Subgroups — C₇×#61162 #13238378

Order 1792.

2162 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₄×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₇×#3331	C₂	1	2	yes	maximal, complemented
5	C₇×#3316	C₂	1	4	yes	maximal, complemented
6	C₇×#3314	C₂	1	4	yes	maximal, complemented
7	C₇×#3299	C₂	1	2	yes	maximal, complemented
8	C₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3092	C₂	1	2	yes	maximal, complemented
11	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3056	C₂	1	2	yes	maximal, complemented
13	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#417	C₂	1	2	yes	maximal, complemented
18	C₂²×C₇×#41	C₂²	1	2	yes	—
19	C₂×C₇×#137	C₂²	1	1	yes	characteristic
20	C₂×C₇×#137	C₂²	1	2	yes	complemented
21	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
22	C₇×#554	—	2	1	no	—
23	C₇×#554	—	2	2	no	—
24	C₇×#554	—	2	1	no	—
25	C₇×#554	C₂²	1	2	yes	—
26	C₇×#554	C₂²	1	4	yes	complemented
27	C₇×#554	C₂²	1	2	yes	complemented
28	C₇×#550	C₂²	1	1	yes	characteristic
29	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
30	C₇×#548	C₂²	1	2	yes	—
31	C₇×#547	—	2	1	no	—
32	C₇×#547	C₂²	1	1	yes	characteristic
33	C₇×#546	—	2	2	no	—
34	C₇×#546	C₂²	1	2	yes	—
35	C₇×D₄²	—	2	1	no	—
36	C₇×D₄²	C₂²	1	1	yes	characteristic
37	C₇×#532	—	2	1	no	—
38	C₇×#532	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#125	—	2	1	no	—
41	C₇×#525	—	2	2	no	—
42	C₇×#525	C₂²	1	2	yes	—
43	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
44	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×C₇×D₄	—	2	1	no	—
48	C₂×C₄×C₇×D₄	—	2	1	no	—
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
51	C₇×#489	C₂²	1	4	yes	complemented
52	C₇×#487	C₂²	1	2	yes	complemented
53	C₇×#486	C₂²	1	2	yes	complemented
54	C₇×#484	C₂²	1	4	yes	complemented
55	C₇×#483	C₂²	1	4	yes	complemented
56	C₇×#481	C₂²	1	4	yes	complemented
57	C₇×#480	C₂²	1	4	yes	complemented
58	C₇×#477	C₂²	1	2	yes	complemented
59	C₇×#476	C₂²	1	2	yes	complemented
60	C₇×#475	C₂²	1	2	yes	complemented
61	C₇×#474	C₂²	1	2	yes	complemented
62	C₇×#470	C₂²	1	4	yes	complemented
63	C₇×#468	C₂²	1	4	yes	complemented
64	C₇×#467	C₂²	1	4	yes	complemented
65	C₇×#465	C₂²	1	4	yes	complemented
66	C₇×#464	C₂²	1	4	yes	complemented
67	C₇×#462	C₂²	1	2	yes	complemented
68	C₇×#460	C₂²	1	2	yes	complemented
69	C₇×#452	C₂²	1	4	yes	complemented
70	C₇×#452	C₂²	1	4	yes	complemented
71	C₇×#451	C₂²	1	4	yes	complemented
72	C₇×#450	C₂²	1	4	yes	complemented
73	C₇×#441	C₂²	1	2	yes	complemented
74	C₇×#440	C₂²	1	2	yes	complemented
75	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
77	C₇×#436	C₂²	1	2	yes	complemented
78	C₇×#435	C₂²	1	4	yes	complemented
79	C₇×C₈×D₄	C₂²	1	2	yes	—
80	C₇×#428	C₂²	1	1	yes	characteristic, complemented
81	C₇×#428	C₂²	1	2	yes	complemented
82	C₇×#423	C₂²	1	1	yes	characteristic, complemented
83	C₇×#419	C₂²	1	1	yes	characteristic, complemented
84	C₇×#417	C₂²	1	1	yes	characteristic
85	C₇×#417	C₂²	1	2	yes	—
86	C₇×#417	C₂²	1	2	yes	complemented
87	C₇×#417	C₂²	1	2	yes	complemented
88	C₇×#417	C₂²	1	2	yes	complemented
89	C₇×#417	C₂²	1	4	yes	complemented
90	C₇×#417	C₂²	1	4	yes	complemented
91	C₂×C₇×#103	C₂²	1	4	yes	complemented
92	C₂×C₇×#102	C₂²	1	4	yes	complemented
93	C₇×#407	C₂²	1	2	yes	complemented
94	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	#61162	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	—	2	2	no	—
98	C₂×C₇×#41	—	2	8	no	—
99	C₂×C₇×#41	—	4	4	no	—
100	C₂×C₇×#41	C₂³	1	2	yes	—
101	C₂×C₇×#41	C₂³	1	2	yes	—
102	C₂×C₇×#41	C₂³	1	2	yes	—
103	C₂×C₇×#41	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	—	2	1	no	—
105	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×Q₈	C₂³	1	2	yes	—
107	C₂²×C₇×D₄	—	2	2	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂³×C₄×C₇	—	2	2	no	—
112	C₂³×C₄×C₇	—	2	2	no	—
113	C₂³×C₄×C₇	C₂³	1	2	yes	—
114	C₇×#137	—	2	4	no	—
115	C₇×#137	—	4	4	no	—
116	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
117	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
118	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₇×M₁₆	—	4	4	no	—
121	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×M₁₆	C₂³	1	2	yes	—
124	C₂×C₇×M₁₆	C₂³	1	4	yes	—
125	C₂²×C₇×C₈	C₂³	1	4	yes	—
126	C₇×C₄⋊Q₈	—	2	1	no	—
127	C₇×C₄⋊Q₈	—	2	1	no	—
128	C₇×C₄⋊Q₈	—	2	1	no	—
129	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₇×#127	—	2	1	no	—
133	C₇×#127	C₂³	1	1	yes	characteristic
134	C₇×#125	—	2	2	no	—
135	C₇×#125	—	2	2	no	—
136	C₇×#125	—	2	4	no	—
137	C₇×#124	—	2	2	no	—
138	C₇×#124	C₂³	1	2	yes	—
139	C₇×#123	—	2	2	no	—
140	C₇×#123	—	2	2	no	—
141	C₇×#123	—	2	2	no	—
142	C₇×C₂²⋊Q₈	—	2	2	no	—
143	C₇×C₂²⋊Q₈	—	2	2	no	—
144	C₇×C₂²⋊Q₈	—	2	2	no	—
145	C₇×C₂²⋊Q₈	—	2	4	no	—
146	C₇×C₂²⋊Q₈	—	2	4	no	—
147	C₇×C₂²⋊Q₈	—	2	4	no	—
148	C₇×C₂²⋊Q₈	—	2	4	no	—
149	C₇×C₂²⋊Q₈	—	2	2	no	—
150	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₇×#121	—	2	2	no	—
155	C₇×#121	—	2	1	no	—
156	C₇×#121	—	2	1	no	—
157	C₇×#121	—	2	1	no	—
158	C₇×#121	—	2	1	no	—
159	C₇×#121	—	2	2	no	—
160	C₇×#121	—	2	2	no	—
161	C₇×#121	C₂³	1	2	yes	—
162	C₇×#121	C₂³	1	2	yes	—
163	C₇×#120	—	2	2	no	—
164	C₇×#120	—	2	2	no	—
165	C₇×#120	—	2	2	no	—
166	C₄×C₇×Q₈	—	2	1	no	—
167	C₄×C₇×Q₈	—	2	1	no	—
168	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
169	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
170	C₄×C₇×Q₈	C₂³	1	2	yes	—
171	C₄×C₇×Q₈	C₂³	1	2	yes	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	—	2	2	no	—
174	C₄×C₇×D₄	—	2	4	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	—	2	2	no	—
177	C₄×C₇×D₄	—	2	1	no	—
178	C₄×C₇×D₄	—	2	1	no	—
179	C₄×C₇×D₄	—	2	2	no	—
180	C₄×C₇×D₄	—	2	1	no	—
181	C₄×C₇×D₄	—	2	2	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	—	2	1	no	—
184	C₄×C₇×D₄	D₄	1	1	yes	characteristic
185	C₄×C₇×D₄	D₄	1	2	yes	—
186	C₄×C₇×D₄	D₄	1	1	yes	characteristic
187	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
188	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
189	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
190	C₄×C₇×D₄	C₂³	1	2	yes	—
191	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₇×#117	—	2	1	no	—
193	C₇×#117	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₄⋊C₄	—	2	2	no	—
195	C₂×C₇×C₄⋊C₄	—	2	2	no	—
196	C₂×C₇×C₄⋊C₄	—	2	2	no	—
197	C₂×C₇×C₄⋊C₄	—	2	1	no	—
198	C₂×C₇×C₄⋊C₄	—	2	1	no	—
199	C₂×C₇×C₄⋊C₄	—	2	2	no	—
200	C₂×C₇×C₄⋊C₄	—	2	1	no	—
201	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
209	C₂×C₄²×C₇	—	2	1	no	—
210	C₂×C₄²×C₇	—	2	1	no	—
211	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
212	C₇×#107	C₂³	1	4	yes	—
213	C₇×#107	C₂³	1	2	yes	—
214	C₇×#106	C₂³	1	4	yes	—
215	C₇×#106	C₂³	1	2	yes	—
216	C₇×C₄⋊C₈	C₂³	1	2	yes	—
217	C₇×C₄⋊C₈	C₂³	1	2	yes	—
218	C₇×#103	C₂³	1	2	yes	—
219	C₇×#103	C₂³	1	4	yes	—
220	C₇×#103	C₂³	1	2	yes	—
221	C₇×#103	C₂³	1	4	yes	—
222	C₇×#103	C₂³	1	4	yes	—
223	C₇×#103	C₂³	1	4	yes	—
224	C₇×#103	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	4	yes	—
227	C₇×#102	C₂³	1	4	yes	—
228	C₇×#102	C₂³	1	4	yes	—
229	C₇×#102	C₂³	1	2	yes	—
230	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₇×#97	C₂³	1	2	yes	—
233	C₄×C₇×C₈	C₂³	1	2	yes	—
234	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
235	D₄×#41	C₂×C₇	1	1	yes	characteristic
236	#3333	C₂×C₇	1	2	yes	complemented
237	#3331	C₂×C₇	1	2	yes	complemented
238	#3316	C₂×C₇	1	4	yes	complemented
239	#3314	C₂×C₇	1	4	yes	complemented
240	#3299	C₂×C₇	1	2	yes	complemented
241	#3295	C₂×C₇	1	2	yes	complemented
242	#3141	C₂×C₇	1	1	yes	characteristic, complemented
243	#3092	C₂×C₇	1	2	yes	complemented
244	#3079	C₂×C₇	1	1	yes	characteristic, complemented
245	#3056	C₂×C₇	1	2	yes	complemented
246	#3037	C₂×C₇	1	1	yes	characteristic, complemented
247	#3007	C₂×C₇	1	2	yes	complemented
248	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
249	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
250	C₂×#417	C₂×C₇	1	2	yes	complemented
251	C₂⁴×C₇	—	2	2	no	—
252	C₂⁴×C₇	C₂×D₄	1	2	yes	—
253	C₇×#41	—	2	2	no	—
254	C₇×#41	—	2	4	no	—
255	C₇×#41	—	2	4	no	—
256	C₇×#41	—	2	4	no	—
257	C₇×#41	—	2	4	no	—
258	C₇×#41	—	4	8	no	—
259	C₇×#41	—	4	2	no	—
260	C₇×#41	—	4	2	no	—
261	C₇×#41	—	4	8	no	—
262	C₇×#41	#41	1	4	yes	—
263	C₂×C₇×Q₈	—	2	1	no	—
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	4	no	—
268	C₂×C₇×Q₈	—	2	2	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	4	2	no	—
271	C₂×C₇×Q₈	—	8	2	no	—
272	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
273	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
274	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×D₄	—	2	1	no	—
276	C₂×C₇×D₄	—	2	4	no	—
277	C₂×C₇×D₄	—	2	4	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	2	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	1	no	—
284	C₂×C₇×D₄	—	2	2	no	—
285	C₂×C₇×D₄	—	2	1	no	—
286	C₂×C₇×D₄	—	4	2	no	—
287	C₂×C₇×D₄	—	4	8	no	—
288	C₂×C₇×D₄	—	4	4	no	—
289	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
290	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
291	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
292	C₂×C₇×D₄	C₂⁴	1	2	yes	—
293	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	—	2	1	no	—
295	C₂²×C₄×C₇	—	2	4	no	—
296	C₂²×C₄×C₇	—	2	4	no	—
297	C₂²×C₄×C₇	—	2	1	no	—
298	C₂²×C₄×C₇	—	2	1	no	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	4	no	—
302	C₂²×C₄×C₇	—	2	4	no	—
303	C₂²×C₄×C₇	—	2	1	no	—
304	C₂²×C₄×C₇	—	2	2	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	2	no	—
307	C₂²×C₄×C₇	—	2	1	no	—
308	C₂²×C₄×C₇	—	4	8	no	—
309	C₂²×C₄×C₇	—	8	4	no	—
310	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
313	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
314	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₇×Q₁₆	—	2	4	no	—
319	C₇×Q₁₆	—	4	4	no	—
320	C₇×SD₁₆	—	2	4	no	—
321	C₇×SD₁₆	—	4	4	no	—
322	C₇×M₁₆	—	2	2	no	—
323	C₇×M₁₆	—	2	2	no	—
324	C₇×M₁₆	—	2	4	no	—
325	C₇×M₁₆	—	4	4	no	—
326	C₂×C₇×C₈	—	4	4	no	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₂×C₇×C₈	C₂⁴	1	2	yes	—
329	C₂×C₇×C₈	C₂⁴	1	4	yes	—
330	C₇×C₄⋊C₄	—	2	1	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	4	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	1	no	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	4	no	—
341	C₇×C₄⋊C₄	—	2	4	no	—
342	C₇×C₄⋊C₄	—	2	1	no	—
343	C₇×C₄⋊C₄	—	2	1	no	—
344	C₇×C₄⋊C₄	—	2	1	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
347	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
348	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
349	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
351	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
352	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
353	C₇×C₂²⋊C₄	—	2	2	no	—
354	C₇×C₂²⋊C₄	—	2	4	no	—
355	C₇×C₂²⋊C₄	—	2	4	no	—
356	C₇×C₂²⋊C₄	—	2	1	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	1	no	—
361	C₇×C₂²⋊C₄	—	2	1	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
367	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
368	C₄²×C₇	—	2	1	no	—
369	C₄²×C₇	—	2	1	no	—
370	C₄²×C₇	—	2	1	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₇	C₂⁴	1	1	yes	characteristic
376	C₄²×C₇	C₂⁴	1	1	yes	characteristic
377	C₂²×#41	C₂²×C₇	1	2	yes	—
378	C₂×#137	C₂²×C₇	1	1	yes	characteristic
379	C₂×#137	C₂²×C₇	1	2	yes	complemented
380	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
381	#554	—	2	1	no	—
382	#554	—	2	2	no	—
383	#554	—	2	1	no	—
384	#554	C₂²×C₇	1	2	yes	—
385	#554	C₂²×C₇	1	2	yes	complemented
386	#554	C₂²×C₇	1	4	yes	complemented
387	#550	C₂²×C₇	1	1	yes	characteristic
388	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
389	#548	C₂²×C₇	1	2	yes	—
390	#547	—	2	1	no	—
391	#547	C₂²×C₇	1	1	yes	characteristic
392	#546	—	2	2	no	—
393	#546	C₂²×C₇	1	2	yes	—
394	D₄²	—	2	1	no	—
395	D₄²	C₂²×C₇	1	1	yes	characteristic
396	#532	—	2	1	no	—
397	#532	C₂²×C₇	1	1	yes	characteristic
398	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
399	C₂×#125	—	2	1	no	—
400	#525	—	2	2	no	—
401	#525	C₂²×C₇	1	2	yes	—
402	C₂×C₂²⋊Q₈	—	2	2	no	—
403	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
404	C₄×#41	C₂²×C₇	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
406	C₂×C₄×D₄	—	2	1	no	—
407	C₂×C₄×D₄	—	2	1	no	—
408	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
410	#489	C₂²×C₇	1	4	yes	complemented
411	#487	C₂²×C₇	1	2	yes	complemented
412	#486	C₂²×C₇	1	2	yes	complemented
413	#484	C₂²×C₇	1	4	yes	complemented
414	#483	C₂²×C₇	1	4	yes	complemented
415	#481	C₂²×C₇	1	4	yes	complemented
416	#480	C₂²×C₇	1	4	yes	complemented
417	#477	C₂²×C₇	1	2	yes	complemented
418	#476	C₂²×C₇	1	2	yes	complemented
419	#475	C₂²×C₇	1	2	yes	complemented
420	#474	C₂²×C₇	1	2	yes	complemented
421	#470	C₂²×C₇	1	4	yes	complemented
422	#468	C₂²×C₇	1	4	yes	complemented
423	#467	C₂²×C₇	1	4	yes	complemented
424	#465	C₂²×C₇	1	4	yes	complemented
425	#464	C₂²×C₇	1	4	yes	complemented
426	#462	C₂²×C₇	1	2	yes	complemented
427	#460	C₂²×C₇	1	2	yes	complemented
428	#452	C₂²×C₇	1	4	yes	complemented
429	#452	C₂²×C₇	1	4	yes	complemented
430	#451	C₂²×C₇	1	4	yes	complemented
431	#450	C₂²×C₇	1	4	yes	complemented
432	#441	C₂²×C₇	1	2	yes	complemented
433	#440	C₂²×C₇	1	2	yes	complemented
434	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
435	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
436	#436	C₂²×C₇	1	2	yes	complemented
437	#435	C₂²×C₇	1	4	yes	complemented
438	C₈×D₄	C₂²×C₇	1	2	yes	—
439	#428	C₂²×C₇	1	2	yes	complemented
440	#428	C₂²×C₇	1	1	yes	characteristic, complemented
441	#423	C₂²×C₇	1	1	yes	characteristic, complemented
442	#419	C₂²×C₇	1	1	yes	characteristic, complemented
443	#417	C₂²×C₇	1	2	yes	—
444	#417	C₂²×C₇	1	1	yes	characteristic
445	#417	C₂²×C₇	1	4	yes	complemented
446	#417	C₂²×C₇	1	4	yes	complemented
447	#417	C₂²×C₇	1	2	yes	complemented
448	#417	C₂²×C₇	1	2	yes	complemented
449	#417	C₂²×C₇	1	2	yes	complemented
450	C₂×#103	C₂²×C₇	1	4	yes	complemented
451	C₂×#102	C₂²×C₇	1	4	yes	complemented
452	#407	C₂²×C₇	1	2	yes	complemented
453	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
454	C₂³×C₇	—	2	4	no	—
455	C₂³×C₇	—	2	4	no	—
456	C₂³×C₇	—	2	1	no	—
457	C₂³×C₇	—	2	2	no	—
458	C₂³×C₇	—	4	2	no	—
459	C₂³×C₇	—	4	4	no	—
460	C₂³×C₇	—	4	4	no	—
461	C₂³×C₇	—	8	2	no	—
462	C₂³×C₇	C₂²×D₄	1	2	yes	—
463	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₇	C₂²×D₄	1	2	yes	—
465	C₇×Q₈	—	2	1	no	—
466	C₇×Q₈	—	2	2	no	—
467	C₇×Q₈	—	2	2	no	—
468	C₇×Q₈	—	2	2	no	—
469	C₇×Q₈	—	2	2	no	—
470	C₇×Q₈	—	4	4	no	—
471	C₇×Q₈	—	4	2	no	—
472	C₇×Q₈	—	8	2	no	—
473	C₇×Q₈	—	8	2	no	—
474	C₇×Q₈	C₂×#41	1	2	yes	—
475	C₇×D₄	—	2	4	no	—
476	C₇×D₄	—	2	4	no	—
477	C₇×D₄	—	2	2	no	—
478	C₇×D₄	—	2	2	no	—
479	C₇×D₄	—	2	1	no	—
480	C₇×D₄	—	2	2	no	—
481	C₇×D₄	—	4	4	no	—
482	C₇×D₄	—	4	4	no	—
483	C₇×D₄	—	4	4	no	—
484	C₇×D₄	—	4	4	no	—
485	C₇×D₄	—	4	4	no	—
486	C₇×D₄	—	4	2	no	—
487	C₇×D₄	—	8	1	no	—
488	C₇×D₄	—	8	2	no	—
489	C₇×D₄	#137	1	4	yes	complemented
490	C₇×D₄	C₂×#41	1	2	yes	—
491	C₂×C₄×C₇	—	2	4	no	—
492	C₂×C₄×C₇	—	2	1	no	—
493	C₂×C₄×C₇	—	2	4	no	—
494	C₂×C₄×C₇	—	2	4	no	—
495	C₂×C₄×C₇	—	2	4	no	—
496	C₂×C₄×C₇	—	2	2	no	—
497	C₂×C₄×C₇	—	2	2	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	2	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	4	no	—
507	C₂×C₄×C₇	—	4	1	no	—
508	C₂×C₄×C₇	—	4	4	no	—
509	C₂×C₄×C₇	—	4	4	no	—
510	C₂×C₄×C₇	—	4	4	no	—
511	C₂×C₄×C₇	—	4	2	no	—
512	C₂×C₄×C₇	—	4	4	no	—
513	C₂×C₄×C₇	—	4	2	no	—
514	C₂×C₄×C₇	—	4	4	no	—
515	C₂×C₄×C₇	—	4	2	no	—
516	C₂×C₄×C₇	—	8	1	no	—
517	C₂×C₄×C₇	—	8	4	no	—
518	C₂×C₄×C₇	—	8	4	no	—
519	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₇	C₂×#41	1	2	yes	—
527	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
528	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
529	C₇×C₈	—	2	2	no	—
530	C₇×C₈	—	2	2	no	—
531	C₇×C₈	—	2	4	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	2	8	no	—
535	C₂×#41	—	4	4	no	—
536	C₂×#41	C₂³×C₇	1	2	yes	—
537	C₂×#41	C₂³×C₇	1	2	yes	—
538	C₂×#41	C₂³×C₇	1	2	yes	—
539	C₂×#41	C₂³×C₇	1	1	yes	characteristic
540	C₂²×Q₈	—	2	1	no	—
541	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₇	1	2	yes	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	—	2	1	no	—
545	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₇	1	2	yes	—
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	—	2	2	no	—
549	C₂³×C₄	C₂³×C₇	1	2	yes	—
550	#137	—	2	4	no	—
551	#137	—	4	4	no	—
552	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
553	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
556	C₂×M₁₆	—	4	4	no	—
557	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
558	C₂×M₁₆	C₂³×C₇	1	2	yes	—
559	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
560	C₂×M₁₆	C₂³×C₇	1	4	yes	—
561	C₂²×C₈	C₂³×C₇	1	4	yes	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
566	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
568	#127	—	2	1	no	—
569	#127	C₂³×C₇	1	1	yes	characteristic
570	#125	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	—	2	4	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₇	1	2	yes	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
587	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
588	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₇	1	2	yes	—
598	#121	C₂³×C₇	1	2	yes	—
599	#120	—	2	2	no	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	C₂³×C₇	1	2	yes	—
605	C₄×Q₈	C₂³×C₇	1	2	yes	—
606	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	C₇×D₄	1	1	yes	characteristic
621	C₄×D₄	C₇×D₄	1	2	yes	—
622	C₄×D₄	C₇×D₄	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₇	1	2	yes	—
627	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
628	#117	—	2	1	no	—
629	#117	C₂³×C₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
641	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
642	C₂×C₂²⋊C₄	—	2	2	no	—
643	C₂×C₂²⋊C₄	—	2	2	no	—
644	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
648	#107	C₂³×C₇	1	2	yes	—
649	#107	C₂³×C₇	1	4	yes	—
650	#106	C₂³×C₇	1	2	yes	—
651	#106	C₂³×C₇	1	4	yes	—
652	C₄⋊C₈	C₂³×C₇	1	2	yes	—
653	C₄⋊C₈	C₂³×C₇	1	2	yes	—
654	#103	C₂³×C₇	1	2	yes	—
655	#103	C₂³×C₇	1	4	yes	—
656	#103	C₂³×C₇	1	4	yes	—
657	#103	C₂³×C₇	1	4	yes	—
658	#103	C₂³×C₇	1	4	yes	—
659	#103	C₂³×C₇	1	2	yes	—
660	#103	C₂³×C₇	1	2	yes	—
661	#102	C₂³×C₇	1	2	yes	—
662	#102	C₂³×C₇	1	4	yes	—
663	#102	C₂³×C₇	1	4	yes	—
664	#102	C₂³×C₇	1	4	yes	—
665	#102	C₂³×C₇	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
668	#97	C₂³×C₇	1	2	yes	—
669	C₄×C₈	C₂³×C₇	1	2	yes	—
670	C₂²×C₇	—	2	1	no	—
671	C₂²×C₇	—	2	2	no	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	1	no	—
674	C₂²×C₇	—	2	2	no	—
675	C₂²×C₇	—	2	2	no	—
676	C₂²×C₇	—	2	2	no	—
677	C₂²×C₇	—	2	2	no	—
678	C₂²×C₇	—	4	8	no	—
679	C₂²×C₇	—	4	1	no	—
680	C₂²×C₇	—	4	1	no	—
681	C₂²×C₇	—	4	2	no	—
682	C₂²×C₇	—	4	2	no	—
683	C₂²×C₇	—	4	2	no	—
684	C₂²×C₇	—	8	8	no	—
685	C₂²×C₇	#546	1	2	yes	—
686	C₂²×C₇	C₂×#137	1	4	yes	—
687	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
688	C₄×C₇	—	2	1	no	—
689	C₄×C₇	—	2	1	no	—
690	C₄×C₇	—	2	2	no	—
691	C₄×C₇	—	2	2	no	—
692	C₄×C₇	—	2	2	no	—
693	C₄×C₇	—	2	1	no	—
694	C₄×C₇	—	4	2	no	—
695	C₄×C₇	—	4	4	no	—
696	C₄×C₇	—	4	1	no	—
697	C₄×C₇	—	4	2	no	—
698	C₄×C₇	—	4	2	no	—
699	C₄×C₇	—	4	1	no	—
700	C₄×C₇	#546	1	2	yes	—
701	C₄×C₇	C₂×#137	1	2	yes	—
702	C₄×C₇	C₂²×#41	1	1	yes	characteristic
703	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂⁴	—	2	2	no	—
705	C₂⁴	C₂×C₇×D₄	1	2	yes	—
706	#41	—	2	2	no	—
707	#41	—	2	4	no	—
708	#41	—	2	4	no	—
709	#41	—	2	4	no	—
710	#41	—	2	4	no	—
711	#41	—	4	8	no	—
712	#41	—	4	2	no	—
713	#41	—	4	2	no	—
714	#41	—	4	8	no	—
715	#41	C₇×#41	1	4	yes	—
716	C₂×Q₈	—	2	1	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	—	8	2	no	—
725	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
726	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	8	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
743	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
744	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
745	C₂×D₄	C₂⁴×C₇	1	2	yes	—
746	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	4	8	no	—
762	C₂²×C₄	—	8	4	no	—
763	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
764	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
765	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
766	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
767	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
771	Q₁₆	—	2	4	no	—
772	Q₁₆	—	4	4	no	—
773	SD₁₆	—	2	4	no	—
774	SD₁₆	—	4	4	no	—
775	M₁₆	—	2	2	no	—
776	M₁₆	—	2	2	no	—
777	M₁₆	—	2	4	no	—
778	M₁₆	—	4	4	no	—
779	C₂×C₈	—	4	4	no	—
780	C₂×C₈	C₂⁴×C₇	1	2	yes	—
781	C₂×C₈	C₂⁴×C₇	1	2	yes	—
782	C₂×C₈	C₂⁴×C₇	1	4	yes	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
800	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
801	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
804	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
805	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	1	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
818	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
819	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
820	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
821	C₄²	—	2	1	no	—
822	C₄²	—	2	1	no	—
823	C₄²	—	2	1	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
827	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
828	C₄²	C₂⁴×C₇	1	1	yes	characteristic
829	C₄²	C₂⁴×C₇	1	1	yes	characteristic
830	C₂×C₇	—	2	2	no	—
831	C₂×C₇	—	2	4	no	—
832	C₂×C₇	—	4	2	no	—
833	C₂×C₇	—	4	2	no	—
834	C₂×C₇	—	8	2	no	—
835	C₂×C₇	C₂×#546	1	1	yes	characteristic
836	C₂×C₇	C₂²×#137	1	1	yes	characteristic
837	C₂×C₇	#3585	1	1	yes	characteristic
838	C₂³	—	2	1	no	—
839	C₂³	—	2	4	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	4	2	no	—
843	C₂³	—	4	4	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	8	2	no	—
846	C₂³	C₂²×C₇×D₄	1	2	yes	—
847	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
848	C₂³	C₂²×C₇×D₄	1	2	yes	—
849	Q₈	—	2	1	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	4	4	no	—
855	Q₈	—	4	2	no	—
856	Q₈	—	8	2	no	—
857	Q₈	—	8	2	no	—
858	Q₈	C₂×C₇×#41	1	2	yes	—
859	D₄	—	2	4	no	—
860	D₄	—	2	4	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	1	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	4	4	no	—
870	D₄	—	4	2	no	—
871	D₄	—	8	1	no	—
872	D₄	—	8	2	no	—
873	D₄	C₇×#137	1	4	yes	complemented
874	D₄	C₂×C₇×#41	1	2	yes	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	4	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	4	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	8	1	no	—
901	C₂×C₄	—	8	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
904	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
905	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
906	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
907	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
908	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
909	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
910	C₂×C₄	C₂×C₇×#41	1	2	yes	—
911	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
912	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
913	C₈	—	2	2	no	—
914	C₈	—	2	2	no	—
915	C₈	—	2	4	no	—
916	C₇	#61162	1	1	yes	characteristic, direct product factor, Sylow
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	8	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	8	8	no	—
932	C₂²	C₇×#546	1	2	yes	—
933	C₂²	C₂×C₇×#137	1	4	yes	—
934	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	4	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	C₇×#546	1	2	yes	—
948	C₄	C₂×C₇×#137	1	2	yes	—
949	C₄	C₂²×C₇×#41	1	1	yes	characteristic
950	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
951	C₂	—	2	2	no	—
952	C₂	—	2	4	no	—
953	C₂	—	4	2	no	—
954	C₂	—	4	2	no	—
955	C₂	—	8	2	no	—
956	C₂	C₂×C₇×#546	1	1	yes	characteristic
957	C₂	C₂²×C₇×#137	1	1	yes	characteristic
958	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×D₄×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#554	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3331	C₂	semidirect
5. C₇×#3316	C₂	semidirect
6. C₇×#3314	C₂	semidirect
7. C₇×#3299	C₂	semidirect
8. C₇×#3295	C₂	semidirect
9. C₇×#3141	C₂	semidirect
10. C₇×#3092	C₂	semidirect
11. C₇×#3079	C₂	semidirect
12. C₇×#3056	C₂	semidirect
13. C₇×#3037	C₂	semidirect
14. C₇×#3007	C₂	semidirect
15. C₄×C₇×#137	C₂	semidirect
16. C₇×D₄×M₁₆	C₂	semidirect
17. C₂×C₇×#417	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
21. C₂²×C₇×M₁₆	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#554	C₂²	semidirect
39. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₄×C₇×Q₈	C₂²	semidirect
50. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
51. C₇×#489	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
53. C₇×#486	C₂²	semidirect
54. C₇×#484	C₂²	semidirect
55. C₇×#483	C₂²	semidirect
56. C₇×#481	C₂²	semidirect
57. C₇×#480	C₂²	semidirect
58. C₇×#477	C₂²	semidirect
59. C₇×#476	C₂²	semidirect
60. C₇×#475	C₂²	semidirect
61. C₇×#474	C₂²	semidirect
62. C₇×#470	C₂²	semidirect
63. C₇×#468	C₂²	semidirect
64. C₇×#467	C₂²	semidirect
65. C₇×#465	C₂²	semidirect
66. C₇×#464	C₂²	semidirect
67. C₇×#462	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#452	C₂²	semidirect
70. C₇×#452	C₂²	semidirect
71. C₇×#451	C₂²	semidirect
72. C₇×#450	C₂²	semidirect
73. C₇×#441	C₂²	semidirect
74. C₇×#440	C₂²	semidirect
75. C₄×C₇×Q₁₆	C₂²	semidirect
76. C₄×C₇×SD₁₆	C₂²	semidirect
77. C₇×#436	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
80. C₇×#428	C₂²	semidirect
81. C₇×#428	C₂²	semidirect
82. C₇×#423	C₂²	semidirect
83. C₇×#419	C₂²	semidirect
86. C₇×#417	C₂²	semidirect
87. C₇×#417	C₂²	semidirect
88. C₇×#417	C₂²	semidirect
89. C₇×#417	C₂²	semidirect
90. C₇×#417	C₂²	semidirect
91. C₂×C₇×#103	C₂²	semidirect
92. C₂×C₇×#102	C₂²	semidirect
93. C₇×#407	C₂²	semidirect
94. C₄×C₇×M₁₆	C₂²	semidirect
95. #61162	C₇	direct (N × H)
234. C₂×#554	C₂×C₇	semidirect
236. #3333	C₂×C₇	semidirect
237. #3331	C₂×C₇	semidirect
238. #3316	C₂×C₇	semidirect
239. #3314	C₂×C₇	semidirect
240. #3299	C₂×C₇	semidirect
241. #3295	C₂×C₇	semidirect
242. #3141	C₂×C₇	semidirect
243. #3092	C₂×C₇	semidirect
244. #3079	C₂×C₇	semidirect
245. #3056	C₂×C₇	semidirect
246. #3037	C₂×C₇	semidirect
247. #3007	C₂×C₇	semidirect
248. C₄×#137	C₂×C₇	semidirect
249. D₄×M₁₆	C₂×C₇	semidirect
250. C₂×#417	C₂×C₇	semidirect
379. C₂×#137	C₂²×C₇	semidirect
380. C₂²×M₁₆	C₂²×C₇	semidirect
385. #554	C₂²×C₇	semidirect
386. #554	C₂²×C₇	semidirect
398. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
403. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
405. C₂×C₄×Q₈	C₂²×C₇	semidirect
409. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
410. #489	C₂²×C₇	semidirect
411. #487	C₂²×C₇	semidirect
412. #486	C₂²×C₇	semidirect
413. #484	C₂²×C₇	semidirect
414. #483	C₂²×C₇	semidirect
415. #481	C₂²×C₇	semidirect
416. #480	C₂²×C₇	semidirect
417. #477	C₂²×C₇	semidirect
418. #476	C₂²×C₇	semidirect
419. #475	C₂²×C₇	semidirect
420. #474	C₂²×C₇	semidirect
421. #470	C₂²×C₇	semidirect
422. #468	C₂²×C₇	semidirect
423. #467	C₂²×C₇	semidirect
424. #465	C₂²×C₇	semidirect
425. #464	C₂²×C₇	semidirect
426. #462	C₂²×C₇	semidirect
427. #460	C₂²×C₇	semidirect
428. #452	C₂²×C₇	semidirect
429. #452	C₂²×C₇	semidirect
430. #451	C₂²×C₇	semidirect
431. #450	C₂²×C₇	semidirect
432. #441	C₂²×C₇	semidirect
433. #440	C₂²×C₇	semidirect
434. C₄×Q₁₆	C₂²×C₇	semidirect
435. C₄×SD₁₆	C₂²×C₇	semidirect
436. #436	C₂²×C₇	semidirect
437. #435	C₂²×C₇	semidirect
439. #428	C₂²×C₇	semidirect
440. #428	C₂²×C₇	semidirect
441. #423	C₂²×C₇	semidirect
442. #419	C₂²×C₇	semidirect
445. #417	C₂²×C₇	semidirect
446. #417	C₂²×C₇	semidirect
447. #417	C₂²×C₇	semidirect
448. #417	C₂²×C₇	semidirect
449. #417	C₂²×C₇	semidirect
450. C₂×#103	C₂²×C₇	semidirect
451. C₂×#102	C₂²×C₇	semidirect
452. #407	C₂²×C₇	semidirect
453. C₄×M₁₆	C₂²×C₇	semidirect
489. C₇×D₄	#137	semidirect
873. D₄	C₇×#137	semidirect
916. C₇	#61162	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#554	2
C₇×D₄×#41	2
C₇×#3333	2
C₇×#3331	2
C₇×#3316	2
C₇×#3314	2
C₇×#3299	2
C₇×#3295	2
C₇×#3141	2
C₇×#3092	2
C₇×#3079	2
C₇×#3056	2
C₇×#3037	2
C₇×#3007	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₂×C₇×#417	2
#61162	7

Subgroups — C7×#61162 #13238378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61162 #13238378