Subgroups — C₇×#62021 #13239237

Order 1792.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3401	C₂	1	2	yes	maximal, complemented
4	C₇×#3369	C₂	1	2	yes	maximal, complemented
5	C₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₇×#3306	C₂	1	2	yes	maximal, complemented
7	C₇×#3298	C₂	1	2	yes	maximal, complemented
8	C₇×#3282	C₂	1	2	yes	maximal, complemented
9	C₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₇×#3270	C₂	1	2	yes	maximal, complemented
11	C₇×#3263	C₂	1	2	yes	maximal, complemented
12	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3225	C₂	1	2	yes	maximal, complemented
14	C₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3125	C₂	1	2	yes	maximal, complemented
16	C₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3046	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×#137	C₂²	1	2	yes	complemented
21	C₂×C₇×#135	C₂²	1	2	yes	—
22	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
24	C₇×#563	—	2	1	no	—
25	C₇×#562	—	2	1	no	—
26	C₇×#559	—	2	1	no	—
27	C₇×#559	C₂²	1	1	yes	characteristic, complemented
28	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
29	C₇×#556	C₂²	1	2	yes	—
30	C₇×#554	—	2	1	no	—
31	C₇×#554	C₂²	1	1	yes	characteristic, complemented
32	C₇×#551	—	2	2	no	—
33	C₇×#550	C₂²	1	1	yes	characteristic, complemented
34	C₇×D₄×Q₈	C₂²	1	2	yes	—
35	C₇×#548	C₂²	1	2	yes	—
36	C₇×#548	C₂²	1	2	yes	—
37	C₇×#547	—	2	2	no	—
38	C₇×#547	C₂²	1	2	yes	—
39	C₇×#546	C₂²	1	2	yes	—
40	C₇×#543	—	2	1	no	—
41	C₇×#542	—	2	2	no	—
42	C₇×#542	—	2	2	no	—
43	C₇×#542	C₂²	1	2	yes	—
44	C₇×#542	C₂²	1	2	yes	complemented
45	C₇×#538	—	2	1	no	—
46	C₇×#536	C₂²	1	2	yes	—
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₇×#532	—	2	1	no	—
49	C₇×#532	C₂²	1	1	yes	characteristic
50	C₇×#529	—	2	1	no	—
51	C₇×#529	C₂²	1	1	yes	characteristic
52	C₂×C₇×#124	C₂²	1	1	yes	characteristic
53	C₇×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
55	C₇×#497	C₂²	1	2	yes	complemented
56	C₇×#496	C₂²	1	2	yes	—
57	C₇×#495	C₂²	1	2	yes	—
58	C₇×#489	C₂²	1	2	yes	—
59	C₇×#489	C₂²	1	2	yes	—
60	C₇×#487	C₂²	1	2	yes	complemented
61	C₇×#483	C₂²	1	2	yes	—
62	C₇×#483	C₂²	1	2	yes	complemented
63	C₇×#481	C₂²	1	2	yes	—
64	C₇×#476	C₂²	1	2	yes	—
65	C₇×#476	C₂²	1	2	yes	complemented
66	C₇×#475	C₂²	1	2	yes	complemented
67	C₇×#475	C₂²	1	1	yes	characteristic, complemented
68	C₇×#475	C₂²	1	2	yes	complemented
69	C₇×#475	C₂²	1	1	yes	characteristic, complemented
70	C₇×#470	C₂²	1	2	yes	complemented
71	C₇×#469	C₂²	1	2	yes	—
72	C₇×#465	C₂²	1	2	yes	—
73	C₇×#465	C₂²	1	2	yes	—
74	C₇×#465	C₂²	1	2	yes	—
75	C₇×#465	C₂²	1	2	yes	complemented
76	C₇×#464	C₂²	1	2	yes	—
77	C₇×#464	C₂²	1	2	yes	—
78	C₇×#464	C₂²	1	2	yes	—
79	C₇×#464	C₂²	1	2	yes	—
80	C₇×#464	C₂²	1	2	yes	—
81	C₇×#464	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	—
83	C₇×#463	C₂²	1	2	yes	—
84	C₇×#463	C₂²	1	2	yes	—
85	C₇×#463	C₂²	1	2	yes	—
86	C₇×#462	C₂²	1	1	yes	characteristic, complemented
87	C₇×#462	C₂²	1	2	yes	complemented
88	C₇×#462	C₂²	1	1	yes	characteristic, complemented
89	C₇×#461	C₂²	1	2	yes	complemented
90	C₇×#461	C₂²	1	2	yes	complemented
91	C₇×#460	C₂²	1	2	yes	complemented
92	C₇×#452	C₂²	1	2	yes	—
93	C₇×#452	C₂²	1	2	yes	complemented
94	C₇×#451	C₂²	1	2	yes	—
95	C₇×#451	C₂²	1	2	yes	complemented
96	C₇×#449	C₂²	1	2	yes	—
97	C₇×#449	C₂²	1	2	yes	—
98	C₇×#448	C₂²	1	2	yes	—
99	C₇×#448	C₂²	1	2	yes	complemented
100	C₇×#447	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#442	C₂²	1	2	yes	—
103	C₇×#441	C₂²	1	2	yes	complemented
104	C₇×#441	C₂²	1	2	yes	complemented
105	C₇×#441	C₂²	1	2	yes	complemented
106	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
107	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	—
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×C₈×D₄	C₂²	1	2	yes	—
111	C₇×#433	C₂²	1	2	yes	complemented
112	C₇×#432	C₂²	1	1	yes	characteristic
113	C₇×#424	C₂²	1	2	yes	complemented
114	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₇×#417	C₂²	1	2	yes	—
116	C₂×C₇×#103	C₂²	1	1	yes	characteristic
117	C₂×C₇×#103	C₂²	1	2	yes	complemented
118	C₂×C₇×#102	C₂²	1	1	yes	characteristic
119	#62021	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	—	2	2	no	—
121	C₂×C₇×#41	—	2	1	no	—
122	C₂×C₇×#41	C₂³	1	2	yes	—
123	C₂×C₇×#41	C₂³	1	2	yes	—
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×Q₈	C₂³	1	2	yes	—
127	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₇×#137	—	4	4	no	—
129	C₇×#135	—	4	4	no	—
130	C₂×C₇×Q₁₆	—	4	2	no	—
131	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
135	C₂×C₇×SD₁₆	—	4	2	no	—
136	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
137	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
142	C₂×C₇×D₈	C₂³	1	2	yes	—
143	C₂×C₇×D₈	C₂³	1	2	yes	—
144	C₂×C₇×M₁₆	C₂³	1	2	yes	—
145	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
146	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	2	yes	—
148	C₇×C₄⋊Q₈	—	2	1	no	—
149	C₇×C₄⋊Q₈	—	2	2	no	—
150	C₇×C₄⋊Q₈	—	2	2	no	—
151	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₇×#127	—	2	1	no	—
157	C₇×#127	C₂³	1	1	yes	characteristic
158	C₇×#126	—	2	2	no	—
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	—	2	2	no	—
162	C₇×#126	D₄	1	2	yes	—
163	C₇×#125	—	2	1	no	—
164	C₇×#125	—	2	1	no	—
165	C₇×#125	D₄	1	1	yes	characteristic
166	C₇×#124	—	2	1	no	—
167	C₇×#124	—	2	2	no	—
168	C₇×#124	—	2	2	no	—
169	C₇×#124	—	2	2	no	—
170	C₇×#124	—	2	2	no	—
171	C₇×#124	—	2	1	no	—
172	C₇×#124	—	2	1	no	—
173	C₇×#124	—	2	1	no	—
174	C₇×#124	D₄	1	1	yes	characteristic
175	C₇×#124	C₂³	1	2	yes	—
176	C₇×#124	C₂³	1	2	yes	—
177	C₇×#124	C₂³	1	2	yes	—
178	C₇×#124	C₂³	1	2	yes	—
179	C₇×#123	—	2	2	no	—
180	C₇×#123	—	2	2	no	—
181	C₇×#123	—	2	2	no	—
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×#123	—	2	2	no	—
187	C₇×#123	D₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	—	2	1	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	—	2	1	no	—
207	C₇×#121	—	2	2	no	—
208	C₇×#121	—	2	2	no	—
209	C₇×#121	D₄	1	1	yes	characteristic
210	C₇×#121	C₂³	1	2	yes	—
211	C₇×#121	C₂³	1	2	yes	—
212	C₇×#121	C₂³	1	2	yes	—
213	C₇×#120	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	1	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	2	no	—
232	C₄×C₇×D₄	—	2	2	no	—
233	C₄×C₇×D₄	—	2	2	no	—
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	C₂³	1	2	yes	—
236	C₄×C₇×D₄	C₂³	1	2	yes	—
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	2	yes	—
239	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
240	C₇×#117	—	2	1	no	—
241	C₇×#117	—	2	2	no	—
242	C₇×#117	—	2	2	no	—
243	C₇×#117	C₂³	1	2	yes	—
244	C₂×C₇×C₄⋊C₄	—	2	1	no	—
245	C₂×C₇×C₄⋊C₄	—	2	2	no	—
246	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²×C₇	—	2	1	no	—
252	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
253	C₇×#106	C₂³	1	2	yes	—
254	C₇×#106	C₂³	1	2	yes	—
255	C₇×#106	C₂³	1	2	yes	—
256	C₇×#106	C₂³	1	2	yes	—
257	C₇×C₄⋊C₈	C₂³	1	2	yes	—
258	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₈	C₂³	1	2	yes	—
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	2	yes	—
262	C₇×C₄⋊C₈	C₂³	1	2	yes	—
263	C₇×#103	C₂³	1	2	yes	—
264	C₇×#103	C₂³	1	2	yes	—
265	C₇×#103	C₂³	1	2	yes	—
266	C₇×#103	C₂³	1	2	yes	—
267	C₇×#103	C₂³	1	2	yes	—
268	C₇×#103	C₂³	1	2	yes	—
269	C₇×#103	C₂³	1	2	yes	—
270	C₇×#103	C₂³	1	2	yes	—
271	C₇×#103	C₂³	1	2	yes	—
272	C₇×#103	C₂³	1	2	yes	—
273	C₇×#102	C₂³	1	2	yes	—
274	C₇×#102	C₂³	1	2	yes	—
275	C₇×#102	C₂³	1	2	yes	—
276	C₇×#102	C₂³	1	2	yes	—
277	C₇×#102	C₂³	1	2	yes	—
278	C₇×#102	C₂³	1	2	yes	—
279	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₇×#97	C₂³	1	2	yes	—
283	C₇×#97	C₂³	1	2	yes	—
284	C₄×C₇×C₈	C₂³	1	2	yes	—
285	#3561	C₂×C₇	1	1	yes	characteristic, complemented
286	#3522	C₂×C₇	1	1	yes	characteristic, complemented
287	#3401	C₂×C₇	1	2	yes	complemented
288	#3369	C₂×C₇	1	2	yes	complemented
289	#3316	C₂×C₇	1	2	yes	complemented
290	#3306	C₂×C₇	1	2	yes	complemented
291	#3298	C₂×C₇	1	2	yes	complemented
292	#3282	C₂×C₇	1	2	yes	complemented
293	#3271	C₂×C₇	1	2	yes	complemented
294	#3270	C₂×C₇	1	2	yes	complemented
295	#3263	C₂×C₇	1	2	yes	complemented
296	#3246	C₂×C₇	1	1	yes	characteristic, complemented
297	#3225	C₂×C₇	1	2	yes	complemented
298	#3213	C₂×C₇	1	1	yes	characteristic, complemented
299	#3125	C₂×C₇	1	2	yes	complemented
300	#3113	C₂×C₇	1	1	yes	characteristic, complemented
301	#3046	C₂×C₇	1	2	yes	complemented
302	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
303	#2992	C₂×C₇	1	1	yes	characteristic, complemented
304	C₂⁴×C₇	—	2	1	no	—
305	C₇×#41	—	2	4	no	—
306	C₇×#41	—	4	2	no	—
307	C₇×#41	—	4	2	no	—
308	C₇×#41	—	4	2	no	—
309	C₇×#41	—	8	2	no	—
310	C₇×#41	—	8	4	no	—
311	C₂×C₇×Q₈	—	2	1	no	—
312	C₂×C₇×Q₈	—	2	1	no	—
313	C₂×C₇×Q₈	—	2	2	no	—
314	C₂×C₇×Q₈	—	2	1	no	—
315	C₂×C₇×Q₈	—	2	2	no	—
316	C₂×C₇×Q₈	—	2	1	no	—
317	C₂×C₇×Q₈	—	2	2	no	—
318	C₂×C₇×Q₈	—	4	1	no	—
319	C₂×C₇×Q₈	—	4	1	no	—
320	C₂×C₇×Q₈	—	4	2	no	—
321	C₂×C₇×Q₈	—	4	1	no	—
322	C₂×C₇×Q₈	—	4	2	no	—
323	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
325	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
326	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×C₇×D₄	—	2	2	no	—
329	C₂×C₇×D₄	—	2	2	no	—
330	C₂×C₇×D₄	—	2	2	no	—
331	C₂×C₇×D₄	—	2	2	no	—
332	C₂×C₇×D₄	—	2	2	no	—
333	C₂×C₇×D₄	—	2	1	no	—
334	C₂×C₇×D₄	—	2	1	no	—
335	C₂×C₇×D₄	—	2	1	no	—
336	C₂×C₇×D₄	—	4	1	no	—
337	C₂×C₇×D₄	—	4	1	no	—
338	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
339	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
340	C₂×C₇×D₄	C₂⁴	1	2	yes	—
341	C₂×C₇×D₄	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₇	—	2	1	no	—
343	C₂²×C₄×C₇	—	2	1	no	—
344	C₂²×C₄×C₇	—	2	1	no	—
345	C₂²×C₄×C₇	—	2	2	no	—
346	C₂²×C₄×C₇	—	2	2	no	—
347	C₂²×C₄×C₇	—	2	2	no	—
348	C₂²×C₄×C₇	—	2	2	no	—
349	C₂²×C₄×C₇	—	2	2	no	—
350	C₂²×C₄×C₇	—	2	2	no	—
351	C₂²×C₄×C₇	—	2	2	no	—
352	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
356	C₇×Q₁₆	—	2	4	no	—
357	C₇×Q₁₆	—	2	4	no	—
358	C₇×Q₁₆	—	4	2	no	—
359	C₇×Q₁₆	—	4	2	no	—
360	C₇×SD₁₆	—	2	4	no	—
361	C₇×SD₁₆	—	4	2	no	—
362	C₇×SD₁₆	—	4	2	no	—
363	C₇×SD₁₆	—	4	2	no	—
364	C₇×SD₁₆	—	4	2	no	—
365	C₇×SD₁₆	—	4	2	no	—
366	C₇×D₈	—	4	2	no	—
367	C₇×D₈	—	4	2	no	—
368	C₇×M₁₆	—	4	2	no	—
369	C₂×C₇×C₈	—	4	1	no	—
370	C₂×C₇×C₈	—	4	1	no	—
371	C₂×C₇×C₈	—	4	2	no	—
372	C₂×C₇×C₈	C₂⁴	1	2	yes	—
373	C₂×C₇×C₈	C₂⁴	1	2	yes	—
374	C₂×C₇×C₈	C₂⁴	1	2	yes	—
375	C₂×C₇×C₈	C₂⁴	1	2	yes	—
376	C₇×C₄⋊C₄	—	2	1	no	—
377	C₇×C₄⋊C₄	—	2	2	no	—
378	C₇×C₄⋊C₄	—	2	2	no	—
379	C₇×C₄⋊C₄	—	2	1	no	—
380	C₇×C₄⋊C₄	—	2	1	no	—
381	C₇×C₄⋊C₄	—	2	1	no	—
382	C₇×C₄⋊C₄	—	2	1	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	1	no	—
385	C₇×C₄⋊C₄	—	2	1	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	1	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₇×C₂²⋊C₄	—	2	2	no	—
406	C₇×C₂²⋊C₄	—	2	2	no	—
407	C₇×C₂²⋊C₄	—	2	2	no	—
408	C₇×C₂²⋊C₄	—	2	2	no	—
409	C₇×C₂²⋊C₄	—	2	2	no	—
410	C₇×C₂²⋊C₄	—	2	2	no	—
411	C₇×C₂²⋊C₄	—	2	2	no	—
412	C₇×C₂²⋊C₄	—	2	2	no	—
413	C₇×C₂²⋊C₄	—	2	2	no	—
414	C₇×C₂²⋊C₄	—	2	2	no	—
415	C₇×C₂²⋊C₄	—	2	2	no	—
416	C₇×C₂²⋊C₄	—	2	2	no	—
417	C₇×C₂²⋊C₄	—	2	2	no	—
418	C₇×C₂²⋊C₄	—	2	2	no	—
419	C₇×C₂²⋊C₄	—	2	2	no	—
420	C₇×C₂²⋊C₄	—	2	2	no	—
421	C₇×C₂²⋊C₄	—	2	2	no	—
422	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₄²×C₇	—	2	1	no	—
428	C₄²×C₇	—	2	1	no	—
429	C₄²×C₇	—	2	1	no	—
430	C₄²×C₇	—	2	1	no	—
431	C₄²×C₇	—	2	2	no	—
432	C₄²×C₇	—	2	2	no	—
433	C₄²×C₇	—	2	2	no	—
434	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₇	C₂⁴	1	2	yes	—
437	C₄²×C₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₇	C₂⁴	1	1	yes	characteristic
439	C₂×#137	C₂²×C₇	1	2	yes	complemented
440	C₂×#135	C₂²×C₇	1	2	yes	—
441	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
443	#563	—	2	1	no	—
444	#562	—	2	1	no	—
445	#559	—	2	1	no	—
446	#559	C₂²×C₇	1	1	yes	characteristic, complemented
447	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
448	#556	C₂²×C₇	1	2	yes	—
449	#554	—	2	1	no	—
450	#554	C₂²×C₇	1	1	yes	characteristic, complemented
451	#551	—	2	2	no	—
452	#550	C₂²×C₇	1	1	yes	characteristic, complemented
453	D₄×Q₈	C₂²×C₇	1	2	yes	—
454	#548	C₂²×C₇	1	2	yes	—
455	#548	C₂²×C₇	1	2	yes	—
456	#547	—	2	2	no	—
457	#547	C₂²×C₇	1	2	yes	—
458	#546	C₂²×C₇	1	2	yes	—
459	#543	—	2	1	no	—
460	#542	—	2	2	no	—
461	#542	—	2	2	no	—
462	#542	C₂²×C₇	1	2	yes	—
463	#542	C₂²×C₇	1	2	yes	complemented
464	#538	—	2	1	no	—
465	#536	C₂²×C₇	1	2	yes	—
466	#533	C₂²×C₇	1	1	yes	characteristic
467	#532	—	2	1	no	—
468	#532	C₂²×C₇	1	1	yes	characteristic
469	#529	—	2	1	no	—
470	#529	C₂²×C₇	1	1	yes	characteristic
471	C₂×#124	C₂²×C₇	1	1	yes	characteristic
472	#520	C₂²×C₇	1	2	yes	complemented
473	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
474	#497	C₂²×C₇	1	2	yes	complemented
475	#496	C₂²×C₇	1	2	yes	—
476	#495	C₂²×C₇	1	2	yes	—
477	#489	C₂²×C₇	1	2	yes	—
478	#489	C₂²×C₇	1	2	yes	—
479	#487	C₂²×C₇	1	2	yes	complemented
480	#483	C₂²×C₇	1	2	yes	—
481	#483	C₂²×C₇	1	2	yes	complemented
482	#481	C₂²×C₇	1	2	yes	—
483	#476	C₂²×C₇	1	2	yes	—
484	#476	C₂²×C₇	1	2	yes	complemented
485	#475	C₂²×C₇	1	1	yes	characteristic, complemented
486	#475	C₂²×C₇	1	1	yes	characteristic, complemented
487	#475	C₂²×C₇	1	2	yes	complemented
488	#475	C₂²×C₇	1	2	yes	complemented
489	#470	C₂²×C₇	1	2	yes	complemented
490	#469	C₂²×C₇	1	2	yes	—
491	#465	C₂²×C₇	1	2	yes	—
492	#465	C₂²×C₇	1	2	yes	—
493	#465	C₂²×C₇	1	2	yes	—
494	#465	C₂²×C₇	1	2	yes	complemented
495	#464	C₂²×C₇	1	2	yes	—
496	#464	C₂²×C₇	1	2	yes	—
497	#464	C₂²×C₇	1	2	yes	—
498	#464	C₂²×C₇	1	2	yes	—
499	#464	C₂²×C₇	1	2	yes	—
500	#464	C₂²×C₇	1	2	yes	complemented
501	#463	C₂²×C₇	1	2	yes	—
502	#463	C₂²×C₇	1	2	yes	—
503	#463	C₂²×C₇	1	2	yes	—
504	#463	C₂²×C₇	1	2	yes	—
505	#462	C₂²×C₇	1	1	yes	characteristic, complemented
506	#462	C₂²×C₇	1	1	yes	characteristic, complemented
507	#462	C₂²×C₇	1	2	yes	complemented
508	#461	C₂²×C₇	1	2	yes	complemented
509	#461	C₂²×C₇	1	2	yes	complemented
510	#460	C₂²×C₇	1	2	yes	complemented
511	#452	C₂²×C₇	1	2	yes	—
512	#452	C₂²×C₇	1	2	yes	complemented
513	#451	C₂²×C₇	1	2	yes	—
514	#451	C₂²×C₇	1	2	yes	complemented
515	#449	C₂²×C₇	1	2	yes	—
516	#449	C₂²×C₇	1	2	yes	—
517	#448	C₂²×C₇	1	2	yes	—
518	#448	C₂²×C₇	1	2	yes	complemented
519	#447	C₂²×C₇	1	2	yes	—
520	#446	C₂²×C₇	1	2	yes	complemented
521	#442	C₂²×C₇	1	2	yes	—
522	#441	C₂²×C₇	1	2	yes	complemented
523	#441	C₂²×C₇	1	2	yes	complemented
524	#441	C₂²×C₇	1	2	yes	complemented
525	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
526	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
527	#435	C₂²×C₇	1	2	yes	—
528	#435	C₂²×C₇	1	2	yes	complemented
529	C₈×D₄	C₂²×C₇	1	2	yes	—
530	#433	C₂²×C₇	1	2	yes	complemented
531	#432	C₂²×C₇	1	1	yes	characteristic
532	#424	C₂²×C₇	1	2	yes	complemented
533	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
534	#417	C₂²×C₇	1	2	yes	—
535	C₂×#103	C₂²×C₇	1	1	yes	characteristic
536	C₂×#103	C₂²×C₇	1	2	yes	complemented
537	C₂×#102	C₂²×C₇	1	1	yes	characteristic
538	C₂³×C₇	—	2	2	no	—
539	C₂³×C₇	—	2	2	no	—
540	C₂³×C₇	—	4	2	no	—
541	C₂³×C₇	—	8	1	no	—
542	C₂³×C₇	—	8	1	no	—
543	C₂³×C₇	C₂²×D₄	1	2	yes	—
544	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
545	C₇×Q₈	—	2	1	no	—
546	C₇×Q₈	—	2	2	no	—
547	C₇×Q₈	—	2	1	no	—
548	C₇×Q₈	—	2	2	no	—
549	C₇×Q₈	—	2	2	no	—
550	C₇×Q₈	—	2	1	no	—
551	C₇×Q₈	—	2	2	no	—
552	C₇×Q₈	—	4	1	no	—
553	C₇×Q₈	—	4	2	no	—
554	C₇×Q₈	—	8	1	no	—
555	C₇×Q₈	—	8	2	no	—
556	C₇×Q₈	—	8	1	no	—
557	C₇×Q₈	—	8	1	no	—
558	C₇×Q₈	—	8	2	no	—
559	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
560	C₇×D₄	—	2	4	no	—
561	C₇×D₄	—	2	2	no	—
562	C₇×D₄	—	2	2	no	—
563	C₇×D₄	—	2	2	no	—
564	C₇×D₄	—	2	2	no	—
565	C₇×D₄	—	4	1	no	—
566	C₇×D₄	—	4	4	no	—
567	C₇×D₄	—	4	2	no	—
568	C₇×D₄	—	4	4	no	—
569	C₇×D₄	—	8	1	no	—
570	C₇×D₄	—	8	1	no	—
571	C₇×D₄	—	8	2	no	—
572	C₇×D₄	—	8	2	no	—
573	C₇×D₄	—	8	2	no	—
574	C₂×C₄×C₇	—	2	2	no	—
575	C₂×C₄×C₇	—	2	1	no	—
576	C₂×C₄×C₇	—	2	1	no	—
577	C₂×C₄×C₇	—	2	2	no	—
578	C₂×C₄×C₇	—	2	1	no	—
579	C₂×C₄×C₇	—	2	2	no	—
580	C₂×C₄×C₇	—	2	1	no	—
581	C₂×C₄×C₇	—	2	2	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	2	no	—
585	C₂×C₄×C₇	—	2	2	no	—
586	C₂×C₄×C₇	—	2	2	no	—
587	C₂×C₄×C₇	—	4	1	no	—
588	C₂×C₄×C₇	—	4	4	no	—
589	C₂×C₄×C₇	—	4	2	no	—
590	C₂×C₄×C₇	—	4	2	no	—
591	C₂×C₄×C₇	—	8	2	no	—
592	C₂×C₄×C₇	—	8	2	no	—
593	C₂×C₄×C₇	—	8	2	no	—
594	C₂×C₄×C₇	—	8	2	no	—
595	C₂×C₄×C₇	—	8	2	no	—
596	C₂×C₄×C₇	—	8	1	no	—
597	C₂×C₄×C₇	—	8	2	no	—
598	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
603	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
606	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
607	C₇×C₈	—	2	2	no	—
608	C₇×C₈	—	2	2	no	—
609	C₇×C₈	—	2	2	no	—
610	C₇×C₈	—	2	2	no	—
611	C₂×#41	—	2	2	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	C₂³×C₇	1	2	yes	—
614	C₂×#41	C₂³×C₇	1	2	yes	—
615	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₇	1	2	yes	—
618	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
619	#137	—	4	4	no	—
620	#135	—	4	4	no	—
621	C₂×Q₁₆	—	4	2	no	—
622	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
623	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
624	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
625	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
626	C₂×SD₁₆	—	4	2	no	—
627	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
633	C₂×D₈	C₂³×C₇	1	2	yes	—
634	C₂×D₈	C₂³×C₇	1	2	yes	—
635	C₂×M₁₆	C₂³×C₇	1	2	yes	—
636	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
638	C₂²×C₈	C₂³×C₇	1	2	yes	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
644	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
647	#127	—	2	1	no	—
648	#127	C₂³×C₇	1	1	yes	characteristic
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	C₇×D₄	1	2	yes	—
654	#125	—	2	1	no	—
655	#125	—	2	1	no	—
656	#125	C₇×D₄	1	1	yes	characteristic
657	#124	—	2	1	no	—
658	#124	—	2	2	no	—
659	#124	—	2	2	no	—
660	#124	—	2	2	no	—
661	#124	—	2	2	no	—
662	#124	—	2	1	no	—
663	#124	—	2	1	no	—
664	#124	—	2	1	no	—
665	#124	C₇×D₄	1	1	yes	characteristic
666	#124	C₂³×C₇	1	2	yes	—
667	#124	C₂³×C₇	1	2	yes	—
668	#124	C₂³×C₇	1	2	yes	—
669	#124	C₂³×C₇	1	2	yes	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	C₇×D₄	1	2	yes	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	C₇×D₄	1	1	yes	characteristic
701	#121	C₂³×C₇	1	2	yes	—
702	#121	C₂³×C₇	1	2	yes	—
703	#121	C₂³×C₇	1	2	yes	—
704	#120	—	2	2	no	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
710	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
711	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₇	1	2	yes	—
714	C₄×Q₈	C₂³×C₇	1	2	yes	—
715	C₄×Q₈	C₂³×C₇	1	2	yes	—
716	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	C₂³×C₇	1	2	yes	—
727	C₄×D₄	C₂³×C₇	1	2	yes	—
728	C₄×D₄	C₂³×C₇	1	2	yes	—
729	C₄×D₄	C₂³×C₇	1	2	yes	—
730	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
731	#117	—	2	1	no	—
732	#117	—	2	2	no	—
733	#117	—	2	2	no	—
734	#117	C₂³×C₇	1	2	yes	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	2	no	—
737	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
739	C₂×C₂²⋊C₄	—	2	1	no	—
740	C₂×C₂²⋊C₄	—	2	1	no	—
741	C₂×C₂²⋊C₄	—	2	2	no	—
742	C₂×C₄²	—	2	1	no	—
743	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
744	#106	C₂³×C₇	1	2	yes	—
745	#106	C₂³×C₇	1	2	yes	—
746	#106	C₂³×C₇	1	2	yes	—
747	#106	C₂³×C₇	1	2	yes	—
748	C₄⋊C₈	C₂³×C₇	1	2	yes	—
749	C₄⋊C₈	C₂³×C₇	1	2	yes	—
750	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₇	1	2	yes	—
752	C₄⋊C₈	C₂³×C₇	1	2	yes	—
753	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
754	#103	C₂³×C₇	1	2	yes	—
755	#103	C₂³×C₇	1	2	yes	—
756	#103	C₂³×C₇	1	2	yes	—
757	#103	C₂³×C₇	1	2	yes	—
758	#103	C₂³×C₇	1	2	yes	—
759	#103	C₂³×C₇	1	2	yes	—
760	#103	C₂³×C₇	1	2	yes	—
761	#103	C₂³×C₇	1	2	yes	—
762	#103	C₂³×C₇	1	2	yes	—
763	#103	C₂³×C₇	1	2	yes	—
764	#102	C₂³×C₇	1	2	yes	—
765	#102	C₂³×C₇	1	2	yes	—
766	#102	C₂³×C₇	1	2	yes	—
767	#102	C₂³×C₇	1	2	yes	—
768	#102	C₂³×C₇	1	2	yes	—
769	#102	C₂³×C₇	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
773	#97	C₂³×C₇	1	2	yes	—
774	#97	C₂³×C₇	1	2	yes	—
775	C₄×C₈	C₂³×C₇	1	2	yes	—
776	C₂²×C₇	—	2	1	no	—
777	C₂²×C₇	—	2	1	no	—
778	C₂²×C₇	—	2	2	no	—
779	C₂²×C₇	—	2	2	no	—
780	C₂²×C₇	—	2	2	no	—
781	C₂²×C₇	—	4	2	no	—
782	C₂²×C₇	—	4	2	no	—
783	C₂²×C₇	—	4	2	no	—
784	C₂²×C₇	—	4	2	no	—
785	C₂²×C₇	—	4	2	no	—
786	C₂²×C₇	—	4	2	no	—
787	C₂²×C₇	—	16	2	no	—
788	C₂²×C₇	#577	1	2	yes	—
789	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
790	C₄×C₇	—	2	1	no	—
791	C₄×C₇	—	2	1	no	—
792	C₄×C₇	—	2	2	no	—
793	C₄×C₇	—	2	2	no	—
794	C₄×C₇	—	2	1	no	—
795	C₄×C₇	—	2	2	no	—
796	C₄×C₇	—	2	1	no	—
797	C₄×C₇	—	2	1	no	—
798	C₄×C₇	—	2	2	no	—
799	C₄×C₇	—	4	2	no	—
800	C₄×C₇	—	4	1	no	—
801	C₄×C₇	—	4	2	no	—
802	C₄×C₇	—	4	2	no	—
803	C₄×C₇	—	4	1	no	—
804	C₄×C₇	—	4	1	no	—
805	C₄×C₇	—	4	2	no	—
806	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
807	C₄×C₇	#585	1	1	yes	characteristic
808	C₂⁴	—	2	1	no	—
809	#41	—	2	4	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	4	2	no	—
813	#41	—	8	2	no	—
814	#41	—	8	4	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	2	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	4	1	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	2	no	—
825	C₂×Q₈	—	4	1	no	—
826	C₂×Q₈	—	4	2	no	—
827	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
828	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
829	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
830	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
831	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	1	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	4	1	no	—
841	C₂×D₄	—	4	1	no	—
842	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
843	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
844	C₂×D₄	C₂⁴×C₇	1	2	yes	—
845	C₂×D₄	C₂⁴×C₇	1	2	yes	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
860	Q₁₆	—	2	4	no	—
861	Q₁₆	—	2	4	no	—
862	Q₁₆	—	4	2	no	—
863	Q₁₆	—	4	2	no	—
864	SD₁₆	—	2	4	no	—
865	SD₁₆	—	4	2	no	—
866	SD₁₆	—	4	2	no	—
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	2	no	—
869	SD₁₆	—	4	2	no	—
870	D₈	—	4	2	no	—
871	D₈	—	4	2	no	—
872	M₁₆	—	4	2	no	—
873	C₂×C₈	—	4	1	no	—
874	C₂×C₈	—	4	1	no	—
875	C₂×C₈	—	4	2	no	—
876	C₂×C₈	C₂⁴×C₇	1	2	yes	—
877	C₂×C₈	C₂⁴×C₇	1	2	yes	—
878	C₂×C₈	C₂⁴×C₇	1	2	yes	—
879	C₂×C₈	C₂⁴×C₇	1	2	yes	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
900	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
901	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
902	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
903	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
904	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
905	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
906	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
907	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
908	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
927	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
928	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
929	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
930	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
931	C₄²	—	2	1	no	—
932	C₄²	—	2	1	no	—
933	C₄²	—	2	1	no	—
934	C₄²	—	2	1	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
939	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
940	C₄²	C₂⁴×C₇	1	2	yes	—
941	C₄²	C₂⁴×C₇	1	1	yes	characteristic
942	C₄²	C₂⁴×C₇	1	1	yes	characteristic
943	C₂×C₇	—	2	2	no	—
944	C₂×C₇	—	4	2	no	—
945	C₂×C₇	—	8	2	no	—
946	C₂×C₇	—	8	2	no	—
947	C₂×C₇	#3488	1	1	yes	characteristic
948	C₂×C₇	C₂×#577	1	1	yes	characteristic
949	C₂×C₇	#3586	1	1	yes	characteristic
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	4	2	no	—
953	C₂³	—	8	1	no	—
954	C₂³	—	8	1	no	—
955	C₂³	C₂²×C₇×D₄	1	2	yes	—
956	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
957	Q₈	—	2	1	no	—
958	Q₈	—	2	2	no	—
959	Q₈	—	2	1	no	—
960	Q₈	—	2	2	no	—
961	Q₈	—	2	2	no	—
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	4	1	no	—
965	Q₈	—	4	2	no	—
966	Q₈	—	8	1	no	—
967	Q₈	—	8	2	no	—
968	Q₈	—	8	1	no	—
969	Q₈	—	8	1	no	—
970	Q₈	—	8	2	no	—
971	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
972	D₄	—	2	4	no	—
973	D₄	—	2	2	no	—
974	D₄	—	2	2	no	—
975	D₄	—	2	2	no	—
976	D₄	—	2	2	no	—
977	D₄	—	4	1	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	2	no	—
980	D₄	—	4	4	no	—
981	D₄	—	8	1	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	4	4	no	—
1001	C₂×C₄	—	4	2	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	8	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	—	8	2	no	—
1006	C₂×C₄	—	8	2	no	—
1007	C₂×C₄	—	8	2	no	—
1008	C₂×C₄	—	8	1	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1011	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1012	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1013	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1014	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1015	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1016	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1017	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1018	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₇	#62021	1	1	yes	characteristic, direct product factor, Sylow
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	16	2	no	—
1036	C₂²	C₇×#577	1	2	yes	—
1037	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1055	C₄	C₇×#585	1	1	yes	characteristic
1056	C₂	—	2	2	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	8	2	no	—
1059	C₂	—	8	2	no	—
1060	C₂	C₇×#3488	1	1	yes	characteristic
1061	C₂	C₂×C₇×#577	1	1	yes	characteristic
1062	C₂	C₇×#3586	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×#3561	C₂	semidirect
2. C₇×#3522	C₂	semidirect
3. C₇×#3401	C₂	semidirect
4. C₇×#3369	C₂	semidirect
5. C₇×#3316	C₂	semidirect
6. C₇×#3306	C₂	semidirect
7. C₇×#3298	C₂	semidirect
8. C₇×#3282	C₂	semidirect
9. C₇×#3271	C₂	semidirect
10. C₇×#3270	C₂	semidirect
11. C₇×#3263	C₂	semidirect
12. C₇×#3246	C₂	semidirect
13. C₇×#3225	C₂	semidirect
14. C₇×#3213	C₂	semidirect
15. C₇×#3125	C₂	semidirect
16. C₇×#3113	C₂	semidirect
17. C₇×#3046	C₂	semidirect
18. C₂×C₇×#464	C₂	semidirect
19. C₇×#2992	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
27. C₇×#559	C₂²	semidirect
28. C₇×Q₈²	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
33. C₇×#550	C₂²	semidirect
44. C₇×#542	C₂²	semidirect
53. C₇×#520	C₂²	semidirect
55. C₇×#497	C₂²	semidirect
60. C₇×#487	C₂²	semidirect
62. C₇×#483	C₂²	semidirect
65. C₇×#476	C₂²	semidirect
66. C₇×#475	C₂²	semidirect
67. C₇×#475	C₂²	semidirect
68. C₇×#475	C₂²	semidirect
69. C₇×#475	C₂²	semidirect
70. C₇×#470	C₂²	semidirect
75. C₇×#465	C₂²	semidirect
81. C₇×#464	C₂²	semidirect
86. C₇×#462	C₂²	semidirect
87. C₇×#462	C₂²	semidirect
88. C₇×#462	C₂²	semidirect
89. C₇×#461	C₂²	semidirect
90. C₇×#461	C₂²	semidirect
91. C₇×#460	C₂²	semidirect
93. C₇×#452	C₂²	semidirect
95. C₇×#451	C₂²	semidirect
99. C₇×#448	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
103. C₇×#441	C₂²	semidirect
104. C₇×#441	C₂²	semidirect
105. C₇×#441	C₂²	semidirect
107. C₄×C₇×SD₁₆	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
111. C₇×#433	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
117. C₂×C₇×#103	C₂²	semidirect
119. #62021	C₇	direct (N × H)
285. #3561	C₂×C₇	semidirect
286. #3522	C₂×C₇	semidirect
287. #3401	C₂×C₇	semidirect
288. #3369	C₂×C₇	semidirect
289. #3316	C₂×C₇	semidirect
290. #3306	C₂×C₇	semidirect
291. #3298	C₂×C₇	semidirect
292. #3282	C₂×C₇	semidirect
293. #3271	C₂×C₇	semidirect
294. #3270	C₂×C₇	semidirect
295. #3263	C₂×C₇	semidirect
296. #3246	C₂×C₇	semidirect
297. #3225	C₂×C₇	semidirect
298. #3213	C₂×C₇	semidirect
299. #3125	C₂×C₇	semidirect
300. #3113	C₂×C₇	semidirect
301. #3046	C₂×C₇	semidirect
302. C₂×#464	C₂×C₇	semidirect
303. #2992	C₂×C₇	semidirect
439. C₂×#137	C₂²×C₇	semidirect
446. #559	C₂²×C₇	semidirect
447. Q₈²	C₂²×C₇	semidirect
450. #554	C₂²×C₇	semidirect
452. #550	C₂²×C₇	semidirect
463. #542	C₂²×C₇	semidirect
472. #520	C₂²×C₇	semidirect
474. #497	C₂²×C₇	semidirect
479. #487	C₂²×C₇	semidirect
481. #483	C₂²×C₇	semidirect
484. #476	C₂²×C₇	semidirect
485. #475	C₂²×C₇	semidirect
486. #475	C₂²×C₇	semidirect
487. #475	C₂²×C₇	semidirect
488. #475	C₂²×C₇	semidirect
489. #470	C₂²×C₇	semidirect
494. #465	C₂²×C₇	semidirect
500. #464	C₂²×C₇	semidirect
505. #462	C₂²×C₇	semidirect
506. #462	C₂²×C₇	semidirect
507. #462	C₂²×C₇	semidirect
508. #461	C₂²×C₇	semidirect
509. #461	C₂²×C₇	semidirect
510. #460	C₂²×C₇	semidirect
512. #452	C₂²×C₇	semidirect
514. #451	C₂²×C₇	semidirect
518. #448	C₂²×C₇	semidirect
520. #446	C₂²×C₇	semidirect
522. #441	C₂²×C₇	semidirect
523. #441	C₂²×C₇	semidirect
524. #441	C₂²×C₇	semidirect
526. C₄×SD₁₆	C₂²×C₇	semidirect
528. #435	C₂²×C₇	semidirect
530. #433	C₂²×C₇	semidirect
532. #424	C₂²×C₇	semidirect
536. C₂×#103	C₂²×C₇	semidirect
1023. C₇	#62021	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×#3561	2
C₇×#3522	2
C₇×#3401	2
C₇×#3369	2
C₇×#3316	2
C₇×#3306	2
C₇×#3298	2
C₇×#3282	2
C₇×#3271	2
C₇×#3270	2
C₇×#3263	2
C₇×#3246	2
C₇×#3225	2
C₇×#3213	2
C₇×#3125	2
C₇×#3113	2
C₇×#3046	2
C₂×C₇×#464	2
C₇×#2992	2
#62021	7

Subgroups — C7×#62021 #13239237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62021 #13239237