Subgroups — C₇×#60949 #13238165

Order 1792.

2092 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3251	C₂	1	4	yes	maximal, complemented
4	C₇×#3239	C₂	1	2	yes	maximal, complemented
5	C₇×#3234	C₂	1	2	yes	maximal, complemented
6	C₇×#3217	C₂	1	2	yes	maximal, complemented
7	C₇×#3213	C₂	1	2	yes	maximal, complemented
8	C₇×#3193	C₂	1	2	yes	maximal, complemented
9	C₇×#3192	C₂	1	2	yes	maximal, complemented
10	C₇×#3171	C₂	1	4	yes	maximal, complemented
11	C₇×#3105	C₂	1	4	yes	maximal, complemented
12	C₇×#3103	C₂	1	2	yes	maximal, complemented
13	C₇×#3100	C₂	1	2	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	—	2	1	no	—
16	C₇×#532	—	2	1	no	—
17	C₇×#532	—	2	1	no	—
18	C₇×#532	—	2	1	no	—
19	C₇×#532	—	2	1	no	—
20	C₇×#532	C₂²	1	2	yes	—
21	C₇×#532	C₂²	1	2	yes	—
22	C₇×#532	C₂²	1	2	yes	complemented
23	C₇×#532	C₂²	1	2	yes	complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×#127	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	—
32	C₇×#529	C₂²	1	2	yes	complemented
33	C₇×#529	C₂²	1	2	yes	complemented
34	C₂×C₇×#126	—	2	1	no	—
35	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₇×#124	—	2	1	no	—
37	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#123	—	2	1	no	—
39	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×#121	—	2	1	no	—
41	C₂×C₇×#121	C₂²	1	1	yes	characteristic
42	C₂×C₇×#121	C₂²	1	2	yes	—
43	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×C₇×D₄	—	2	1	no	—
45	C₂×C₄×C₇×D₄	—	2	1	no	—
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
48	C₂×C₇×#117	—	2	1	no	—
49	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
50	C₇×#501	C₂²	1	4	yes	complemented
51	C₇×#496	C₂²	1	4	yes	complemented
52	C₇×#490	C₂²	1	4	yes	complemented
53	C₇×#489	C₂²	1	4	yes	complemented
54	C₇×#484	C₂²	1	4	yes	complemented
55	C₇×#481	C₂²	1	4	yes	—
56	C₇×#481	C₂²	1	4	yes	complemented
57	C₇×#480	C₂²	1	4	yes	complemented
58	C₇×#478	C₂²	1	8	yes	complemented
59	C₇×#475	C₂²	1	4	yes	complemented
60	C₇×#474	C₂²	1	4	yes	complemented
61	C₇×#469	C₂²	1	8	yes	complemented
62	C₇×#468	C₂²	1	8	yes	complemented
63	C₇×#463	C₂²	1	8	yes	complemented
64	C₇×#460	C₂²	1	4	yes	complemented
65	C₇×#459	C₂²	1	4	yes	complemented
66	C₇×#450	C₂²	1	4	yes	complemented
67	C₇×#448	C₂²	1	4	yes	complemented
68	C₇×#447	C₂²	1	4	yes	—
69	C₇×#447	C₂²	1	4	yes	complemented
70	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
71	C₄×C₇×D₈	C₂²	1	8	yes	complemented
72	C₇×#432	C₂²	1	2	yes	complemented
73	C₇×#432	C₂²	1	2	yes	complemented
74	C₇×#431	C₂²	1	2	yes	complemented
75	C₇×#431	C₂²	1	2	yes	complemented
76	C₇×#423	C₂²	1	2	yes	complemented
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
79	#60949	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	2	no	—
81	C₂×C₇×#41	—	2	2	no	—
82	C₂×C₇×#41	—	2	2	no	—
83	C₂×C₇×#41	—	2	2	no	—
84	C₂×C₇×#41	—	4	8	no	—
85	C₂²×C₇×Q₈	—	2	1	no	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	—	2	2	no	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	—	2	1	no	—
90	C₂²×C₇×D₄	—	2	1	no	—
91	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₇×D₄	C₂³	1	2	yes	—
93	C₂³×C₄×C₇	—	2	2	no	—
94	C₂³×C₄×C₇	—	2	1	no	—
95	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
96	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
99	C₂×C₇×D₈	C₂³	1	8	yes	—
100	C₂×C₇×M₁₆	C₂³	1	4	yes	—
101	C₇×C₄⋊Q₈	—	2	1	no	—
102	C₇×C₄⋊Q₈	—	2	1	no	—
103	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
105	C₇×#127	—	2	1	no	—
106	C₇×#127	—	2	1	no	—
107	C₇×#127	C₂³	1	2	yes	—
108	C₇×#127	C₂³	1	2	yes	—
109	C₇×#126	—	2	2	no	—
110	C₇×#126	—	2	2	no	—
111	C₇×#126	—	2	2	no	—
112	C₇×#126	—	2	2	no	—
113	C₇×#125	—	2	1	no	—
114	C₇×#125	—	2	1	no	—
115	C₇×#125	C₂³	1	2	yes	—
116	C₇×#125	C₂³	1	2	yes	—
117	C₇×#124	—	2	2	no	—
118	C₇×#124	—	2	2	no	—
119	C₇×#124	—	2	2	no	—
120	C₇×#124	—	2	2	no	—
121	C₇×#124	—	2	1	no	—
122	C₇×#124	—	2	1	no	—
123	C₇×#124	C₂³	1	2	yes	—
124	C₇×#124	C₂³	1	2	yes	—
125	C₇×#123	—	2	2	no	—
126	C₇×#123	—	2	2	no	—
127	C₇×#123	—	2	2	no	—
128	C₇×#123	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	1	no	—
130	C₇×C₂²⋊Q₈	—	2	1	no	—
131	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
132	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₇×#121	—	2	2	no	—
134	C₇×#121	—	2	2	no	—
135	C₇×#121	—	2	2	no	—
136	C₇×#121	—	2	2	no	—
137	C₇×#121	—	2	1	no	—
138	C₇×#121	—	2	1	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	C₂³	1	4	yes	—
142	C₇×#121	C₂³	1	2	yes	—
143	C₇×#121	C₂³	1	4	yes	—
144	C₇×#121	C₂³	1	2	yes	—
145	C₄×C₇×Q₈	—	2	1	no	—
146	C₄×C₇×Q₈	—	2	1	no	—
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	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	1	no	—
158	C₄×C₇×D₄	—	2	1	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	C₂³	1	2	yes	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	4	yes	—
165	C₇×#117	—	2	2	no	—
166	C₇×#117	—	2	2	no	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	—	2	2	no	—
169	C₂×C₇×C₄⋊C₄	—	2	1	no	—
170	C₂×C₇×C₄⋊C₄	—	2	1	no	—
171	C₂×C₇×C₄⋊C₄	—	2	1	no	—
172	C₂×C₇×C₄⋊C₄	—	2	1	no	—
173	C₂×C₇×C₄⋊C₄	—	2	1	no	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
183	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₄²×C₇	—	2	1	no	—
185	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
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	C₂³	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	C₇×#107	C₂³	1	8	yes	—
198	C₇×#106	C₂³	1	8	yes	—
199	C₇×C₄⋊C₈	C₂³	1	4	yes	—
200	C₇×C₄⋊C₈	C₂³	1	4	yes	—
201	C₇×#103	C₂³	1	8	yes	—
202	C₇×#102	C₂³	1	8	yes	—
203	C₇×#102	C₂³	1	8	yes	—
204	C₇×#102	C₂³	1	8	yes	—
205	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
206	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
207	C₇×#97	C₂³	1	4	yes	—
208	C₄×C₇×C₈	C₂³	1	4	yes	—
209	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
210	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
211	#3251	C₂×C₇	1	4	yes	complemented
212	#3239	C₂×C₇	1	2	yes	complemented
213	#3234	C₂×C₇	1	2	yes	complemented
214	#3217	C₂×C₇	1	2	yes	complemented
215	#3213	C₂×C₇	1	2	yes	complemented
216	#3193	C₂×C₇	1	2	yes	complemented
217	#3192	C₂×C₇	1	2	yes	complemented
218	#3171	C₂×C₇	1	4	yes	complemented
219	#3105	C₂×C₇	1	4	yes	complemented
220	#3103	C₂×C₇	1	2	yes	complemented
221	#3100	C₂×C₇	1	2	yes	complemented
222	#2920	C₂×C₇	1	1	yes	characteristic, complemented
223	C₂⁴×C₇	—	2	1	no	—
224	C₂⁴×C₇	—	2	2	no	—
225	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
226	C₇×#41	—	4	8	no	—
227	C₇×#41	—	4	8	no	—
228	C₇×#41	—	4	8	no	—
229	C₇×#41	—	4	8	no	—
230	C₂×C₇×Q₈	—	2	1	no	—
231	C₂×C₇×Q₈	—	2	2	no	—
232	C₂×C₇×Q₈	—	2	2	no	—
233	C₂×C₇×Q₈	—	4	2	no	—
234	C₂×C₇×Q₈	—	4	4	no	—
235	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
236	C₂×C₇×D₄	—	2	2	no	—
237	C₂×C₇×D₄	—	2	2	no	—
238	C₂×C₇×D₄	—	2	4	no	—
239	C₂×C₇×D₄	—	2	4	no	—
240	C₂×C₇×D₄	—	2	1	no	—
241	C₂×C₇×D₄	—	2	2	no	—
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	2	no	—
246	C₂×C₇×D₄	—	4	4	no	—
247	C₂×C₇×D₄	—	4	2	no	—
248	C₂×C₇×D₄	—	4	4	no	—
249	C₂×C₇×D₄	—	4	4	no	—
250	C₂×C₇×D₄	—	4	4	no	—
251	C₂×C₇×D₄	—	4	8	no	—
252	C₂×C₇×D₄	C₂⁴	1	2	yes	—
253	C₂×C₇×D₄	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₇	—	2	4	no	—
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	2	4	no	—
261	C₂²×C₄×C₇	—	2	2	no	—
262	C₂²×C₄×C₇	—	2	4	no	—
263	C₂²×C₄×C₇	—	4	2	no	—
264	C₂²×C₄×C₇	—	4	2	no	—
265	C₂²×C₄×C₇	—	4	8	no	—
266	C₂²×C₄×C₇	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₇×SD₁₆	—	4	8	no	—
286	C₇×D₈	—	4	8	no	—
287	C₇×M₁₆	—	4	4	no	—
288	C₂×C₇×C₈	C₂⁴	1	8	yes	—
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	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	1	no	—
301	C₇×C₄⋊C₄	—	2	1	no	—
302	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
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	4	no	—
312	C₇×C₂²⋊C₄	—	2	4	no	—
313	C₇×C₂²⋊C₄	—	2	2	no	—
314	C₇×C₂²⋊C₄	—	2	2	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	2	no	—
318	C₇×C₂²⋊C₄	—	2	2	no	—
319	C₄²×C₇	—	2	2	no	—
320	C₄²×C₇	—	2	2	no	—
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	C₂×D₄	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	C₄²×C₇	C₂⁴	1	1	yes	characteristic
337	C₂²×#41	—	2	1	no	—
338	#532	—	2	1	no	—
339	#532	—	2	1	no	—
340	#532	—	2	1	no	—
341	#532	—	2	1	no	—
342	#532	C₂²×C₇	1	2	yes	—
343	#532	C₂²×C₇	1	2	yes	—
344	#532	C₂²×C₇	1	2	yes	complemented
345	#532	C₂²×C₇	1	2	yes	complemented
346	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
347	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
348	#529	—	2	1	no	—
349	#529	—	2	1	no	—
350	#529	—	2	1	no	—
351	#529	—	2	1	no	—
352	#529	C₂²×C₇	1	2	yes	—
353	#529	C₂²×C₇	1	2	yes	—
354	#529	C₂²×C₇	1	2	yes	complemented
355	#529	C₂²×C₇	1	2	yes	complemented
356	C₂×#126	—	2	1	no	—
357	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×#124	—	2	1	no	—
359	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂×#123	—	2	1	no	—
361	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
362	C₂×#121	—	2	1	no	—
363	C₂×#121	C₂²×C₇	1	1	yes	characteristic
364	C₂×#121	C₂²×C₇	1	2	yes	—
365	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×C₄×D₄	—	2	1	no	—
367	C₂×C₄×D₄	—	2	1	no	—
368	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
370	C₂×#117	—	2	1	no	—
371	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
372	#501	C₂²×C₇	1	4	yes	complemented
373	#496	C₂²×C₇	1	4	yes	complemented
374	#490	C₂²×C₇	1	4	yes	complemented
375	#489	C₂²×C₇	1	4	yes	complemented
376	#484	C₂²×C₇	1	4	yes	complemented
377	#481	C₂²×C₇	1	4	yes	—
378	#481	C₂²×C₇	1	4	yes	complemented
379	#480	C₂²×C₇	1	4	yes	complemented
380	#478	C₂²×C₇	1	8	yes	complemented
381	#475	C₂²×C₇	1	4	yes	complemented
382	#474	C₂²×C₇	1	4	yes	complemented
383	#469	C₂²×C₇	1	8	yes	complemented
384	#468	C₂²×C₇	1	8	yes	complemented
385	#463	C₂²×C₇	1	8	yes	complemented
386	#460	C₂²×C₇	1	4	yes	complemented
387	#459	C₂²×C₇	1	4	yes	complemented
388	#450	C₂²×C₇	1	4	yes	complemented
389	#448	C₂²×C₇	1	4	yes	complemented
390	#447	C₂²×C₇	1	4	yes	—
391	#447	C₂²×C₇	1	4	yes	complemented
392	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
393	C₄×D₈	C₂²×C₇	1	8	yes	complemented
394	#432	C₂²×C₇	1	2	yes	complemented
395	#432	C₂²×C₇	1	2	yes	complemented
396	#431	C₂²×C₇	1	2	yes	complemented
397	#431	C₂²×C₇	1	2	yes	complemented
398	#423	C₂²×C₇	1	2	yes	complemented
399	#407	C₂²×C₇	1	2	yes	—
400	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	2	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	2	4	no	—
405	C₂³×C₇	—	4	1	no	—
406	C₂³×C₇	—	4	4	no	—
407	C₂³×C₇	—	4	2	no	—
408	C₂³×C₇	—	4	4	no	—
409	C₂³×C₇	—	4	2	no	—
410	C₂³×C₇	—	4	2	no	—
411	C₂³×C₇	—	4	4	no	—
412	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
415	C₇×Q₈	—	2	4	no	—
416	C₇×Q₈	—	4	2	no	—
417	C₇×Q₈	—	4	4	no	—
418	C₇×Q₈	—	4	4	no	—
419	C₇×D₄	—	2	4	no	—
420	C₇×D₄	—	2	8	no	—
421	C₇×D₄	—	4	4	no	—
422	C₇×D₄	—	4	2	no	—
423	C₇×D₄	—	4	4	no	—
424	C₇×D₄	—	4	4	no	—
425	C₇×D₄	—	4	4	no	—
426	C₇×D₄	—	4	4	no	—
427	C₇×D₄	—	4	8	no	—
428	C₇×D₄	—	4	8	no	—
429	C₇×D₄	—	4	4	no	—
430	C₇×D₄	—	4	4	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	2	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	1	no	—
449	C₂×C₄×C₇	—	4	1	no	—
450	C₂×C₄×C₇	—	4	1	no	—
451	C₂×C₄×C₇	—	4	1	no	—
452	C₂×C₄×C₇	—	4	8	no	—
453	C₂×C₄×C₇	—	4	4	no	—
454	C₂×C₄×C₇	—	4	2	no	—
455	C₂×C₄×C₇	—	4	2	no	—
456	C₂×C₄×C₇	—	4	2	no	—
457	C₂×C₄×C₇	—	4	4	no	—
458	C₂×C₄×C₇	—	4	4	no	—
459	C₂×C₄×C₇	—	4	8	no	—
460	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
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	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
473	C₇×C₈	—	2	8	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	4	8	no	—
479	C₂²×Q₈	—	2	1	no	—
480	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₇	1	2	yes	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
490	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
492	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
493	C₂×D₈	C₂³×C₇	1	8	yes	—
494	C₂×M₁₆	C₂³×C₇	1	4	yes	—
495	C₄⋊Q₈	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
498	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
499	#127	—	2	1	no	—
500	#127	—	2	1	no	—
501	#127	C₂³×C₇	1	2	yes	—
502	#127	C₂³×C₇	1	2	yes	—
503	#126	—	2	2	no	—
504	#126	—	2	2	no	—
505	#126	—	2	2	no	—
506	#126	—	2	2	no	—
507	#125	—	2	1	no	—
508	#125	—	2	1	no	—
509	#125	C₂³×C₇	1	2	yes	—
510	#125	C₂³×C₇	1	2	yes	—
511	#124	—	2	2	no	—
512	#124	—	2	2	no	—
513	#124	—	2	2	no	—
514	#124	—	2	2	no	—
515	#124	—	2	1	no	—
516	#124	—	2	1	no	—
517	#124	C₂³×C₇	1	2	yes	—
518	#124	C₂³×C₇	1	2	yes	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
526	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	C₂³×C₇	1	2	yes	—
536	#121	C₂³×C₇	1	2	yes	—
537	#121	C₂³×C₇	1	4	yes	—
538	#121	C₂³×C₇	1	4	yes	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	C₂³×C₇	1	2	yes	—
542	C₄×Q₈	C₂³×C₇	1	2	yes	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	C₂³×C₇	1	2	yes	—
556	C₄×D₄	C₂³×C₇	1	2	yes	—
557	C₄×D₄	C₂³×C₇	1	4	yes	—
558	C₄×D₄	C₂³×C₇	1	4	yes	—
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	—	2	2	no	—
562	#117	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	2	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	2	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₄²	—	2	1	no	—
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	C₇×D₄	1	1	yes	characteristic
584	C₂×C₄²	C₇×D₄	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	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
591	#107	C₂³×C₇	1	8	yes	—
592	#106	C₂³×C₇	1	8	yes	—
593	C₄⋊C₈	C₂³×C₇	1	4	yes	—
594	C₄⋊C₈	C₂³×C₇	1	4	yes	—
595	#103	C₂³×C₇	1	8	yes	—
596	#102	C₂³×C₇	1	8	yes	—
597	#102	C₂³×C₇	1	8	yes	—
598	#102	C₂³×C₇	1	8	yes	—
599	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
601	#97	C₂³×C₇	1	4	yes	—
602	C₄×C₈	C₂³×C₇	1	4	yes	—
603	C₂²×C₇	—	2	1	no	—
604	C₂²×C₇	—	2	1	no	—
605	C₂²×C₇	—	2	1	no	—
606	C₂²×C₇	—	2	1	no	—
607	C₂²×C₇	—	2	1	no	—
608	C₂²×C₇	—	2	1	no	—
609	C₂²×C₇	—	2	1	no	—
610	C₂²×C₇	—	4	4	no	—
611	C₂²×C₇	—	4	2	no	—
612	C₂²×C₇	—	4	4	no	—
613	C₂²×C₇	—	4	4	no	—
614	C₂²×C₇	—	4	2	no	—
615	C₂²×C₇	—	4	4	no	—
616	C₂²×C₇	—	4	2	no	—
617	C₂²×C₇	—	8	8	no	—
618	C₂²×C₇	—	8	4	no	—
619	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
620	C₂²×C₇	#575	1	2	yes	—
621	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
622	C₄×C₇	—	2	1	no	—
623	C₄×C₇	—	2	1	no	—
624	C₄×C₇	—	2	1	no	—
625	C₄×C₇	—	2	1	no	—
626	C₄×C₇	—	2	1	no	—
627	C₄×C₇	—	2	1	no	—
628	C₄×C₇	—	2	1	no	—
629	C₄×C₇	—	2	1	no	—
630	C₄×C₇	—	2	1	no	—
631	C₄×C₇	—	4	2	no	—
632	C₄×C₇	—	4	2	no	—
633	C₄×C₇	—	4	4	no	—
634	C₄×C₇	—	4	2	no	—
635	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
636	C₄×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
637	C₄×C₇	#585	1	2	yes	—
638	C₂⁴	—	2	1	no	—
639	C₂⁴	—	2	2	no	—
640	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
641	#41	—	4	8	no	—
642	#41	—	4	8	no	—
643	#41	—	4	8	no	—
644	#41	—	4	8	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	4	no	—
650	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	C₂⁴×C₇	1	2	yes	—
668	C₂×D₄	C₂⁴×C₇	1	4	yes	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	8	no	—
681	C₂²×C₄	—	4	4	no	—
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	C₂×C₇×D₄	1	1	yes	characteristic
689	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
690	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
691	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
692	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
694	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
696	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
700	SD₁₆	—	4	8	no	—
701	D₈	—	4	8	no	—
702	M₁₆	—	4	4	no	—
703	C₂×C₈	C₂⁴×C₇	1	8	yes	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
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	C₂×C₇×D₄	1	1	yes	characteristic
744	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
745	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
746	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
747	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
748	C₄²	C₂⁴×C₇	1	1	yes	characteristic
749	C₄²	C₂⁴×C₇	1	1	yes	characteristic
750	C₄²	C₂⁴×C₇	1	1	yes	characteristic
751	C₄²	C₂⁴×C₇	1	1	yes	characteristic
752	C₂×C₇	—	2	2	no	—
753	C₂×C₇	—	2	2	no	—
754	C₂×C₇	—	4	1	no	—
755	C₂×C₇	—	8	4	no	—
756	C₂×C₇	—	8	2	no	—
757	C₂×C₇	#3449	1	1	yes	characteristic
758	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
759	C₂×C₇	C₂×#575	1	1	yes	characteristic
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	4	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	2	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	2	no	—
770	C₂³	—	4	4	no	—
771	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
772	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
773	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
774	Q₈	—	2	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	4	4	no	—
777	Q₈	—	4	4	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	8	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	2	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	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	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	8	no	—
819	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
820	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
821	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
822	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
823	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
827	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
830	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
832	C₈	—	2	8	no	—
833	C₇	#60949	1	1	yes	characteristic, direct product factor, Sylow
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	8	8	no	—
849	C₂²	—	8	4	no	—
850	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
851	C₂²	C₇×#575	1	2	yes	—
852	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	4	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
867	C₄	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
868	C₄	C₇×#585	1	2	yes	—
869	C₂	—	2	2	no	—
870	C₂	—	2	2	no	—
871	C₂	—	4	1	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	2	no	—
874	C₂	C₇×#3449	1	1	yes	characteristic
875	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
876	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. C₂×C₇×#532	C₂	semidirect
2. C₂×C₇×#529	C₂	semidirect
3. C₇×#3251	C₂	semidirect
4. C₇×#3239	C₂	semidirect
5. C₇×#3234	C₂	semidirect
6. C₇×#3217	C₂	semidirect
7. C₇×#3213	C₂	semidirect
8. C₇×#3193	C₂	semidirect
9. C₇×#3192	C₂	semidirect
10. C₇×#3171	C₂	semidirect
11. C₇×#3105	C₂	semidirect
12. C₇×#3103	C₂	semidirect
13. C₇×#3100	C₂	semidirect
14. C₇×#2920	C₂	semidirect
22. C₇×#532	C₂²	semidirect
23. C₇×#532	C₂²	semidirect
24. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₇×#127	C₂²	semidirect
32. C₇×#529	C₂²	semidirect
33. C₇×#529	C₂²	semidirect
35. C₂×C₇×#125	C₂²	semidirect
37. C₂×C₇×#124	C₂²	semidirect
43. C₂×C₄×C₇×Q₈	C₂²	semidirect
46. C₂×C₄×C₇×D₄	C₂²	semidirect
47. C₂×C₄×C₇×D₄	C₂²	semidirect
50. C₇×#501	C₂²	semidirect
51. C₇×#496	C₂²	semidirect
52. C₇×#490	C₂²	semidirect
53. C₇×#489	C₂²	semidirect
54. C₇×#484	C₂²	semidirect
56. C₇×#481	C₂²	semidirect
57. C₇×#480	C₂²	semidirect
58. C₇×#478	C₂²	semidirect
59. C₇×#475	C₂²	semidirect
60. C₇×#474	C₂²	semidirect
61. C₇×#469	C₂²	semidirect
62. C₇×#468	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#460	C₂²	semidirect
65. C₇×#459	C₂²	semidirect
66. C₇×#450	C₂²	semidirect
67. C₇×#448	C₂²	semidirect
69. C₇×#447	C₂²	semidirect
70. C₄×C₇×SD₁₆	C₂²	semidirect
71. C₄×C₇×D₈	C₂²	semidirect
72. C₇×#432	C₂²	semidirect
73. C₇×#432	C₂²	semidirect
74. C₇×#431	C₂²	semidirect
75. C₇×#431	C₂²	semidirect
76. C₇×#423	C₂²	semidirect
78. C₄×C₇×M₁₆	C₂²	semidirect
79. #60949	C₇	direct (N × H)
209. C₂×#532	C₂×C₇	semidirect
210. C₂×#529	C₂×C₇	semidirect
211. #3251	C₂×C₇	semidirect
212. #3239	C₂×C₇	semidirect
213. #3234	C₂×C₇	semidirect
214. #3217	C₂×C₇	semidirect
215. #3213	C₂×C₇	semidirect
216. #3193	C₂×C₇	semidirect
217. #3192	C₂×C₇	semidirect
218. #3171	C₂×C₇	semidirect
219. #3105	C₂×C₇	semidirect
220. #3103	C₂×C₇	semidirect
221. #3100	C₂×C₇	semidirect
222. #2920	C₂×C₇	semidirect
344. #532	C₂²×C₇	semidirect
345. #532	C₂²×C₇	semidirect
346. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
347. C₂×#127	C₂²×C₇	semidirect
354. #529	C₂²×C₇	semidirect
355. #529	C₂²×C₇	semidirect
357. C₂×#125	C₂²×C₇	semidirect
359. C₂×#124	C₂²×C₇	semidirect
365. C₂×C₄×Q₈	C₂²×C₇	semidirect
368. C₂×C₄×D₄	C₂²×C₇	semidirect
369. C₂×C₄×D₄	C₂²×C₇	semidirect
372. #501	C₂²×C₇	semidirect
373. #496	C₂²×C₇	semidirect
374. #490	C₂²×C₇	semidirect
375. #489	C₂²×C₇	semidirect
376. #484	C₂²×C₇	semidirect
378. #481	C₂²×C₇	semidirect
379. #480	C₂²×C₇	semidirect
380. #478	C₂²×C₇	semidirect
381. #475	C₂²×C₇	semidirect
382. #474	C₂²×C₇	semidirect
383. #469	C₂²×C₇	semidirect
384. #468	C₂²×C₇	semidirect
385. #463	C₂²×C₇	semidirect
386. #460	C₂²×C₇	semidirect
387. #459	C₂²×C₇	semidirect
388. #450	C₂²×C₇	semidirect
389. #448	C₂²×C₇	semidirect
391. #447	C₂²×C₇	semidirect
392. C₄×SD₁₆	C₂²×C₇	semidirect
393. C₄×D₈	C₂²×C₇	semidirect
394. #432	C₂²×C₇	semidirect
395. #432	C₂²×C₇	semidirect
396. #431	C₂²×C₇	semidirect
397. #431	C₂²×C₇	semidirect
398. #423	C₂²×C₇	semidirect
400. C₄×M₁₆	C₂²×C₇	semidirect
833. C₇	#60949	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×#532	2
C₂×C₇×#529	2
C₇×#3251	2
C₇×#3239	2
C₇×#3234	2
C₇×#3217	2
C₇×#3213	2
C₇×#3193	2
C₇×#3192	2
C₇×#3171	2
C₇×#3105	2
C₇×#3103	2
C₇×#3100	2
C₇×#2920	2
#60949	7

Subgroups — C7×#60949 #13238165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60949 #13238165