Subgroups — C₇×#62053 #13239269

Order 1792.

1956 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3314	C₂	1	2	yes	maximal, complemented
9	C₇×#3295	C₂	1	2	yes	maximal, complemented
10	C₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3280	C₂	1	2	yes	maximal, complemented
13	C₇×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3264	C₂	1	2	yes	maximal, complemented
15	C₇×#3257	C₂	1	2	yes	maximal, complemented
16	C₇×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3224	C₂	1	2	yes	maximal, complemented
18	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3119	C₂	1	2	yes	maximal, complemented
20	C₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3045	C₂	1	2	yes	maximal, complemented
22	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₇×#135	C₂²	1	2	yes	complemented
26	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
27	C₇×#560	—	2	2	no	—
28	C₇×#559	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	C₂²	1	1	yes	characteristic, complemented
30	C₇×#554	C₂²	1	2	yes	complemented
31	C₇×#552	—	2	1	no	—
32	C₇×#551	—	2	2	no	—
33	C₇×#550	C₂²	1	1	yes	characteristic, complemented
34	C₇×#550	C₂²	1	1	yes	characteristic, complemented
35	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₇×#548	—	2	1	no	—
37	C₇×#547	C₂²	1	1	yes	characteristic, complemented
38	C₇×#547	C₂²	1	1	yes	characteristic, complemented
39	C₇×#546	—	2	1	no	—
40	C₇×#546	C₂²	1	2	yes	—
41	C₇×#546	C₂²	1	2	yes	complemented
42	C₇×D₄²	—	2	1	no	—
43	C₇×D₄²	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic, complemented
45	C₇×#542	C₂²	1	2	yes	complemented
46	C₇×#540	—	2	1	no	—
47	C₇×#540	C₂²	1	2	yes	complemented
48	C₇×#539	—	2	2	no	—
49	C₇×#535	—	2	1	no	—
50	C₇×#535	C₂²	1	2	yes	complemented
51	C₇×#534	—	2	2	no	—
52	C₇×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₇×#127	C₂²	1	1	yes	characteristic
54	C₇×#529	C₂²	1	1	yes	characteristic
55	C₇×#529	C₂²	1	1	yes	characteristic
56	C₇×#525	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
58	C₇×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	complemented
62	C₇×#492	C₂²	1	1	yes	characteristic, complemented
63	C₇×#492	C₂²	1	1	yes	characteristic, complemented
64	C₇×#489	C₂²	1	2	yes	complemented
65	C₇×#486	C₂²	1	1	yes	characteristic, complemented
66	C₇×#486	C₂²	1	1	yes	characteristic, complemented
67	C₇×#486	C₂²	1	2	yes	complemented
68	C₇×#484	C₂²	1	1	yes	characteristic, complemented
69	C₇×#481	C₂²	1	1	yes	characteristic
70	C₇×#481	C₂²	1	2	yes	complemented
71	C₇×#480	C₂²	1	2	yes	complemented
72	C₇×#479	C₂²	1	2	yes	complemented
73	C₇×#478	C₂²	1	1	yes	characteristic, complemented
74	C₇×#478	C₂²	1	1	yes	characteristic, complemented
75	C₇×#476	C₂²	1	2	yes	complemented
76	C₇×#475	C₂²	1	1	yes	characteristic, complemented
77	C₇×#474	C₂²	1	1	yes	characteristic, complemented
78	C₇×#474	C₂²	1	2	yes	complemented
79	C₇×#469	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#467	C₂²	1	2	yes	complemented
82	C₇×#466	C₂²	1	2	yes	complemented
83	C₇×#465	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	complemented
85	C₇×#464	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	1	yes	characteristic, complemented
88	C₇×#463	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	complemented
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	1	yes	characteristic, complemented
92	C₇×#462	C₂²	1	1	yes	characteristic, complemented
93	C₇×#461	C₂²	1	1	yes	characteristic, complemented
94	C₇×#460	C₂²	1	2	yes	complemented
95	C₇×#460	C₂²	1	2	yes	complemented
96	C₇×#460	C₂²	1	2	yes	complemented
97	C₇×#459	C₂²	1	1	yes	characteristic
98	C₇×#459	C₂²	1	1	yes	characteristic
99	C₇×#459	C₂²	1	2	yes	complemented
100	C₇×#459	C₂²	1	2	yes	complemented
101	C₇×#459	C₂²	1	1	yes	characteristic, complemented
102	C₇×#459	C₂²	1	2	yes	complemented
103	C₇×#459	C₂²	1	1	yes	characteristic, complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#450	C₂²	1	2	yes	complemented
106	C₇×#450	C₂²	1	2	yes	complemented
107	C₇×#450	C₂²	1	2	yes	complemented
108	C₇×#450	C₂²	1	1	yes	characteristic, complemented
109	C₇×#449	C₂²	1	2	yes	complemented
110	C₇×#449	C₂²	1	2	yes	complemented
111	C₇×#449	C₂²	1	2	yes	complemented
112	C₇×#447	C₂²	1	1	yes	characteristic
113	C₇×#447	C₂²	1	2	yes	complemented
114	C₇×#446	C₂²	1	1	yes	characteristic, complemented
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₇×#442	C₂²	1	2	yes	complemented
117	C₇×#440	C₂²	1	2	yes	complemented
118	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
120	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×D₈	C₂²	1	2	yes	complemented
123	C₄×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₇×#436	C₂²	1	1	yes	characteristic, complemented
125	C₇×#435	C₂²	1	2	yes	complemented
126	C₇×C₈×D₄	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₇×#433	C₂²	1	2	yes	complemented
129	C₇×#431	C₂²	1	1	yes	characteristic, complemented
130	C₇×#424	C₂²	1	2	yes	complemented
131	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₇×#417	C₂²	1	2	yes	complemented
133	C₂×C₇×#102	C₂²	1	2	yes	complemented
134	C₂×C₇×#102	C₂²	1	2	yes	complemented
135	#62053	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	—	2	1	no	—
141	C₂²×C₇×D₄	—	2	2	no	—
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	—	2	1	no	—
144	C₂²×C₇×D₄	—	2	1	no	—
145	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
146	C₂²×C₇×D₄	C₂³	1	2	yes	—
147	C₂²×C₇×D₄	C₂³	1	2	yes	—
148	C₂³×C₄×C₇	—	2	1	no	—
149	C₇×AGL(1,ℤ/8)	—	4	4	no	—
150	C₇×#135	—	4	4	no	—
151	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×D₈	—	4	4	no	—
160	C₂×C₇×D₈	C₂³	1	2	yes	—
161	C₂×C₇×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
163	C₂×C₇×D₈	C₂³	1	2	yes	—
164	C₂×C₇×D₈	C₂³	1	2	yes	—
165	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
166	C₂×C₇×M₁₆	C₂³	1	2	yes	—
167	C₂²×C₇×C₈	C₂³	1	2	yes	—
168	C₂²×C₇×C₈	C₂³	1	2	yes	—
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×#127	—	2	1	no	—
173	C₇×#127	—	2	1	no	—
174	C₇×#127	—	2	1	no	—
175	C₇×#127	C₂³	1	1	yes	characteristic
176	C₇×#127	C₂³	1	1	yes	characteristic
177	C₇×#127	C₂³	1	2	yes	—
178	C₇×#127	C₂³	1	2	yes	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	1	no	—
182	C₇×#126	D₄	1	2	yes	—
183	C₇×#125	—	2	2	no	—
184	C₇×#125	—	2	1	no	—
185	C₇×#125	D₄	1	1	yes	characteristic
186	C₇×#125	C₂³	1	1	yes	characteristic
187	C₇×#124	—	2	1	no	—
188	C₇×#124	—	2	2	no	—
189	C₇×#124	D₄	1	1	yes	characteristic
190	C₇×#124	C₂³	1	2	yes	—
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#123	—	2	1	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	D₄	1	2	yes	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	2	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	D₄	1	1	yes	characteristic
228	C₇×#121	C₂³	1	2	yes	—
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	1	yes	characteristic
232	C₇×#120	—	2	2	no	—
233	C₇×#120	—	2	2	no	—
234	C₇×#120	—	2	2	no	—
235	C₇×#120	—	2	2	no	—
236	C₇×#120	—	2	2	no	—
237	C₇×#120	—	2	2	no	—
238	C₇×#120	—	2	2	no	—
239	C₄×C₇×Q₈	—	2	1	no	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	2	yes	—
242	C₄×C₇×Q₈	C₂³	1	2	yes	—
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	2	yes	—
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	—	2	2	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₇×C₄⋊C₈	C₂³	1	2	yes	—
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
294	C₇×#102	C₂³	1	2	yes	—
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	2	yes	—
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3543	C₂×C₇	1	1	yes	characteristic, complemented
317	#3520	C₂×C₇	1	1	yes	characteristic, complemented
318	#3397	C₂×C₇	1	1	yes	characteristic, complemented
319	#3394	C₂×C₇	1	1	yes	characteristic, complemented
320	#3373	C₂×C₇	1	1	yes	characteristic, complemented
321	#3358	C₂×C₇	1	1	yes	characteristic, complemented
322	#3332	C₂×C₇	1	1	yes	characteristic, complemented
323	#3314	C₂×C₇	1	2	yes	complemented
324	#3295	C₂×C₇	1	2	yes	complemented
325	#3294	C₂×C₇	1	1	yes	characteristic, complemented
326	#3284	C₂×C₇	1	1	yes	characteristic, complemented
327	#3280	C₂×C₇	1	2	yes	complemented
328	#3272	C₂×C₇	1	1	yes	characteristic, complemented
329	#3264	C₂×C₇	1	2	yes	complemented
330	#3257	C₂×C₇	1	2	yes	complemented
331	#3248	C₂×C₇	1	1	yes	characteristic, complemented
332	#3224	C₂×C₇	1	2	yes	complemented
333	#3208	C₂×C₇	1	1	yes	characteristic, complemented
334	#3119	C₂×C₇	1	2	yes	complemented
335	#3105	C₂×C₇	1	1	yes	characteristic, complemented
336	#3045	C₂×C₇	1	2	yes	complemented
337	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	1	no	—
340	C₂⁴×C₇	—	2	2	no	—
341	C₂⁴×C₇	—	2	2	no	—
342	C₇×#41	—	2	4	no	—
343	C₇×#41	—	4	2	no	—
344	C₇×#41	—	4	2	no	—
345	C₇×#41	—	4	2	no	—
346	C₇×#41	—	8	2	no	—
347	C₇×#41	—	8	2	no	—
348	C₂×C₇×Q₈	—	2	1	no	—
349	C₂×C₇×Q₈	—	2	2	no	—
350	C₂×C₇×Q₈	—	8	2	no	—
351	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
352	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
354	C₂×C₇×D₄	—	2	2	no	—
355	C₂×C₇×D₄	—	2	2	no	—
356	C₂×C₇×D₄	—	2	1	no	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	—	2	2	no	—
359	C₂×C₇×D₄	—	2	2	no	—
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	1	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	1	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	—	2	1	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	2	no	—
371	C₂×C₇×D₄	—	2	1	no	—
372	C₂×C₇×D₄	—	4	1	no	—
373	C₂×C₇×D₄	—	4	2	no	—
374	C₂×C₇×D₄	—	4	2	no	—
375	C₂×C₇×D₄	—	4	2	no	—
376	C₂×C₇×D₄	—	4	2	no	—
377	C₂×C₇×D₄	—	8	2	no	—
378	C₂×C₇×D₄	—	8	2	no	—
379	C₂×C₇×D₄	—	8	2	no	—
380	C₂×C₇×D₄	—	8	4	no	—
381	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
382	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
383	C₂×C₇×D₄	C₂⁴	1	2	yes	—
384	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×D₄	C₂⁴	1	2	yes	—
386	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
387	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₇	—	2	1	no	—
389	C₂²×C₄×C₇	—	2	2	no	—
390	C₂²×C₄×C₇	—	2	2	no	—
391	C₂²×C₄×C₇	—	2	1	no	—
392	C₂²×C₄×C₇	—	2	1	no	—
393	C₂²×C₄×C₇	—	2	1	no	—
394	C₂²×C₄×C₇	—	2	2	no	—
395	C₂²×C₄×C₇	—	2	2	no	—
396	C₂²×C₄×C₇	—	2	2	no	—
397	C₂²×C₄×C₇	—	2	1	no	—
398	C₂²×C₄×C₇	—	2	2	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	8	2	no	—
401	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
405	C₇×Q₁₆	—	4	2	no	—
406	C₇×SD₁₆	—	2	2	no	—
407	C₇×SD₁₆	—	4	2	no	—
408	C₇×SD₁₆	—	4	1	no	—
409	C₇×SD₁₆	—	4	2	no	—
410	C₇×SD₁₆	—	4	2	no	—
411	C₇×SD₁₆	—	4	2	no	—
412	C₇×SD₁₆	—	4	2	no	—
413	C₇×D₈	—	2	4	no	—
414	C₇×D₈	—	2	4	no	—
415	C₇×D₈	—	2	2	no	—
416	C₇×D₈	—	4	2	no	—
417	C₇×D₈	—	4	2	no	—
418	C₇×D₈	—	4	1	no	—
419	C₇×M₁₆	—	4	2	no	—
420	C₂×C₇×C₈	—	4	2	no	—
421	C₂×C₇×C₈	—	4	2	no	—
422	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₇×C₈	C₂⁴	1	2	yes	—
426	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
427	C₂×C₇×C₈	C₂⁴	1	2	yes	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	2	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	1	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
445	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
447	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
448	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
451	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₇×C₂²⋊C₄	—	2	1	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	1	no	—
457	C₇×C₂²⋊C₄	—	2	1	no	—
458	C₇×C₂²⋊C₄	—	2	1	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	2	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	1	no	—
469	C₇×C₂²⋊C₄	—	2	2	no	—
470	C₇×C₂²⋊C₄	—	2	2	no	—
471	C₇×C₂²⋊C₄	—	2	1	no	—
472	C₇×C₂²⋊C₄	—	2	2	no	—
473	C₇×C₂²⋊C₄	—	2	2	no	—
474	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
475	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
476	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
477	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
478	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
479	C₄²×C₇	—	2	2	no	—
480	C₄²×C₇	—	2	2	no	—
481	C₄²×C₇	—	2	1	no	—
482	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
483	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
484	C₄²×C₇	C₂⁴	1	1	yes	characteristic
485	C₄²×C₇	C₂⁴	1	2	yes	—
486	C₄²×C₇	C₂⁴	1	1	yes	characteristic
487	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
488	C₂×#135	C₂²×C₇	1	2	yes	complemented
489	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
490	#560	—	2	2	no	—
491	#559	C₂²×C₇	1	1	yes	characteristic, complemented
492	#556	C₂²×C₇	1	1	yes	characteristic, complemented
493	#554	C₂²×C₇	1	2	yes	complemented
494	#552	—	2	1	no	—
495	#551	—	2	2	no	—
496	#550	C₂²×C₇	1	1	yes	characteristic, complemented
497	#550	C₂²×C₇	1	1	yes	characteristic, complemented
498	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
499	#548	—	2	1	no	—
500	#547	C₂²×C₇	1	1	yes	characteristic, complemented
501	#547	C₂²×C₇	1	1	yes	characteristic, complemented
502	#546	—	2	1	no	—
503	#546	C₂²×C₇	1	2	yes	—
504	#546	C₂²×C₇	1	2	yes	complemented
505	D₄²	—	2	1	no	—
506	D₄²	C₂²×C₇	1	2	yes	—
507	D₄²	C₂²×C₇	1	1	yes	characteristic, complemented
508	#542	C₂²×C₇	1	2	yes	complemented
509	#540	—	2	1	no	—
510	#540	C₂²×C₇	1	2	yes	complemented
511	#539	—	2	2	no	—
512	#535	—	2	1	no	—
513	#535	C₂²×C₇	1	2	yes	complemented
514	#534	—	2	2	no	—
515	#533	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂×#127	C₂²×C₇	1	1	yes	characteristic
517	#529	C₂²×C₇	1	1	yes	characteristic
518	#529	C₂²×C₇	1	1	yes	characteristic
519	#525	—	2	1	no	—
520	C₂×C₂²⋊Q₈	—	2	1	no	—
521	#520	C₂²×C₇	1	2	yes	complemented
522	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
523	#496	C₂²×C₇	1	2	yes	complemented
524	#495	C₂²×C₇	1	2	yes	complemented
525	#492	C₂²×C₇	1	1	yes	characteristic, complemented
526	#492	C₂²×C₇	1	1	yes	characteristic, complemented
527	#489	C₂²×C₇	1	2	yes	complemented
528	#486	C₂²×C₇	1	1	yes	characteristic, complemented
529	#486	C₂²×C₇	1	2	yes	complemented
530	#486	C₂²×C₇	1	1	yes	characteristic, complemented
531	#484	C₂²×C₇	1	1	yes	characteristic, complemented
532	#481	C₂²×C₇	1	1	yes	characteristic
533	#481	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	1	yes	characteristic, complemented
537	#478	C₂²×C₇	1	1	yes	characteristic, complemented
538	#476	C₂²×C₇	1	2	yes	complemented
539	#475	C₂²×C₇	1	1	yes	characteristic, complemented
540	#474	C₂²×C₇	1	1	yes	characteristic, complemented
541	#474	C₂²×C₇	1	2	yes	complemented
542	#469	C₂²×C₇	1	2	yes	complemented
543	#468	C₂²×C₇	1	2	yes	complemented
544	#467	C₂²×C₇	1	2	yes	complemented
545	#466	C₂²×C₇	1	2	yes	complemented
546	#465	C₂²×C₇	1	2	yes	—
547	#465	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#464	C₂²×C₇	1	2	yes	complemented
550	#463	C₂²×C₇	1	1	yes	characteristic, complemented
551	#463	C₂²×C₇	1	1	yes	characteristic, complemented
552	#463	C₂²×C₇	1	2	yes	complemented
553	#463	C₂²×C₇	1	2	yes	complemented
554	#463	C₂²×C₇	1	2	yes	complemented
555	#462	C₂²×C₇	1	1	yes	characteristic, complemented
556	#461	C₂²×C₇	1	1	yes	characteristic, complemented
557	#460	C₂²×C₇	1	2	yes	complemented
558	#460	C₂²×C₇	1	2	yes	complemented
559	#460	C₂²×C₇	1	2	yes	complemented
560	#459	C₂²×C₇	1	1	yes	characteristic
561	#459	C₂²×C₇	1	1	yes	characteristic
562	#459	C₂²×C₇	1	1	yes	characteristic, complemented
563	#459	C₂²×C₇	1	2	yes	complemented
564	#459	C₂²×C₇	1	1	yes	characteristic, complemented
565	#459	C₂²×C₇	1	2	yes	complemented
566	#459	C₂²×C₇	1	2	yes	complemented
567	#452	C₂²×C₇	1	2	yes	complemented
568	#450	C₂²×C₇	1	1	yes	characteristic, complemented
569	#450	C₂²×C₇	1	2	yes	complemented
570	#450	C₂²×C₇	1	2	yes	complemented
571	#450	C₂²×C₇	1	2	yes	complemented
572	#449	C₂²×C₇	1	2	yes	complemented
573	#449	C₂²×C₇	1	2	yes	complemented
574	#449	C₂²×C₇	1	2	yes	complemented
575	#447	C₂²×C₇	1	1	yes	characteristic
576	#447	C₂²×C₇	1	2	yes	complemented
577	#446	C₂²×C₇	1	1	yes	characteristic, complemented
578	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
579	#442	C₂²×C₇	1	2	yes	complemented
580	#440	C₂²×C₇	1	2	yes	complemented
581	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
582	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
583	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
584	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
585	C₄×D₈	C₂²×C₇	1	2	yes	complemented
586	C₄×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
587	#436	C₂²×C₇	1	1	yes	characteristic, complemented
588	#435	C₂²×C₇	1	2	yes	complemented
589	C₈×D₄	C₂²×C₇	1	2	yes	complemented
590	C₈×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
591	#433	C₂²×C₇	1	2	yes	complemented
592	#431	C₂²×C₇	1	1	yes	characteristic, complemented
593	#424	C₂²×C₇	1	2	yes	complemented
594	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
595	#417	C₂²×C₇	1	2	yes	complemented
596	C₂×#102	C₂²×C₇	1	2	yes	complemented
597	C₂×#102	C₂²×C₇	1	2	yes	complemented
598	C₂³×C₇	—	2	1	no	—
599	C₂³×C₇	—	2	1	no	—
600	C₂³×C₇	—	2	1	no	—
601	C₂³×C₇	—	2	2	no	—
602	C₂³×C₇	—	2	2	no	—
603	C₂³×C₇	—	4	2	no	—
604	C₂³×C₇	—	4	2	no	—
605	C₂³×C₇	—	4	4	no	—
606	C₂³×C₇	—	8	1	no	—
607	C₂³×C₇	—	8	2	no	—
608	C₂³×C₇	—	8	2	no	—
609	C₂³×C₇	—	8	2	no	—
610	C₂³×C₇	—	8	2	no	—
611	C₂³×C₇	—	8	2	no	—
612	C₂³×C₇	C₂²×D₄	1	2	yes	—
613	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
614	C₇×Q₈	—	2	2	no	—
615	C₇×Q₈	—	2	1	no	—
616	C₇×Q₈	—	2	2	no	—
617	C₇×Q₈	—	2	2	no	—
618	C₇×Q₈	—	2	1	no	—
619	C₇×Q₈	—	4	2	no	—
620	C₇×Q₈	—	8	2	no	—
621	C₇×D₄	—	2	4	no	—
622	C₇×D₄	—	2	2	no	—
623	C₇×D₄	—	2	2	no	—
624	C₇×D₄	—	2	2	no	—
625	C₇×D₄	—	2	1	no	—
626	C₇×D₄	—	2	1	no	—
627	C₇×D₄	—	2	1	no	—
628	C₇×D₄	—	2	1	no	—
629	C₇×D₄	—	2	1	no	—
630	C₇×D₄	—	2	2	no	—
631	C₇×D₄	—	2	2	no	—
632	C₇×D₄	—	4	2	no	—
633	C₇×D₄	—	4	4	no	—
634	C₇×D₄	—	4	2	no	—
635	C₇×D₄	—	4	2	no	—
636	C₇×D₄	—	4	2	no	—
637	C₇×D₄	—	8	2	no	—
638	C₇×D₄	—	8	2	no	—
639	C₇×D₄	—	8	2	no	—
640	C₇×D₄	—	8	1	no	—
641	C₇×D₄	—	8	2	no	—
642	C₇×D₄	—	8	1	no	—
643	C₇×D₄	—	8	2	no	—
644	C₇×D₄	—	8	2	no	—
645	C₇×D₄	—	8	2	no	—
646	C₇×D₄	—	8	2	no	—
647	C₇×D₄	—	8	2	no	—
648	C₇×D₄	—	8	2	no	—
649	C₇×D₄	H(5,𝔽₂)	1	2	yes	—
650	C₂×C₄×C₇	—	2	2	no	—
651	C₂×C₄×C₇	—	2	2	no	—
652	C₂×C₄×C₇	—	2	1	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	1	no	—
655	C₂×C₄×C₇	—	2	2	no	—
656	C₂×C₄×C₇	—	2	2	no	—
657	C₂×C₄×C₇	—	2	1	no	—
658	C₂×C₄×C₇	—	2	1	no	—
659	C₂×C₄×C₇	—	2	1	no	—
660	C₂×C₄×C₇	—	2	2	no	—
661	C₂×C₄×C₇	—	2	1	no	—
662	C₂×C₄×C₇	—	2	1	no	—
663	C₂×C₄×C₇	—	4	4	no	—
664	C₂×C₄×C₇	—	4	2	no	—
665	C₂×C₄×C₇	—	4	2	no	—
666	C₂×C₄×C₇	—	4	2	no	—
667	C₂×C₄×C₇	—	8	1	no	—
668	C₂×C₄×C₇	—	8	1	no	—
669	C₂×C₄×C₇	—	8	2	no	—
670	C₂×C₄×C₇	—	8	2	no	—
671	C₂×C₄×C₇	—	8	2	no	—
672	C₂×C₄×C₇	—	8	2	no	—
673	C₂×C₄×C₇	—	8	1	no	—
674	C₂×C₄×C₇	—	8	2	no	—
675	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
680	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
681	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
682	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
683	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
684	C₇×C₈	—	2	2	no	—
685	C₇×C₈	—	2	1	no	—
686	C₇×C₈	—	2	2	no	—
687	C₇×C₈	—	2	1	no	—
688	C₇×C₈	—	2	1	no	—
689	C₇×C₈	—	2	1	no	—
690	C₂×#41	—	2	1	no	—
691	C₂×#41	—	2	1	no	—
692	C₂×#41	C₂³×C₇	1	2	yes	—
693	C₂×#41	C₂³×C₇	1	2	yes	—
694	C₂²×Q₈	—	2	1	no	—
695	C₂²×D₄	—	2	2	no	—
696	C₂²×D₄	—	2	1	no	—
697	C₂²×D₄	—	2	1	no	—
698	C₂²×D₄	—	2	1	no	—
699	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₇	1	2	yes	—
701	C₂²×D₄	C₂³×C₇	1	2	yes	—
702	C₂³×C₄	—	2	1	no	—
703	AGL(1,ℤ/8)	—	4	4	no	—
704	#135	—	4	4	no	—
705	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
713	C₂×D₈	—	4	4	no	—
714	C₂×D₈	C₂³×C₇	1	2	yes	—
715	C₂×D₈	C₂³×C₇	1	2	yes	—
716	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
717	C₂×D₈	C₂³×C₇	1	2	yes	—
718	C₂×D₈	C₂³×C₇	1	2	yes	—
719	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₇	1	2	yes	—
721	C₂²×C₈	C₂³×C₇	1	2	yes	—
722	C₂²×C₈	C₂³×C₇	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
726	#127	—	2	1	no	—
727	#127	—	2	1	no	—
728	#127	—	2	1	no	—
729	#127	C₂³×C₇	1	2	yes	—
730	#127	C₂³×C₇	1	1	yes	characteristic
731	#127	C₂³×C₇	1	1	yes	characteristic
732	#127	C₂³×C₇	1	2	yes	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	1	no	—
736	#126	C₇×D₄	1	2	yes	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	C₇×D₄	1	1	yes	characteristic
740	#125	C₂³×C₇	1	1	yes	characteristic
741	#124	—	2	1	no	—
742	#124	—	2	2	no	—
743	#124	C₇×D₄	1	1	yes	characteristic
744	#124	C₂³×C₇	1	1	yes	characteristic
745	#124	C₂³×C₇	1	2	yes	—
746	#124	C₂³×C₇	1	2	yes	—
747	#123	—	2	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	C₇×D₄	1	2	yes	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
766	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
769	#121	—	2	1	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	C₇×D₄	1	1	yes	characteristic
782	#121	C₂³×C₇	1	1	yes	characteristic
783	#121	C₂³×C₇	1	2	yes	—
784	#121	C₂³×C₇	1	2	yes	—
785	#121	C₂³×C₇	1	2	yes	—
786	#120	—	2	2	no	—
787	#120	—	2	2	no	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	#120	—	2	2	no	—
792	#120	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	C₂³×C₇	1	2	yes	—
795	C₄×Q₈	C₂³×C₇	1	2	yes	—
796	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₇	1	2	yes	—
811	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₇	1	2	yes	—
813	C₄×D₄	C₂³×C₇	1	2	yes	—
814	C₄×D₄	C₂³×C₇	1	2	yes	—
815	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	C₂³×C₇	1	2	yes	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
829	#107	C₂³×C₇	1	1	yes	characteristic
830	#107	C₂³×C₇	1	2	yes	—
831	#107	C₂³×C₇	1	1	yes	characteristic
832	#106	C₂³×C₇	1	1	yes	characteristic
833	#106	C₂³×C₇	1	1	yes	characteristic
834	#106	C₂³×C₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₇	1	2	yes	—
836	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₇	1	2	yes	—
840	C₄⋊C₈	C₂³×C₇	1	2	yes	—
841	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
842	#103	C₂³×C₇	1	1	yes	characteristic
843	#103	C₂³×C₇	1	2	yes	—
844	#103	C₂³×C₇	1	2	yes	—
845	#103	C₂³×C₇	1	1	yes	characteristic
846	#103	C₂³×C₇	1	2	yes	—
847	#102	C₂³×C₇	1	1	yes	characteristic
848	#102	C₂³×C₇	1	2	yes	—
849	#102	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	2	yes	—
855	#102	C₂³×C₇	1	1	yes	characteristic
856	#102	C₂³×C₇	1	2	yes	—
857	#102	C₂³×C₇	1	1	yes	characteristic
858	#102	C₂³×C₇	1	1	yes	characteristic
859	#102	C₂³×C₇	1	1	yes	characteristic
860	#102	C₂³×C₇	1	1	yes	characteristic
861	#102	C₂³×C₇	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
863	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
864	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
866	#97	C₂³×C₇	1	2	yes	—
867	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₇	1	2	yes	—
870	C₂²×C₇	—	2	1	no	—
871	C₂²×C₇	—	2	1	no	—
872	C₂²×C₇	—	2	2	no	—
873	C₂²×C₇	—	2	2	no	—
874	C₂²×C₇	—	2	2	no	—
875	C₂²×C₇	—	2	2	no	—
876	C₂²×C₇	—	4	1	no	—
877	C₂²×C₇	—	4	1	no	—
878	C₂²×C₇	—	4	2	no	—
879	C₂²×C₇	—	4	1	no	—
880	C₂²×C₇	—	4	2	no	—
881	C₂²×C₇	—	4	1	no	—
882	C₂²×C₇	—	4	1	no	—
883	C₂²×C₇	—	4	1	no	—
884	C₂²×C₇	—	4	2	no	—
885	C₂²×C₇	—	4	2	no	—
886	C₂²×C₇	—	4	2	no	—
887	C₂²×C₇	—	4	1	no	—
888	C₂²×C₇	—	4	2	no	—
889	C₂²×C₇	—	4	1	no	—
890	C₂²×C₇	—	8	4	no	—
891	C₂²×C₇	—	16	4	no	—
892	C₂²×C₇	—	16	4	no	—
893	C₂²×C₇	#577	1	2	yes	—
894	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
895	C₄×C₇	—	2	2	no	—
896	C₄×C₇	—	2	1	no	—
897	C₄×C₇	—	2	1	no	—
898	C₄×C₇	—	2	2	no	—
899	C₄×C₇	—	2	1	no	—
900	C₄×C₇	—	2	1	no	—
901	C₄×C₇	—	2	2	no	—
902	C₄×C₇	—	4	2	no	—
903	C₄×C₇	—	4	1	no	—
904	C₄×C₇	—	4	1	no	—
905	C₄×C₇	—	4	1	no	—
906	C₄×C₇	—	4	1	no	—
907	C₄×C₇	—	4	2	no	—
908	C₄×C₇	—	4	1	no	—
909	C₄×C₇	#576	1	2	yes	—
910	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
911	C₄×C₇	#585	1	1	yes	characteristic
912	C₂⁴	—	2	1	no	—
913	C₂⁴	—	2	2	no	—
914	C₂⁴	—	2	2	no	—
915	#41	—	2	4	no	—
916	#41	—	4	2	no	—
917	#41	—	4	2	no	—
918	#41	—	4	2	no	—
919	#41	—	8	2	no	—
920	#41	—	8	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	—	8	2	no	—
924	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	4	1	no	—
946	C₂×D₄	—	4	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	—	8	2	no	—
952	C₂×D₄	—	8	2	no	—
953	C₂×D₄	—	8	4	no	—
954	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
955	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
956	C₂×D₄	C₂⁴×C₇	1	2	yes	—
957	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₇	1	2	yes	—
959	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	8	2	no	—
974	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
975	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
978	Q₁₆	—	4	2	no	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	4	2	no	—
981	SD₁₆	—	4	1	no	—
982	SD₁₆	—	4	2	no	—
983	SD₁₆	—	4	2	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	2	no	—
986	D₈	—	2	4	no	—
987	D₈	—	2	4	no	—
988	D₈	—	2	2	no	—
989	D₈	—	4	2	no	—
990	D₈	—	4	2	no	—
991	D₈	—	4	1	no	—
992	M₁₆	—	4	2	no	—
993	C₂×C₈	—	4	2	no	—
994	C₂×C₈	—	4	2	no	—
995	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₇	1	2	yes	—
999	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	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	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
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	C₂×C₇×D₄	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1020	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1023	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1048	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1049	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1050	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1051	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1052	C₄²	—	2	2	no	—
1053	C₄²	—	2	2	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1056	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1058	C₄²	C₂⁴×C₇	1	2	yes	—
1059	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1060	C₂×C₇	—	2	2	no	—
1061	C₂×C₇	—	4	2	no	—
1062	C₂×C₇	—	4	2	no	—
1063	C₂×C₇	—	8	1	no	—
1064	C₂×C₇	—	8	2	no	—
1065	C₂×C₇	—	8	1	no	—
1066	C₂×C₇	—	8	2	no	—
1067	C₂×C₇	#3488	1	1	yes	characteristic
1068	C₂×C₇	C₂×#576	1	1	yes	characteristic
1069	C₂×C₇	C₂×#577	1	1	yes	characteristic
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	2	no	—
1075	C₂³	—	4	2	no	—
1076	C₂³	—	4	2	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	8	1	no	—
1079	C₂³	—	8	2	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	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	2	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	4	2	no	—
1092	Q₈	—	8	2	no	—
1093	D₄	—	2	4	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	4	4	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	1	no	—
1113	D₄	—	8	2	no	—
1114	D₄	—	8	1	no	—
1115	D₄	—	8	2	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	C₇×H(5,𝔽₂)	1	2	yes	—
1122	C₂×C₄	—	2	2	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	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	4	4	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	8	1	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	2	no	—
1142	C₂×C₄	—	8	2	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	1	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1148	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1149	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1150	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1151	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1152	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1153	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1154	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1155	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1156	C₈	—	2	2	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	2	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	1	no	—
1161	C₈	—	2	1	no	—
1162	C₇	#62053	1	1	yes	characteristic, direct product factor, Sylow
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	2	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	8	4	no	—
1184	C₂²	—	16	4	no	—
1185	C₂²	—	16	4	no	—
1186	C₂²	C₇×#577	1	2	yes	—
1187	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1188	C₄	—	2	1	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	C₇×#576	1	2	yes	—
1203	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1204	C₄	C₇×#585	1	1	yes	characteristic
1205	C₂	—	2	2	no	—
1206	C₂	—	4	2	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	8	1	no	—
1209	C₂	—	8	1	no	—
1210	C₂	—	8	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	C₇×#3488	1	1	yes	characteristic
1213	C₂	C₂×C₇×#576	1	1	yes	characteristic
1214	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3543	C₂	semidirect
2. C₇×#3520	C₂	semidirect
3. C₇×#3397	C₂	semidirect
4. C₇×#3394	C₂	semidirect
5. C₇×#3373	C₂	semidirect
6. C₇×#3358	C₂	semidirect
7. C₇×#3332	C₂	semidirect
8. C₇×#3314	C₂	semidirect
9. C₇×#3295	C₂	semidirect
10. C₇×#3294	C₂	semidirect
11. C₇×#3284	C₂	semidirect
12. C₇×#3280	C₂	semidirect
13. C₇×#3272	C₂	semidirect
14. C₇×#3264	C₂	semidirect
15. C₇×#3257	C₂	semidirect
16. C₇×#3248	C₂	semidirect
17. C₇×#3224	C₂	semidirect
18. C₇×#3208	C₂	semidirect
19. C₇×#3119	C₂	semidirect
20. C₇×#3105	C₂	semidirect
21. C₇×#3045	C₂	semidirect
22. C₂×C₇×#459	C₂	semidirect
23. C₇×#2994	C₂	semidirect
24. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₇×#135	C₂²	semidirect
26. C₂²×C₇×D₈	C₂²	semidirect
28. C₇×#559	C₂²	semidirect
29. C₇×#556	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
33. C₇×#550	C₂²	semidirect
34. C₇×#550	C₂²	semidirect
35. C₇×D₄×Q₈	C₂²	semidirect
37. C₇×#547	C₂²	semidirect
38. C₇×#547	C₂²	semidirect
41. C₇×#546	C₂²	semidirect
44. C₇×D₄²	C₂²	semidirect
45. C₇×#542	C₂²	semidirect
47. C₇×#540	C₂²	semidirect
50. C₇×#535	C₂²	semidirect
52. C₇×#533	C₂²	semidirect
58. C₇×#520	C₂²	semidirect
59. C₂×C₄×C₇×D₄	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
61. C₇×#495	C₂²	semidirect
62. C₇×#492	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
64. C₇×#489	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#486	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#484	C₂²	semidirect
70. C₇×#481	C₂²	semidirect
71. C₇×#480	C₂²	semidirect
72. C₇×#479	C₂²	semidirect
73. C₇×#478	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#476	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#469	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#467	C₂²	semidirect
82. C₇×#466	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
85. C₇×#464	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#463	C₂²	semidirect
89. C₇×#463	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#462	C₂²	semidirect
93. C₇×#461	C₂²	semidirect
94. C₇×#460	C₂²	semidirect
95. C₇×#460	C₂²	semidirect
96. C₇×#460	C₂²	semidirect
99. C₇×#459	C₂²	semidirect
100. C₇×#459	C₂²	semidirect
101. C₇×#459	C₂²	semidirect
102. C₇×#459	C₂²	semidirect
103. C₇×#459	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#450	C₂²	semidirect
106. C₇×#450	C₂²	semidirect
107. C₇×#450	C₂²	semidirect
108. C₇×#450	C₂²	semidirect
109. C₇×#449	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
111. C₇×#449	C₂²	semidirect
113. C₇×#447	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#442	C₂²	semidirect
117. C₇×#440	C₂²	semidirect
118. C₄×C₇×SD₁₆	C₂²	semidirect
119. C₄×C₇×SD₁₆	C₂²	semidirect
120. C₄×C₇×SD₁₆	C₂²	semidirect
121. C₄×C₇×D₈	C₂²	semidirect
122. C₄×C₇×D₈	C₂²	semidirect
123. C₄×C₇×D₈	C₂²	semidirect
124. C₇×#436	C₂²	semidirect
125. C₇×#435	C₂²	semidirect
126. C₇×C₈×D₄	C₂²	semidirect
127. C₇×C₈×D₄	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₂×C₇×C₄⋊C₈	C₂²	semidirect
132. C₇×#417	C₂²	semidirect
133. C₂×C₇×#102	C₂²	semidirect
134. C₂×C₇×#102	C₂²	semidirect
135. #62053	C₇	direct (N × H)
316. #3543	C₂×C₇	semidirect
317. #3520	C₂×C₇	semidirect
318. #3397	C₂×C₇	semidirect
319. #3394	C₂×C₇	semidirect
320. #3373	C₂×C₇	semidirect
321. #3358	C₂×C₇	semidirect
322. #3332	C₂×C₇	semidirect
323. #3314	C₂×C₇	semidirect
324. #3295	C₂×C₇	semidirect
325. #3294	C₂×C₇	semidirect
326. #3284	C₂×C₇	semidirect
327. #3280	C₂×C₇	semidirect
328. #3272	C₂×C₇	semidirect
329. #3264	C₂×C₇	semidirect
330. #3257	C₂×C₇	semidirect
331. #3248	C₂×C₇	semidirect
332. #3224	C₂×C₇	semidirect
333. #3208	C₂×C₇	semidirect
334. #3119	C₂×C₇	semidirect
335. #3105	C₂×C₇	semidirect
336. #3045	C₂×C₇	semidirect
337. C₂×#459	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
487. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
488. C₂×#135	C₂²×C₇	semidirect
489. C₂²×D₈	C₂²×C₇	semidirect
491. #559	C₂²×C₇	semidirect
492. #556	C₂²×C₇	semidirect
493. #554	C₂²×C₇	semidirect
496. #550	C₂²×C₇	semidirect
497. #550	C₂²×C₇	semidirect
498. D₄×Q₈	C₂²×C₇	semidirect
500. #547	C₂²×C₇	semidirect
501. #547	C₂²×C₇	semidirect
504. #546	C₂²×C₇	semidirect
507. D₄²	C₂²×C₇	semidirect
508. #542	C₂²×C₇	semidirect
510. #540	C₂²×C₇	semidirect
513. #535	C₂²×C₇	semidirect
515. #533	C₂²×C₇	semidirect
521. #520	C₂²×C₇	semidirect
522. C₂×C₄×D₄	C₂²×C₇	semidirect
523. #496	C₂²×C₇	semidirect
524. #495	C₂²×C₇	semidirect
525. #492	C₂²×C₇	semidirect
526. #492	C₂²×C₇	semidirect
527. #489	C₂²×C₇	semidirect
528. #486	C₂²×C₇	semidirect
529. #486	C₂²×C₇	semidirect
530. #486	C₂²×C₇	semidirect
531. #484	C₂²×C₇	semidirect
533. #481	C₂²×C₇	semidirect
534. #480	C₂²×C₇	semidirect
535. #479	C₂²×C₇	semidirect
536. #478	C₂²×C₇	semidirect
537. #478	C₂²×C₇	semidirect
538. #476	C₂²×C₇	semidirect
539. #475	C₂²×C₇	semidirect
540. #474	C₂²×C₇	semidirect
541. #474	C₂²×C₇	semidirect
542. #469	C₂²×C₇	semidirect
543. #468	C₂²×C₇	semidirect
544. #467	C₂²×C₇	semidirect
545. #466	C₂²×C₇	semidirect
547. #465	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
549. #464	C₂²×C₇	semidirect
550. #463	C₂²×C₇	semidirect
551. #463	C₂²×C₇	semidirect
552. #463	C₂²×C₇	semidirect
553. #463	C₂²×C₇	semidirect
554. #463	C₂²×C₇	semidirect
555. #462	C₂²×C₇	semidirect
556. #461	C₂²×C₇	semidirect
557. #460	C₂²×C₇	semidirect
558. #460	C₂²×C₇	semidirect
559. #460	C₂²×C₇	semidirect
562. #459	C₂²×C₇	semidirect
563. #459	C₂²×C₇	semidirect
564. #459	C₂²×C₇	semidirect
565. #459	C₂²×C₇	semidirect
566. #459	C₂²×C₇	semidirect
567. #452	C₂²×C₇	semidirect
568. #450	C₂²×C₇	semidirect
569. #450	C₂²×C₇	semidirect
570. #450	C₂²×C₇	semidirect
571. #450	C₂²×C₇	semidirect
572. #449	C₂²×C₇	semidirect
573. #449	C₂²×C₇	semidirect
574. #449	C₂²×C₇	semidirect
576. #447	C₂²×C₇	semidirect
577. #446	C₂²×C₇	semidirect
578. C₈×Q₈	C₂²×C₇	semidirect
579. #442	C₂²×C₇	semidirect
580. #440	C₂²×C₇	semidirect
581. C₄×SD₁₆	C₂²×C₇	semidirect
582. C₄×SD₁₆	C₂²×C₇	semidirect
583. C₄×SD₁₆	C₂²×C₇	semidirect
584. C₄×D₈	C₂²×C₇	semidirect
585. C₄×D₈	C₂²×C₇	semidirect
586. C₄×D₈	C₂²×C₇	semidirect
587. #436	C₂²×C₇	semidirect
588. #435	C₂²×C₇	semidirect
589. C₈×D₄	C₂²×C₇	semidirect
590. C₈×D₄	C₂²×C₇	semidirect
591. #433	C₂²×C₇	semidirect
592. #431	C₂²×C₇	semidirect
593. #424	C₂²×C₇	semidirect
594. C₂×C₄⋊C₈	C₂²×C₇	semidirect
595. #417	C₂²×C₇	semidirect
596. C₂×#102	C₂²×C₇	semidirect
597. C₂×#102	C₂²×C₇	semidirect
1162. C₇	#62053	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×#3543	2
C₇×#3520	2
C₇×#3397	2
C₇×#3394	2
C₇×#3373	2
C₇×#3358	2
C₇×#3332	2
C₇×#3314	2
C₇×#3295	2
C₇×#3294	2
C₇×#3284	2
C₇×#3280	2
C₇×#3272	2
C₇×#3264	2
C₇×#3257	2
C₇×#3248	2
C₇×#3224	2
C₇×#3208	2
C₇×#3119	2
C₇×#3105	2
C₇×#3045	2
C₂×C₇×#459	2
C₇×#2994	2
#62053	7

Subgroups — C7×#62053 #13239269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62053 #13239269