Subgroups — C₇×#61330 #13238546

Order 1792.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3374	C₂	1	2	yes	maximal, complemented
4	C₇×#3372	C₂	1	2	yes	maximal, complemented
5	C₇×#3369	C₂	1	2	yes	maximal, complemented
6	C₇×#3367	C₂	1	2	yes	maximal, complemented
7	C₇×#3364	C₂	1	2	yes	maximal, complemented
8	C₇×#3363	C₂	1	2	yes	maximal, complemented
9	C₇×#3360	C₂	1	2	yes	maximal, complemented
10	C₇×#3359	C₂	1	2	yes	maximal, complemented
11	C₇×#3137	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3082	C₂	1	2	yes	maximal, complemented
14	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3046	C₂	1	2	yes	maximal
16	C₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2947	C₂	1	2	yes	maximal, complemented
19	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
20	C₂×C₇×#137	C₂²	1	2	yes	—
21	C₂×C₇×#135	C₂²	1	1	yes	characteristic
22	C₇×Q₈²	C₂²	1	2	yes	—
23	C₇×#557	C₂²	1	2	yes	—
24	C₇×#557	C₂²	1	2	yes	—
25	C₇×#557	C₂²	1	2	yes	—
26	C₇×#556	C₂²	1	2	yes	—
27	C₇×#556	C₂²	1	2	yes	—
28	C₇×#554	—	2	2	no	—
29	C₇×#554	C₂²	1	2	yes	—
30	C₇×#552	—	2	2	no	—
31	C₇×#552	—	2	2	no	—
32	C₇×D₄×Q₈	—	2	2	no	—
33	C₇×D₄×Q₈	C₂²	1	2	yes	—
34	C₇×#544	—	2	2	no	—
35	C₇×#544	C₂²	1	2	yes	—
36	C₇×#541	—	2	2	no	—
37	C₇×#536	C₂²	1	2	yes	—
38	C₇×#533	—	2	1	no	—
39	C₇×#533	—	2	1	no	—
40	C₇×#533	—	2	1	no	—
41	C₇×#533	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
45	C₇×#520	C₂²	1	2	yes	—
46	C₇×#519	C₂²	1	2	yes	—
47	C₄×C₇×#41	C₂²	1	1	yes	characteristic
48	C₄×C₇×#41	C₂²	1	1	yes	characteristic
49	C₇×#491	C₂²	1	4	yes	—
50	C₇×#489	C₂²	1	4	yes	—
51	C₇×#488	C₂²	1	4	yes	—
52	C₇×#487	C₂²	1	4	yes	—
53	C₇×#487	C₂²	1	2	yes	—
54	C₇×#487	C₂²	1	2	yes	—
55	C₇×#487	C₂²	1	2	yes	—
56	C₇×#487	C₂²	1	2	yes	—
57	C₇×#479	C₂²	1	4	yes	—
58	C₇×#479	C₂²	1	4	yes	—
59	C₇×#477	C₂²	1	2	yes	—
60	C₇×#477	C₂²	1	4	yes	—
61	C₇×#476	C₂²	1	2	yes	—
62	C₇×#475	C₂²	1	2	yes	—
63	C₇×#475	C₂²	1	4	yes	—
64	C₇×#474	C₂²	1	2	yes	—
65	C₇×#464	C₂²	1	4	yes	—
66	C₇×#463	C₂²	1	4	yes	—
67	C₇×#462	C₂²	1	2	yes	—
68	C₇×#462	C₂²	1	2	yes	—
69	C₇×#462	C₂²	1	4	yes	—
70	C₇×#461	C₂²	1	2	yes	—
71	C₇×#461	C₂²	1	2	yes	—
72	C₇×#461	C₂²	1	4	yes	—
73	C₇×#446	C₂²	1	2	yes	—
74	C₇×#446	C₂²	1	2	yes	—
75	C₇×C₈×Q₈	C₂²	1	2	yes	—
76	C₇×C₈×Q₈	C₂²	1	2	yes	—
77	C₇×#441	C₂²	1	4	yes	—
78	C₇×#440	C₂²	1	4	yes	—
79	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
80	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
81	C₄×C₇×Q₁₆	C₂²	1	4	yes	—
82	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
83	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
84	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
85	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
86	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
87	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
88	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
89	C₇×#428	C₂²	1	2	yes	—
90	C₇×#427	C₂²	1	1	yes	characteristic
91	C₇×#424	C₂²	1	2	yes	—
92	C₇×#423	C₂²	1	1	yes	characteristic
93	C₇×#419	C₂²	1	2	yes	—
94	C₇×#417	C₂²	1	2	yes	—
95	C₇×#416	C₂²	1	1	yes	characteristic
96	C₇×#416	C₂²	1	1	yes	characteristic
97	C₂×C₇×#103	C₂²	1	2	yes	—
98	C₂×C₇×#103	C₂²	1	2	yes	—
99	C₇×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
101	#61330	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×C₇×#41	C₂³	1	1	yes	characteristic
103	C₂×C₇×#41	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	—	2	2	no	—
105	C₂²×C₇×Q₈	—	2	1	no	—
106	C₂²×C₇×Q₈	C₂³	1	2	yes	—
107	C₇×#137	—	2	8	no	—
108	C₇×#135	—	2	4	no	—
109	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
115	C₂×C₇×M₁₆	C₂³	1	2	yes	—
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₇×C₄⋊Q₈	—	2	2	no	—
119	C₇×C₄⋊Q₈	—	2	2	no	—
120	C₇×C₄⋊Q₈	—	2	2	no	—
121	C₇×C₄⋊Q₈	—	2	4	no	—
122	C₇×C₄⋊Q₈	—	2	1	no	—
123	C₇×C₄⋊Q₈	—	2	1	no	—
124	C₇×C₄⋊Q₈	—	2	1	no	—
125	C₇×C₄⋊Q₈	—	2	1	no	—
126	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
127	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₇×#126	—	2	4	no	—
135	C₇×#126	—	2	4	no	—
136	C₇×#125	—	2	2	no	—
137	C₇×#125	—	2	2	no	—
138	C₇×#125	—	2	2	no	—
139	C₇×#125	—	2	4	no	—
140	C₇×#125	—	2	4	no	—
141	C₇×#125	—	2	4	no	—
142	C₇×#125	D₄	1	2	yes	—
143	C₇×#125	C₂³	1	4	yes	—
144	C₇×#124	C₂³	1	4	yes	—
145	C₇×#123	—	2	4	no	—
146	C₇×C₂²⋊Q₈	—	2	2	no	—
147	C₇×C₂²⋊Q₈	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₇×C₂²⋊Q₈	—	2	2	no	—
150	C₇×C₂²⋊Q₈	—	2	2	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	4	no	—
153	C₇×C₂²⋊Q₈	—	2	4	no	—
154	C₇×C₂²⋊Q₈	—	2	4	no	—
155	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
156	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
157	C₄×C₇×Q₈	—	2	2	no	—
158	C₄×C₇×Q₈	—	2	2	no	—
159	C₄×C₇×Q₈	—	2	2	no	—
160	C₄×C₇×Q₈	—	2	2	no	—
161	C₄×C₇×Q₈	—	2	2	no	—
162	C₄×C₇×Q₈	—	2	2	no	—
163	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
164	C₄×C₇×Q₈	C₂³	1	4	yes	—
165	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
166	C₄×C₇×Q₈	C₂³	1	4	yes	—
167	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
168	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
169	C₄×C₇×Q₈	C₂³	1	4	yes	—
170	C₄×C₇×Q₈	C₂³	1	2	yes	—
171	C₄×C₇×Q₈	C₂³	1	2	yes	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	1	no	—
176	C₄×C₇×D₄	—	2	4	no	—
177	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
178	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
179	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
180	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
181	C₄×C₇×D₄	C₂³	1	4	yes	—
182	C₇×#117	—	2	2	no	—
183	C₇×#117	—	2	2	no	—
184	C₇×#117	—	2	2	no	—
185	C₇×#117	—	2	4	no	—
186	C₇×#117	—	2	1	no	—
187	C₇×#117	—	2	1	no	—
188	C₇×#117	C₂³	1	1	yes	characteristic
189	C₇×#117	C₂³	1	1	yes	characteristic
190	C₇×#117	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	—	2	1	no	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	—	2	1	no	—
194	C₂×C₇×C₄⋊C₄	—	2	2	no	—
195	C₂×C₇×C₄⋊C₄	—	2	2	no	—
196	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄²×C₇	—	2	1	no	—
198	C₂×C₄²×C₇	—	2	1	no	—
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₇×#107	C₂³	1	4	yes	—
201	C₇×#107	C₂³	1	1	yes	characteristic
202	C₇×#107	C₂³	1	1	yes	characteristic
203	C₇×#106	C₂³	1	1	yes	characteristic
204	C₇×#106	C₂³	1	4	yes	—
205	C₇×#106	C₂³	1	1	yes	characteristic
206	C₇×C₄⋊C₈	C₂³	1	2	yes	—
207	C₇×C₄⋊C₈	C₂³	1	4	yes	—
208	C₇×C₄⋊C₈	C₂³	1	2	yes	—
209	C₇×C₄⋊C₈	C₂³	1	4	yes	—
210	C₇×#103	C₂³	1	4	yes	—
211	C₇×#103	C₂³	1	4	yes	—
212	C₇×#103	C₂³	1	4	yes	—
213	C₇×#103	C₂³	1	4	yes	—
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	1	yes	characteristic
216	C₇×#103	C₂³	1	4	yes	—
217	C₇×#103	C₂³	1	4	yes	—
218	C₇×#103	C₂³	1	1	yes	characteristic
219	C₇×#103	C₂³	1	1	yes	characteristic
220	C₇×#103	C₂³	1	1	yes	characteristic
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	1	yes	characteristic
223	C₇×#102	C₂³	1	1	yes	characteristic
224	C₇×#102	C₂³	1	1	yes	characteristic
225	C₇×#102	C₂³	1	1	yes	characteristic
226	C₇×#97	C₂³	1	4	yes	—
227	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
229	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
230	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×C₈	C₂³	1	4	yes	—
232	#3509	C₂×C₇	1	1	yes	characteristic, complemented
233	#3503	C₂×C₇	1	1	yes	characteristic, complemented
234	#3374	C₂×C₇	1	2	yes	complemented
235	#3372	C₂×C₇	1	2	yes	complemented
236	#3369	C₂×C₇	1	2	yes	complemented
237	#3367	C₂×C₇	1	2	yes	complemented
238	#3364	C₂×C₇	1	2	yes	complemented
239	#3363	C₂×C₇	1	2	yes	complemented
240	#3360	C₂×C₇	1	2	yes	complemented
241	#3359	C₂×C₇	1	2	yes	complemented
242	#3137	C₂×C₇	1	2	yes	complemented
243	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
244	#3082	C₂×C₇	1	2	yes	complemented
245	#3079	C₂×C₇	1	1	yes	characteristic, complemented
246	#3046	C₂×C₇	1	2	yes	—
247	#3039	C₂×C₇	1	1	yes	characteristic, complemented
248	#2960	C₂×C₇	1	1	yes	characteristic, complemented
249	#2947	C₂×C₇	1	2	yes	complemented
250	C₄×#135	C₂×C₇	1	1	yes	characteristic
251	C₇×#41	—	2	2	no	—
252	C₇×#41	—	2	2	no	—
253	C₇×#41	—	2	2	no	—
254	C₇×#41	#41	1	4	yes	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	2	4	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	2	4	no	—
260	C₂×C₇×Q₈	—	2	4	no	—
261	C₂×C₇×Q₈	—	8	2	no	—
262	C₂×C₇×Q₈	—	8	4	no	—
263	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
264	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
265	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
266	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×D₄	—	2	1	no	—
269	C₂×C₇×D₄	—	2	1	no	—
270	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
271	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇	—	2	1	no	—
273	C₂²×C₄×C₇	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	1	no	—
276	C₂²×C₄×C₇	—	2	1	no	—
277	C₂²×C₄×C₇	—	2	1	no	—
278	C₂²×C₄×C₇	—	2	1	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	2	4	no	—
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₇×Q₁₆	—	2	2	no	—
285	C₇×Q₁₆	—	2	8	no	—
286	C₇×SD₁₆	—	2	2	no	—
287	C₇×SD₁₆	—	2	2	no	—
288	C₇×SD₁₆	—	2	8	no	—
289	C₇×D₈	—	2	2	no	—
290	C₇×M₁₆	—	2	4	no	—
291	C₂×C₇×C₈	—	2	2	no	—
292	C₂×C₇×C₈	—	2	2	no	—
293	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
294	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
295	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
296	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
297	C₂×C₇×C₈	C₂⁴	1	4	yes	—
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	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	4	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	1	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	4	no	—
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	—	2	4	no	—
316	C₇×C₄⋊C₄	—	2	4	no	—
317	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
322	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
326	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
327	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₇×C₂²⋊C₄	—	2	1	no	—
329	C₇×C₂²⋊C₄	—	2	1	no	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	1	no	—
332	C₇×C₂²⋊C₄	—	2	4	no	—
333	C₇×C₂²⋊C₄	—	2	1	no	—
334	C₇×C₂²⋊C₄	—	2	1	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
338	C₄²×C₇	—	2	1	no	—
339	C₄²×C₇	—	2	1	no	—
340	C₄²×C₇	—	2	1	no	—
341	C₄²×C₇	—	2	1	no	—
342	C₄²×C₇	—	2	1	no	—
343	C₄²×C₇	—	2	1	no	—
344	C₄²×C₇	—	2	4	no	—
345	C₄²×C₇	—	2	4	no	—
346	C₄²×C₇	—	2	4	no	—
347	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₇	C₂⁴	1	1	yes	characteristic
351	C₄²×C₇	C₂⁴	1	4	yes	—
352	C₂×#137	C₂²×C₇	1	2	yes	—
353	C₂×#135	C₂²×C₇	1	1	yes	characteristic
354	Q₈²	C₂²×C₇	1	2	yes	—
355	#557	C₂²×C₇	1	2	yes	—
356	#557	C₂²×C₇	1	2	yes	—
357	#557	C₂²×C₇	1	2	yes	—
358	#556	C₂²×C₇	1	2	yes	—
359	#556	C₂²×C₇	1	2	yes	—
360	#554	—	2	2	no	—
361	#554	C₂²×C₇	1	2	yes	—
362	#552	—	2	2	no	—
363	#552	—	2	2	no	—
364	D₄×Q₈	—	2	2	no	—
365	D₄×Q₈	C₂²×C₇	1	2	yes	—
366	#544	—	2	2	no	—
367	#544	C₂²×C₇	1	2	yes	—
368	#541	—	2	2	no	—
369	#536	C₂²×C₇	1	2	yes	—
370	#533	—	2	1	no	—
371	#533	—	2	1	no	—
372	#533	—	2	1	no	—
373	#533	C₂²×C₇	1	1	yes	characteristic
374	C₂×C₄⋊Q₈	—	2	1	no	—
375	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
376	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
377	#520	C₂²×C₇	1	2	yes	—
378	#519	C₂²×C₇	1	2	yes	—
379	C₄×#41	C₂²×C₇	1	1	yes	characteristic
380	C₄×#41	C₂²×C₇	1	1	yes	characteristic
381	#491	C₂²×C₇	1	4	yes	—
382	#489	C₂²×C₇	1	4	yes	—
383	#488	C₂²×C₇	1	4	yes	—
384	#487	C₂²×C₇	1	4	yes	—
385	#487	C₂²×C₇	1	2	yes	—
386	#487	C₂²×C₇	1	2	yes	—
387	#487	C₂²×C₇	1	2	yes	—
388	#487	C₂²×C₇	1	2	yes	—
389	#479	C₂²×C₇	1	4	yes	—
390	#479	C₂²×C₇	1	4	yes	—
391	#477	C₂²×C₇	1	2	yes	—
392	#477	C₂²×C₇	1	4	yes	—
393	#476	C₂²×C₇	1	2	yes	—
394	#475	C₂²×C₇	1	2	yes	—
395	#475	C₂²×C₇	1	4	yes	—
396	#474	C₂²×C₇	1	2	yes	—
397	#464	C₂²×C₇	1	4	yes	—
398	#463	C₂²×C₇	1	4	yes	—
399	#462	C₂²×C₇	1	2	yes	—
400	#462	C₂²×C₇	1	4	yes	—
401	#462	C₂²×C₇	1	2	yes	—
402	#461	C₂²×C₇	1	2	yes	—
403	#461	C₂²×C₇	1	4	yes	—
404	#461	C₂²×C₇	1	2	yes	—
405	#446	C₂²×C₇	1	2	yes	—
406	#446	C₂²×C₇	1	2	yes	—
407	C₈×Q₈	C₂²×C₇	1	2	yes	—
408	C₈×Q₈	C₂²×C₇	1	2	yes	—
409	#441	C₂²×C₇	1	4	yes	—
410	#440	C₂²×C₇	1	4	yes	—
411	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
412	C₄×Q₁₆	C₂²×C₇	1	4	yes	—
413	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
414	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
415	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
416	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
417	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
418	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
419	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
420	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
421	#428	C₂²×C₇	1	2	yes	—
422	#427	C₂²×C₇	1	1	yes	characteristic
423	#424	C₂²×C₇	1	2	yes	—
424	#423	C₂²×C₇	1	1	yes	characteristic
425	#419	C₂²×C₇	1	2	yes	—
426	#417	C₂²×C₇	1	2	yes	—
427	#416	C₂²×C₇	1	1	yes	characteristic
428	#416	C₂²×C₇	1	1	yes	characteristic
429	C₂×#103	C₂²×C₇	1	2	yes	—
430	C₂×#103	C₂²×C₇	1	2	yes	—
431	#405	C₂²×C₇	1	2	yes	—
432	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
433	C₂³×C₇	—	2	1	no	—
434	C₂³×C₇	—	2	1	no	—
435	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
436	C₇×Q₈	—	2	4	no	—
437	C₇×Q₈	—	2	4	no	—
438	C₇×Q₈	—	2	1	no	—
439	C₇×Q₈	—	2	4	no	—
440	C₇×Q₈	—	2	1	no	—
441	C₇×Q₈	—	2	4	no	—
442	C₇×Q₈	—	2	1	no	—
443	C₇×Q₈	—	4	4	no	—
444	C₇×Q₈	—	4	4	no	—
445	C₇×Q₈	—	8	2	no	—
446	C₇×Q₈	—	8	4	no	—
447	C₇×Q₈	C₂×#41	1	2	yes	—
448	C₇×D₄	—	2	4	no	—
449	C₇×D₄	—	2	1	no	—
450	C₇×D₄	—	2	1	no	—
451	C₇×D₄	—	2	1	no	—
452	C₇×D₄	—	4	2	no	—
453	C₇×D₄	C₂×#41	1	2	yes	—
454	C₂×C₄×C₇	—	2	1	no	—
455	C₂×C₄×C₇	—	2	4	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	1	no	—
459	C₂×C₄×C₇	—	2	1	no	—
460	C₂×C₄×C₇	—	2	1	no	—
461	C₂×C₄×C₇	—	2	4	no	—
462	C₂×C₄×C₇	—	2	1	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	4	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	—	4	2	no	—
469	C₂×C₄×C₇	—	4	2	no	—
470	C₂×C₄×C₇	—	4	2	no	—
471	C₂×C₄×C₇	—	8	4	no	—
472	C₂×C₄×C₇	—	8	2	no	—
473	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
474	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
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	C₂×#41	1	2	yes	—
481	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
482	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
483	C₇×C₈	—	2	1	no	—
484	C₇×C₈	—	2	1	no	—
485	C₇×C₈	—	2	4	no	—
486	C₇×C₈	—	2	1	no	—
487	C₇×C₈	—	2	1	no	—
488	C₂×#41	C₂³×C₇	1	1	yes	characteristic
489	C₂×#41	C₂³×C₇	1	1	yes	characteristic
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	C₂³×C₇	1	2	yes	—
493	#137	—	2	8	no	—
494	#135	—	2	4	no	—
495	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
496	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
498	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
499	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
500	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
501	C₂×M₁₆	C₂³×C₇	1	2	yes	—
502	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	2	4	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
513	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
517	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
520	#126	—	2	4	no	—
521	#126	—	2	4	no	—
522	#125	—	2	2	no	—
523	#125	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	4	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	C₇×D₄	1	2	yes	—
529	#125	C₂³×C₇	1	4	yes	—
530	#124	C₂³×C₇	1	4	yes	—
531	#123	—	2	4	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
542	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
552	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
553	C₄×Q₈	C₂³×C₇	1	4	yes	—
554	C₄×Q₈	C₂³×C₇	1	4	yes	—
555	C₄×Q₈	C₂³×C₇	1	4	yes	—
556	C₄×Q₈	C₂³×C₇	1	2	yes	—
557	C₄×Q₈	C₂³×C₇	1	2	yes	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
564	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
565	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
566	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
567	C₄×D₄	C₂³×C₇	1	4	yes	—
568	#117	—	2	2	no	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	2	4	no	—
572	#117	—	2	1	no	—
573	#117	—	2	1	no	—
574	#117	C₂³×C₇	1	1	yes	characteristic
575	#117	C₂³×C₇	1	1	yes	characteristic
576	#117	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄²	—	2	1	no	—
584	C₂×C₄²	—	2	1	no	—
585	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
586	#107	C₂³×C₇	1	1	yes	characteristic
587	#107	C₂³×C₇	1	1	yes	characteristic
588	#107	C₂³×C₇	1	4	yes	—
589	#106	C₂³×C₇	1	1	yes	characteristic
590	#106	C₂³×C₇	1	1	yes	characteristic
591	#106	C₂³×C₇	1	4	yes	—
592	C₄⋊C₈	C₂³×C₇	1	2	yes	—
593	C₄⋊C₈	C₂³×C₇	1	2	yes	—
594	C₄⋊C₈	C₂³×C₇	1	4	yes	—
595	C₄⋊C₈	C₂³×C₇	1	4	yes	—
596	#103	C₂³×C₇	1	4	yes	—
597	#103	C₂³×C₇	1	4	yes	—
598	#103	C₂³×C₇	1	4	yes	—
599	#103	C₂³×C₇	1	4	yes	—
600	#103	C₂³×C₇	1	1	yes	characteristic
601	#103	C₂³×C₇	1	1	yes	characteristic
602	#103	C₂³×C₇	1	1	yes	characteristic
603	#103	C₂³×C₇	1	1	yes	characteristic
604	#103	C₂³×C₇	1	4	yes	—
605	#103	C₂³×C₇	1	4	yes	—
606	#103	C₂³×C₇	1	4	yes	—
607	#102	C₂³×C₇	1	1	yes	characteristic
608	#102	C₂³×C₇	1	1	yes	characteristic
609	#102	C₂³×C₇	1	1	yes	characteristic
610	#102	C₂³×C₇	1	1	yes	characteristic
611	#102	C₂³×C₇	1	4	yes	—
612	#97	C₂³×C₇	1	4	yes	—
613	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
614	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
615	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
616	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
617	C₄×C₈	C₂³×C₇	1	4	yes	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	2	no	—
621	C₂²×C₇	—	4	1	no	—
622	C₂²×C₇	—	4	1	no	—
623	C₂²×C₇	—	4	1	no	—
624	C₂²×C₇	—	4	1	no	—
625	C₂²×C₇	—	4	1	no	—
626	C₂²×C₇	#548	1	2	yes	—
627	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
628	C₄×C₇	—	2	2	no	—
629	C₄×C₇	—	2	1	no	—
630	C₄×C₇	—	2	4	no	—
631	C₄×C₇	—	2	1	no	—
632	C₄×C₇	—	2	4	no	—
633	C₄×C₇	—	4	1	no	—
634	C₄×C₇	—	4	4	no	—
635	C₄×C₇	—	4	1	no	—
636	C₄×C₇	—	4	1	no	—
637	C₄×C₇	—	4	4	no	—
638	C₄×C₇	—	4	1	no	—
639	C₄×C₇	—	4	1	no	—
640	C₄×C₇	#548	1	2	yes	—
641	C₄×C₇	#577	1	2	yes	—
642	C₄×C₇	#578	1	2	yes	—
643	C₄×C₇	C₂²×#41	1	1	yes	characteristic
644	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
645	#41	—	2	2	no	—
646	#41	—	2	2	no	—
647	#41	—	2	2	no	—
648	#41	C₇×#41	1	4	yes	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	8	2	no	—
656	C₂×Q₈	—	8	4	no	—
657	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
658	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
659	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
660	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
661	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
665	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
676	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
678	Q₁₆	—	2	2	no	—
679	Q₁₆	—	2	8	no	—
680	SD₁₆	—	2	2	no	—
681	SD₁₆	—	2	2	no	—
682	SD₁₆	—	2	8	no	—
683	D₈	—	2	2	no	—
684	M₁₆	—	2	4	no	—
685	C₂×C₈	—	2	2	no	—
686	C₂×C₈	—	2	2	no	—
687	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
688	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
689	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
690	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
691	C₂×C₈	C₂⁴×C₇	1	4	yes	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	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	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
712	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
713	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
714	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
715	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
716	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
717	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
718	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	4	no	—
741	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
742	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
743	C₄²	C₂⁴×C₇	1	1	yes	characteristic
744	C₄²	C₂⁴×C₇	1	1	yes	characteristic
745	C₄²	C₂⁴×C₇	1	4	yes	—
746	C₂×C₇	—	2	2	no	—
747	C₂×C₇	—	4	2	no	—
748	C₂×C₇	—	8	1	no	—
749	C₂×C₇	C₂×#548	1	1	yes	characteristic
750	C₂×C₇	C₂×#577	1	1	yes	characteristic
751	C₂×C₇	C₂×#578	1	1	yes	characteristic
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
755	Q₈	—	2	1	no	—
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	4	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	4	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	8	2	no	—
765	Q₈	—	8	4	no	—
766	Q₈	C₂×C₇×#41	1	2	yes	—
767	D₄	—	2	4	no	—
768	D₄	—	2	1	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	1	no	—
771	D₄	—	4	2	no	—
772	D₄	C₂×C₇×#41	1	2	yes	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
793	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
794	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂×C₇×#41	1	2	yes	—
800	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
801	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	2	4	no	—
805	C₈	—	2	1	no	—
806	C₈	—	2	1	no	—
807	C₇	#61330	1	1	yes	characteristic, direct product factor, Sylow
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	C₇×#548	1	2	yes	—
817	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	4	no	—
830	C₄	C₇×#548	1	2	yes	—
831	C₄	C₇×#577	1	2	yes	—
832	C₄	C₇×#578	1	2	yes	—
833	C₄	C₂²×C₇×#41	1	1	yes	characteristic
834	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
835	C₂	—	2	2	no	—
836	C₂	—	4	2	no	—
837	C₂	—	8	1	no	—
838	C₂	C₂×C₇×#548	1	1	yes	characteristic
839	C₂	C₂×C₇×#577	1	1	yes	characteristic
840	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3509	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3374	C₂	semidirect
4. C₇×#3372	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3367	C₂	semidirect
7. C₇×#3364	C₂	semidirect
8. C₇×#3363	C₂	semidirect
9. C₇×#3360	C₂	semidirect
10. C₇×#3359	C₂	semidirect
11. C₇×#3137	C₂	semidirect
12. C₂×C₇×#487	C₂	semidirect
13. C₇×#3082	C₂	semidirect
14. C₇×#3079	C₂	semidirect
16. C₇×#3039	C₂	semidirect
17. C₇×#2960	C₂	semidirect
18. C₇×#2947	C₂	semidirect
101. #61330	C₇	direct (N × H)
232. #3509	C₂×C₇	semidirect
233. #3503	C₂×C₇	semidirect
234. #3374	C₂×C₇	semidirect
235. #3372	C₂×C₇	semidirect
236. #3369	C₂×C₇	semidirect
237. #3367	C₂×C₇	semidirect
238. #3364	C₂×C₇	semidirect
239. #3363	C₂×C₇	semidirect
240. #3360	C₂×C₇	semidirect
241. #3359	C₂×C₇	semidirect
242. #3137	C₂×C₇	semidirect
243. C₂×#487	C₂×C₇	semidirect
244. #3082	C₂×C₇	semidirect
245. #3079	C₂×C₇	semidirect
247. #3039	C₂×C₇	semidirect
248. #2960	C₂×C₇	semidirect
249. #2947	C₂×C₇	semidirect
807. C₇	#61330	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×#3509	2
C₇×#3503	2
C₇×#3374	2
C₇×#3372	2
C₇×#3369	2
C₇×#3367	2
C₇×#3364	2
C₇×#3363	2
C₇×#3360	2
C₇×#3359	2
C₇×#3137	2
C₂×C₇×#487	2
C₇×#3082	2
C₇×#3079	2
C₇×#3046	2
C₇×#3039	2
C₇×#2960	2
C₇×#2947	2
C₄×C₇×#135	2
#61330	7

Subgroups — C7×#61330 #13238546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61330 #13238546