C₇	1	2	yes	—
475	C₂²×Q₈	C₂³×C₇	1	2	yes	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
479	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
481	#137	—	2	16	no	—
482	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
483	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
484	C₂×M₁₆	C₂³×C₇	1	4	yes	—
485	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
486	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
488	#127	C₂³×C₇	1	1	yes	characteristic
489	#126	—	2	2	no	—
490	#126	—	2	2	no	—
491	#125	—	2	1	no	—
492	#125	—	2	1	no	—
493	#125	C₂³×C₇	1	2	yes	—
494	#124	—	2	1	no	—
495	#124	—	2	1	no	—
496	#124	C₂³×C₇	1	2	yes	—
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	#123	—	2	2	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	—	2	1	no	—
510	#121	C₂³×C₇	1	2	yes	—
511	#121	C₂³×C₇	1	2	yes	—
512	#120	—	2	2	no	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	C₂³×C₇	1	4	yes	—
530	C₄×Q₈	C₂³×C₇	1	4	yes	—
531	C₄×Q₈	C₂³×C₇	1	4	yes	—
532	C₄×Q₈	C₂³×C₇	1	4	yes	—
533	C₄×Q₈	C₂³×C₇	1	2	yes	—
534	C₄×Q₈	C₂³×C₇	1	2	yes	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	C₂³×C₇	1	2	yes	—
546	C₄×D₄	C₂³×C₇	1	2	yes	—
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	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	—	2	2	no	—
557	C₂×C₄⋊C₄	—	2	2	no	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₄²	—	2	2	no	—
566	C₂×C₄²	—	2	2	no	—
567	C₂×C₄²	—	2	2	no	—
568	C₂×C₄²	—	2	2	no	—
569	C₂×C₄²	—	2	2	no	—
570	C₂×C₄²	—	2	2	no	—
571	C₂×C₄²	—	2	2	no	—
572	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
573	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
574	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
575	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
576	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
577	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
584	#107	C₂³×C₇	1	8	yes	—
585	#106	C₂³×C₇	1	8	yes	—
586	C₄⋊C₈	C₂³×C₇	1	4	yes	—
587	C₄⋊C₈	C₂³×C₇	1	4	yes	—
588	#103	C₂³×C₇	1	8	yes	—
589	#103	C₂³×C₇	1	8	yes	—
590	#103	C₂³×C₇	1	8	yes	—
591	#102	C₂³×C₇	1	8	yes	—
592	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
593	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
594	#97	C₂³×C₇	1	4	yes	—
595	C₄×C₈	C₂³×C₇	1	4	yes	—
596	C₂²×C₇	—	2	8	no	—
597	C₂²×C₇	—	2	1	no	—
598	C₂²×C₇	—	2	1	no	—
599	C₂²×C₇	—	2	1	no	—
600	C₂²×C₇	—	2	1	no	—
601	C₂²×C₇	—	2	1	no	—
602	C₂²×C₇	—	2	1	no	—
603	C₂²×C₇	—	4	2	no	—
604	C₂²×C₇	—	4	2	no	—
605	C₂²×C₇	—	4	2	no	—
606	C₂²×C₇	#525	1	2	yes	—
607	C₂²×C₇	C₂×#137	1	2	yes	—
608	C₂²×C₇	#575	1	2	yes	—
609	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
610	C₄×C₇	—	2	8	no	—
611	C₄×C₇	—	2	1	no	—
612	C₄×C₇	—	2	1	no	—
613	C₄×C₇	—	2	1	no	—
614	C₄×C₇	—	2	1	no	—
615	C₄×C₇	—	2	1	no	—
616	C₄×C₇	—	2	1	no	—
617	C₄×C₇	—	2	1	no	—
618	C₄×C₇	—	2	1	no	—
619	C₄×C₇	—	4	2	no	—
620	C₄×C₇	—	4	2	no	—
621	C₄×C₇	—	4	4	no	—
622	C₄×C₇	—	4	2	no	—
623	C₄×C₇	#525	1	2	yes	—
624	C₄×C₇	C₂×#137	1	2	yes	—
625	C₄×C₇	C₂×#137	1	2	yes	—
626	C₄×C₇	C₂²×#41	1	2	yes	—
627	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
628	#41	—	2	8	no	—
629	#41	—	4	4	no	—
630	#41	—	4	4	no	—
631	C₂×Q₈	—	2	8	no	—
632	C₂×Q₈	—	2	8	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	2	8	no	—
635	C₂×Q₈	—	2	8	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	C₇×#41	1	8	yes	complemented
643	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
644	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	C₂⁴×C₇	1	2	yes	—
651	C₂²×C₄	—	2	8	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	4	no	—
665	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
666	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
683	Q₁₆	—	2	16	no	—
684	SD₁₆	—	2	16	no	—
685	M₁₆	—	2	8	no	—
686	C₂×C₈	C₂⁴×C₇	1	8	yes	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	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	C₂⁴×C₇	1	4	yes	—
705	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₄²	—	2	4	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	4	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
724	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
725	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
726	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
727	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
728	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
729	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
730	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
736	C₄²	C₂⁴×C₇	1	1	yes	characteristic
737	C₄²	C₂⁴×C₇	1	1	yes	characteristic
738	C₄²	C₂⁴×C₇	1	1	yes	characteristic
739	C₂×C₇	—	2	2	no	—
740	C₂×C₇	—	2	2	no	—
741	C₂×C₇	—	2	2	no	—
742	C₂×C₇	—	8	2	no	—
743	C₂×C₇	C₂×#525	1	1	yes	characteristic
744	C₂×C₇	C₂²×#137	1	1	yes	characteristic
745	C₂×C₇	C₂×#575	1	1	yes	characteristic
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
751	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
752	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
753	Q₈	—	2	8	no	—
754	Q₈	—	2	8	no	—
755	Q₈	—	2	4	no	—
756	Q₈	—	2	8	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	4	2	no	—
759	Q₈	—	4	2	no	—
760	Q₈	C₂×C₇×#41	1	8	yes	—
761	D₄	—	2	4	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	8	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	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	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	C₇×#137	1	4	yes	complemented
798	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
800	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
806	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
807	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
808	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
809	C₂×C₄	C₂×C₇×#41	1	4	yes	—
810	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
811	C₈	—	2	8	no	—
812	C₇	#60560	1	1	yes	characteristic, direct product factor, Sylow
813	C₂²	—	2	8	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	C₇×#525	1	2	yes	—
824	C₂²	C₂×C₇×#137	1	2	yes	—
825	C₂²	C₇×#575	1	2	yes	—
826	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	8	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	4	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	C₇×#525	1	2	yes	—
841	C₄	C₂×C₇×#137	1	2	yes	—
842	C₄	C₂×C₇×#137	1	2	yes	—
843	C₄	C₂²×C₇×#41	1	2	yes	—
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	2	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₇×#525	1	1	yes	characteristic
849	C₂	C₂²×C₇×#137	1	1	yes	characteristic
850	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	C₇×#3444	C₂
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
2. C₂²×C₄×C₇×Q₈	C₂	semidirect
3. C₇×#3117	C₂	semidirect
4. C₇×#3113	C₂	semidirect
5. C₇×#3112	C₂	semidirect
6. C₇×#3108	C₂	semidirect
7. C₇×#3104	C₂	semidirect
8. C₇×#3103	C₂	semidirect
9. C₇×#3092	C₂	semidirect
10. C₇×#3078	C₂	semidirect
11. C₇×#3037	C₂	semidirect
12. C₇×#3004	C₂	semidirect
13. C₄×C₇×#137	C₂	semidirect
14. C₇×#2920	C₂	semidirect
55. C₇×#479	C₂²	semidirect
56. C₇×#477	C₂²	semidirect
57. C₇×#475	C₂²	semidirect
58. C₇×#464	C₂²	semidirect
59. C₇×#462	C₂²	semidirect
60. C₇×#460	C₂²	semidirect
65. C₇×#441	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₄×C₇×Q₁₆	C₂²	semidirect
68. C₄×C₇×SD₁₆	C₂²	semidirect
79. #60560	C₇	direct (N × H)
211. C₂²×C₄×Q₈	C₂×C₇	semidirect
212. #3117	C₂×C₇	semidirect
213. #3113	C₂×C₇	semidirect
214. #3112	C₂×C₇	semidirect
215. #3108	C₂×C₇	semidirect
216. #3104	C₂×C₇	semidirect
217. #3103	C₂×C₇	semidirect
218. #3092	C₂×C₇	semidirect
219. #3078	C₂×C₇	semidirect
220. #3037	C₂×C₇	semidirect
221. #3004	C₂×C₇	semidirect
222. C₄×#137	C₂×C₇	semidirect
223. #2920	C₂×C₇	semidirect
239. C₂×C₇×Q₈	#41	semidirect
376. #479	C₂²×C₇	semidirect
377. #477	C₂²×C₇	semidirect
378. #475	C₂²×C₇	semidirect
379. #464	C₂²×C₇	semidirect
380. #462	C₂²×C₇	semidirect
381. #460	C₂²×C₇	semidirect
386. #441	C₂²×C₇	semidirect
387. #440	C₂²×C₇	semidirect
388. C₄×Q₁₆	C₂²×C₇	semidirect
389. C₄×SD₁₆	C₂²×C₇	semidirect
451. C₂×C₄×C₇	#137	semidirect
642. C₂×Q₈	C₇×#41	semidirect
797. C₂×C₄	C₇×#137	semidirect
812. C₇	#60560	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
C₂²×C₄×C₇×Q₈	2
C₇×#3117	2
C₇×#3113	2
C₇×#3112	2
C₇×#3108	2
C₇×#3104	2
C₇×#3103	2
C₇×#3092	2
C₇×#3078	2
C₇×#3037	2
C₇×#3004	2
C₄×C₇×#137	2
C₇×#2920	2
#60560	7

Subgroups — C7×#60560 #13237776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60560 #13237776