Subgroups — C₇×#62045 #13239261

Order 1792.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3332	C₂	1	2	yes	maximal, complemented
8	C₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3306	C₂	1	2	yes	maximal, complemented
10	C₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3275	C₂	1	2	yes	maximal, complemented
13	C₇×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3271	C₂	1	2	yes	maximal, complemented
15	C₇×#3263	C₂	1	2	yes	maximal, complemented
16	C₇×#3253	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3224	C₂	1	2	yes	maximal, complemented
18	C₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3125	C₂	1	2	yes	maximal, complemented
20	C₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3045	C₂	1	2	yes	maximal, complemented
22	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	complemented
25	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₇×#135	C₂²	1	2	yes	complemented
27	C₇×#560	—	2	2	no	—
28	C₇×#559	—	2	1	no	—
29	C₇×#559	C₂²	1	1	yes	characteristic, complemented
30	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
31	C₇×#556	C₂²	1	1	yes	characteristic
32	C₇×#554	—	2	1	no	—
33	C₇×#554	C₂²	1	1	yes	characteristic
34	C₇×#553	—	2	1	no	—
35	C₇×#550	C₂²	1	2	yes	—
36	C₇×#550	C₂²	1	1	yes	characteristic
37	C₇×#550	C₂²	1	1	yes	characteristic
38	C₇×#548	C₂²	1	2	yes	complemented
39	C₇×#547	—	2	2	no	—
40	C₇×#547	C₂²	1	1	yes	characteristic
41	C₇×#547	C₂²	1	2	yes	complemented
42	C₇×#546	—	2	1	no	—
43	C₇×#546	C₂²	1	2	yes	—
44	C₇×D₄²	C₂²	1	1	yes	characteristic
45	C₇×#542	—	2	2	no	—
46	C₇×#542	C₂²	1	2	yes	—
47	C₇×#542	C₂²	1	2	yes	complemented
48	C₇×#538	—	2	2	no	—
49	C₇×#537	—	2	1	no	—
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	2	yes	—
52	C₇×#532	—	2	1	no	—
53	C₇×#532	C₂²	1	1	yes	characteristic
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₇×#532	C₂²	1	1	yes	characteristic, complemented
56	C₇×#529	—	2	1	no	—
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₇×#496	C₂²	1	2	yes	complemented
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#493	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	1	yes	characteristic, complemented
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic, complemented
66	C₇×#486	C₂²	1	1	yes	characteristic
67	C₇×#486	C₂²	1	2	yes	complemented
68	C₇×#483	C₂²	1	2	yes	complemented
69	C₇×#481	C₂²	1	2	yes	—
70	C₇×#481	C₂²	1	1	yes	characteristic
71	C₇×#481	C₂²	1	1	yes	characteristic, complemented
72	C₇×#476	C₂²	1	1	yes	characteristic
73	C₇×#476	C₂²	1	2	yes	complemented
74	C₇×#476	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×#475	C₂²	1	2	yes	complemented
78	C₇×#475	C₂²	1	1	yes	characteristic, complemented
79	C₇×#470	C₂²	1	2	yes	complemented
80	C₇×#469	C₂²	1	2	yes	—
81	C₇×#469	C₂²	1	2	yes	—
82	C₇×#469	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	—
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#464	C₂²	1	2	yes	complemented
88	C₇×#464	C₂²	1	2	yes	complemented
89	C₇×#463	C₂²	1	2	yes	—
90	C₇×#463	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#463	C₂²	1	2	yes	complemented
93	C₇×#462	C₂²	1	1	yes	characteristic, complemented
94	C₇×#462	C₂²	1	1	yes	characteristic, complemented
95	C₇×#460	C₂²	1	1	yes	characteristic
96	C₇×#460	C₂²	1	1	yes	characteristic
97	C₇×#460	C₂²	1	1	yes	characteristic
98	C₇×#460	C₂²	1	1	yes	characteristic
99	C₇×#460	C₂²	1	2	yes	complemented
100	C₇×#459	C₂²	1	2	yes	—
101	C₇×#459	C₂²	1	1	yes	characteristic
102	C₇×#459	C₂²	1	1	yes	characteristic, complemented
103	C₇×#459	C₂²	1	2	yes	complemented
104	C₇×#452	C₂²	1	2	yes	complemented
105	C₇×#452	C₂²	1	2	yes	complemented
106	C₇×#450	C₂²	1	2	yes	—
107	C₇×#449	C₂²	1	2	yes	—
108	C₇×#449	C₂²	1	2	yes	complemented
109	C₇×#449	C₂²	1	2	yes	complemented
110	C₇×#449	C₂²	1	2	yes	complemented
111	C₇×#448	C₂²	1	1	yes	characteristic
112	C₇×#448	C₂²	1	1	yes	characteristic, complemented
113	C₇×#447	C₂²	1	2	yes	—
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×#441	C₂²	1	2	yes	complemented
118	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#436	C₂²	1	2	yes	complemented
126	C₇×#435	C₂²	1	2	yes	complemented
127	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
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	C₇×#423	C₂²	1	1	yes	characteristic, complemented
132	C₇×#417	C₂²	1	2	yes	complemented
133	C₇×#417	C₂²	1	2	yes	complemented
134	C₂×C₇×#102	C₂²	1	2	yes	—
135	#62045	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	1	no	—
137	C₂×C₇×#41	—	2	2	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	C₂³	1	2	yes	—
141	C₂×C₇×#41	C₂³	1	2	yes	—
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×D₄	—	2	1	no	—
145	C₂²×C₇×D₄	C₂³	1	2	yes	—
146	C₇×#137	—	4	4	no	—
147	C₇×AGL(1,ℤ/8)	—	4	4	no	—
148	C₇×#135	—	4	4	no	—
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×D₈	C₂³	1	2	yes	—
160	C₂×C₇×D₈	C₂³	1	2	yes	—
161	C₂×C₇×D₈	C₂³	1	2	yes	—
162	C₂×C₇×D₈	C₂³	1	2	yes	—
163	C₂×C₇×M₁₆	C₂³	1	2	yes	—
164	C₂×C₇×M₁₆	C₂³	1	2	yes	—
165	C₂²×C₇×C₈	C₂³	1	2	yes	—
166	C₇×C₄⋊Q₈	—	2	1	no	—
167	C₇×C₄⋊Q₈	—	2	2	no	—
168	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₇×#127	—	2	1	no	—
173	C₇×#127	—	2	2	no	—
174	C₇×#127	C₂³	1	1	yes	characteristic
175	C₇×#127	C₂³	1	2	yes	—
176	C₇×#127	C₂³	1	1	yes	characteristic
177	C₇×#127	C₂³	1	1	yes	characteristic
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	D₄	1	2	yes	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	D₄	1	1	yes	characteristic
184	C₇×#124	—	2	1	no	—
185	C₇×#124	—	2	2	no	—
186	C₇×#124	—	2	2	no	—
187	C₇×#124	—	2	2	no	—
188	C₇×#124	—	2	1	no	—
189	C₇×#124	—	2	1	no	—
190	C₇×#124	D₄	1	1	yes	characteristic
191	C₇×#124	C₂³	1	2	yes	—
192	C₇×#124	C₂³	1	2	yes	—
193	C₇×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₇×#121	—	2	2	no	—
212	C₇×#121	—	2	1	no	—
213	C₇×#121	—	2	1	no	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	2	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	D₄	1	1	yes	characteristic
227	C₇×#121	C₂³	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	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	—	2	1	no	—
238	C₄×C₇×Q₈	—	2	1	no	—
239	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	2	yes	—
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
263	C₄×C₇×D₄	C₂³	1	2	yes	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	2	no	—
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#106	C₂³	1	1	yes	characteristic
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
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	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	1	yes	characteristic
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
316	#3546	C₂×C₇	1	1	yes	characteristic, complemented
317	#3522	C₂×C₇	1	1	yes	characteristic, complemented
318	#3399	C₂×C₇	1	1	yes	characteristic, complemented
319	#3394	C₂×C₇	1	1	yes	characteristic, complemented
320	#3369	C₂×C₇	1	1	yes	characteristic, complemented
321	#3362	C₂×C₇	1	1	yes	characteristic, complemented
322	#3332	C₂×C₇	1	2	yes	complemented
323	#3331	C₂×C₇	1	1	yes	characteristic, complemented
324	#3306	C₂×C₇	1	2	yes	complemented
325	#3295	C₂×C₇	1	1	yes	characteristic, complemented
326	#3284	C₂×C₇	1	1	yes	characteristic, complemented
327	#3275	C₂×C₇	1	2	yes	complemented
328	#3274	C₂×C₇	1	1	yes	characteristic, complemented
329	#3271	C₂×C₇	1	2	yes	complemented
330	#3263	C₂×C₇	1	2	yes	complemented
331	#3253	C₂×C₇	1	1	yes	characteristic, complemented
332	#3224	C₂×C₇	1	2	yes	complemented
333	#3207	C₂×C₇	1	1	yes	characteristic, complemented
334	#3125	C₂×C₇	1	2	yes	complemented
335	#3103	C₂×C₇	1	1	yes	characteristic, complemented
336	#3045	C₂×C₇	1	2	yes	complemented
337	#3037	C₂×C₇	1	1	yes	characteristic, complemented
338	#2993	C₂×C₇	1	1	yes	characteristic, complemented
339	C₂⁴×C₇	—	2	2	no	—
340	C₇×#41	—	2	4	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	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	C₇×#41	—	8	4	no	—
349	C₇×#41	—	8	2	no	—
350	C₂×C₇×Q₈	—	2	1	no	—
351	C₂×C₇×Q₈	—	2	1	no	—
352	C₂×C₇×Q₈	—	2	2	no	—
353	C₂×C₇×Q₈	—	2	1	no	—
354	C₂×C₇×Q₈	—	2	2	no	—
355	C₂×C₇×Q₈	—	4	1	no	—
356	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
358	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₇×D₄	—	2	2	no	—
361	C₂×C₇×D₄	—	2	2	no	—
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	2	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	1	no	—
369	C₂×C₇×D₄	—	2	1	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	1	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	2	no	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	4	2	no	—
378	C₂×C₇×D₄	—	4	2	no	—
379	C₂×C₇×D₄	—	8	2	no	—
380	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
381	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
382	C₂×C₇×D₄	C₂⁴	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	C₂²×C₄×C₇	—	2	1	no	—
387	C₂²×C₄×C₇	—	2	1	no	—
388	C₂²×C₄×C₇	—	2	2	no	—
389	C₂²×C₄×C₇	—	2	2	no	—
390	C₂²×C₄×C₇	—	2	1	no	—
391	C₂²×C₄×C₇	—	2	1	no	—
392	C₂²×C₄×C₇	—	2	2	no	—
393	C₂²×C₄×C₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
401	C₇×Q₁₆	—	2	4	no	—
402	C₇×Q₁₆	—	4	2	no	—
403	C₇×SD₁₆	—	2	2	no	—
404	C₇×SD₁₆	—	2	2	no	—
405	C₇×SD₁₆	—	2	4	no	—
406	C₇×SD₁₆	—	4	1	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×D₈	—	4	2	no	—
412	C₇×D₈	—	4	2	no	—
413	C₇×D₈	—	4	2	no	—
414	C₇×D₈	—	4	2	no	—
415	C₇×M₁₆	—	4	2	no	—
416	C₇×M₁₆	—	4	2	no	—
417	C₂×C₇×C₈	—	4	2	no	—
418	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₇×C₈	C₂⁴	1	2	yes	—
422	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₇×C₈	C₂⁴	1	2	yes	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	1	no	—
429	C₇×C₄⋊C₄	—	2	1	no	—
430	C₇×C₄⋊C₄	—	2	1	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	1	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	2	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	2	no	—
439	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
445	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
447	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
449	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	1	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	2	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	—	2	1	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	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	2	no	—
467	C₇×C₂²⋊C₄	—	2	1	no	—
468	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
472	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
473	C₄²×C₇	—	2	1	no	—
474	C₄²×C₇	—	2	1	no	—
475	C₄²×C₇	—	2	1	no	—
476	C₄²×C₇	—	2	1	no	—
477	C₄²×C₇	—	2	2	no	—
478	C₄²×C₇	—	2	2	no	—
479	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
480	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₇	C₂⁴	1	1	yes	characteristic
482	C₄²×C₇	C₂⁴	1	2	yes	—
483	C₄²×C₇	C₂⁴	1	1	yes	characteristic
484	C₂×#137	C₂²×C₇	1	2	yes	complemented
485	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
486	C₂×#135	C₂²×C₇	1	2	yes	complemented
487	#560	—	2	2	no	—
488	#559	—	2	1	no	—
489	#559	C₂²×C₇	1	1	yes	characteristic, complemented
490	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
491	#556	C₂²×C₇	1	1	yes	characteristic
492	#554	—	2	1	no	—
493	#554	C₂²×C₇	1	1	yes	characteristic
494	#553	—	2	1	no	—
495	#550	C₂²×C₇	1	2	yes	—
496	#550	C₂²×C₇	1	1	yes	characteristic
497	#550	C₂²×C₇	1	1	yes	characteristic
498	#548	C₂²×C₇	1	2	yes	complemented
499	#547	—	2	2	no	—
500	#547	C₂²×C₇	1	1	yes	characteristic
501	#547	C₂²×C₇	1	2	yes	complemented
502	#546	—	2	1	no	—
503	#546	C₂²×C₇	1	2	yes	—
504	D₄²	C₂²×C₇	1	1	yes	characteristic
505	#542	—	2	2	no	—
506	#542	C₂²×C₇	1	2	yes	—
507	#542	C₂²×C₇	1	2	yes	complemented
508	#538	—	2	2	no	—
509	#537	—	2	1	no	—
510	#535	—	2	1	no	—
511	#535	C₂²×C₇	1	2	yes	—
512	#532	—	2	1	no	—
513	#532	C₂²×C₇	1	1	yes	characteristic
514	#532	C₂²×C₇	1	1	yes	characteristic
515	#532	C₂²×C₇	1	1	yes	characteristic, complemented
516	#529	—	2	1	no	—
517	#529	C₂²×C₇	1	1	yes	characteristic
518	#520	C₂²×C₇	1	2	yes	complemented
519	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
520	#496	C₂²×C₇	1	2	yes	complemented
521	#495	C₂²×C₇	1	2	yes	—
522	#493	C₂²×C₇	1	1	yes	characteristic
523	#492	C₂²×C₇	1	1	yes	characteristic, complemented
524	#489	C₂²×C₇	1	2	yes	—
525	#487	C₂²×C₇	1	1	yes	characteristic, complemented
526	#486	C₂²×C₇	1	1	yes	characteristic
527	#486	C₂²×C₇	1	2	yes	complemented
528	#483	C₂²×C₇	1	2	yes	complemented
529	#481	C₂²×C₇	1	2	yes	—
530	#481	C₂²×C₇	1	1	yes	characteristic
531	#481	C₂²×C₇	1	1	yes	characteristic, complemented
532	#476	C₂²×C₇	1	1	yes	characteristic
533	#476	C₂²×C₇	1	1	yes	characteristic, complemented
534	#476	C₂²×C₇	1	2	yes	complemented
535	#476	C₂²×C₇	1	2	yes	complemented
536	#475	C₂²×C₇	1	2	yes	complemented
537	#475	C₂²×C₇	1	1	yes	characteristic, complemented
538	#475	C₂²×C₇	1	1	yes	characteristic, complemented
539	#470	C₂²×C₇	1	2	yes	complemented
540	#469	C₂²×C₇	1	2	yes	—
541	#469	C₂²×C₇	1	2	yes	—
542	#469	C₂²×C₇	1	2	yes	complemented
543	#465	C₂²×C₇	1	2	yes	—
544	#465	C₂²×C₇	1	2	yes	complemented
545	#464	C₂²×C₇	1	2	yes	—
546	#464	C₂²×C₇	1	2	yes	complemented
547	#464	C₂²×C₇	1	2	yes	complemented
548	#464	C₂²×C₇	1	2	yes	complemented
549	#463	C₂²×C₇	1	2	yes	—
550	#463	C₂²×C₇	1	2	yes	complemented
551	#463	C₂²×C₇	1	2	yes	complemented
552	#463	C₂²×C₇	1	2	yes	complemented
553	#462	C₂²×C₇	1	1	yes	characteristic, complemented
554	#462	C₂²×C₇	1	1	yes	characteristic, complemented
555	#460	C₂²×C₇	1	1	yes	characteristic
556	#460	C₂²×C₇	1	1	yes	characteristic
557	#460	C₂²×C₇	1	1	yes	characteristic
558	#460	C₂²×C₇	1	1	yes	characteristic
559	#460	C₂²×C₇	1	2	yes	complemented
560	#459	C₂²×C₇	1	1	yes	characteristic
561	#459	C₂²×C₇	1	2	yes	—
562	#459	C₂²×C₇	1	2	yes	complemented
563	#459	C₂²×C₇	1	1	yes	characteristic, complemented
564	#452	C₂²×C₇	1	2	yes	complemented
565	#452	C₂²×C₇	1	2	yes	complemented
566	#450	C₂²×C₇	1	2	yes	—
567	#449	C₂²×C₇	1	2	yes	—
568	#449	C₂²×C₇	1	2	yes	complemented
569	#449	C₂²×C₇	1	2	yes	complemented
570	#449	C₂²×C₇	1	2	yes	complemented
571	#448	C₂²×C₇	1	1	yes	characteristic
572	#448	C₂²×C₇	1	1	yes	characteristic, complemented
573	#447	C₂²×C₇	1	2	yes	—
574	#446	C₂²×C₇	1	1	yes	characteristic, complemented
575	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
576	#442	C₂²×C₇	1	2	yes	complemented
577	#441	C₂²×C₇	1	2	yes	complemented
578	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
579	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
580	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
581	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
582	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
583	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
584	#436	C₂²×C₇	1	1	yes	characteristic
585	#436	C₂²×C₇	1	2	yes	complemented
586	#435	C₂²×C₇	1	2	yes	complemented
587	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
588	#433	C₂²×C₇	1	2	yes	complemented
589	#431	C₂²×C₇	1	1	yes	characteristic, complemented
590	#424	C₂²×C₇	1	2	yes	complemented
591	#423	C₂²×C₇	1	1	yes	characteristic, complemented
592	#417	C₂²×C₇	1	2	yes	complemented
593	#417	C₂²×C₇	1	2	yes	complemented
594	C₂×#102	C₂²×C₇	1	2	yes	—
595	C₂³×C₇	—	2	2	no	—
596	C₂³×C₇	—	2	1	no	—
597	C₂³×C₇	—	2	2	no	—
598	C₂³×C₇	—	2	1	no	—
599	C₂³×C₇	—	8	2	no	—
600	C₂³×C₇	—	8	2	no	—
601	C₂³×C₇	—	8	2	no	—
602	C₂³×C₇	C₂²×D₄	1	2	yes	—
603	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
604	C₇×Q₈	—	2	2	no	—
605	C₇×Q₈	—	2	1	no	—
606	C₇×Q₈	—	2	1	no	—
607	C₇×Q₈	—	2	2	no	—
608	C₇×Q₈	—	2	1	no	—
609	C₇×Q₈	—	2	2	no	—
610	C₇×Q₈	—	4	2	no	—
611	C₇×Q₈	—	8	1	no	—
612	C₇×Q₈	—	8	2	no	—
613	C₇×Q₈	—	8	1	no	—
614	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
615	C₇×D₄	—	2	2	no	—
616	C₇×D₄	—	2	2	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	2	1	no	—
619	C₇×D₄	—	2	2	no	—
620	C₇×D₄	—	2	2	no	—
621	C₇×D₄	—	2	2	no	—
622	C₇×D₄	—	2	1	no	—
623	C₇×D₄	—	2	1	no	—
624	C₇×D₄	—	4	2	no	—
625	C₇×D₄	—	4	4	no	—
626	C₇×D₄	—	4	4	no	—
627	C₇×D₄	—	4	2	no	—
628	C₇×D₄	—	4	2	no	—
629	C₇×D₄	—	8	1	no	—
630	C₇×D₄	—	8	1	no	—
631	C₇×D₄	—	8	2	no	—
632	C₇×D₄	—	8	2	no	—
633	C₇×D₄	—	8	1	no	—
634	C₇×D₄	—	8	1	no	—
635	C₇×D₄	—	8	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	1	no	—
641	C₇×D₄	—	8	1	no	—
642	C₂×C₄×C₇	—	2	1	no	—
643	C₂×C₄×C₇	—	2	2	no	—
644	C₂×C₄×C₇	—	2	2	no	—
645	C₂×C₄×C₇	—	2	1	no	—
646	C₂×C₄×C₇	—	2	2	no	—
647	C₂×C₄×C₇	—	2	1	no	—
648	C₂×C₄×C₇	—	2	1	no	—
649	C₂×C₄×C₇	—	2	1	no	—
650	C₂×C₄×C₇	—	2	1	no	—
651	C₂×C₄×C₇	—	2	1	no	—
652	C₂×C₄×C₇	—	2	2	no	—
653	C₂×C₄×C₇	—	2	2	no	—
654	C₂×C₄×C₇	—	2	1	no	—
655	C₂×C₄×C₇	—	4	1	no	—
656	C₂×C₄×C₇	—	4	4	no	—
657	C₂×C₄×C₇	—	4	2	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	—	8	2	no	—
662	C₂×C₄×C₇	—	8	2	no	—
663	C₂×C₄×C₇	—	8	2	no	—
664	C₂×C₄×C₇	—	8	2	no	—
665	C₂×C₄×C₇	—	8	2	no	—
666	C₂×C₄×C₇	—	8	2	no	—
667	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
668	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
669	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
670	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
671	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
672	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
673	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
674	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
675	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
676	C₇×C₈	—	2	1	no	—
677	C₇×C₈	—	2	2	no	—
678	C₇×C₈	—	2	1	no	—
679	C₇×C₈	—	2	2	no	—
680	C₇×C₈	—	2	1	no	—
681	C₇×C₈	—	2	1	no	—
682	C₂×#41	—	2	1	no	—
683	C₂×#41	—	2	2	no	—
684	C₂×#41	—	2	1	no	—
685	C₂×#41	—	2	1	no	—
686	C₂×#41	C₂³×C₇	1	2	yes	—
687	C₂×#41	C₂³×C₇	1	2	yes	—
688	C₂×#41	C₂³×C₇	1	2	yes	—
689	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
690	C₂²×D₄	—	2	1	no	—
691	C₂²×D₄	C₂³×C₇	1	2	yes	—
692	#137	—	4	4	no	—
693	AGL(1,ℤ/8)	—	4	4	no	—
694	#135	—	4	4	no	—
695	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
696	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
703	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
704	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
705	C₂×D₈	C₂³×C₇	1	2	yes	—
706	C₂×D₈	C₂³×C₇	1	2	yes	—
707	C₂×D₈	C₂³×C₇	1	2	yes	—
708	C₂×D₈	C₂³×C₇	1	2	yes	—
709	C₂×M₁₆	C₂³×C₇	1	2	yes	—
710	C₂×M₁₆	C₂³×C₇	1	2	yes	—
711	C₂²×C₈	C₂³×C₇	1	2	yes	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
718	#127	—	2	1	no	—
719	#127	—	2	2	no	—
720	#127	C₂³×C₇	1	1	yes	characteristic
721	#127	C₂³×C₇	1	1	yes	characteristic
722	#127	C₂³×C₇	1	1	yes	characteristic
723	#127	C₂³×C₇	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	C₇×D₄	1	2	yes	—
728	#125	—	2	1	no	—
729	#125	C₇×D₄	1	1	yes	characteristic
730	#124	—	2	1	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	C₇×D₄	1	1	yes	characteristic
737	#124	C₂³×C₇	1	2	yes	—
738	#124	C₂³×C₇	1	2	yes	—
739	#124	C₂³×C₇	1	2	yes	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	C₇×D₄	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
757	#121	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	C₇×D₄	1	1	yes	characteristic
773	#121	C₂³×C₇	1	1	yes	characteristic
774	#121	C₂³×C₇	1	1	yes	characteristic
775	#121	C₂³×C₇	1	2	yes	—
776	#121	C₂³×C₇	1	2	yes	—
777	#121	C₂³×C₇	1	2	yes	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₇	1	2	yes	—
791	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
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	1	no	—
803	C₄×D₄	C₂³×C₇	1	2	yes	—
804	C₄×D₄	C₂³×C₇	1	2	yes	—
805	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₇	1	2	yes	—
808	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₇	1	2	yes	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	C₂³×C₇	1	2	yes	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
818	C₂×C₂²⋊C₄	—	2	2	no	—
819	C₂×C₄²	—	2	1	no	—
820	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
821	#106	C₂³×C₇	1	1	yes	characteristic
822	#106	C₂³×C₇	1	1	yes	characteristic
823	#106	C₂³×C₇	1	1	yes	characteristic
824	#106	C₂³×C₇	1	1	yes	characteristic
825	#106	C₂³×C₇	1	2	yes	—
826	#106	C₂³×C₇	1	2	yes	—
827	C₄⋊C₈	C₂³×C₇	1	2	yes	—
828	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₇	1	2	yes	—
832	C₄⋊C₈	C₂³×C₇	1	2	yes	—
833	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
834	#103	C₂³×C₇	1	2	yes	—
835	#103	C₂³×C₇	1	2	yes	—
836	#103	C₂³×C₇	1	2	yes	—
837	#103	C₂³×C₇	1	1	yes	characteristic
838	#103	C₂³×C₇	1	1	yes	characteristic
839	#103	C₂³×C₇	1	1	yes	characteristic
840	#103	C₂³×C₇	1	1	yes	characteristic
841	#103	C₂³×C₇	1	2	yes	—
842	#102	C₂³×C₇	1	1	yes	characteristic
843	#102	C₂³×C₇	1	2	yes	—
844	#102	C₂³×C₇	1	2	yes	—
845	#102	C₂³×C₇	1	2	yes	—
846	#102	C₂³×C₇	1	1	yes	characteristic
847	#102	C₂³×C₇	1	2	yes	—
848	#102	C₂³×C₇	1	2	yes	—
849	#102	C₂³×C₇	1	1	yes	characteristic
850	#102	C₂³×C₇	1	2	yes	—
851	#102	C₂³×C₇	1	1	yes	characteristic
852	#102	C₂³×C₇	1	2	yes	—
853	#102	C₂³×C₇	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
858	#97	C₂³×C₇	1	2	yes	—
859	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₇	1	2	yes	—
862	C₂²×C₇	—	2	1	no	—
863	C₂²×C₇	—	2	2	no	—
864	C₂²×C₇	—	2	1	no	—
865	C₂²×C₇	—	2	2	no	—
866	C₂²×C₇	—	2	1	no	—
867	C₂²×C₇	—	2	2	no	—
868	C₂²×C₇	—	4	2	no	—
869	C₂²×C₇	—	4	1	no	—
870	C₂²×C₇	—	4	2	no	—
871	C₂²×C₇	—	4	1	no	—
872	C₂²×C₇	—	4	2	no	—
873	C₂²×C₇	—	4	1	no	—
874	C₂²×C₇	—	4	2	no	—
875	C₂²×C₇	—	4	1	no	—
876	C₂²×C₇	—	4	1	no	—
877	C₂²×C₇	—	4	1	no	—
878	C₂²×C₇	—	4	2	no	—
879	C₂²×C₇	—	4	2	no	—
880	C₂²×C₇	—	16	4	no	—
881	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
882	C₄×C₇	—	2	1	no	—
883	C₄×C₇	—	2	1	no	—
884	C₄×C₇	—	2	2	no	—
885	C₄×C₇	—	2	2	no	—
886	C₄×C₇	—	2	1	no	—
887	C₄×C₇	—	2	2	no	—
888	C₄×C₇	—	2	1	no	—
889	C₄×C₇	—	2	2	no	—
890	C₄×C₇	—	4	1	no	—
891	C₄×C₇	—	4	1	no	—
892	C₄×C₇	—	4	2	no	—
893	C₄×C₇	—	4	1	no	—
894	C₄×C₇	—	4	2	no	—
895	C₄×C₇	—	4	1	no	—
896	C₄×C₇	—	4	1	no	—
897	C₄×C₇	#577	1	2	yes	—
898	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
899	C₄×C₇	#585	1	1	yes	characteristic
900	C₂⁴	—	2	2	no	—
901	#41	—	2	4	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	2	no	—
908	#41	—	8	2	no	—
909	#41	—	8	4	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	2	2	no	—
916	C₂×Q₈	—	4	1	no	—
917	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
919	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	8	2	no	—
941	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
942	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
943	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₇	1	2	yes	—
945	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₇	1	2	yes	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
959	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
962	Q₁₆	—	2	4	no	—
963	Q₁₆	—	4	2	no	—
964	SD₁₆	—	2	2	no	—
965	SD₁₆	—	2	2	no	—
966	SD₁₆	—	2	4	no	—
967	SD₁₆	—	4	1	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	1	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	D₈	—	4	2	no	—
973	D₈	—	4	2	no	—
974	D₈	—	4	2	no	—
975	D₈	—	4	2	no	—
976	M₁₆	—	4	2	no	—
977	M₁₆	—	4	2	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₇	1	2	yes	—
983	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₇	1	2	yes	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1001	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1003	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1004	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1005	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1030	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1031	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1032	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1033	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1041	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₇	1	2	yes	—
1044	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1045	C₂×C₇	—	4	1	no	—
1046	C₂×C₇	—	4	2	no	—
1047	C₂×C₇	—	8	2	no	—
1048	C₂×C₇	—	8	1	no	—
1049	C₂×C₇	—	8	2	no	—
1050	C₂×C₇	—	8	1	no	—
1051	C₂×C₇	#3488	1	1	yes	characteristic
1052	C₂×C₇	C₂×#577	1	1	yes	characteristic
1053	C₂×C₇	#3585	1	1	yes	characteristic
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	8	2	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	C₂²×C₇×D₄	1	2	yes	—
1062	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	4	2	no	—
1070	Q₈	—	8	1	no	—
1071	Q₈	—	8	1	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	1	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	2	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1127	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1128	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1129	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1130	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1131	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1132	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1133	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1134	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	1	no	—
1140	C₈	—	2	1	no	—
1141	C₇	#62045	1	1	yes	characteristic, direct product factor, Sylow
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	16	4	no	—
1161	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	1	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	2	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	2	no	—
1177	C₄	C₇×#577	1	2	yes	—
1178	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1179	C₄	C₇×#585	1	1	yes	characteristic
1180	C₂	—	4	2	no	—
1181	C₂	—	4	1	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	2	no	—
1184	C₂	—	8	1	no	—
1185	C₂	—	8	2	no	—
1186	C₂	C₇×#3488	1	1	yes	characteristic
1187	C₂	C₂×C₇×#577	1	1	yes	characteristic
1188	C₂	C₇×#3585	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×#3546	C₂	semidirect
2. C₇×#3522	C₂	semidirect
3. C₇×#3399	C₂	semidirect
4. C₇×#3394	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3362	C₂	semidirect
7. C₇×#3332	C₂	semidirect
8. C₇×#3331	C₂	semidirect
9. C₇×#3306	C₂	semidirect
10. C₇×#3295	C₂	semidirect
11. C₇×#3284	C₂	semidirect
12. C₇×#3275	C₂	semidirect
13. C₇×#3274	C₂	semidirect
14. C₇×#3271	C₂	semidirect
15. C₇×#3263	C₂	semidirect
16. C₇×#3253	C₂	semidirect
17. C₇×#3224	C₂	semidirect
18. C₇×#3207	C₂	semidirect
19. C₇×#3125	C₂	semidirect
20. C₇×#3103	C₂	semidirect
21. C₇×#3045	C₂	semidirect
22. C₇×#3037	C₂	semidirect
23. C₇×#2993	C₂	semidirect
24. C₂×C₇×#137	C₂²	semidirect
26. C₂×C₇×#135	C₂²	semidirect
29. C₇×#559	C₂²	semidirect
30. C₇×Q₈²	C₂²	semidirect
38. C₇×#548	C₂²	semidirect
41. C₇×#547	C₂²	semidirect
47. C₇×#542	C₂²	semidirect
55. C₇×#532	C₂²	semidirect
58. C₇×#520	C₂²	semidirect
59. C₂×C₄×C₇×Q₈	C₂²	semidirect
60. C₇×#496	C₂²	semidirect
63. C₇×#492	C₂²	semidirect
65. C₇×#487	C₂²	semidirect
67. C₇×#486	C₂²	semidirect
68. C₇×#483	C₂²	semidirect
71. C₇×#481	C₂²	semidirect
73. C₇×#476	C₂²	semidirect
74. C₇×#476	C₂²	semidirect
75. C₇×#476	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
77. C₇×#475	C₂²	semidirect
78. C₇×#475	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
82. C₇×#469	C₂²	semidirect
84. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#464	C₂²	semidirect
88. C₇×#464	C₂²	semidirect
90. C₇×#463	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#463	C₂²	semidirect
93. C₇×#462	C₂²	semidirect
94. C₇×#462	C₂²	semidirect
99. C₇×#460	C₂²	semidirect
102. C₇×#459	C₂²	semidirect
103. C₇×#459	C₂²	semidirect
104. C₇×#452	C₂²	semidirect
105. C₇×#452	C₂²	semidirect
108. C₇×#449	C₂²	semidirect
109. C₇×#449	C₂²	semidirect
110. C₇×#449	C₂²	semidirect
112. C₇×#448	C₂²	semidirect
114. C₇×#446	C₂²	semidirect
115. C₇×C₈×Q₈	C₂²	semidirect
116. C₇×#442	C₂²	semidirect
117. C₇×#441	C₂²	semidirect
120. C₄×C₇×SD₁₆	C₂²	semidirect
121. C₄×C₇×SD₁₆	C₂²	semidirect
122. C₄×C₇×SD₁₆	C₂²	semidirect
123. C₄×C₇×SD₁₆	C₂²	semidirect
125. C₇×#436	C₂²	semidirect
126. C₇×#435	C₂²	semidirect
128. C₇×#433	C₂²	semidirect
129. C₇×#431	C₂²	semidirect
130. C₇×#424	C₂²	semidirect
131. C₇×#423	C₂²	semidirect
132. C₇×#417	C₂²	semidirect
133. C₇×#417	C₂²	semidirect
135. #62045	C₇	direct (N × H)
316. #3546	C₂×C₇	semidirect
317. #3522	C₂×C₇	semidirect
318. #3399	C₂×C₇	semidirect
319. #3394	C₂×C₇	semidirect
320. #3369	C₂×C₇	semidirect
321. #3362	C₂×C₇	semidirect
322. #3332	C₂×C₇	semidirect
323. #3331	C₂×C₇	semidirect
324. #3306	C₂×C₇	semidirect
325. #3295	C₂×C₇	semidirect
326. #3284	C₂×C₇	semidirect
327. #3275	C₂×C₇	semidirect
328. #3274	C₂×C₇	semidirect
329. #3271	C₂×C₇	semidirect
330. #3263	C₂×C₇	semidirect
331. #3253	C₂×C₇	semidirect
332. #3224	C₂×C₇	semidirect
333. #3207	C₂×C₇	semidirect
334. #3125	C₂×C₇	semidirect
335. #3103	C₂×C₇	semidirect
336. #3045	C₂×C₇	semidirect
337. #3037	C₂×C₇	semidirect
338. #2993	C₂×C₇	semidirect
484. C₂×#137	C₂²×C₇	semidirect
486. C₂×#135	C₂²×C₇	semidirect
489. #559	C₂²×C₇	semidirect
490. Q₈²	C₂²×C₇	semidirect
498. #548	C₂²×C₇	semidirect
501. #547	C₂²×C₇	semidirect
507. #542	C₂²×C₇	semidirect
515. #532	C₂²×C₇	semidirect
518. #520	C₂²×C₇	semidirect
519. C₂×C₄×Q₈	C₂²×C₇	semidirect
520. #496	C₂²×C₇	semidirect
523. #492	C₂²×C₇	semidirect
525. #487	C₂²×C₇	semidirect
527. #486	C₂²×C₇	semidirect
528. #483	C₂²×C₇	semidirect
531. #481	C₂²×C₇	semidirect
533. #476	C₂²×C₇	semidirect
534. #476	C₂²×C₇	semidirect
535. #476	C₂²×C₇	semidirect
536. #475	C₂²×C₇	semidirect
537. #475	C₂²×C₇	semidirect
538. #475	C₂²×C₇	semidirect
539. #470	C₂²×C₇	semidirect
542. #469	C₂²×C₇	semidirect
544. #465	C₂²×C₇	semidirect
546. #464	C₂²×C₇	semidirect
547. #464	C₂²×C₇	semidirect
548. #464	C₂²×C₇	semidirect
550. #463	C₂²×C₇	semidirect
551. #463	C₂²×C₇	semidirect
552. #463	C₂²×C₇	semidirect
553. #462	C₂²×C₇	semidirect
554. #462	C₂²×C₇	semidirect
559. #460	C₂²×C₇	semidirect
562. #459	C₂²×C₇	semidirect
563. #459	C₂²×C₇	semidirect
564. #452	C₂²×C₇	semidirect
565. #452	C₂²×C₇	semidirect
568. #449	C₂²×C₇	semidirect
569. #449	C₂²×C₇	semidirect
570. #449	C₂²×C₇	semidirect
572. #448	C₂²×C₇	semidirect
574. #446	C₂²×C₇	semidirect
575. C₈×Q₈	C₂²×C₇	semidirect
576. #442	C₂²×C₇	semidirect
577. #441	C₂²×C₇	semidirect
580. C₄×SD₁₆	C₂²×C₇	semidirect
581. C₄×SD₁₆	C₂²×C₇	semidirect
582. C₄×SD₁₆	C₂²×C₇	semidirect
583. C₄×SD₁₆	C₂²×C₇	semidirect
585. #436	C₂²×C₇	semidirect
586. #435	C₂²×C₇	semidirect
588. #433	C₂²×C₇	semidirect
589. #431	C₂²×C₇	semidirect
590. #424	C₂²×C₇	semidirect
591. #423	C₂²×C₇	semidirect
592. #417	C₂²×C₇	semidirect
593. #417	C₂²×C₇	semidirect
1141. C₇	#62045	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×#3546	2
C₇×#3522	2
C₇×#3399	2
C₇×#3394	2
C₇×#3369	2
C₇×#3362	2
C₇×#3332	2
C₇×#3331	2
C₇×#3306	2
C₇×#3295	2
C₇×#3284	2
C₇×#3275	2
C₇×#3274	2
C₇×#3271	2
C₇×#3263	2
C₇×#3253	2
C₇×#3224	2
C₇×#3207	2
C₇×#3125	2
C₇×#3103	2
C₇×#3045	2
C₇×#3037	2
C₇×#2993	2
#62045	7

Subgroups — C7×#62045 #13239261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62045 #13239261