Subgroups — C₇×#60782 #13237998

Order 1792.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 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×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3212	C₂	1	4	yes	maximal, complemented
4	C₇×#3211	C₂	1	4	yes	maximal, complemented
5	C₇×#3210	C₂	1	2	yes	maximal, complemented
6	C₇×#3209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3207	C₂	1	2	yes	maximal, complemented
9	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3147	C₂	1	2	yes	maximal, complemented
12	C₇×#3131	C₂	1	2	yes	maximal, complemented
13	C₇×#3035	C₂	1	4	yes	maximal, complemented
14	C₇×#3002	C₂	1	4	yes	maximal, complemented
15	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	2	yes	—
17	C₂×C₇×#135	C₂²	1	8	yes	complemented
18	C₇×#533	C₂²	1	1	yes	characteristic
19	C₇×#533	C₂²	1	1	yes	characteristic, complemented
20	C₇×#533	C₂²	1	1	yes	characteristic, complemented
21	C₇×#532	—	2	1	no	—
22	C₇×#532	—	2	1	no	—
23	C₇×#532	—	2	1	no	—
24	C₇×#532	—	2	1	no	—
25	C₇×#532	C₂²	1	2	yes	—
26	C₇×#532	C₂²	1	2	yes	—
27	C₇×#532	C₂²	1	2	yes	—
28	C₇×#532	C₂²	1	2	yes	—
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₇×#532	C₂²	1	1	yes	characteristic, complemented
31	C₇×#532	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×#127	C₂²	1	1	yes	characteristic
34	C₇×#529	—	2	1	no	—
35	C₇×#529	—	2	1	no	—
36	C₇×#529	—	2	1	no	—
37	C₇×#529	—	2	1	no	—
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	2	yes	complemented
40	C₂×C₇×#124	C₂²	1	2	yes	—
41	C₇×#525	—	2	1	no	—
42	C₇×#525	—	2	1	no	—
43	C₇×#525	C₂²	1	2	yes	—
44	C₂×C₇×#121	—	2	1	no	—
45	C₂×C₇×#121	—	2	1	no	—
46	C₄×C₇×#41	—	2	1	no	—
47	C₄×C₇×#41	—	2	1	no	—
48	C₄×C₇×#41	C₂²	1	2	yes	complemented
49	C₂×C₄×C₇×D₄	—	2	1	no	—
50	C₂×C₄×C₇×D₄	—	2	1	no	—
51	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
52	C₇×#495	C₂²	1	8	yes	complemented
53	C₇×#494	C₂²	1	2	yes	complemented
54	C₇×#493	C₂²	1	2	yes	complemented
55	C₇×#492	C₂²	1	2	yes	complemented
56	C₇×#492	C₂²	1	2	yes	complemented
57	C₇×#488	C₂²	1	8	yes	complemented
58	C₇×#487	C₂²	1	2	yes	complemented
59	C₇×#487	C₂²	1	2	yes	complemented
60	C₇×#486	C₂²	1	2	yes	complemented
61	C₇×#486	C₂²	1	2	yes	complemented
62	C₇×#464	C₂²	1	8	yes	complemented
63	C₇×#463	C₂²	1	8	yes	complemented
64	C₇×#462	C₂²	1	4	yes	complemented
65	C₇×#461	C₂²	1	4	yes	complemented
66	C₇×#460	C₂²	1	4	yes	complemented
67	C₇×#459	C₂²	1	4	yes	complemented
68	C₇×#452	C₂²	1	8	yes	complemented
69	C₇×#451	C₂²	1	4	yes	—
70	C₇×#450	C₂²	1	4	yes	—
71	C₇×#449	C₂²	1	8	yes	complemented
72	C₇×#448	C₂²	1	4	yes	—
73	C₇×#447	C₂²	1	4	yes	—
74	C₇×#431	C₂²	1	1	yes	characteristic
75	C₇×#431	C₂²	1	1	yes	characteristic
76	C₇×#431	C₂²	1	2	yes	—
77	C₇×#431	C₂²	1	2	yes	complemented
78	C₇×#431	C₂²	1	2	yes	complemented
79	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
80	C₇×#416	C₂²	1	8	yes	complemented
81	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
82	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
83	#60782	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₇×#41	—	2	2	no	—
85	C₂×C₇×#41	—	2	2	no	—
86	C₂×C₇×#41	—	2	1	no	—
87	C₂×C₇×#41	—	2	1	no	—
88	C₂×C₇×#41	—	4	8	no	—
89	C₂×C₇×#41	C₂³	1	4	yes	—
90	C₂×C₇×#41	C₂³	1	2	yes	—
91	C₂×C₇×#41	C₂³	1	4	yes	—
92	C₂²×C₇×Q₈	C₂³	1	2	yes	—
93	C₂²×C₇×D₄	—	2	2	no	—
94	C₂²×C₇×D₄	—	2	1	no	—
95	C₂²×C₇×D₄	—	2	1	no	—
96	C₂²×C₇×D₄	C₂³	1	2	yes	—
97	C₂³×C₄×C₇	—	2	2	no	—
98	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
99	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
101	C₇×#135	—	4	16	no	—
102	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
103	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
104	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
105	C₂×C₇×D₈	C₂³	1	8	yes	—
106	C₂²×C₇×C₈	C₂³	1	4	yes	—
107	C₇×C₄⋊Q₈	—	2	1	no	—
108	C₇×C₄⋊Q₈	—	2	1	no	—
109	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₇×#127	—	2	1	no	—
115	C₇×#127	—	2	1	no	—
116	C₇×#127	C₂³	1	2	yes	—
117	C₇×#127	C₂³	1	1	yes	characteristic
118	C₇×#127	C₂³	1	2	yes	—
119	C₇×#126	—	2	2	no	—
120	C₇×#126	—	2	2	no	—
121	C₇×#125	—	2	1	no	—
122	C₇×#125	—	2	1	no	—
123	C₇×#125	C₂³	1	2	yes	—
124	C₇×#124	—	2	2	no	—
125	C₇×#124	—	2	2	no	—
126	C₇×#124	—	2	1	no	—
127	C₇×#124	—	2	1	no	—
128	C₇×#124	C₂³	1	4	yes	—
129	C₇×#124	C₂³	1	2	yes	—
130	C₇×#124	C₂³	1	4	yes	—
131	C₇×#123	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	1	no	—
135	C₇×C₂²⋊Q₈	—	2	1	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	2	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	2	no	—
146	C₇×#121	—	2	2	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	1	no	—
149	C₇×#121	—	2	1	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	—	2	1	no	—
152	C₇×#121	C₂³	1	2	yes	—
153	C₇×#121	C₂³	1	2	yes	—
154	C₇×#120	—	2	2	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×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	2	no	—
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	1	no	—
176	C₄×C₇×D₄	—	2	1	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	1	no	—
179	C₄×C₇×D₄	C₂³	1	2	yes	—
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₇×#117	—	2	1	no	—
182	C₇×#117	—	2	1	no	—
183	C₇×#117	—	2	2	no	—
184	C₇×#117	—	2	2	no	—
185	C₇×#117	—	2	2	no	—
186	C₇×#117	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	—	2	1	no	—
188	C₂×C₇×C₄⋊C₄	—	2	1	no	—
189	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
190	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
191	C₂×C₄²×C₇	—	2	2	no	—
192	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₇×C₄⋊C₈	C₂³	1	2	yes	—
205	C₇×C₄⋊C₈	C₂³	1	2	yes	—
206	C₇×C₄⋊C₈	C₂³	1	4	yes	—
207	C₇×#103	C₂³	1	8	yes	—
208	C₇×#103	C₂³	1	8	yes	—
209	C₇×#102	C₂³	1	8	yes	—
210	C₇×#102	C₂³	1	8	yes	—
211	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₄×C₇×C₈	C₂³	1	2	yes	—
215	C₄×C₇×C₈	C₂³	1	2	yes	—
216	C₄×C₇×C₈	C₂³	1	4	yes	—
217	#3444	C₂×C₇	1	1	yes	characteristic, complemented
218	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
219	#3212	C₂×C₇	1	4	yes	complemented
220	#3211	C₂×C₇	1	4	yes	complemented
221	#3210	C₂×C₇	1	2	yes	complemented
222	#3209	C₂×C₇	1	1	yes	characteristic, complemented
223	#3208	C₂×C₇	1	1	yes	characteristic, complemented
224	#3207	C₂×C₇	1	2	yes	complemented
225	#3206	C₂×C₇	1	1	yes	characteristic, complemented
226	#3205	C₂×C₇	1	1	yes	characteristic, complemented
227	#3147	C₂×C₇	1	2	yes	complemented
228	#3131	C₂×C₇	1	2	yes	complemented
229	#3035	C₂×C₇	1	4	yes	complemented
230	#3002	C₂×C₇	1	4	yes	complemented
231	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
232	C₂⁴×C₇	—	2	2	no	—
233	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
234	C₇×#41	—	2	8	no	—
235	C₇×#41	—	2	16	no	—
236	C₇×#41	—	4	8	no	—
237	C₇×#41	—	4	4	no	—
238	C₇×#41	—	4	8	no	—
239	C₇×#41	—	4	8	no	—
240	C₇×#41	—	4	4	no	—
241	C₂×C₇×Q₈	—	2	1	no	—
242	C₂×C₇×Q₈	—	2	1	no	—
243	C₂×C₇×Q₈	—	2	2	no	—
244	C₂×C₇×Q₈	—	4	4	no	—
245	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
246	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	2	4	no	—
252	C₂×C₇×D₄	—	2	1	no	—
253	C₂×C₇×D₄	—	2	1	no	—
254	C₂×C₇×D₄	—	2	2	no	—
255	C₂×C₇×D₄	—	2	2	no	—
256	C₂×C₇×D₄	—	2	2	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	2	no	—
259	C₂×C₇×D₄	—	4	4	no	—
260	C₂×C₇×D₄	—	4	4	no	—
261	C₂×C₇×D₄	—	4	8	no	—
262	C₂×C₇×D₄	—	4	4	no	—
263	C₂×C₇×D₄	C₂⁴	1	4	yes	—
264	C₂×C₇×D₄	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	4	no	—
271	C₂²×C₄×C₇	—	2	2	no	—
272	C₂²×C₄×C₇	—	2	4	no	—
273	C₂²×C₄×C₇	—	4	2	no	—
274	C₂²×C₄×C₇	—	4	8	no	—
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	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₇×Q₁₆	—	4	8	no	—
294	C₇×SD₁₆	—	4	8	no	—
295	C₇×SD₁₆	—	4	8	no	—
296	C₇×D₈	—	4	8	no	—
297	C₂×C₇×C₈	—	2	8	no	—
298	C₂×C₇×C₈	C₂⁴	1	4	yes	—
299	C₂×C₇×C₈	C₂⁴	1	4	yes	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	1	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	2	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₇×C₂²⋊C₄	—	2	2	no	—
317	C₇×C₂²⋊C₄	—	2	2	no	—
318	C₇×C₂²⋊C₄	—	2	2	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	4	no	—
321	C₇×C₂²⋊C₄	—	2	4	no	—
322	C₇×C₂²⋊C₄	—	2	4	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	2	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₄²×C₇	—	2	2	no	—
330	C₄²×C₇	—	2	2	no	—
331	C₄²×C₇	—	2	2	no	—
332	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₇	C₂⁴	1	1	yes	characteristic
345	C₄²×C₇	C₂⁴	1	1	yes	characteristic
346	C₄²×C₇	C₂⁴	1	1	yes	characteristic
347	C₄²×C₇	C₂⁴	1	1	yes	characteristic
348	C₂²×#41	C₂²×C₇	1	2	yes	—
349	C₂×#135	C₂²×C₇	1	8	yes	complemented
350	#533	C₂²×C₇	1	1	yes	characteristic
351	#533	C₂²×C₇	1	1	yes	characteristic, complemented
352	#533	C₂²×C₇	1	1	yes	characteristic, complemented
353	#532	—	2	1	no	—
354	#532	—	2	1	no	—
355	#532	—	2	1	no	—
356	#532	—	2	1	no	—
357	#532	C₂²×C₇	1	2	yes	—
358	#532	C₂²×C₇	1	2	yes	—
359	#532	C₂²×C₇	1	2	yes	—
360	#532	C₂²×C₇	1	2	yes	—
361	#532	C₂²×C₇	1	1	yes	characteristic
362	#532	C₂²×C₇	1	1	yes	characteristic, complemented
363	#532	C₂²×C₇	1	1	yes	characteristic, complemented
364	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
365	C₂×#127	C₂²×C₇	1	1	yes	characteristic
366	#529	—	2	1	no	—
367	#529	—	2	1	no	—
368	#529	—	2	1	no	—
369	#529	—	2	1	no	—
370	#529	C₂²×C₇	1	2	yes	—
371	#529	C₂²×C₇	1	2	yes	complemented
372	C₂×#124	C₂²×C₇	1	2	yes	—
373	#525	—	2	1	no	—
374	#525	—	2	1	no	—
375	#525	C₂²×C₇	1	2	yes	—
376	C₂×#121	—	2	1	no	—
377	C₂×#121	—	2	1	no	—
378	C₄×#41	—	2	1	no	—
379	C₄×#41	—	2	1	no	—
380	C₄×#41	C₂²×C₇	1	2	yes	complemented
381	C₂×C₄×D₄	—	2	1	no	—
382	C₂×C₄×D₄	—	2	1	no	—
383	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
384	#495	C₂²×C₇	1	8	yes	complemented
385	#494	C₂²×C₇	1	2	yes	complemented
386	#493	C₂²×C₇	1	2	yes	complemented
387	#492	C₂²×C₇	1	2	yes	complemented
388	#492	C₂²×C₇	1	2	yes	complemented
389	#488	C₂²×C₇	1	8	yes	complemented
390	#487	C₂²×C₇	1	2	yes	complemented
391	#487	C₂²×C₇	1	2	yes	complemented
392	#486	C₂²×C₇	1	2	yes	complemented
393	#486	C₂²×C₇	1	2	yes	complemented
394	#464	C₂²×C₇	1	8	yes	complemented
395	#463	C₂²×C₇	1	8	yes	complemented
396	#462	C₂²×C₇	1	4	yes	complemented
397	#461	C₂²×C₇	1	4	yes	complemented
398	#460	C₂²×C₇	1	4	yes	complemented
399	#459	C₂²×C₇	1	4	yes	complemented
400	#452	C₂²×C₇	1	8	yes	complemented
401	#451	C₂²×C₇	1	4	yes	—
402	#450	C₂²×C₇	1	4	yes	—
403	#449	C₂²×C₇	1	8	yes	complemented
404	#448	C₂²×C₇	1	4	yes	—
405	#447	C₂²×C₇	1	4	yes	—
406	#431	C₂²×C₇	1	1	yes	characteristic
407	#431	C₂²×C₇	1	1	yes	characteristic
408	#431	C₂²×C₇	1	2	yes	—
409	#431	C₂²×C₇	1	2	yes	complemented
410	#431	C₂²×C₇	1	2	yes	complemented
411	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
412	#416	C₂²×C₇	1	8	yes	complemented
413	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
414	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	2	4	no	—
419	C₂³×C₇	—	4	1	no	—
420	C₂³×C₇	—	4	4	no	—
421	C₂³×C₇	—	4	4	no	—
422	C₂³×C₇	—	4	4	no	—
423	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
424	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₇×Q₈	—	2	4	no	—
427	C₇×Q₈	—	2	8	no	—
428	C₇×Q₈	—	4	4	no	—
429	C₇×Q₈	—	4	2	no	—
430	C₇×Q₈	—	4	2	no	—
431	C₇×D₄	—	2	4	no	—
432	C₇×D₄	—	2	8	no	—
433	C₇×D₄	—	4	4	no	—
434	C₇×D₄	—	4	4	no	—
435	C₇×D₄	—	4	8	no	—
436	C₇×D₄	—	4	4	no	—
437	C₇×D₄	—	4	8	no	—
438	C₇×D₄	—	4	4	no	—
439	C₇×D₄	—	4	4	no	—
440	C₇×D₄	—	4	4	no	—
441	C₇×D₄	—	4	4	no	—
442	C₇×D₄	—	4	2	no	—
443	C₇×D₄	—	4	4	no	—
444	C₇×D₄	—	4	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	2	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	4	no	—
462	C₂×C₄×C₇	—	4	1	no	—
463	C₂×C₄×C₇	—	4	1	no	—
464	C₂×C₄×C₇	—	4	1	no	—
465	C₂×C₄×C₇	—	4	8	no	—
466	C₂×C₄×C₇	—	4	4	no	—
467	C₂×C₄×C₇	—	4	4	no	—
468	C₂×C₄×C₇	—	4	8	no	—
469	C₂×C₄×C₇	—	4	4	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	#135	1	4	yes	complemented
472	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
484	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
485	C₇×C₈	—	2	4	no	—
486	C₇×C₈	—	2	4	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	4	8	no	—
492	C₂×#41	C₂³×C₇	1	2	yes	—
493	C₂×#41	C₂³×C₇	1	4	yes	—
494	C₂×#41	C₂³×C₇	1	4	yes	—
495	C₂²×Q₈	C₂³×C₇	1	2	yes	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	C₂³×C₇	1	2	yes	—
500	C₂³×C₄	—	2	2	no	—
501	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
502	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
504	#135	—	4	16	no	—
505	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
506	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
507	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
508	C₂×D₈	C₂³×C₇	1	8	yes	—
509	C₂²×C₈	C₂³×C₇	1	4	yes	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	#127	—	2	1	no	—
518	#127	—	2	1	no	—
519	#127	C₂³×C₇	1	2	yes	—
520	#127	C₂³×C₇	1	2	yes	—
521	#127	C₂³×C₇	1	1	yes	characteristic
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#125	—	2	1	no	—
525	#125	—	2	1	no	—
526	#125	C₂³×C₇	1	2	yes	—
527	#124	—	2	2	no	—
528	#124	—	2	2	no	—
529	#124	—	2	1	no	—
530	#124	—	2	1	no	—
531	#124	C₂³×C₇	1	4	yes	—
532	#124	C₂³×C₇	1	4	yes	—
533	#124	C₂³×C₇	1	2	yes	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	#123	—	2	2	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
542	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	1	no	—
552	#121	—	2	1	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	C₂³×C₇	1	2	yes	—
556	#121	C₂³×C₇	1	2	yes	—
557	#120	—	2	2	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	C₂³×C₇	1	2	yes	—
563	C₄×Q₈	C₂³×C₇	1	2	yes	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	C₂³×C₇	1	2	yes	—
583	C₄×D₄	C₂³×C₇	1	2	yes	—
584	#117	—	2	1	no	—
585	#117	—	2	1	no	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	2	no	—
593	C₂×C₂²⋊C₄	—	2	2	no	—
594	C₂×C₄²	—	2	2	no	—
595	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
596	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
597	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
598	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
599	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
600	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
607	C₄⋊C₈	C₂³×C₇	1	2	yes	—
608	C₄⋊C₈	C₂³×C₇	1	2	yes	—
609	C₄⋊C₈	C₂³×C₇	1	4	yes	—
610	#103	C₂³×C₇	1	8	yes	—
611	#103	C₂³×C₇	1	8	yes	—
612	#102	C₂³×C₇	1	8	yes	—
613	#102	C₂³×C₇	1	8	yes	—
614	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
615	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
616	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
617	C₄×C₈	C₂³×C₇	1	2	yes	—
618	C₄×C₈	C₂³×C₇	1	2	yes	—
619	C₄×C₈	C₂³×C₇	1	4	yes	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	1	no	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	4	4	no	—
628	C₂²×C₇	—	4	4	no	—
629	C₂²×C₇	—	4	2	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	4	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	4	4	no	—
634	C₂²×C₇	—	8	8	no	—
635	C₂²×C₇	#535	1	2	yes	—
636	C₂²×C₇	C₂×#135	1	2	yes	—
637	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	4	4	no	—
646	C₄×C₇	—	4	2	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	#535	1	2	yes	—
650	C₄×C₇	C₂×#135	1	2	yes	—
651	C₄×C₇	C₂×#135	1	2	yes	—
652	C₄×C₇	#575	1	2	yes	—
653	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
656	#41	—	2	8	no	—
657	#41	—	2	16	no	—
658	#41	—	4	8	no	—
659	#41	—	4	8	no	—
660	#41	—	4	8	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	4	4	no	—
667	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
668	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	4	8	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	C₂⁴×C₇	1	4	yes	—
686	C₂×D₄	C₂⁴×C₇	1	2	yes	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
698	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
699	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
700	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
710	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
711	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
715	Q₁₆	—	4	8	no	—
716	SD₁₆	—	4	8	no	—
717	SD₁₆	—	4	8	no	—
718	D₈	—	4	8	no	—
719	C₂×C₈	—	2	8	no	—
720	C₂×C₈	C₂⁴×C₇	1	4	yes	—
721	C₂×C₈	C₂⁴×C₇	1	4	yes	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
755	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
756	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
757	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
758	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
759	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
760	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
762	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
765	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
766	C₄²	C₂⁴×C₇	1	1	yes	characteristic
767	C₄²	C₂⁴×C₇	1	1	yes	characteristic
768	C₄²	C₂⁴×C₇	1	1	yes	characteristic
769	C₄²	C₂⁴×C₇	1	1	yes	characteristic
770	C₂×C₇	—	2	2	no	—
771	C₂×C₇	—	2	2	no	—
772	C₂×C₇	—	4	1	no	—
773	C₂×C₇	—	8	2	no	—
774	C₂×C₇	—	8	4	no	—
775	C₂×C₇	C₂×#535	1	1	yes	characteristic
776	C₂×C₇	C₂²×#135	1	1	yes	characteristic
777	C₂×C₇	C₂×#575	1	1	yes	characteristic
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	4	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
787	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
788	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
789	Q₈	—	2	4	no	—
790	Q₈	—	2	8	no	—
791	Q₈	—	4	4	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	4	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	8	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	4	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	C₇×#135	1	4	yes	complemented
835	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
838	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
839	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
842	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
843	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
844	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
846	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
847	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
848	C₈	—	2	4	no	—
849	C₈	—	2	4	no	—
850	C₇	#60782	1	1	yes	characteristic, direct product factor, Sylow
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	4	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	8	8	no	—
866	C₂²	C₇×#535	1	2	yes	—
867	C₂²	C₂×C₇×#135	1	2	yes	—
868	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	2	no	—
880	C₄	C₇×#535	1	2	yes	—
881	C₄	C₂×C₇×#135	1	2	yes	—
882	C₄	C₂×C₇×#135	1	2	yes	—
883	C₄	C₇×#575	1	2	yes	—
884	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	4	no	—
889	C₂	—	8	2	no	—
890	C₂	C₂×C₇×#535	1	1	yes	characteristic
891	C₂	C₂²×C₇×#135	1	1	yes	characteristic
892	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×C₇×#532	C₂	semidirect
3. C₇×#3212	C₂	semidirect
4. C₇×#3211	C₂	semidirect
5. C₇×#3210	C₂	semidirect
6. C₇×#3209	C₂	semidirect
7. C₇×#3208	C₂	semidirect
8. C₇×#3207	C₂	semidirect
9. C₇×#3206	C₂	semidirect
10. C₇×#3205	C₂	semidirect
11. C₇×#3147	C₂	semidirect
12. C₇×#3131	C₂	semidirect
13. C₇×#3035	C₂	semidirect
14. C₇×#3002	C₂	semidirect
15. C₂×C₇×#431	C₂	semidirect
17. C₂×C₇×#135	C₂²	semidirect
19. C₇×#533	C₂²	semidirect
20. C₇×#533	C₂²	semidirect
30. C₇×#532	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
39. C₇×#529	C₂²	semidirect
48. C₄×C₇×#41	C₂²	semidirect
52. C₇×#495	C₂²	semidirect
53. C₇×#494	C₂²	semidirect
54. C₇×#493	C₂²	semidirect
55. C₇×#492	C₂²	semidirect
56. C₇×#492	C₂²	semidirect
57. C₇×#488	C₂²	semidirect
58. C₇×#487	C₂²	semidirect
59. C₇×#487	C₂²	semidirect
60. C₇×#486	C₂²	semidirect
61. C₇×#486	C₂²	semidirect
62. C₇×#464	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#459	C₂²	semidirect
68. C₇×#452	C₂²	semidirect
71. C₇×#449	C₂²	semidirect
77. C₇×#431	C₂²	semidirect
78. C₇×#431	C₂²	semidirect
79. C₂×C₇×C₄⋊C₈	C₂²	semidirect
80. C₇×#416	C₂²	semidirect
82. C₂×C₄×C₇×C₈	C₂²	semidirect
83. #60782	C₇	direct (N × H)
217. #3444	C₂×C₇	semidirect
218. C₂×#532	C₂×C₇	semidirect
219. #3212	C₂×C₇	semidirect
220. #3211	C₂×C₇	semidirect
221. #3210	C₂×C₇	semidirect
222. #3209	C₂×C₇	semidirect
223. #3208	C₂×C₇	semidirect
224. #3207	C₂×C₇	semidirect
225. #3206	C₂×C₇	semidirect
226. #3205	C₂×C₇	semidirect
227. #3147	C₂×C₇	semidirect
228. #3131	C₂×C₇	semidirect
229. #3035	C₂×C₇	semidirect
230. #3002	C₂×C₇	semidirect
231. C₂×#431	C₂×C₇	semidirect
349. C₂×#135	C₂²×C₇	semidirect
351. #533	C₂²×C₇	semidirect
352. #533	C₂²×C₇	semidirect
362. #532	C₂²×C₇	semidirect
363. #532	C₂²×C₇	semidirect
371. #529	C₂²×C₇	semidirect
380. C₄×#41	C₂²×C₇	semidirect
384. #495	C₂²×C₇	semidirect
385. #494	C₂²×C₇	semidirect
386. #493	C₂²×C₇	semidirect
387. #492	C₂²×C₇	semidirect
388. #492	C₂²×C₇	semidirect
389. #488	C₂²×C₇	semidirect
390. #487	C₂²×C₇	semidirect
391. #487	C₂²×C₇	semidirect
392. #486	C₂²×C₇	semidirect
393. #486	C₂²×C₇	semidirect
394. #464	C₂²×C₇	semidirect
395. #463	C₂²×C₇	semidirect
396. #462	C₂²×C₇	semidirect
397. #461	C₂²×C₇	semidirect
398. #460	C₂²×C₇	semidirect
399. #459	C₂²×C₇	semidirect
400. #452	C₂²×C₇	semidirect
403. #449	C₂²×C₇	semidirect
409. #431	C₂²×C₇	semidirect
410. #431	C₂²×C₇	semidirect
411. C₂×C₄⋊C₈	C₂²×C₇	semidirect
412. #416	C₂²×C₇	semidirect
414. C₂×C₄×C₈	C₂²×C₇	semidirect
471. C₂×C₄×C₇	#135	semidirect
834. C₂×C₄	C₇×#135	semidirect
850. C₇	#60782	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×C₇×#532	2
C₇×#3212	2
C₇×#3211	2
C₇×#3210	2
C₇×#3209	2
C₇×#3208	2
C₇×#3207	2
C₇×#3206	2
C₇×#3205	2
C₇×#3147	2
C₇×#3131	2
C₇×#3035	2
C₇×#3002	2
C₂×C₇×#431	2
#60782	7

Subgroups — C7×#60782 #13237998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60782 #13237998