Subgroups — C₇×#60570 #13237786

Order 1792.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3124	C₂	1	2	yes	maximal, complemented
4	C₇×#3122	C₂	1	2	yes	maximal, complemented
5	C₇×#3119	C₂	1	2	yes	maximal, complemented
6	C₇×#3118	C₂	1	2	yes	maximal, complemented
7	C₇×#3106	C₂	1	2	yes	maximal, complemented
8	C₇×#3105	C₂	1	2	yes	maximal, complemented
9	C₇×#3102	C₂	1	2	yes	maximal, complemented
10	C₇×#3100	C₂	1	2	yes	maximal, complemented
11	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₇×#135	C₂²	1	1	yes	characteristic
28	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
29	C₇×#544	C₂²	1	1	yes	characteristic, complemented
30	C₇×#542	—	2	1	no	—
31	C₇×#542	C₂²	1	2	yes	complemented
32	C₇×#540	—	2	1	no	—
33	C₇×#540	C₂²	1	2	yes	complemented
34	C₇×#538	—	2	2	no	—
35	C₇×#537	C₂²	1	1	yes	characteristic
36	C₇×#535	C₂²	1	1	yes	characteristic
37	C₇×#535	C₂²	1	1	yes	characteristic, complemented
38	C₇×#532	—	2	1	no	—
39	C₇×#532	C₂²	1	2	yes	complemented
40	C₇×#529	—	2	1	no	—
41	C₇×#529	C₂²	1	2	yes	complemented
42	C₇×#525	—	2	2	no	—
43	C₇×#520	—	2	1	no	—
44	C₇×#520	C₂²	1	1	yes	characteristic
45	C₇×#520	C₂²	1	1	yes	characteristic
46	C₇×#520	C₂²	1	2	yes	complemented
47	C₇×#518	—	2	2	no	—
48	C₇×#518	—	2	1	no	—
49	C₇×#518	C₂²	1	1	yes	characteristic
50	C₇×#518	C₂²	1	2	yes	complemented
51	C₄×C₇×#41	—	2	1	no	—
52	C₄×C₇×#41	C₂²	1	1	yes	characteristic
53	C₄×C₇×#41	C₂²	1	1	yes	characteristic
54	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₇×#41	C₂²	1	2	yes	complemented
56	C₂×C₄×C₇×D₄	—	2	1	no	—
57	C₂×C₄×C₇×D₄	—	2	2	no	—
58	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
61	C₇×#485	C₂²	1	2	yes	complemented
62	C₇×#484	C₂²	1	2	yes	complemented
63	C₇×#482	C₂²	1	2	yes	complemented
64	C₇×#482	C₂²	1	2	yes	complemented
65	C₇×#482	C₂²	1	2	yes	complemented
66	C₇×#481	C₂²	1	2	yes	complemented
67	C₇×#480	C₂²	1	2	yes	complemented
68	C₇×#480	C₂²	1	2	yes	complemented
69	C₇×#479	C₂²	1	2	yes	complemented
70	C₇×#478	C₂²	1	2	yes	complemented
71	C₇×#478	C₂²	1	2	yes	complemented
72	C₇×#478	C₂²	1	2	yes	complemented
73	C₇×#477	C₂²	1	2	yes	complemented
74	C₇×#476	C₂²	1	2	yes	complemented
75	C₇×#474	C₂²	1	2	yes	complemented
76	C₇×#474	C₂²	1	2	yes	complemented
77	C₇×#464	C₂²	1	2	yes	complemented
78	C₇×#463	C₂²	1	2	yes	complemented
79	C₇×#463	C₂²	1	2	yes	complemented
80	C₇×#463	C₂²	1	2	yes	complemented
81	C₇×#460	C₂²	1	2	yes	complemented
82	C₇×#459	C₂²	1	2	yes	complemented
83	C₇×#459	C₂²	1	2	yes	complemented
84	C₇×#459	C₂²	1	2	yes	complemented
85	C₇×#452	C₂²	1	2	yes	complemented
86	C₇×#450	C₂²	1	2	yes	complemented
87	C₇×#449	C₂²	1	2	yes	—
88	C₇×#449	C₂²	1	2	yes	—
89	C₇×#449	C₂²	1	2	yes	complemented
90	C₇×#447	C₂²	1	2	yes	—
91	C₇×#447	C₂²	1	2	yes	—
92	C₇×#447	C₂²	1	2	yes	complemented
93	C₇×#442	C₂²	1	2	yes	complemented
94	C₇×#442	C₂²	1	2	yes	complemented
95	C₇×#440	C₂²	1	2	yes	complemented
96	C₇×#440	C₂²	1	2	yes	complemented
97	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×D₈	C₂²	1	2	yes	complemented
106	C₄×C₇×D₈	C₂²	1	2	yes	complemented
107	C₄×C₇×D₈	C₂²	1	2	yes	complemented
108	C₄×C₇×D₈	C₂²	1	2	yes	complemented
109	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₇×D₈	C₂²	1	2	yes	complemented
112	C₄×C₇×D₈	C₂²	1	2	yes	complemented
113	C₇×#433	C₂²	1	2	yes	complemented
114	C₇×#433	C₂²	1	2	yes	complemented
115	C₇×#431	C₂²	1	2	yes	complemented
116	C₇×#431	C₂²	1	2	yes	complemented
117	C₇×#428	C₂²	1	1	yes	characteristic, complemented
118	C₇×#428	C₂²	1	1	yes	characteristic, complemented
119	C₇×#427	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
121	C₇×#424	C₂²	1	1	yes	characteristic, complemented
122	C₇×#424	C₂²	1	1	yes	characteristic, complemented
123	C₇×#418	C₂²	1	1	yes	characteristic
124	C₇×#418	C₂²	1	1	yes	characteristic, complemented
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic, complemented
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#102	C₂²	1	1	yes	characteristic
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
131	C₇×#408	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
135	#60570	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×H(5,𝔽₂)	—	2	4	no	—
137	C₇×H(5,𝔽₂)	—	2	4	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	C₂³	1	2	yes	—
141	C₂×C₇×#41	C₂³	1	1	yes	characteristic
142	C₂×C₇×#41	C₂³	1	1	yes	characteristic
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₇×D₄	—	2	2	no	—
145	C₂²×C₇×D₄	—	2	1	no	—
146	C₂²×C₇×D₄	C₂³	1	2	yes	—
147	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
148	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₇	—	2	1	no	—
150	C₂³×C₄×C₇	—	2	2	no	—
151	C₂³×C₄×C₇	—	2	1	no	—
152	C₇×AGL(1,ℤ/8)	—	2	4	no	—
153	C₇×AGL(1,ℤ/8)	—	2	4	no	—
154	C₇×#135	—	2	4	no	—
155	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₇×D₈	—	2	4	no	—
161	C₂×C₇×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	2	yes	—
163	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
164	C₂×C₇×D₈	C₂³	1	2	yes	—
165	C₂×C₇×D₈	C₂³	1	2	yes	—
166	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
168	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
169	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	—	2	1	no	—
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×#127	—	2	1	no	—
173	C₇×#127	C₂³	1	2	yes	—
174	C₇×#126	—	2	2	no	—
175	C₇×#126	—	2	2	no	—
176	C₇×#125	—	2	1	no	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	—	2	2	no	—
180	C₇×#124	—	2	2	no	—
181	C₇×#124	C₂³	1	2	yes	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×C₂²⋊Q₈	—	2	1	no	—
187	C₇×C₂²⋊Q₈	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₇×#121	—	2	2	no	—
191	C₇×#121	—	2	1	no	—
192	C₇×#121	—	2	2	no	—
193	C₇×#121	—	2	1	no	—
194	C₇×#121	—	2	1	no	—
195	C₇×#121	—	2	2	no	—
196	C₇×#121	—	2	2	no	—
197	C₇×#121	C₂³	1	2	yes	—
198	C₇×#121	C₂³	1	2	yes	—
199	C₇×#121	C₂³	1	2	yes	—
200	C₇×#120	—	2	2	no	—
201	C₇×#120	—	2	2	no	—
202	C₄×C₇×Q₈	—	2	1	no	—
203	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
204	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
205	C₄×C₇×Q₈	C₂³	1	2	yes	—
206	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
207	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
208	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
209	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
210	C₄×C₇×D₄	—	2	2	no	—
211	C₄×C₇×D₄	—	2	1	no	—
212	C₄×C₇×D₄	—	2	1	no	—
213	C₄×C₇×D₄	—	2	2	no	—
214	C₄×C₇×D₄	—	2	1	no	—
215	C₄×C₇×D₄	—	2	2	no	—
216	C₄×C₇×D₄	—	2	1	no	—
217	C₄×C₇×D₄	—	2	1	no	—
218	C₄×C₇×D₄	—	2	2	no	—
219	C₄×C₇×D₄	—	2	1	no	—
220	C₄×C₇×D₄	—	2	2	no	—
221	C₄×C₇×D₄	—	2	1	no	—
222	C₄×C₇×D₄	—	2	2	no	—
223	C₄×C₇×D₄	—	2	2	no	—
224	C₄×C₇×D₄	—	2	2	no	—
225	C₄×C₇×D₄	—	2	2	no	—
226	C₄×C₇×D₄	—	2	1	no	—
227	C₄×C₇×D₄	—	2	2	no	—
228	C₄×C₇×D₄	—	2	1	no	—
229	C₄×C₇×D₄	—	2	2	no	—
230	C₄×C₇×D₄	—	2	1	no	—
231	C₄×C₇×D₄	—	2	1	no	—
232	C₄×C₇×D₄	—	2	2	no	—
233	C₄×C₇×D₄	D₄	1	2	yes	—
234	C₄×C₇×D₄	D₄	1	1	yes	characteristic
235	C₄×C₇×D₄	D₄	1	2	yes	—
236	C₄×C₇×D₄	D₄	1	1	yes	characteristic
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	2	yes	—
239	C₄×C₇×D₄	C₂³	1	2	yes	—
240	C₄×C₇×D₄	C₂³	1	2	yes	—
241	C₄×C₇×D₄	C₂³	1	2	yes	—
242	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
243	C₄×C₇×D₄	C₂³	1	2	yes	—
244	C₄×C₇×D₄	C₂³	1	2	yes	—
245	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
247	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
248	C₇×#117	—	2	1	no	—
249	C₇×#117	—	2	2	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	2	no	—
252	C₇×#117	—	2	1	no	—
253	C₇×#117	—	2	2	no	—
254	C₇×#117	C₂³	1	2	yes	—
255	C₇×#117	C₂³	1	1	yes	characteristic
256	C₇×#117	C₂³	1	1	yes	characteristic
257	C₇×#117	C₂³	1	1	yes	characteristic
258	C₇×#117	C₂³	1	2	yes	—
259	C₂×C₇×C₄⋊C₄	—	2	1	no	—
260	C₂×C₇×C₄⋊C₄	—	2	2	no	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²×C₇	—	2	1	no	—
271	C₂×C₄²×C₇	—	2	2	no	—
272	C₂×C₄²×C₇	—	2	1	no	—
273	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₇	C₂³	1	2	yes	—
275	C₇×#107	C₂³	1	1	yes	characteristic
276	C₇×#107	C₂³	1	2	yes	—
277	C₇×#107	C₂³	1	2	yes	—
278	C₇×#107	C₂³	1	2	yes	—
279	C₇×#107	C₂³	1	2	yes	—
280	C₇×#107	C₂³	1	1	yes	characteristic
281	C₇×#106	C₂³	1	1	yes	characteristic
282	C₇×#106	C₂³	1	2	yes	—
283	C₇×#106	C₂³	1	1	yes	characteristic
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	1	yes	characteristic
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	2	yes	—
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₇×#97	C₂³	1	2	yes	—
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
316	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
317	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
318	C₄×C₇×C₈	C₂³	1	2	yes	—
319	#3460	C₂×C₇	1	1	yes	characteristic, complemented
320	C₄×H(5,𝔽₂)	C₂×C₇	1	1	yes	characteristic, complemented
321	#3124	C₂×C₇	1	2	yes	complemented
322	#3122	C₂×C₇	1	2	yes	complemented
323	#3119	C₂×C₇	1	2	yes	complemented
324	#3118	C₂×C₇	1	2	yes	complemented
325	#3106	C₂×C₇	1	2	yes	complemented
326	#3105	C₂×C₇	1	2	yes	complemented
327	#3102	C₂×C₇	1	2	yes	complemented
328	#3100	C₂×C₇	1	2	yes	complemented
329	#3098	C₂×C₇	1	1	yes	characteristic, complemented
330	#3096	C₂×C₇	1	1	yes	characteristic, complemented
331	#3083	C₂×C₇	1	1	yes	characteristic, complemented
332	#3081	C₂×C₇	1	1	yes	characteristic, complemented
333	#3045	C₂×C₇	1	1	yes	characteristic, complemented
334	#3041	C₂×C₇	1	1	yes	characteristic, complemented
335	#3012	C₂×C₇	1	1	yes	characteristic, complemented
336	#3008	C₂×C₇	1	1	yes	characteristic, complemented
337	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
338	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
339	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
340	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
341	#2922	C₂×C₇	1	1	yes	characteristic, complemented
342	C₂⁴×C₇	—	2	2	no	—
343	C₂⁴×C₇	—	2	1	no	—
344	C₂⁴×C₇	—	2	1	no	—
345	C₇×#41	—	2	8	no	—
346	C₇×#41	—	2	4	no	—
347	C₇×#41	—	2	4	no	—
348	C₇×#41	—	2	2	no	—
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	8	4	no	—
354	C₇×#41	#41	1	4	yes	complemented
355	C₂×C₇×Q₈	—	2	2	no	—
356	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×D₄	—	2	16	no	—
360	C₂×C₇×D₄	—	2	8	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	4	no	—
364	C₂×C₇×D₄	—	2	4	no	—
365	C₂×C₇×D₄	—	2	1	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	2	no	—
368	C₂×C₇×D₄	—	2	2	no	—
369	C₂×C₇×D₄	—	2	2	no	—
370	C₂×C₇×D₄	—	2	1	no	—
371	C₂×C₇×D₄	—	2	1	no	—
372	C₂×C₇×D₄	—	2	2	no	—
373	C₂×C₇×D₄	—	2	2	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	2	no	—
376	C₂×C₇×D₄	—	2	2	no	—
377	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
378	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
379	C₂×C₇×D₄	#41	1	4	yes	complemented
380	C₂×C₇×D₄	C₂⁴	1	2	yes	—
381	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
382	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
383	C₂×C₇×D₄	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₇	—	2	2	no	—
385	C₂²×C₄×C₇	—	2	1	no	—
386	C₂²×C₄×C₇	—	2	2	no	—
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	1	no	—
389	C₂²×C₄×C₇	—	2	1	no	—
390	C₂²×C₄×C₇	—	2	1	no	—
391	C₂²×C₄×C₇	—	2	2	no	—
392	C₂²×C₄×C₇	—	2	1	no	—
393	C₂²×C₄×C₇	—	2	2	no	—
394	C₂²×C₄×C₇	—	2	1	no	—
395	C₂²×C₄×C₇	—	2	2	no	—
396	C₂²×C₄×C₇	—	2	1	no	—
397	C₂²×C₄×C₇	—	2	2	no	—
398	C₂²×C₄×C₇	—	2	2	no	—
399	C₂²×C₄×C₇	—	2	2	no	—
400	C₂²×C₄×C₇	—	2	2	no	—
401	C₂²×C₄×C₇	—	8	2	no	—
402	C₂²×C₄×C₇	—	8	2	no	—
403	C₂²×C₄×C₇	—	8	4	no	—
404	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
406	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
408	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₇×Q₁₆	—	2	2	no	—
411	C₇×SD₁₆	—	2	2	no	—
412	C₇×SD₁₆	—	2	4	no	—
413	C₇×SD₁₆	—	2	2	no	—
414	C₇×SD₁₆	—	2	4	no	—
415	C₇×D₈	—	2	4	no	—
416	C₇×D₈	—	2	4	no	—
417	C₇×D₈	—	2	2	no	—
418	C₇×D₈	—	2	4	no	—
419	C₇×D₈	—	2	4	no	—
420	C₇×M₁₆	—	2	2	no	—
421	C₇×M₁₆	—	2	2	no	—
422	C₂×C₇×C₈	—	2	2	no	—
423	C₂×C₇×C₈	—	2	2	no	—
424	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
426	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
427	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₇×C₈	C₂⁴	1	2	yes	—
429	C₂×C₇×C₈	C₂⁴	1	2	yes	—
430	C₇×C₄⋊C₄	—	2	1	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	1	no	—
434	C₇×C₄⋊C₄	—	2	1	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	1	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	no	—
442	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
444	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
450	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	1	no	—
454	C₇×C₂²⋊C₄	—	2	1	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	2	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	—	2	2	no	—
464	C₇×C₂²⋊C₄	—	2	2	no	—
465	C₇×C₂²⋊C₄	—	2	1	no	—
466	C₇×C₂²⋊C₄	—	2	1	no	—
467	C₇×C₂²⋊C₄	—	2	2	no	—
468	C₇×C₂²⋊C₄	—	2	2	no	—
469	C₇×C₂²⋊C₄	—	2	2	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	2	no	—
472	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
474	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₄²×C₇	—	2	1	no	—
476	C₄²×C₇	—	2	2	no	—
477	C₄²×C₇	—	2	2	no	—
478	C₄²×C₇	—	2	1	no	—
479	C₄²×C₇	—	2	1	no	—
480	C₄²×C₇	—	2	1	no	—
481	C₄²×C₇	—	2	1	no	—
482	C₄²×C₇	—	2	1	no	—
483	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₇	C₂×D₄	1	2	yes	—
485	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₇	C₂×D₄	1	2	yes	—
487	C₄²×C₇	C₂⁴	1	1	yes	characteristic
488	C₄²×C₇	C₂⁴	1	2	yes	—
489	C₄²×C₇	C₂⁴	1	1	yes	characteristic
490	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
491	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
492	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
493	C₂×#135	C₂²×C₇	1	1	yes	characteristic
494	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
495	#544	C₂²×C₇	1	1	yes	characteristic, complemented
496	#542	—	2	1	no	—
497	#542	C₂²×C₇	1	2	yes	complemented
498	#540	—	2	1	no	—
499	#540	C₂²×C₇	1	2	yes	complemented
500	#538	—	2	2	no	—
501	#537	C₂²×C₇	1	1	yes	characteristic
502	#535	C₂²×C₇	1	1	yes	characteristic
503	#535	C₂²×C₇	1	1	yes	characteristic, complemented
504	#532	—	2	1	no	—
505	#532	C₂²×C₇	1	2	yes	complemented
506	#529	—	2	1	no	—
507	#529	C₂²×C₇	1	2	yes	complemented
508	#525	—	2	2	no	—
509	#520	—	2	1	no	—
510	#520	C₂²×C₇	1	1	yes	characteristic
511	#520	C₂²×C₇	1	1	yes	characteristic
512	#520	C₂²×C₇	1	2	yes	complemented
513	#518	—	2	2	no	—
514	#518	—	2	1	no	—
515	#518	C₂²×C₇	1	1	yes	characteristic
516	#518	C₂²×C₇	1	2	yes	complemented
517	C₄×#41	—	2	1	no	—
518	C₄×#41	C₂²×C₇	1	1	yes	characteristic
519	C₄×#41	C₂²×C₇	1	1	yes	characteristic
520	C₄×#41	C₂²×C₇	1	2	yes	complemented
521	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
522	C₂×C₄×D₄	—	2	1	no	—
523	C₂×C₄×D₄	—	2	2	no	—
524	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
526	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
527	#485	C₂²×C₇	1	2	yes	complemented
528	#484	C₂²×C₇	1	2	yes	complemented
529	#482	C₂²×C₇	1	2	yes	complemented
530	#482	C₂²×C₇	1	2	yes	complemented
531	#482	C₂²×C₇	1	2	yes	complemented
532	#481	C₂²×C₇	1	2	yes	complemented
533	#480	C₂²×C₇	1	2	yes	complemented
534	#480	C₂²×C₇	1	2	yes	complemented
535	#479	C₂²×C₇	1	2	yes	complemented
536	#478	C₂²×C₇	1	2	yes	complemented
537	#478	C₂²×C₇	1	2	yes	complemented
538	#478	C₂²×C₇	1	2	yes	complemented
539	#477	C₂²×C₇	1	2	yes	complemented
540	#476	C₂²×C₇	1	2	yes	complemented
541	#474	C₂²×C₇	1	2	yes	complemented
542	#474	C₂²×C₇	1	2	yes	complemented
543	#464	C₂²×C₇	1	2	yes	complemented
544	#463	C₂²×C₇	1	2	yes	complemented
545	#463	C₂²×C₇	1	2	yes	complemented
546	#463	C₂²×C₇	1	2	yes	complemented
547	#460	C₂²×C₇	1	2	yes	complemented
548	#459	C₂²×C₇	1	2	yes	complemented
549	#459	C₂²×C₇	1	2	yes	complemented
550	#459	C₂²×C₇	1	2	yes	complemented
551	#452	C₂²×C₇	1	2	yes	complemented
552	#450	C₂²×C₇	1	2	yes	complemented
553	#449	C₂²×C₇	1	2	yes	—
554	#449	C₂²×C₇	1	2	yes	—
555	#449	C₂²×C₇	1	2	yes	complemented
556	#447	C₂²×C₇	1	2	yes	—
557	#447	C₂²×C₇	1	2	yes	—
558	#447	C₂²×C₇	1	2	yes	complemented
559	#442	C₂²×C₇	1	2	yes	complemented
560	#442	C₂²×C₇	1	2	yes	complemented
561	#440	C₂²×C₇	1	2	yes	complemented
562	#440	C₂²×C₇	1	2	yes	complemented
563	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
564	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
565	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
566	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
567	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
568	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
569	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
570	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
571	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
572	C₄×D₈	C₂²×C₇	1	2	yes	complemented
573	C₄×D₈	C₂²×C₇	1	2	yes	complemented
574	C₄×D₈	C₂²×C₇	1	2	yes	complemented
575	C₄×D₈	C₂²×C₇	1	2	yes	complemented
576	C₄×D₈	C₂²×C₇	1	2	yes	complemented
577	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
578	C₄×D₈	C₂²×C₇	1	2	yes	complemented
579	#433	C₂²×C₇	1	2	yes	complemented
580	#433	C₂²×C₇	1	2	yes	complemented
581	#431	C₂²×C₇	1	2	yes	complemented
582	#431	C₂²×C₇	1	2	yes	complemented
583	#428	C₂²×C₇	1	1	yes	characteristic, complemented
584	#428	C₂²×C₇	1	1	yes	characteristic, complemented
585	#427	C₂²×C₇	1	1	yes	characteristic, complemented
586	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
587	#424	C₂²×C₇	1	1	yes	characteristic, complemented
588	#424	C₂²×C₇	1	1	yes	characteristic, complemented
589	#418	C₂²×C₇	1	1	yes	characteristic
590	#418	C₂²×C₇	1	1	yes	characteristic, complemented
591	#417	C₂²×C₇	1	1	yes	characteristic
592	#417	C₂²×C₇	1	1	yes	characteristic, complemented
593	#416	C₂²×C₇	1	1	yes	characteristic
594	#416	C₂²×C₇	1	1	yes	characteristic, complemented
595	C₂×#102	C₂²×C₇	1	1	yes	characteristic
596	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
597	#408	C₂²×C₇	1	1	yes	characteristic
598	#408	C₂²×C₇	1	1	yes	characteristic
599	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
600	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
601	C₂³×C₇	—	2	8	no	—
602	C₂³×C₇	—	2	2	no	—
603	C₂³×C₇	—	2	1	no	—
604	C₂³×C₇	—	2	4	no	—
605	C₂³×C₇	—	2	2	no	—
606	C₂³×C₇	—	2	1	no	—
607	C₂³×C₇	—	4	2	no	—
608	C₂³×C₇	—	8	1	no	—
609	C₂³×C₇	—	8	1	no	—
610	C₂³×C₇	—	8	2	no	—
611	C₂³×C₇	—	8	1	no	—
612	C₂³×C₇	—	8	1	no	—
613	C₂³×C₇	—	8	2	no	—
614	C₂³×C₇	C₂²×D₄	1	2	yes	—
615	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
616	C₇×Q₈	—	2	2	no	—
617	C₇×Q₈	—	2	1	no	—
618	C₇×Q₈	—	2	1	no	—
619	C₇×Q₈	—	2	1	no	—
620	C₇×Q₈	—	8	2	no	—
621	C₇×Q₈	C₂×#41	1	2	yes	—
622	C₇×D₄	—	2	8	no	—
623	C₇×D₄	—	2	8	no	—
624	C₇×D₄	—	2	4	no	—
625	C₇×D₄	—	2	4	no	—
626	C₇×D₄	—	2	2	no	—
627	C₇×D₄	—	2	4	no	—
628	C₇×D₄	—	2	2	no	—
629	C₇×D₄	—	2	1	no	—
630	C₇×D₄	—	2	2	no	—
631	C₇×D₄	—	2	1	no	—
632	C₇×D₄	—	2	2	no	—
633	C₇×D₄	—	2	1	no	—
634	C₇×D₄	—	4	2	no	—
635	C₇×D₄	—	4	2	no	—
636	C₇×D₄	—	8	2	no	—
637	C₇×D₄	—	8	2	no	—
638	C₇×D₄	—	8	2	no	—
639	C₇×D₄	—	8	2	no	—
640	C₇×D₄	—	8	2	no	—
641	C₇×D₄	C₂×#41	1	2	yes	—
642	C₇×D₄	C₂×#41	1	4	yes	—
643	C₂×C₄×C₇	—	2	8	no	—
644	C₂×C₄×C₇	—	2	1	no	—
645	C₂×C₄×C₇	—	2	4	no	—
646	C₂×C₄×C₇	—	2	2	no	—
647	C₂×C₄×C₇	—	2	4	no	—
648	C₂×C₄×C₇	—	2	2	no	—
649	C₂×C₄×C₇	—	2	2	no	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	1	no	—
652	C₂×C₄×C₇	—	2	1	no	—
653	C₂×C₄×C₇	—	2	1	no	—
654	C₂×C₄×C₇	—	2	2	no	—
655	C₂×C₄×C₇	—	2	1	no	—
656	C₂×C₄×C₇	—	2	2	no	—
657	C₂×C₄×C₇	—	4	1	no	—
658	C₂×C₄×C₇	—	4	2	no	—
659	C₂×C₄×C₇	—	4	2	no	—
660	C₂×C₄×C₇	—	4	2	no	—
661	C₂×C₄×C₇	—	4	4	no	—
662	C₂×C₄×C₇	—	4	4	no	—
663	C₂×C₄×C₇	—	4	2	no	—
664	C₂×C₄×C₇	—	8	1	no	—
665	C₂×C₄×C₇	—	8	1	no	—
666	C₂×C₄×C₇	—	8	2	no	—
667	C₂×C₄×C₇	—	8	2	no	—
668	C₂×C₄×C₇	—	8	2	no	—
669	C₂×C₄×C₇	—	8	2	no	—
670	C₂×C₄×C₇	—	8	2	no	—
671	C₂×C₄×C₇	—	8	1	no	—
672	C₂×C₄×C₇	—	8	2	no	—
673	C₂×C₄×C₇	—	8	1	no	—
674	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
675	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
676	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
677	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
678	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
679	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
680	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
681	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
682	C₂×C₄×C₇	C₂×#41	1	2	yes	—
683	C₂×C₄×C₇	C₂×#41	1	2	yes	—
684	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
685	C₇×C₈	—	2	1	no	—
686	C₇×C₈	—	2	1	no	—
687	C₇×C₈	—	2	1	no	—
688	C₇×C₈	—	2	1	no	—
689	C₇×C₈	—	2	2	no	—
690	C₇×C₈	—	2	2	no	—
691	H(5,𝔽₂)	—	2	4	no	—
692	H(5,𝔽₂)	—	2	4	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	2	2	no	—
695	C₂×#41	C₂³×C₇	1	2	yes	—
696	C₂×#41	C₂³×C₇	1	1	yes	characteristic
697	C₂×#41	C₂³×C₇	1	1	yes	characteristic
698	C₂×#41	C₂³×C₇	1	1	yes	characteristic
699	C₂²×D₄	—	2	2	no	—
700	C₂²×D₄	—	2	1	no	—
701	C₂²×D₄	C₂³×C₇	1	2	yes	—
702	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
703	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	C₂³×C₄	—	2	2	no	—
706	C₂³×C₄	—	2	1	no	—
707	AGL(1,ℤ/8)	—	2	4	no	—
708	AGL(1,ℤ/8)	—	2	4	no	—
709	#135	—	2	4	no	—
710	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
715	C₂×D₈	—	2	4	no	—
716	C₂×D₈	C₂³×C₇	1	2	yes	—
717	C₂×D₈	C₂³×C₇	1	2	yes	—
718	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
719	C₂×D₈	C₂³×C₇	1	2	yes	—
720	C₂×D₈	C₂³×C₇	1	2	yes	—
721	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
722	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
724	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
727	#127	—	2	1	no	—
728	#127	C₂³×C₇	1	2	yes	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	C₂³×C₇	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	2	no	—
735	#124	—	2	2	no	—
736	#124	C₂³×C₇	1	2	yes	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
745	#121	—	2	2	no	—
746	#121	—	2	1	no	—
747	#121	—	2	2	no	—
748	#121	—	2	1	no	—
749	#121	—	2	1	no	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	C₂³×C₇	1	2	yes	—
753	#121	C₂³×C₇	1	2	yes	—
754	#121	C₂³×C₇	1	2	yes	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
759	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
760	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₇	1	2	yes	—
763	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	C₇×D₄	1	2	yes	—
789	C₄×D₄	C₇×D₄	1	1	yes	characteristic
790	C₄×D₄	C₇×D₄	1	2	yes	—
791	C₄×D₄	C₇×D₄	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₇	1	2	yes	—
793	C₄×D₄	C₂³×C₇	1	2	yes	—
794	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₇	1	2	yes	—
796	C₄×D₄	C₂³×C₇	1	2	yes	—
797	C₄×D₄	C₂³×C₇	1	2	yes	—
798	C₄×D₄	C₂³×C₇	1	2	yes	—
799	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₇	1	2	yes	—
801	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	C₂³×C₇	1	1	yes	characteristic
810	#117	C₂³×C₇	1	2	yes	—
811	#117	C₂³×C₇	1	1	yes	characteristic
812	#117	C₂³×C₇	1	1	yes	characteristic
813	#117	C₂³×C₇	1	2	yes	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
819	C₂×C₂²⋊C₄	—	2	1	no	—
820	C₂×C₂²⋊C₄	—	2	2	no	—
821	C₂×C₂²⋊C₄	—	2	1	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	—	2	2	no	—
827	C₂×C₄²	—	2	1	no	—
828	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
829	C₂×C₄²	C₂³×C₇	1	2	yes	—
830	#107	C₂³×C₇	1	2	yes	—
831	#107	C₂³×C₇	1	2	yes	—
832	#107	C₂³×C₇	1	1	yes	characteristic
833	#107	C₂³×C₇	1	1	yes	characteristic
834	#107	C₂³×C₇	1	2	yes	—
835	#107	C₂³×C₇	1	2	yes	—
836	#106	C₂³×C₇	1	1	yes	characteristic
837	#106	C₂³×C₇	1	1	yes	characteristic
838	#106	C₂³×C₇	1	2	yes	—
839	#106	C₂³×C₇	1	2	yes	—
840	C₄⋊C₈	C₂³×C₇	1	2	yes	—
841	C₄⋊C₈	C₂³×C₇	1	2	yes	—
842	C₄⋊C₈	C₂³×C₇	1	2	yes	—
843	C₄⋊C₈	C₂³×C₇	1	2	yes	—
844	#103	C₂³×C₇	1	1	yes	characteristic
845	#103	C₂³×C₇	1	1	yes	characteristic
846	#103	C₂³×C₇	1	1	yes	characteristic
847	#103	C₂³×C₇	1	1	yes	characteristic
848	#103	C₂³×C₇	1	2	yes	—
849	#103	C₂³×C₇	1	2	yes	—
850	#102	C₂³×C₇	1	2	yes	—
851	#102	C₂³×C₇	1	2	yes	—
852	#102	C₂³×C₇	1	2	yes	—
853	#102	C₂³×C₇	1	2	yes	—
854	#102	C₂³×C₇	1	1	yes	characteristic
855	#102	C₂³×C₇	1	1	yes	characteristic
856	#102	C₂³×C₇	1	1	yes	characteristic
857	#102	C₂³×C₇	1	1	yes	characteristic
858	#102	C₂³×C₇	1	2	yes	—
859	#102	C₂³×C₇	1	2	yes	—
860	#102	C₂³×C₇	1	2	yes	—
861	#102	C₂³×C₇	1	2	yes	—
862	#102	C₂³×C₇	1	2	yes	—
863	#102	C₂³×C₇	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
868	#97	C₂³×C₇	1	2	yes	—
869	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₇	1	2	yes	—
874	C₂²×C₇	—	2	1	no	—
875	C₂²×C₇	—	2	1	no	—
876	C₂²×C₇	—	2	2	no	—
877	C₂²×C₇	—	2	2	no	—
878	C₂²×C₇	—	2	4	no	—
879	C₂²×C₇	—	2	2	no	—
880	C₂²×C₇	—	2	2	no	—
881	C₂²×C₇	—	4	2	no	—
882	C₂²×C₇	—	4	1	no	—
883	C₂²×C₇	—	4	2	no	—
884	C₂²×C₇	—	4	1	no	—
885	C₂²×C₇	—	4	1	no	—
886	C₂²×C₇	—	4	2	no	—
887	C₂²×C₇	—	4	1	no	—
888	C₂²×C₇	—	4	2	no	—
889	C₂²×C₇	—	4	2	no	—
890	C₂²×C₇	—	4	1	no	—
891	C₂²×C₇	—	8	4	no	—
892	C₂²×C₇	—	8	4	no	—
893	C₂²×C₇	—	8	8	no	—
894	C₂²×C₇	#525	1	2	yes	—
895	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
896	C₄×C₇	—	2	1	no	—
897	C₄×C₇	—	2	1	no	—
898	C₄×C₇	—	2	2	no	—
899	C₄×C₇	—	2	2	no	—
900	C₄×C₇	—	2	2	no	—
901	C₄×C₇	—	2	1	no	—
902	C₄×C₇	—	2	2	no	—
903	C₄×C₇	—	4	1	no	—
904	C₄×C₇	—	4	1	no	—
905	C₄×C₇	—	4	1	no	—
906	C₄×C₇	—	4	2	no	—
907	C₄×C₇	—	4	1	no	—
908	C₄×C₇	—	4	2	no	—
909	C₄×C₇	—	4	1	no	—
910	C₄×C₇	#525	1	2	yes	—
911	C₄×C₇	#576	1	2	yes	—
912	C₄×C₇	C₂²×#41	1	1	yes	characteristic
913	C₄×C₇	C₂²×#41	1	1	yes	characteristic
914	C₂⁴	—	2	2	no	—
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	1	no	—
917	#41	—	2	8	no	—
918	#41	—	2	4	no	—
919	#41	—	2	4	no	—
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	—	2	2	no	—
923	#41	—	2	2	no	—
924	#41	—	2	2	no	—
925	#41	—	8	4	no	—
926	#41	C₇×#41	1	4	yes	complemented
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
929	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
930	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
931	C₂×D₄	—	2	16	no	—
932	C₂×D₄	—	2	8	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	4	no	—
936	C₂×D₄	—	2	4	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
950	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
951	C₂×D₄	C₇×#41	1	4	yes	complemented
952	C₂×D₄	C₂⁴×C₇	1	2	yes	—
953	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
955	C₂×D₄	C₂⁴×C₇	1	2	yes	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	8	2	no	—
974	C₂²×C₄	—	8	2	no	—
975	C₂²×C₄	—	8	4	no	—
976	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
977	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
978	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
979	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
981	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
982	Q₁₆	—	2	2	no	—
983	SD₁₆	—	2	2	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	2	2	no	—
986	SD₁₆	—	2	4	no	—
987	D₈	—	2	4	no	—
988	D₈	—	2	4	no	—
989	D₈	—	2	2	no	—
990	D₈	—	2	4	no	—
991	D₈	—	2	4	no	—
992	M₁₆	—	2	2	no	—
993	M₁₆	—	2	2	no	—
994	C₂×C₈	—	2	2	no	—
995	C₂×C₈	—	2	2	no	—
996	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1016	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1017	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1045	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1046	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1056	C₄²	C₂×C₇×D₄	1	2	yes	—
1057	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1058	C₄²	C₂×C₇×D₄	1	2	yes	—
1059	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₇	1	2	yes	—
1062	C₂×C₇	—	2	2	no	—
1063	C₂×C₇	—	4	2	no	—
1064	C₂×C₇	—	4	4	no	—
1065	C₂×C₇	—	4	2	no	—
1066	C₂×C₇	—	8	1	no	—
1067	C₂×C₇	—	8	2	no	—
1068	C₂×C₇	C₂×#525	1	1	yes	characteristic
1069	C₂×C₇	C₂×#576	1	1	yes	characteristic
1070	C₂×C₇	#3584	1	1	yes	characteristic
1071	C₂³	—	2	8	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	4	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	4	2	no	—
1078	C₂³	—	8	1	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	C₂²×C₇×D₄	1	2	yes	—
1085	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	8	2	no	—
1091	Q₈	C₂×C₇×#41	1	2	yes	—
1092	D₄	—	2	8	no	—
1093	D₄	—	2	8	no	—
1094	D₄	—	2	4	no	—
1095	D₄	—	2	4	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	4	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	C₂×C₇×#41	1	2	yes	—
1112	D₄	C₂×C₇×#41	1	4	yes	—
1113	C₂×C₄	—	2	8	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	4	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	8	1	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	2	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	2	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1145	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1146	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1147	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1148	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1149	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1150	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1151	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1152	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1153	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1154	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	—	2	2	no	—
1161	C₇	#60570	1	1	yes	characteristic, direct product factor, Sylow
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	4	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	8	4	no	—
1180	C₂²	—	8	4	no	—
1181	C₂²	—	8	8	no	—
1182	C₂²	C₇×#525	1	2	yes	—
1183	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1184	C₄	—	2	1	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	C₇×#525	1	2	yes	—
1199	C₄	C₇×#576	1	2	yes	—
1200	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1201	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1202	C₂	—	2	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	4	4	no	—
1205	C₂	—	4	2	no	—
1206	C₂	—	8	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	C₂×C₇×#525	1	1	yes	characteristic
1209	C₂	C₂×C₇×#576	1	1	yes	characteristic
1210	C₂	C₇×#3584	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3460	C₂	semidirect
2. C₄×C₇×H(5,𝔽₂)	C₂	semidirect
3. C₇×#3124	C₂	semidirect
4. C₇×#3122	C₂	semidirect
5. C₇×#3119	C₂	semidirect
6. C₇×#3118	C₂	semidirect
7. C₇×#3106	C₂	semidirect
8. C₇×#3105	C₂	semidirect
9. C₇×#3102	C₂	semidirect
10. C₇×#3100	C₂	semidirect
11. C₇×#3098	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3083	C₂	semidirect
14. C₇×#3081	C₂	semidirect
15. C₇×#3045	C₂	semidirect
16. C₇×#3041	C₂	semidirect
17. C₇×#3012	C₂	semidirect
18. C₇×#3008	C₂	semidirect
19. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
20. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
21. C₄×C₇×#135	C₂	semidirect
22. C₂×C₄×C₇×D₈	C₂	semidirect
23. C₇×#2922	C₂	semidirect
29. C₇×#544	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
33. C₇×#540	C₂²	semidirect
37. C₇×#535	C₂²	semidirect
39. C₇×#532	C₂²	semidirect
41. C₇×#529	C₂²	semidirect
46. C₇×#520	C₂²	semidirect
50. C₇×#518	C₂²	semidirect
54. C₄×C₇×#41	C₂²	semidirect
55. C₄×C₇×#41	C₂²	semidirect
59. C₂×C₄×C₇×D₄	C₂²	semidirect
60. C₂×C₄×C₇×D₄	C₂²	semidirect
61. C₇×#485	C₂²	semidirect
62. C₇×#484	C₂²	semidirect
63. C₇×#482	C₂²	semidirect
64. C₇×#482	C₂²	semidirect
65. C₇×#482	C₂²	semidirect
66. C₇×#481	C₂²	semidirect
67. C₇×#480	C₂²	semidirect
68. C₇×#480	C₂²	semidirect
69. C₇×#479	C₂²	semidirect
70. C₇×#478	C₂²	semidirect
71. C₇×#478	C₂²	semidirect
72. C₇×#478	C₂²	semidirect
73. C₇×#477	C₂²	semidirect
74. C₇×#476	C₂²	semidirect
75. C₇×#474	C₂²	semidirect
76. C₇×#474	C₂²	semidirect
77. C₇×#464	C₂²	semidirect
78. C₇×#463	C₂²	semidirect
79. C₇×#463	C₂²	semidirect
80. C₇×#463	C₂²	semidirect
81. C₇×#460	C₂²	semidirect
82. C₇×#459	C₂²	semidirect
83. C₇×#459	C₂²	semidirect
84. C₇×#459	C₂²	semidirect
85. C₇×#452	C₂²	semidirect
86. C₇×#450	C₂²	semidirect
89. C₇×#449	C₂²	semidirect
92. C₇×#447	C₂²	semidirect
93. C₇×#442	C₂²	semidirect
94. C₇×#442	C₂²	semidirect
95. C₇×#440	C₂²	semidirect
96. C₇×#440	C₂²	semidirect
97. C₄×C₇×Q₁₆	C₂²	semidirect
98. C₄×C₇×Q₁₆	C₂²	semidirect
99. C₄×C₇×SD₁₆	C₂²	semidirect
100. C₄×C₇×SD₁₆	C₂²	semidirect
101. C₄×C₇×SD₁₆	C₂²	semidirect
102. C₄×C₇×SD₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
104. C₄×C₇×SD₁₆	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₄×C₇×D₈	C₂²	semidirect
107. C₄×C₇×D₈	C₂²	semidirect
108. C₄×C₇×D₈	C₂²	semidirect
109. C₄×C₇×D₈	C₂²	semidirect
110. C₄×C₇×D₈	C₂²	semidirect
111. C₄×C₇×D₈	C₂²	semidirect
112. C₄×C₇×D₈	C₂²	semidirect
113. C₇×#433	C₂²	semidirect
114. C₇×#433	C₂²	semidirect
115. C₇×#431	C₂²	semidirect
116. C₇×#431	C₂²	semidirect
117. C₇×#428	C₂²	semidirect
118. C₇×#428	C₂²	semidirect
119. C₇×#427	C₂²	semidirect
120. C₂×C₇×#107	C₂²	semidirect
121. C₇×#424	C₂²	semidirect
122. C₇×#424	C₂²	semidirect
124. C₇×#418	C₂²	semidirect
126. C₇×#417	C₂²	semidirect
128. C₇×#416	C₂²	semidirect
130. C₂×C₇×#102	C₂²	semidirect
133. C₄×C₇×M₁₆	C₂²	semidirect
134. C₂×C₄×C₇×C₈	C₂²	semidirect
135. #60570	C₇	direct (N × H)
319. #3460	C₂×C₇	semidirect
320. C₄×H(5,𝔽₂)	C₂×C₇	semidirect
321. #3124	C₂×C₇	semidirect
322. #3122	C₂×C₇	semidirect
323. #3119	C₂×C₇	semidirect
324. #3118	C₂×C₇	semidirect
325. #3106	C₂×C₇	semidirect
326. #3105	C₂×C₇	semidirect
327. #3102	C₂×C₇	semidirect
328. #3100	C₂×C₇	semidirect
329. #3098	C₂×C₇	semidirect
330. #3096	C₂×C₇	semidirect
331. #3083	C₂×C₇	semidirect
332. #3081	C₂×C₇	semidirect
333. #3045	C₂×C₇	semidirect
334. #3041	C₂×C₇	semidirect
335. #3012	C₂×C₇	semidirect
336. #3008	C₂×C₇	semidirect
337. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
338. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
339. C₄×#135	C₂×C₇	semidirect
340. C₂×C₄×D₈	C₂×C₇	semidirect
341. #2922	C₂×C₇	semidirect
354. C₇×#41	#41	semidirect
379. C₂×C₇×D₄	#41	semidirect
495. #544	C₂²×C₇	semidirect
497. #542	C₂²×C₇	semidirect
499. #540	C₂²×C₇	semidirect
503. #535	C₂²×C₇	semidirect
505. #532	C₂²×C₇	semidirect
507. #529	C₂²×C₇	semidirect
512. #520	C₂²×C₇	semidirect
516. #518	C₂²×C₇	semidirect
520. C₄×#41	C₂²×C₇	semidirect
521. C₄×#41	C₂²×C₇	semidirect
525. C₂×C₄×D₄	C₂²×C₇	semidirect
526. C₂×C₄×D₄	C₂²×C₇	semidirect
527. #485	C₂²×C₇	semidirect
528. #484	C₂²×C₇	semidirect
529. #482	C₂²×C₇	semidirect
530. #482	C₂²×C₇	semidirect
531. #482	C₂²×C₇	semidirect
532. #481	C₂²×C₇	semidirect
533. #480	C₂²×C₇	semidirect
534. #480	C₂²×C₇	semidirect
535. #479	C₂²×C₇	semidirect
536. #478	C₂²×C₇	semidirect
537. #478	C₂²×C₇	semidirect
538. #478	C₂²×C₇	semidirect
539. #477	C₂²×C₇	semidirect
540. #476	C₂²×C₇	semidirect
541. #474	C₂²×C₇	semidirect
542. #474	C₂²×C₇	semidirect
543. #464	C₂²×C₇	semidirect
544. #463	C₂²×C₇	semidirect
545. #463	C₂²×C₇	semidirect
546. #463	C₂²×C₇	semidirect
547. #460	C₂²×C₇	semidirect
548. #459	C₂²×C₇	semidirect
549. #459	C₂²×C₇	semidirect
550. #459	C₂²×C₇	semidirect
551. #452	C₂²×C₇	semidirect
552. #450	C₂²×C₇	semidirect
555. #449	C₂²×C₇	semidirect
558. #447	C₂²×C₇	semidirect
559. #442	C₂²×C₇	semidirect
560. #442	C₂²×C₇	semidirect
561. #440	C₂²×C₇	semidirect
562. #440	C₂²×C₇	semidirect
563. C₄×Q₁₆	C₂²×C₇	semidirect
564. C₄×Q₁₆	C₂²×C₇	semidirect
565. C₄×SD₁₆	C₂²×C₇	semidirect
566. C₄×SD₁₆	C₂²×C₇	semidirect
567. C₄×SD₁₆	C₂²×C₇	semidirect
568. C₄×SD₁₆	C₂²×C₇	semidirect
569. C₄×SD₁₆	C₂²×C₇	semidirect
570. C₄×SD₁₆	C₂²×C₇	semidirect
571. C₄×D₈	C₂²×C₇	semidirect
572. C₄×D₈	C₂²×C₇	semidirect
573. C₄×D₈	C₂²×C₇	semidirect
574. C₄×D₈	C₂²×C₇	semidirect
575. C₄×D₈	C₂²×C₇	semidirect
576. C₄×D₈	C₂²×C₇	semidirect
577. C₄×D₈	C₂²×C₇	semidirect
578. C₄×D₈	C₂²×C₇	semidirect
579. #433	C₂²×C₇	semidirect
580. #433	C₂²×C₇	semidirect
581. #431	C₂²×C₇	semidirect
582. #431	C₂²×C₇	semidirect
583. #428	C₂²×C₇	semidirect
584. #428	C₂²×C₇	semidirect
585. #427	C₂²×C₇	semidirect
586. C₂×#107	C₂²×C₇	semidirect
587. #424	C₂²×C₇	semidirect
588. #424	C₂²×C₇	semidirect
590. #418	C₂²×C₇	semidirect
592. #417	C₂²×C₇	semidirect
594. #416	C₂²×C₇	semidirect
596. C₂×#102	C₂²×C₇	semidirect
599. C₄×M₁₆	C₂²×C₇	semidirect
600. C₂×C₄×C₈	C₂²×C₇	semidirect
926. #41	C₇×#41	semidirect
951. C₂×D₄	C₇×#41	semidirect
1161. C₇	#60570	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×#3460	2
C₄×C₇×H(5,𝔽₂)	2
C₇×#3124	2
C₇×#3122	2
C₇×#3119	2
C₇×#3118	2
C₇×#3106	2
C₇×#3105	2
C₇×#3102	2
C₇×#3100	2
C₇×#3098	2
C₇×#3096	2
C₇×#3083	2
C₇×#3081	2
C₇×#3045	2
C₇×#3041	2
C₇×#3012	2
C₇×#3008	2
C₄×C₇×AGL(1,ℤ/8)	2
C₄×C₇×#135	2
C₂×C₄×C₇×D₈	2
C₇×#2922	2
#60570	7

Subgroups — C7×#60570 #13237786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60570 #13237786