Subgroups — C₇×#61329 #13238545

Order 1792.

1896 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	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₇×#3373	C₂	1	2	yes	maximal, complemented
5	C₇×#3368	C₂	1	2	yes	maximal, complemented
6	C₇×#3366	C₂	1	2	yes	maximal, complemented
7	C₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₇×#3362	C₂	1	2	yes	maximal, complemented
9	C₇×#3361	C₂	1	2	yes	maximal, complemented
10	C₇×#3358	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3081	C₂	1	2	yes	maximal, complemented
14	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3045	C₂	1	2	yes	maximal, complemented
16	C₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₇×#135	C₂²	1	1	yes	characteristic
22	C₇×#559	C₂²	1	2	yes	—
23	C₇×#559	C₂²	1	2	yes	—
24	C₇×Q₈²	C₂²	1	2	yes	complemented
25	C₇×#557	C₂²	1	2	yes	complemented
26	C₇×#554	—	2	2	no	—
27	C₇×#554	C₂²	1	2	yes	complemented
28	C₇×#550	C₂²	1	2	yes	—
29	C₇×#550	C₂²	1	2	yes	—
30	C₇×D₄×Q₈	—	2	2	no	—
31	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
32	C₇×#546	—	2	2	no	—
33	C₇×#546	—	2	2	no	—
34	C₇×#544	—	2	2	no	—
35	C₇×#544	C₂²	1	2	yes	—
36	C₇×#540	—	2	2	no	—
37	C₇×#535	C₂²	1	2	yes	—
38	C₇×#533	—	2	1	no	—
39	C₇×#533	C₂²	1	1	yes	characteristic
40	C₇×#532	—	2	1	no	—
41	C₇×#532	—	2	1	no	—
42	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₇×#127	C₂²	1	1	yes	characteristic
45	C₇×#520	C₂²	1	2	yes	—
46	C₇×#518	C₂²	1	2	yes	—
47	C₄×C₇×#41	C₂²	1	1	yes	characteristic
48	C₄×C₇×#41	C₂²	1	1	yes	characteristic
49	C₇×#490	C₂²	1	4	yes	complemented
50	C₇×#489	C₂²	1	4	yes	complemented
51	C₇×#488	C₂²	1	4	yes	complemented
52	C₇×#486	C₂²	1	2	yes	—
53	C₇×#486	C₂²	1	2	yes	—
54	C₇×#486	C₂²	1	2	yes	—
55	C₇×#486	C₂²	1	2	yes	—
56	C₇×#486	C₂²	1	4	yes	complemented
57	C₇×#478	C₂²	1	4	yes	complemented
58	C₇×#478	C₂²	1	4	yes	complemented
59	C₇×#477	C₂²	1	2	yes	complemented
60	C₇×#476	C₂²	1	2	yes	complemented
61	C₇×#476	C₂²	1	4	yes	complemented
62	C₇×#475	C₂²	1	2	yes	complemented
63	C₇×#474	C₂²	1	2	yes	complemented
64	C₇×#474	C₂²	1	4	yes	complemented
65	C₇×#464	C₂²	1	4	yes	complemented
66	C₇×#463	C₂²	1	4	yes	complemented
67	C₇×#460	C₂²	1	2	yes	—
68	C₇×#460	C₂²	1	2	yes	—
69	C₇×#460	C₂²	1	4	yes	complemented
70	C₇×#459	C₂²	1	2	yes	—
71	C₇×#459	C₂²	1	2	yes	—
72	C₇×#459	C₂²	1	4	yes	complemented
73	C₇×#446	C₂²	1	2	yes	complemented
74	C₇×#446	C₂²	1	2	yes	complemented
75	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
76	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
77	C₇×#442	C₂²	1	4	yes	complemented
78	C₇×#440	C₂²	1	4	yes	complemented
79	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
86	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₇×D₈	C₂²	1	4	yes	complemented
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×#418	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×#102	C₂²	1	2	yes	—
98	C₂×C₇×#102	C₂²	1	2	yes	—
99	C₇×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
101	#61329	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×C₇×#41	—	2	2	no	—
103	C₂×C₇×#41	—	2	2	no	—
104	C₂×C₇×#41	C₂³	1	1	yes	characteristic
105	C₂×C₇×#41	C₂³	1	1	yes	characteristic
106	C₂²×C₇×Q₈	—	2	2	no	—
107	C₂²×C₇×Q₈	—	2	1	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	—	2	1	no	—
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₇×AGL(1,ℤ/8)	—	2	8	no	—
112	C₇×#135	—	2	4	no	—
113	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
118	C₂×C₇×D₈	C₂³	1	4	yes	—
119	C₂×C₇×M₁₆	C₂³	1	2	yes	—
120	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊Q₈	—	2	2	no	—
123	C₇×C₄⋊Q₈	—	2	2	no	—
124	C₇×C₄⋊Q₈	—	2	2	no	—
125	C₇×C₄⋊Q₈	—	2	4	no	—
126	C₇×C₄⋊Q₈	—	2	1	no	—
127	C₇×C₄⋊Q₈	—	2	1	no	—
128	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
129	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₇×#127	—	2	1	no	—
134	C₇×#127	—	2	1	no	—
135	C₇×#127	C₂³	1	2	yes	—
136	C₇×#127	C₂³	1	2	yes	—
137	C₇×#127	C₂³	1	4	yes	—
138	C₇×#125	—	2	2	no	—
139	C₇×#125	—	2	4	no	—
140	C₇×#125	D₄	1	2	yes	—
141	C₇×#125	C₂³	1	4	yes	—
142	C₇×#124	—	2	2	no	—
143	C₇×#124	—	2	2	no	—
144	C₇×#124	C₂³	1	4	yes	—
145	C₇×#123	—	2	4	no	—
146	C₇×#123	—	2	4	no	—
147	C₇×C₂²⋊Q₈	—	2	2	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₇×C₂²⋊Q₈	—	2	4	no	—
150	C₇×C₂²⋊Q₈	—	2	4	no	—
151	C₇×C₂²⋊Q₈	—	2	4	no	—
152	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
153	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
154	C₇×#121	—	2	2	no	—
155	C₇×#121	—	2	2	no	—
156	C₇×#121	—	2	2	no	—
157	C₇×#121	—	2	2	no	—
158	C₇×#121	—	2	4	no	—
159	C₇×#121	—	2	4	no	—
160	C₇×#120	—	2	4	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	1	yes	characteristic
165	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
166	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
167	C₄×C₇×Q₈	C₂³	1	4	yes	—
168	C₄×C₇×Q₈	C₂³	1	2	yes	—
169	C₄×C₇×Q₈	C₂³	1	2	yes	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	—	2	2	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	2	no	—
178	C₄×C₇×D₄	—	2	4	no	—
179	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
180	C₄×C₇×D₄	C₂³	1	4	yes	—
181	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
182	C₄×C₇×D₄	C₂³	1	4	yes	—
183	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
184	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
185	C₄×C₇×D₄	C₂³	1	4	yes	—
186	C₇×#117	—	2	2	no	—
187	C₇×#117	—	2	1	no	—
188	C₇×#117	—	2	1	no	—
189	C₇×#117	C₂³	1	1	yes	characteristic
190	C₇×#117	C₂³	1	1	yes	characteristic
191	C₇×#117	C₂³	1	2	yes	—
192	C₂×C₇×C₄⋊C₄	—	2	1	no	—
193	C₂×C₇×C₄⋊C₄	—	2	2	no	—
194	C₂×C₇×C₄⋊C₄	—	2	2	no	—
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
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	1	yes	characteristic
201	C₇×#107	C₂³	1	4	yes	—
202	C₇×#107	C₂³	1	1	yes	characteristic
203	C₇×#106	C₂³	1	4	yes	—
204	C₇×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	C₇×#103	C₂³	1	1	yes	characteristic
213	C₇×#103	C₂³	1	1	yes	characteristic
214	C₇×#103	C₂³	1	1	yes	characteristic
215	C₇×#102	C₂³	1	4	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	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	#3508	C₂×C₇	1	1	yes	characteristic, complemented
233	#3503	C₂×C₇	1	1	yes	characteristic, complemented
234	#3375	C₂×C₇	1	2	yes	complemented
235	#3373	C₂×C₇	1	2	yes	complemented
236	#3368	C₂×C₇	1	2	yes	complemented
237	#3366	C₂×C₇	1	2	yes	complemented
238	#3365	C₂×C₇	1	2	yes	complemented
239	#3362	C₂×C₇	1	2	yes	complemented
240	#3361	C₂×C₇	1	2	yes	complemented
241	#3358	C₂×C₇	1	2	yes	complemented
242	#3136	C₂×C₇	1	2	yes	complemented
243	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
244	#3081	C₂×C₇	1	2	yes	complemented
245	#3079	C₂×C₇	1	1	yes	characteristic, complemented
246	#3045	C₂×C₇	1	2	yes	complemented
247	#3038	C₂×C₇	1	1	yes	characteristic, complemented
248	#2960	C₂×C₇	1	1	yes	characteristic, complemented
249	#2946	C₂×C₇	1	2	yes	complemented
250	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
251	C₂⁴×C₇	—	2	2	no	—
252	C₇×#41	—	2	2	no	—
253	C₇×#41	—	2	2	no	—
254	C₇×#41	—	2	2	no	—
255	C₇×#41	—	8	4	no	—
256	C₇×#41	—	8	4	no	—
257	C₇×#41	#41	1	4	yes	complemented
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	2	4	no	—
260	C₂×C₇×Q₈	—	2	2	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	1	yes	characteristic
266	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×D₄	—	2	1	no	—
268	C₂×C₇×D₄	—	2	1	no	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	2	4	no	—
274	C₂×C₇×D₄	—	2	2	no	—
275	C₂×C₇×D₄	—	2	2	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	4	no	—
278	C₂×C₇×D₄	—	8	2	no	—
279	C₂×C₇×D₄	—	8	2	no	—
280	C₂×C₇×D₄	C₂⁴	1	4	yes	—
281	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇	—	2	1	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	1	no	—
286	C₂²×C₄×C₇	—	2	1	no	—
287	C₂²×C₄×C₇	—	2	1	no	—
288	C₂²×C₄×C₇	—	2	1	no	—
289	C₂²×C₄×C₇	—	2	1	no	—
290	C₂²×C₄×C₇	—	2	4	no	—
291	C₂²×C₄×C₇	—	2	4	no	—
292	C₂²×C₄×C₇	—	2	4	no	—
293	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
296	C₇×Q₁₆	—	2	2	no	—
297	C₇×SD₁₆	—	2	2	no	—
298	C₇×SD₁₆	—	2	8	no	—
299	C₇×SD₁₆	—	2	2	no	—
300	C₇×D₈	—	2	2	no	—
301	C₇×D₈	—	2	8	no	—
302	C₇×M₁₆	—	2	4	no	—
303	C₂×C₇×C₈	—	2	2	no	—
304	C₂×C₇×C₈	—	2	2	no	—
305	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
306	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
307	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
308	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
309	C₂×C₇×C₈	C₂⁴	1	4	yes	—
310	C₇×C₄⋊C₄	—	2	2	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	—	2	2	no	—
314	C₇×C₄⋊C₄	—	2	4	no	—
315	C₇×C₄⋊C₄	—	2	1	no	—
316	C₇×C₄⋊C₄	—	2	1	no	—
317	C₇×C₄⋊C₄	—	2	1	no	—
318	C₇×C₄⋊C₄	—	2	1	no	—
319	C₇×C₄⋊C₄	—	2	4	no	—
320	C₇×C₄⋊C₄	—	2	4	no	—
321	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
322	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
323	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
325	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
326	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
327	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
329	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
330	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
331	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
332	C₇×C₂²⋊C₄	—	2	1	no	—
333	C₇×C₂²⋊C₄	—	2	1	no	—
334	C₇×C₂²⋊C₄	—	2	4	no	—
335	C₇×C₂²⋊C₄	—	2	4	no	—
336	C₇×C₂²⋊C₄	—	2	1	no	—
337	C₇×C₂²⋊C₄	—	2	1	no	—
338	C₇×C₂²⋊C₄	—	2	1	no	—
339	C₇×C₂²⋊C₄	—	2	1	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
344	C₄²×C₇	—	2	1	no	—
345	C₄²×C₇	—	2	1	no	—
346	C₄²×C₇	—	2	1	no	—
347	C₄²×C₇	—	2	1	no	—
348	C₄²×C₇	—	2	1	no	—
349	C₄²×C₇	—	2	1	no	—
350	C₄²×C₇	—	2	4	no	—
351	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₇	C₂⁴	1	1	yes	characteristic
354	C₄²×C₇	C₂⁴	1	1	yes	characteristic
355	C₄²×C₇	C₂⁴	1	4	yes	—
356	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
357	C₂×#135	C₂²×C₇	1	1	yes	characteristic
358	#559	C₂²×C₇	1	2	yes	—
359	#559	C₂²×C₇	1	2	yes	—
360	Q₈²	C₂²×C₇	1	2	yes	complemented
361	#557	C₂²×C₇	1	2	yes	complemented
362	#554	—	2	2	no	—
363	#554	C₂²×C₇	1	2	yes	complemented
364	#550	C₂²×C₇	1	2	yes	—
365	#550	C₂²×C₇	1	2	yes	—
366	D₄×Q₈	—	2	2	no	—
367	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
368	#546	—	2	2	no	—
369	#546	—	2	2	no	—
370	#544	—	2	2	no	—
371	#544	C₂²×C₇	1	2	yes	—
372	#540	—	2	2	no	—
373	#535	C₂²×C₇	1	2	yes	—
374	#533	—	2	1	no	—
375	#533	C₂²×C₇	1	1	yes	characteristic
376	#532	—	2	1	no	—
377	#532	—	2	1	no	—
378	C₂×C₄⋊Q₈	—	2	1	no	—
379	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
380	C₂×#127	C₂²×C₇	1	1	yes	characteristic
381	#520	C₂²×C₇	1	2	yes	—
382	#518	C₂²×C₇	1	2	yes	—
383	C₄×#41	C₂²×C₇	1	1	yes	characteristic
384	C₄×#41	C₂²×C₇	1	1	yes	characteristic
385	#490	C₂²×C₇	1	4	yes	complemented
386	#489	C₂²×C₇	1	4	yes	complemented
387	#488	C₂²×C₇	1	4	yes	complemented
388	#486	C₂²×C₇	1	2	yes	—
389	#486	C₂²×C₇	1	2	yes	—
390	#486	C₂²×C₇	1	2	yes	—
391	#486	C₂²×C₇	1	2	yes	—
392	#486	C₂²×C₇	1	4	yes	complemented
393	#478	C₂²×C₇	1	4	yes	complemented
394	#478	C₂²×C₇	1	4	yes	complemented
395	#477	C₂²×C₇	1	2	yes	complemented
396	#476	C₂²×C₇	1	2	yes	complemented
397	#476	C₂²×C₇	1	4	yes	complemented
398	#475	C₂²×C₇	1	2	yes	complemented
399	#474	C₂²×C₇	1	2	yes	complemented
400	#474	C₂²×C₇	1	4	yes	complemented
401	#464	C₂²×C₇	1	4	yes	complemented
402	#463	C₂²×C₇	1	4	yes	complemented
403	#460	C₂²×C₇	1	2	yes	—
404	#460	C₂²×C₇	1	2	yes	—
405	#460	C₂²×C₇	1	4	yes	complemented
406	#459	C₂²×C₇	1	2	yes	—
407	#459	C₂²×C₇	1	2	yes	—
408	#459	C₂²×C₇	1	4	yes	complemented
409	#446	C₂²×C₇	1	2	yes	complemented
410	#446	C₂²×C₇	1	2	yes	complemented
411	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
412	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
413	#442	C₂²×C₇	1	4	yes	complemented
414	#440	C₂²×C₇	1	4	yes	complemented
415	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
416	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
417	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
418	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
419	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
420	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
421	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
422	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
423	C₄×D₈	C₂²×C₇	1	4	yes	complemented
424	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
425	#428	C₂²×C₇	1	2	yes	—
426	#427	C₂²×C₇	1	1	yes	characteristic
427	#424	C₂²×C₇	1	2	yes	—
428	#423	C₂²×C₇	1	1	yes	characteristic
429	#418	C₂²×C₇	1	2	yes	—
430	#417	C₂²×C₇	1	2	yes	—
431	#416	C₂²×C₇	1	1	yes	characteristic
432	#416	C₂²×C₇	1	1	yes	characteristic
433	C₂×#102	C₂²×C₇	1	2	yes	—
434	C₂×#102	C₂²×C₇	1	2	yes	—
435	#405	C₂²×C₇	1	2	yes	—
436	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
437	C₂³×C₇	—	2	1	no	—
438	C₂³×C₇	—	2	4	no	—
439	C₂³×C₇	—	2	1	no	—
440	C₂³×C₇	—	4	4	no	—
441	C₂³×C₇	—	8	2	no	—
442	C₂³×C₇	—	8	2	no	—
443	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
444	C₇×Q₈	—	2	4	no	—
445	C₇×Q₈	—	2	4	no	—
446	C₇×Q₈	—	2	1	no	—
447	C₇×Q₈	—	2	1	no	—
448	C₇×Q₈	—	2	1	no	—
449	C₇×Q₈	—	4	4	no	—
450	C₇×Q₈	—	8	2	no	—
451	C₇×Q₈	—	8	4	no	—
452	C₇×Q₈	C₂×#41	1	2	yes	—
453	C₇×D₄	—	2	4	no	—
454	C₇×D₄	—	2	4	no	—
455	C₇×D₄	—	2	1	no	—
456	C₇×D₄	—	2	1	no	—
457	C₇×D₄	—	2	4	no	—
458	C₇×D₄	—	2	1	no	—
459	C₇×D₄	—	4	2	no	—
460	C₇×D₄	—	4	4	no	—
461	C₇×D₄	—	4	4	no	—
462	C₇×D₄	—	4	4	no	—
463	C₇×D₄	—	8	2	no	—
464	C₇×D₄	—	8	2	no	—
465	C₇×D₄	—	8	4	no	—
466	C₇×D₄	—	8	4	no	—
467	C₇×D₄	C₂×#41	1	2	yes	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	4	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	1	no	—
477	C₂×C₄×C₇	—	2	4	no	—
478	C₂×C₄×C₇	—	4	2	no	—
479	C₂×C₄×C₇	—	4	2	no	—
480	C₂×C₄×C₇	—	4	2	no	—
481	C₂×C₄×C₇	—	4	2	no	—
482	C₂×C₄×C₇	—	4	2	no	—
483	C₂×C₄×C₇	—	8	4	no	—
484	C₂×C₄×C₇	—	8	4	no	—
485	C₂×C₄×C₇	—	8	4	no	—
486	C₂×C₄×C₇	—	8	2	no	—
487	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
488	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
491	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₇	C₂×#41	1	2	yes	—
495	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
496	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
497	C₇×C₈	—	2	1	no	—
498	C₇×C₈	—	2	1	no	—
499	C₇×C₈	—	2	4	no	—
500	C₇×C₈	—	2	1	no	—
501	C₇×C₈	—	2	1	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	C₂³×C₇	1	1	yes	characteristic
505	C₂×#41	C₂³×C₇	1	1	yes	characteristic
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂³×C₇	1	2	yes	—
511	AGL(1,ℤ/8)	—	2	8	no	—
512	#135	—	2	4	no	—
513	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
514	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
515	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
516	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
517	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
518	C₂×D₈	C₂³×C₇	1	4	yes	—
519	C₂×M₁₆	C₂³×C₇	1	2	yes	—
520	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	4	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
529	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
533	#127	—	2	1	no	—
534	#127	—	2	1	no	—
535	#127	C₂³×C₇	1	2	yes	—
536	#127	C₂³×C₇	1	2	yes	—
537	#127	C₂³×C₇	1	4	yes	—
538	#125	—	2	2	no	—
539	#125	—	2	4	no	—
540	#125	C₇×D₄	1	2	yes	—
541	#125	C₂³×C₇	1	4	yes	—
542	#124	—	2	2	no	—
543	#124	—	2	2	no	—
544	#124	C₂³×C₇	1	4	yes	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
553	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
554	#121	—	2	2	no	—
555	#121	—	2	2	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	4	no	—
559	#121	—	2	4	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
567	C₄×Q₈	C₂³×C₇	1	4	yes	—
568	C₄×Q₈	C₂³×C₇	1	2	yes	—
569	C₄×Q₈	C₂³×C₇	1	2	yes	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	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	4	no	—
579	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
580	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
581	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
583	C₄×D₄	C₂³×C₇	1	4	yes	—
584	C₄×D₄	C₂³×C₇	1	4	yes	—
585	C₄×D₄	C₂³×C₇	1	4	yes	—
586	#117	—	2	2	no	—
587	#117	—	2	1	no	—
588	#117	—	2	1	no	—
589	#117	C₂³×C₇	1	1	yes	characteristic
590	#117	C₂³×C₇	1	1	yes	characteristic
591	#117	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₂²⋊C₄	—	2	4	no	—
597	C₂×C₄²	—	2	1	no	—
598	C₂×C₄²	—	2	1	no	—
599	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
600	#107	C₂³×C₇	1	1	yes	characteristic
601	#107	C₂³×C₇	1	1	yes	characteristic
602	#107	C₂³×C₇	1	4	yes	—
603	#106	C₂³×C₇	1	1	yes	characteristic
604	#106	C₂³×C₇	1	1	yes	characteristic
605	#106	C₂³×C₇	1	4	yes	—
606	C₄⋊C₈	C₂³×C₇	1	2	yes	—
607	C₄⋊C₈	C₂³×C₇	1	2	yes	—
608	C₄⋊C₈	C₂³×C₇	1	4	yes	—
609	C₄⋊C₈	C₂³×C₇	1	4	yes	—
610	#103	C₂³×C₇	1	1	yes	characteristic
611	#103	C₂³×C₇	1	1	yes	characteristic
612	#103	C₂³×C₇	1	1	yes	characteristic
613	#103	C₂³×C₇	1	1	yes	characteristic
614	#103	C₂³×C₇	1	4	yes	—
615	#102	C₂³×C₇	1	4	yes	—
616	#102	C₂³×C₇	1	4	yes	—
617	#102	C₂³×C₇	1	4	yes	—
618	#102	C₂³×C₇	1	4	yes	—
619	#102	C₂³×C₇	1	1	yes	characteristic
620	#102	C₂³×C₇	1	1	yes	characteristic
621	#102	C₂³×C₇	1	1	yes	characteristic
622	#102	C₂³×C₇	1	1	yes	characteristic
623	#102	C₂³×C₇	1	4	yes	—
624	#102	C₂³×C₇	1	4	yes	—
625	#102	C₂³×C₇	1	4	yes	—
626	#97	C₂³×C₇	1	4	yes	—
627	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
628	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
629	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
630	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
631	C₄×C₈	C₂³×C₇	1	4	yes	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	1	no	—
634	C₂²×C₇	—	2	2	no	—
635	C₂²×C₇	—	4	1	no	—
636	C₂²×C₇	—	4	1	no	—
637	C₂²×C₇	—	4	1	no	—
638	C₂²×C₇	—	4	4	no	—
639	C₂²×C₇	—	4	1	no	—
640	C₂²×C₇	—	4	4	no	—
641	C₂²×C₇	—	4	1	no	—
642	C₂²×C₇	—	4	4	no	—
643	C₂²×C₇	—	16	4	no	—
644	C₂²×C₇	#548	1	2	yes	—
645	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
646	C₄×C₇	—	2	2	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	4	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	4	no	—
651	C₄×C₇	—	4	1	no	—
652	C₄×C₇	—	4	1	no	—
653	C₄×C₇	—	4	1	no	—
654	C₄×C₇	—	4	4	no	—
655	C₄×C₇	—	4	1	no	—
656	C₄×C₇	—	4	1	no	—
657	C₄×C₇	#548	1	2	yes	—
658	C₄×C₇	#576	1	2	yes	—
659	C₄×C₇	#577	1	2	yes	—
660	C₄×C₇	C₂²×#41	1	1	yes	characteristic
661	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
662	C₂⁴	—	2	2	no	—
663	#41	—	2	2	no	—
664	#41	—	2	2	no	—
665	#41	—	2	2	no	—
666	#41	—	8	4	no	—
667	#41	—	8	4	no	—
668	#41	C₇×#41	1	4	yes	complemented
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	8	2	no	—
673	C₂×Q₈	—	8	4	no	—
674	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
675	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
676	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	8	2	no	—
690	C₂×D₄	—	8	2	no	—
691	C₂×D₄	C₂⁴×C₇	1	4	yes	—
692	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
707	Q₁₆	—	2	2	no	—
708	SD₁₆	—	2	2	no	—
709	SD₁₆	—	2	8	no	—
710	SD₁₆	—	2	2	no	—
711	D₈	—	2	2	no	—
712	D₈	—	2	8	no	—
713	M₁₆	—	2	4	no	—
714	C₂×C₈	—	2	2	no	—
715	C₂×C₈	—	2	2	no	—
716	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
717	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
718	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
719	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
720	C₂×C₈	C₂⁴×C₇	1	4	yes	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	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	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
733	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
734	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
735	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
736	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
737	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
739	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	4	no	—
762	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
764	C₄²	C₂⁴×C₇	1	1	yes	characteristic
765	C₄²	C₂⁴×C₇	1	1	yes	characteristic
766	C₄²	C₂⁴×C₇	1	4	yes	—
767	C₂×C₇	—	2	2	no	—
768	C₂×C₇	—	4	2	no	—
769	C₂×C₇	—	8	1	no	—
770	C₂×C₇	—	8	4	no	—
771	C₂×C₇	C₂×#548	1	1	yes	characteristic
772	C₂×C₇	C₂×#576	1	1	yes	characteristic
773	C₂×C₇	C₂×#577	1	1	yes	characteristic
774	C₂³	—	2	1	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	4	no	—
778	C₂³	—	8	2	no	—
779	C₂³	—	8	2	no	—
780	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
781	Q₈	—	2	1	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	8	2	no	—
788	Q₈	—	8	4	no	—
789	Q₈	C₂×C₇×#41	1	2	yes	—
790	D₄	—	2	4	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	1	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	4	no	—
803	D₄	—	8	4	no	—
804	D₄	C₂×C₇×#41	1	2	yes	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	2	no	—
824	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
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	4	yes	—
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	C₂×C₇×#41	1	2	yes	—
832	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
833	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
834	C₈	—	2	1	no	—
835	C₈	—	2	1	no	—
836	C₈	—	2	4	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₇	#61329	1	1	yes	characteristic, direct product factor, Sylow
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	16	4	no	—
852	C₂²	C₇×#548	1	2	yes	—
853	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	C₇×#548	1	2	yes	—
866	C₄	C₇×#576	1	2	yes	—
867	C₄	C₇×#577	1	2	yes	—
868	C₄	C₂²×C₇×#41	1	1	yes	characteristic
869	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×C₇×#548	1	1	yes	characteristic
875	C₂	C₂×C₇×#576	1	1	yes	characteristic
876	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×#3508	C₂	semidirect
2. C₇×#3503	C₂	semidirect
3. C₇×#3375	C₂	semidirect
4. C₇×#3373	C₂	semidirect
5. C₇×#3368	C₂	semidirect
6. C₇×#3366	C₂	semidirect
7. C₇×#3365	C₂	semidirect
8. C₇×#3362	C₂	semidirect
9. C₇×#3361	C₂	semidirect
10. C₇×#3358	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₂×C₇×#486	C₂	semidirect
13. C₇×#3081	C₂	semidirect
14. C₇×#3079	C₂	semidirect
15. C₇×#3045	C₂	semidirect
16. C₇×#3038	C₂	semidirect
17. C₇×#2960	C₂	semidirect
18. C₇×#2946	C₂	semidirect
19. C₄×C₇×#135	C₂	semidirect
24. C₇×Q₈²	C₂²	semidirect
25. C₇×#557	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
31. C₇×D₄×Q₈	C₂²	semidirect
49. C₇×#490	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#488	C₂²	semidirect
56. C₇×#486	C₂²	semidirect
57. C₇×#478	C₂²	semidirect
58. C₇×#478	C₂²	semidirect
59. C₇×#477	C₂²	semidirect
60. C₇×#476	C₂²	semidirect
61. C₇×#476	C₂²	semidirect
62. C₇×#475	C₂²	semidirect
63. C₇×#474	C₂²	semidirect
64. C₇×#474	C₂²	semidirect
65. C₇×#464	C₂²	semidirect
66. C₇×#463	C₂²	semidirect
69. C₇×#460	C₂²	semidirect
72. C₇×#459	C₂²	semidirect
73. C₇×#446	C₂²	semidirect
74. C₇×#446	C₂²	semidirect
75. C₇×C₈×Q₈	C₂²	semidirect
76. C₇×C₈×Q₈	C₂²	semidirect
77. C₇×#442	C₂²	semidirect
78. C₇×#440	C₂²	semidirect
79. C₄×C₇×Q₁₆	C₂²	semidirect
80. C₄×C₇×Q₁₆	C₂²	semidirect
81. C₄×C₇×SD₁₆	C₂²	semidirect
82. C₄×C₇×SD₁₆	C₂²	semidirect
83. C₄×C₇×SD₁₆	C₂²	semidirect
84. C₄×C₇×SD₁₆	C₂²	semidirect
85. C₄×C₇×SD₁₆	C₂²	semidirect
86. C₄×C₇×D₈	C₂²	semidirect
87. C₄×C₇×D₈	C₂²	semidirect
88. C₄×C₇×D₈	C₂²	semidirect
101. #61329	C₇	direct (N × H)
232. #3508	C₂×C₇	semidirect
233. #3503	C₂×C₇	semidirect
234. #3375	C₂×C₇	semidirect
235. #3373	C₂×C₇	semidirect
236. #3368	C₂×C₇	semidirect
237. #3366	C₂×C₇	semidirect
238. #3365	C₂×C₇	semidirect
239. #3362	C₂×C₇	semidirect
240. #3361	C₂×C₇	semidirect
241. #3358	C₂×C₇	semidirect
242. #3136	C₂×C₇	semidirect
243. C₂×#486	C₂×C₇	semidirect
244. #3081	C₂×C₇	semidirect
245. #3079	C₂×C₇	semidirect
246. #3045	C₂×C₇	semidirect
247. #3038	C₂×C₇	semidirect
248. #2960	C₂×C₇	semidirect
249. #2946	C₂×C₇	semidirect
250. C₄×#135	C₂×C₇	semidirect
257. C₇×#41	#41	semidirect
360. Q₈²	C₂²×C₇	semidirect
361. #557	C₂²×C₇	semidirect
363. #554	C₂²×C₇	semidirect
367. D₄×Q₈	C₂²×C₇	semidirect
385. #490	C₂²×C₇	semidirect
386. #489	C₂²×C₇	semidirect
387. #488	C₂²×C₇	semidirect
392. #486	C₂²×C₇	semidirect
393. #478	C₂²×C₇	semidirect
394. #478	C₂²×C₇	semidirect
395. #477	C₂²×C₇	semidirect
396. #476	C₂²×C₇	semidirect
397. #476	C₂²×C₇	semidirect
398. #475	C₂²×C₇	semidirect
399. #474	C₂²×C₇	semidirect
400. #474	C₂²×C₇	semidirect
401. #464	C₂²×C₇	semidirect
402. #463	C₂²×C₇	semidirect
405. #460	C₂²×C₇	semidirect
408. #459	C₂²×C₇	semidirect
409. #446	C₂²×C₇	semidirect
410. #446	C₂²×C₇	semidirect
411. C₈×Q₈	C₂²×C₇	semidirect
412. C₈×Q₈	C₂²×C₇	semidirect
413. #442	C₂²×C₇	semidirect
414. #440	C₂²×C₇	semidirect
415. C₄×Q₁₆	C₂²×C₇	semidirect
416. C₄×Q₁₆	C₂²×C₇	semidirect
417. C₄×SD₁₆	C₂²×C₇	semidirect
418. C₄×SD₁₆	C₂²×C₇	semidirect
419. C₄×SD₁₆	C₂²×C₇	semidirect
420. C₄×SD₁₆	C₂²×C₇	semidirect
421. C₄×SD₁₆	C₂²×C₇	semidirect
422. C₄×D₈	C₂²×C₇	semidirect
423. C₄×D₈	C₂²×C₇	semidirect
424. C₄×D₈	C₂²×C₇	semidirect
668. #41	C₇×#41	semidirect
839. C₇	#61329	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×#3508	2
C₇×#3503	2
C₇×#3375	2
C₇×#3373	2
C₇×#3368	2
C₇×#3366	2
C₇×#3365	2
C₇×#3362	2
C₇×#3361	2
C₇×#3358	2
C₇×#3136	2
C₂×C₇×#486	2
C₇×#3081	2
C₇×#3079	2
C₇×#3045	2
C₇×#3038	2
C₇×#2960	2
C₇×#2946	2
C₄×C₇×#135	2
#61329	7

Subgroups — C7×#61329 #13238545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61329 #13238545