Subgroups — C₇×#60871 #13238087

Order 1792.

1742 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3243	C₂	1	4	yes	maximal, complemented
4	C₇×#3241	C₂	1	4	yes	maximal, complemented
5	C₇×#3238	C₂	1	2	yes	maximal, complemented
6	C₇×#3234	C₂	1	2	yes	maximal, complemented
7	C₇×#3232	C₂	1	2	yes	maximal, complemented
8	C₇×#3226	C₂	1	2	yes	maximal, complemented
9	C₇×#3164	C₂	1	2	yes	maximal, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3083	C₂	1	2	yes	maximal, complemented
16	C₇×#3081	C₂	1	2	yes	maximal, complemented
17	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#555	—	2	1	no	—
19	C₇×#553	—	2	1	no	—
20	C₇×#553	—	2	1	no	—
21	C₇×#551	—	2	2	no	—
22	C₇×#547	—	2	1	no	—
23	C₇×#546	—	2	2	no	—
24	C₇×#544	—	2	2	no	—
25	C₇×#544	—	2	1	no	—
26	C₇×#544	—	2	1	no	—
27	C₇×#544	C₂²	1	1	yes	characteristic
28	C₇×#544	C₂²	1	2	yes	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#544	C₂²	1	4	yes	complemented
31	C₇×#542	C₂²	1	2	yes	—
32	C₇×#540	C₂²	1	2	yes	—
33	C₇×#535	C₂²	1	1	yes	characteristic
34	C₇×#532	C₂²	1	2	yes	—
35	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₇×#529	C₂²	1	2	yes	—
38	C₂×C₇×#125	—	2	1	no	—
39	C₂×C₇×#125	C₂²	1	2	yes	complemented
40	C₇×#525	C₂²	1	1	yes	characteristic
41	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₇×#121	C₂²	1	1	yes	characteristic
43	C₇×#520	C₂²	1	1	yes	characteristic
44	C₇×#518	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	1	yes	characteristic
46	C₂×C₇×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₇×#501	C₂²	1	4	yes	complemented
49	C₇×#501	C₂²	1	4	yes	complemented
50	C₇×#500	C₂²	1	4	yes	complemented
51	C₇×#499	C₂²	1	4	yes	complemented
52	C₇×#490	C₂²	1	4	yes	complemented
53	C₇×#489	C₂²	1	4	yes	complemented
54	C₇×#488	C₂²	1	4	yes	complemented
55	C₇×#486	C₂²	1	4	yes	complemented
56	C₇×#485	C₂²	1	2	yes	complemented
57	C₇×#484	C₂²	1	1	yes	characteristic, complemented
58	C₇×#484	C₂²	1	2	yes	complemented
59	C₇×#483	C₂²	1	2	yes	complemented
60	C₇×#483	C₂²	1	1	yes	characteristic, complemented
61	C₇×#482	C₂²	1	4	yes	—
62	C₇×#482	C₂²	1	2	yes	complemented
63	C₇×#481	C₂²	1	2	yes	—
64	C₇×#481	C₂²	1	1	yes	characteristic, complemented
65	C₇×#481	C₂²	1	2	yes	complemented
66	C₇×#480	C₂²	1	2	yes	—
67	C₇×#480	C₂²	1	2	yes	—
68	C₇×#480	C₂²	1	2	yes	—
69	C₇×#480	C₂²	1	4	yes	—
70	C₇×#480	C₂²	1	1	yes	characteristic, complemented
71	C₇×#480	C₂²	1	2	yes	complemented
72	C₇×#479	C₂²	1	4	yes	complemented
73	C₇×#478	C₂²	1	4	yes	complemented
74	C₇×#478	C₂²	1	4	yes	complemented
75	C₇×#478	C₂²	1	4	yes	complemented
76	C₇×#477	C₂²	1	4	yes	complemented
77	C₇×#476	C₂²	1	4	yes	complemented
78	C₇×#474	C₂²	1	4	yes	complemented
79	C₇×#474	C₂²	1	4	yes	complemented
80	C₇×#433	C₂²	1	4	yes	complemented
81	C₇×#432	C₂²	1	2	yes	complemented
82	C₇×#431	C₂²	1	2	yes	complemented
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	2	yes	—
85	C₇×#427	C₂²	1	2	yes	—
86	C₂×C₇×#107	C₂²	1	2	yes	—
87	C₇×#424	C₂²	1	2	yes	—
88	C₇×#418	C₂²	1	2	yes	—
89	C₇×#417	C₂²	1	2	yes	—
90	C₇×#416	C₂²	1	2	yes	—
91	C₂×C₇×#102	C₂²	1	2	yes	—
92	C₇×#407	C₂²	1	1	yes	characteristic
93	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₇×#405	C₂²	1	2	yes	—
95	#60871	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂²×C₇×Q₈	—	2	2	no	—
99	C₂²×C₇×D₄	—	2	1	no	—
100	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₇	—	2	1	no	—
102	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₇×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₇×C₈	C₂³	1	2	yes	—
105	C₇×C₄⋊Q₈	—	2	2	no	—
106	C₇×C₄⋊Q₈	—	2	2	no	—
107	C₇×C₄⋊Q₈	—	2	4	no	—
108	C₇×C₄⋊Q₈	—	2	1	no	—
109	C₇×C₄⋊Q₈	—	2	2	no	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₇×#127	C₂³	1	2	yes	—
115	C₇×#126	—	2	2	no	—
116	C₇×#126	—	2	2	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	—	2	2	no	—
119	C₇×#125	—	2	4	no	—
120	C₇×#125	—	2	1	no	—
121	C₇×#125	—	2	2	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	C₂³	1	4	yes	—
124	C₇×#125	C₂³	1	4	yes	—
125	C₇×#125	C₂³	1	2	yes	—
126	C₇×#124	—	2	2	no	—
127	C₇×#124	—	2	2	no	—
128	C₇×#124	C₂³	1	2	yes	—
129	C₇×#123	—	2	1	no	—
130	C₇×#123	—	2	2	no	—
131	C₇×#123	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×C₂²⋊Q₈	—	2	2	no	—
135	C₇×C₂²⋊Q₈	—	2	4	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₇×C₂²⋊Q₈	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
142	C₇×#121	—	2	1	no	—
143	C₇×#121	—	2	1	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	1	no	—
146	C₇×#121	—	2	1	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	2	no	—
149	C₇×#121	C₂³	1	2	yes	—
150	C₇×#121	C₂³	1	2	yes	—
151	C₇×#121	C₂³	1	1	yes	characteristic
152	C₇×#121	C₂³	1	1	yes	characteristic
153	C₇×#120	—	2	1	no	—
154	C₇×#120	—	2	2	no	—
155	C₄×C₇×Q₈	C₂³	1	2	yes	—
156	C₄×C₇×D₄	—	2	1	no	—
157	C₄×C₇×D₄	—	2	1	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	1	no	—
160	C₄×C₇×D₄	—	2	1	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	2	yes	—
166	C₇×#117	—	2	1	no	—
167	C₇×#117	—	2	1	no	—
168	C₇×#117	—	2	1	no	—
169	C₇×#117	—	2	2	no	—
170	C₇×#117	D₄	1	2	yes	—
171	C₇×#117	D₄	1	1	yes	characteristic
172	C₇×#117	D₄	1	1	yes	characteristic
173	C₇×#117	C₂³	1	2	yes	—
174	C₇×#117	C₂³	1	2	yes	—
175	C₇×#117	C₂³	1	1	yes	characteristic
176	C₇×#117	C₂³	1	1	yes	characteristic
177	C₇×#117	C₂³	1	1	yes	characteristic
178	C₇×#117	C₂³	1	2	yes	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	—	2	1	no	—
182	C₂×C₇×C₄⋊C₄	—	2	2	no	—
183	C₂×C₇×C₄⋊C₄	—	2	2	no	—
184	C₂×C₇×C₄⋊C₄	—	2	2	no	—
185	C₂×C₇×C₄⋊C₄	—	2	1	no	—
186	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
198	C₂×C₄²×C₇	—	2	1	no	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₇×#107	C₂³	1	2	yes	—
201	C₇×#107	C₂³	1	4	yes	—
202	C₇×#107	C₂³	1	4	yes	—
203	C₇×#107	C₂³	1	4	yes	—
204	C₇×#107	C₂³	1	4	yes	—
205	C₇×#107	C₂³	1	2	yes	—
206	C₇×#106	C₂³	1	2	yes	—
207	C₇×#106	C₂³	1	4	yes	—
208	C₇×#106	C₂³	1	2	yes	—
209	C₇×#106	C₂³	1	4	yes	—
210	C₇×C₄⋊C₈	C₂³	1	4	yes	—
211	C₇×C₄⋊C₈	C₂³	1	4	yes	—
212	C₇×#103	C₂³	1	2	yes	—
213	C₇×#103	C₂³	1	4	yes	—
214	C₇×#103	C₂³	1	2	yes	—
215	C₇×#102	C₂³	1	2	yes	—
216	C₇×#102	C₂³	1	4	yes	—
217	C₇×#102	C₂³	1	4	yes	—
218	C₇×#102	C₂³	1	4	yes	—
219	C₇×#102	C₂³	1	4	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	2	yes	—
222	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₄×C₇×C₈	C₂³	1	4	yes	—
229	#3494	C₂×C₇	1	1	yes	characteristic
230	C₂×#544	C₂×C₇	1	1	yes	characteristic, complemented
231	#3243	C₂×C₇	1	4	yes	complemented
232	#3241	C₂×C₇	1	4	yes	complemented
233	#3238	C₂×C₇	1	2	yes	complemented
234	#3234	C₂×C₇	1	2	yes	complemented
235	#3232	C₂×C₇	1	2	yes	complemented
236	#3226	C₂×C₇	1	2	yes	complemented
237	#3164	C₂×C₇	1	2	yes	complemented
238	#3136	C₂×C₇	1	2	yes	complemented
239	#3094	C₂×C₇	1	1	yes	characteristic, complemented
240	#3092	C₂×C₇	1	1	yes	characteristic, complemented
241	#3091	C₂×C₇	1	1	yes	characteristic, complemented
242	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
243	#3083	C₂×C₇	1	2	yes	complemented
244	#3081	C₂×C₇	1	2	yes	complemented
245	#2924	C₂×C₇	1	1	yes	characteristic, complemented
246	C₂⁴×C₇	—	2	1	no	—
247	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
248	C₇×#41	—	2	4	no	—
249	C₇×#41	—	8	4	no	—
250	C₂×C₇×Q₈	—	2	2	no	—
251	C₂×C₇×Q₈	—	2	4	no	—
252	C₂×C₇×Q₈	—	2	4	no	—
253	C₂×C₇×Q₈	—	8	4	no	—
254	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
255	C₂×C₇×D₄	—	2	1	no	—
256	C₂×C₇×D₄	—	2	1	no	—
257	C₂×C₇×D₄	—	2	2	no	—
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	—	2	2	no	—
260	C₂×C₇×D₄	—	2	1	no	—
261	C₂×C₇×D₄	—	2	2	no	—
262	C₂×C₇×D₄	—	2	2	no	—
263	C₂×C₇×D₄	—	2	4	no	—
264	C₂×C₇×D₄	—	8	2	no	—
265	C₂×C₇×D₄	C₂⁴	1	2	yes	—
266	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇	—	2	4	no	—
268	C₂²×C₄×C₇	—	2	1	no	—
269	C₂²×C₄×C₇	—	2	1	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	1	no	—
272	C₂²×C₄×C₇	—	2	2	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	1	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	8	2	no	—
279	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
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	2	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₇×M₁₆	—	2	4	no	—
288	C₂×C₇×C₈	—	2	4	no	—
289	C₂×C₇×C₈	C₂⁴	1	2	yes	—
290	C₂×C₇×C₈	C₂⁴	1	4	yes	—
291	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	1	no	—
296	C₇×C₄⋊C₄	—	2	2	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	4	no	—
301	C₇×C₄⋊C₄	—	2	4	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
314	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
320	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₂²⋊C₄	—	2	1	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₇×C₂²⋊C₄	—	2	1	no	—
326	C₇×C₂²⋊C₄	—	2	1	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	2	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	1	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	1	no	—
336	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₄²×C₇	—	2	2	no	—
341	C₄²×C₇	—	2	2	no	—
342	C₄²×C₇	—	2	2	no	—
343	C₄²×C₇	—	2	1	no	—
344	C₄²×C₇	C₂×D₄	1	2	yes	—
345	C₄²×C₇	C₂×D₄	1	2	yes	—
346	C₄²×C₇	C₂⁴	1	2	yes	—
347	C₄²×C₇	C₂⁴	1	2	yes	—
348	#555	—	2	1	no	—
349	#553	—	2	1	no	—
350	#553	—	2	1	no	—
351	#551	—	2	2	no	—
352	#547	—	2	1	no	—
353	#546	—	2	2	no	—
354	#544	—	2	2	no	—
355	#544	—	2	1	no	—
356	#544	—	2	1	no	—
357	#544	C₂²×C₇	1	2	yes	—
358	#544	C₂²×C₇	1	2	yes	—
359	#544	C₂²×C₇	1	1	yes	characteristic
360	#544	C₂²×C₇	1	4	yes	complemented
361	#542	C₂²×C₇	1	2	yes	—
362	#540	C₂²×C₇	1	2	yes	—
363	#535	C₂²×C₇	1	1	yes	characteristic
364	#532	C₂²×C₇	1	2	yes	—
365	C₂×C₄⋊Q₈	—	2	1	no	—
366	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
367	#529	C₂²×C₇	1	2	yes	—
368	C₂×#125	—	2	1	no	—
369	C₂×#125	C₂²×C₇	1	2	yes	complemented
370	#525	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₂²⋊Q₈	—	2	2	no	—
372	C₂×#121	C₂²×C₇	1	1	yes	characteristic
373	#520	C₂²×C₇	1	1	yes	characteristic
374	#518	C₂²×C₇	1	1	yes	characteristic
375	C₂×#117	C₂²×C₇	1	1	yes	characteristic
376	C₂×#117	C₂²×C₇	1	1	yes	characteristic
377	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
378	#501	C₂²×C₇	1	4	yes	complemented
379	#501	C₂²×C₇	1	4	yes	complemented
380	#500	C₂²×C₇	1	4	yes	complemented
381	#499	C₂²×C₇	1	4	yes	complemented
382	#490	C₂²×C₇	1	4	yes	complemented
383	#489	C₂²×C₇	1	4	yes	complemented
384	#488	C₂²×C₇	1	4	yes	complemented
385	#486	C₂²×C₇	1	4	yes	complemented
386	#485	C₂²×C₇	1	2	yes	complemented
387	#484	C₂²×C₇	1	1	yes	characteristic, complemented
388	#484	C₂²×C₇	1	2	yes	complemented
389	#483	C₂²×C₇	1	1	yes	characteristic, complemented
390	#483	C₂²×C₇	1	2	yes	complemented
391	#482	C₂²×C₇	1	4	yes	—
392	#482	C₂²×C₇	1	2	yes	complemented
393	#481	C₂²×C₇	1	2	yes	—
394	#481	C₂²×C₇	1	1	yes	characteristic, complemented
395	#481	C₂²×C₇	1	2	yes	complemented
396	#480	C₂²×C₇	1	2	yes	—
397	#480	C₂²×C₇	1	2	yes	—
398	#480	C₂²×C₇	1	4	yes	—
399	#480	C₂²×C₇	1	2	yes	—
400	#480	C₂²×C₇	1	1	yes	characteristic, complemented
401	#480	C₂²×C₇	1	2	yes	complemented
402	#479	C₂²×C₇	1	4	yes	complemented
403	#478	C₂²×C₇	1	4	yes	complemented
404	#478	C₂²×C₇	1	4	yes	complemented
405	#478	C₂²×C₇	1	4	yes	complemented
406	#477	C₂²×C₇	1	4	yes	complemented
407	#476	C₂²×C₇	1	4	yes	complemented
408	#474	C₂²×C₇	1	4	yes	complemented
409	#474	C₂²×C₇	1	4	yes	complemented
410	#433	C₂²×C₇	1	4	yes	complemented
411	#432	C₂²×C₇	1	2	yes	complemented
412	#431	C₂²×C₇	1	2	yes	complemented
413	#428	C₂²×C₇	1	2	yes	—
414	#428	C₂²×C₇	1	2	yes	—
415	#427	C₂²×C₇	1	2	yes	—
416	C₂×#107	C₂²×C₇	1	2	yes	—
417	#424	C₂²×C₇	1	2	yes	—
418	#418	C₂²×C₇	1	2	yes	—
419	#417	C₂²×C₇	1	2	yes	—
420	#416	C₂²×C₇	1	2	yes	—
421	C₂×#102	C₂²×C₇	1	2	yes	—
422	#407	C₂²×C₇	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
424	#405	C₂²×C₇	1	2	yes	—
425	C₂³×C₇	—	2	2	no	—
426	C₂³×C₇	—	2	2	no	—
427	C₂³×C₇	—	2	2	no	—
428	C₂³×C₇	—	2	1	no	—
429	C₂³×C₇	—	4	1	no	—
430	C₂³×C₇	—	4	2	no	—
431	C₂³×C₇	—	8	1	no	—
432	C₂³×C₇	—	8	1	no	—
433	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
435	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
436	C₇×Q₈	—	2	2	no	—
437	C₇×Q₈	—	8	4	no	—
438	C₇×Q₈	—	8	4	no	—
439	C₇×Q₈	—	8	2	no	—
440	C₇×D₄	—	2	4	no	—
441	C₇×D₄	—	2	2	no	—
442	C₇×D₄	—	4	2	no	—
443	C₇×D₄	—	4	4	no	—
444	C₇×D₄	—	4	2	no	—
445	C₇×D₄	—	4	2	no	—
446	C₇×D₄	—	8	2	no	—
447	C₇×D₄	—	8	2	no	—
448	C₇×D₄	—	8	1	no	—
449	C₇×D₄	—	8	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	4	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	1	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	2	no	—
459	C₂×C₄×C₇	—	2	1	no	—
460	C₂×C₄×C₇	—	2	1	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	4	no	—
463	C₂×C₄×C₇	—	4	2	no	—
464	C₂×C₄×C₇	—	4	2	no	—
465	C₂×C₄×C₇	—	4	4	no	—
466	C₂×C₄×C₇	—	4	2	no	—
467	C₂×C₄×C₇	—	4	2	no	—
468	C₂×C₄×C₇	—	8	2	no	—
469	C₂×C₄×C₇	—	8	2	no	—
470	C₂×C₄×C₇	—	8	2	no	—
471	C₂×C₄×C₇	—	8	2	no	—
472	C₂×C₄×C₇	—	8	2	no	—
473	C₂×C₄×C₇	—	8	1	no	—
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
482	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
483	C₇×C₈	—	2	2	no	—
484	C₇×C₈	—	2	2	no	—
485	C₇×C₈	—	2	4	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	C₂³×C₇	1	1	yes	characteristic
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
493	C₂×M₁₆	C₂³×C₇	1	2	yes	—
494	C₂²×C₈	C₂³×C₇	1	2	yes	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	—	2	4	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	2	no	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
502	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
503	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
504	#127	C₂³×C₇	1	2	yes	—
505	#126	—	2	2	no	—
506	#126	—	2	2	no	—
507	#125	—	2	2	no	—
508	#125	—	2	2	no	—
509	#125	—	2	4	no	—
510	#125	—	2	1	no	—
511	#125	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	C₂³×C₇	1	4	yes	—
514	#125	C₂³×C₇	1	4	yes	—
515	#125	C₂³×C₇	1	2	yes	—
516	#124	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	C₂³×C₇	1	2	yes	—
519	#123	—	2	1	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	#123	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
531	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	2	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	C₂³×C₇	1	2	yes	—
540	#121	C₂³×C₇	1	2	yes	—
541	#121	C₂³×C₇	1	1	yes	characteristic
542	#121	C₂³×C₇	1	1	yes	characteristic
543	#120	—	2	1	no	—
544	#120	—	2	2	no	—
545	C₄×Q₈	C₂³×C₇	1	2	yes	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	C₂³×C₇	1	2	yes	—
554	C₄×D₄	C₂³×C₇	1	2	yes	—
555	C₄×D₄	C₂³×C₇	1	2	yes	—
556	#117	—	2	1	no	—
557	#117	—	2	1	no	—
558	#117	—	2	1	no	—
559	#117	—	2	2	no	—
560	#117	C₇×D₄	1	2	yes	—
561	#117	C₇×D₄	1	1	yes	characteristic
562	#117	C₇×D₄	1	1	yes	characteristic
563	#117	C₂³×C₇	1	2	yes	—
564	#117	C₂³×C₇	1	2	yes	—
565	#117	C₂³×C₇	1	1	yes	characteristic
566	#117	C₂³×C₇	1	1	yes	characteristic
567	#117	C₂³×C₇	1	1	yes	characteristic
568	#117	C₂³×C₇	1	2	yes	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	2	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	C₂³×C₇	1	2	yes	—
590	#107	C₂³×C₇	1	4	yes	—
591	#107	C₂³×C₇	1	4	yes	—
592	#107	C₂³×C₇	1	2	yes	—
593	#107	C₂³×C₇	1	2	yes	—
594	#107	C₂³×C₇	1	4	yes	—
595	#107	C₂³×C₇	1	4	yes	—
596	#106	C₂³×C₇	1	2	yes	—
597	#106	C₂³×C₇	1	2	yes	—
598	#106	C₂³×C₇	1	4	yes	—
599	#106	C₂³×C₇	1	4	yes	—
600	C₄⋊C₈	C₂³×C₇	1	4	yes	—
601	C₄⋊C₈	C₂³×C₇	1	4	yes	—
602	#103	C₂³×C₇	1	2	yes	—
603	#103	C₂³×C₇	1	2	yes	—
604	#103	C₂³×C₇	1	4	yes	—
605	#102	C₂³×C₇	1	4	yes	—
606	#102	C₂³×C₇	1	4	yes	—
607	#102	C₂³×C₇	1	2	yes	—
608	#102	C₂³×C₇	1	2	yes	—
609	#102	C₂³×C₇	1	4	yes	—
610	#102	C₂³×C₇	1	4	yes	—
611	#102	C₂³×C₇	1	4	yes	—
612	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
613	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
615	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
616	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
617	#97	C₂³×C₇	1	4	yes	—
618	C₄×C₈	C₂³×C₇	1	4	yes	—
619	C₂²×C₇	—	2	1	no	—
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	—	4	4	no	—
627	C₂²×C₇	—	4	2	no	—
628	C₂²×C₇	—	4	1	no	—
629	C₂²×C₇	—	4	1	no	—
630	C₂²×C₇	—	4	2	no	—
631	C₂²×C₇	—	4	1	no	—
632	C₂²×C₇	—	4	2	no	—
633	C₂²×C₇	—	16	2	no	—
634	C₂²×C₇	#536	1	2	yes	—
635	C₂²×C₇	#576	1	2	yes	—
636	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
637	C₄×C₇	—	2	2	no	—
638	C₄×C₇	—	2	2	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	2	no	—
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	4	2	no	—
644	C₄×C₇	—	4	1	no	—
645	C₄×C₇	—	4	1	no	—
646	C₄×C₇	—	4	4	no	—
647	C₄×C₇	—	4	2	no	—
648	C₄×C₇	—	4	2	no	—
649	C₄×C₇	—	4	1	no	—
650	C₄×C₇	#536	1	2	yes	—
651	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
652	C₂⁴	—	2	1	no	—
653	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
654	#41	—	2	4	no	—
655	#41	—	8	4	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	8	4	no	—
660	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	8	2	no	—
671	C₂×D₄	C₂⁴×C₇	1	2	yes	—
672	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	8	2	no	—
685	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
686	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
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	2	yes	—
690	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
693	M₁₆	—	2	4	no	—
694	C₂×C₈	—	2	4	no	—
695	C₂×C₈	C₂⁴×C₇	1	2	yes	—
696	C₂×C₈	C₂⁴×C₇	1	4	yes	—
697	C₂×C₈	C₂⁴×C₇	1	2	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	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	1	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	C₂×C₇×D₄	1	1	yes	characteristic
717	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
718	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
719	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
720	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
721	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
743	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
744	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
745	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	1	no	—
750	C₄²	C₂×C₇×D₄	1	2	yes	—
751	C₄²	C₂×C₇×D₄	1	2	yes	—
752	C₄²	C₂⁴×C₇	1	2	yes	—
753	C₄²	C₂⁴×C₇	1	2	yes	—
754	C₂×C₇	—	2	2	no	—
755	C₂×C₇	—	2	2	no	—
756	C₂×C₇	—	4	1	no	—
757	C₂×C₇	—	8	1	no	—
758	C₂×C₇	—	8	2	no	—
759	C₂×C₇	C₂×#536	1	1	yes	characteristic
760	C₂×C₇	C₂×#576	1	1	yes	characteristic
761	C₂×C₇	#3586	1	1	yes	characteristic
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	2	no	—
768	C₂³	—	8	1	no	—
769	C₂³	—	8	1	no	—
770	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
771	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
772	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
773	Q₈	—	2	2	no	—
774	Q₈	—	8	4	no	—
775	Q₈	—	8	4	no	—
776	Q₈	—	8	2	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	2	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	2	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	2	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	1	no	—
786	D₄	—	8	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	4	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	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
813	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
815	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
816	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
817	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
818	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
819	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	4	no	—
823	C₇	#60871	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	—	4	4	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	16	2	no	—
839	C₂²	C₇×#536	1	2	yes	—
840	C₂²	C₇×#576	1	2	yes	—
841	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	C₇×#536	1	2	yes	—
856	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
857	C₂	—	2	2	no	—
858	C₂	—	2	2	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₂×C₇×#536	1	1	yes	characteristic
863	C₂	C₂×C₇×#576	1	1	yes	characteristic
864	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#544	C₂	semidirect
3. C₇×#3243	C₂	semidirect
4. C₇×#3241	C₂	semidirect
5. C₇×#3238	C₂	semidirect
6. C₇×#3234	C₂	semidirect
7. C₇×#3232	C₂	semidirect
8. C₇×#3226	C₂	semidirect
9. C₇×#3164	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3094	C₂	semidirect
12. C₇×#3092	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₂×C₇×#480	C₂	semidirect
15. C₇×#3083	C₂	semidirect
16. C₇×#3081	C₂	semidirect
17. C₇×#2924	C₂	semidirect
30. C₇×#544	C₂²	semidirect
36. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₇×#125	C₂²	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#501	C₂²	semidirect
50. C₇×#500	C₂²	semidirect
51. C₇×#499	C₂²	semidirect
52. C₇×#490	C₂²	semidirect
53. C₇×#489	C₂²	semidirect
54. C₇×#488	C₂²	semidirect
55. C₇×#486	C₂²	semidirect
56. C₇×#485	C₂²	semidirect
57. C₇×#484	C₂²	semidirect
58. C₇×#484	C₂²	semidirect
59. C₇×#483	C₂²	semidirect
60. C₇×#483	C₂²	semidirect
62. C₇×#482	C₂²	semidirect
64. C₇×#481	C₂²	semidirect
65. C₇×#481	C₂²	semidirect
70. C₇×#480	C₂²	semidirect
71. C₇×#480	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#478	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#476	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#474	C₂²	semidirect
80. C₇×#433	C₂²	semidirect
81. C₇×#432	C₂²	semidirect
82. C₇×#431	C₂²	semidirect
95. #60871	C₇	direct (N × H)
230. C₂×#544	C₂×C₇	semidirect
231. #3243	C₂×C₇	semidirect
232. #3241	C₂×C₇	semidirect
233. #3238	C₂×C₇	semidirect
234. #3234	C₂×C₇	semidirect
235. #3232	C₂×C₇	semidirect
236. #3226	C₂×C₇	semidirect
237. #3164	C₂×C₇	semidirect
238. #3136	C₂×C₇	semidirect
239. #3094	C₂×C₇	semidirect
240. #3092	C₂×C₇	semidirect
241. #3091	C₂×C₇	semidirect
242. C₂×#480	C₂×C₇	semidirect
243. #3083	C₂×C₇	semidirect
244. #3081	C₂×C₇	semidirect
245. #2924	C₂×C₇	semidirect
360. #544	C₂²×C₇	semidirect
366. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
369. C₂×#125	C₂²×C₇	semidirect
378. #501	C₂²×C₇	semidirect
379. #501	C₂²×C₇	semidirect
380. #500	C₂²×C₇	semidirect
381. #499	C₂²×C₇	semidirect
382. #490	C₂²×C₇	semidirect
383. #489	C₂²×C₇	semidirect
384. #488	C₂²×C₇	semidirect
385. #486	C₂²×C₇	semidirect
386. #485	C₂²×C₇	semidirect
387. #484	C₂²×C₇	semidirect
388. #484	C₂²×C₇	semidirect
389. #483	C₂²×C₇	semidirect
390. #483	C₂²×C₇	semidirect
392. #482	C₂²×C₇	semidirect
394. #481	C₂²×C₇	semidirect
395. #481	C₂²×C₇	semidirect
400. #480	C₂²×C₇	semidirect
401. #480	C₂²×C₇	semidirect
402. #479	C₂²×C₇	semidirect
403. #478	C₂²×C₇	semidirect
404. #478	C₂²×C₇	semidirect
405. #478	C₂²×C₇	semidirect
406. #477	C₂²×C₇	semidirect
407. #476	C₂²×C₇	semidirect
408. #474	C₂²×C₇	semidirect
409. #474	C₂²×C₇	semidirect
410. #433	C₂²×C₇	semidirect
411. #432	C₂²×C₇	semidirect
412. #431	C₂²×C₇	semidirect
823. C₇	#60871	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×#3494	2
C₂×C₇×#544	2
C₇×#3243	2
C₇×#3241	2
C₇×#3238	2
C₇×#3234	2
C₇×#3232	2
C₇×#3226	2
C₇×#3164	2
C₇×#3136	2
C₇×#3094	2
C₇×#3092	2
C₇×#3091	2
C₂×C₇×#480	2
C₇×#3083	2
C₇×#3081	2
C₇×#2924	2
#60871	7

Subgroups — C7×#60871 #13238087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60871 #13238087