Subgroups — C₇×#60812 #13238028

Order 1792.

2218 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3224	C₂	1	4	yes	maximal, complemented
4	C₇×#3222	C₂	1	4	yes	maximal, complemented
5	C₇×#3217	C₂	1	2	yes	maximal, complemented
6	C₇×#3215	C₂	1	2	yes	maximal, complemented
7	C₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₇×#3208	C₂	1	2	yes	maximal, complemented
9	C₇×#3154	C₂	1	2	yes	maximal, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3045	C₂	1	2	yes	maximal, complemented
12	C₇×#3043	C₂	1	2	yes	maximal, complemented
13	C₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₇×#137	C₂²	1	2	yes	complemented
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₇×#135	C₂²	1	2	yes	complemented
23	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
24	C₇×#556	—	2	1	no	—
25	C₇×#554	—	2	1	no	—
26	C₇×#552	—	2	2	no	—
27	C₇×#552	—	2	1	no	—
28	C₇×#552	—	2	1	no	—
29	C₇×#551	—	2	2	no	—
30	C₇×#544	C₂²	1	1	yes	characteristic, complemented
31	C₇×#542	C₂²	1	2	yes	complemented
32	C₇×#541	C₂²	1	2	yes	complemented
33	C₇×#536	C₂²	1	1	yes	characteristic, complemented
34	C₇×#535	—	2	1	no	—
35	C₇×#535	—	2	2	no	—
36	C₇×#535	—	2	1	no	—
37	C₇×#535	C₂²	1	4	yes	—
38	C₇×#535	C₂²	1	2	yes	—
39	C₇×#535	C₂²	1	2	yes	—
40	C₇×#533	C₂²	1	2	yes	complemented
41	C₂×C₇×#127	C₂²	1	2	yes	—
42	C₇×#529	C₂²	1	2	yes	complemented
43	C₂×C₇×#124	C₂²	1	2	yes	—
44	C₇×#525	C₂²	1	1	yes	characteristic
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×#121	—	2	1	no	—
47	C₂×C₇×#121	—	2	1	no	—
48	C₂×C₇×#120	—	2	2	no	—
49	C₇×#520	C₂²	1	1	yes	characteristic, complemented
50	C₇×#519	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₇×#117	C₂²	1	1	yes	characteristic
52	C₇×#497	C₂²	1	4	yes	complemented
53	C₇×#496	C₂²	1	4	yes	complemented
54	C₇×#495	C₂²	1	4	yes	complemented
55	C₇×#492	C₂²	1	4	yes	complemented
56	C₇×#490	C₂²	1	4	yes	complemented
57	C₇×#489	C₂²	1	4	yes	complemented
58	C₇×#488	C₂²	1	4	yes	complemented
59	C₇×#486	C₂²	1	4	yes	complemented
60	C₇×#464	C₂²	1	4	yes	complemented
61	C₇×#464	C₂²	1	4	yes	complemented
62	C₇×#464	C₂²	1	4	yes	complemented
63	C₇×#463	C₂²	1	4	yes	complemented
64	C₇×#460	C₂²	1	4	yes	complemented
65	C₇×#460	C₂²	1	4	yes	complemented
66	C₇×#460	C₂²	1	4	yes	complemented
67	C₇×#459	C₂²	1	4	yes	complemented
68	C₇×#452	C₂²	1	2	yes	complemented
69	C₇×#452	C₂²	1	4	yes	complemented
70	C₇×#451	C₂²	1	2	yes	complemented
71	C₇×#451	C₂²	1	1	yes	characteristic, complemented
72	C₇×#450	C₂²	1	2	yes	—
73	C₇×#450	C₂²	1	2	yes	—
74	C₇×#450	C₂²	1	2	yes	—
75	C₇×#450	C₂²	1	2	yes	complemented
76	C₇×#450	C₂²	1	4	yes	complemented
77	C₇×#450	C₂²	1	1	yes	characteristic, complemented
78	C₇×#450	C₂²	1	2	yes	complemented
79	C₇×#449	C₂²	1	2	yes	complemented
80	C₇×#448	C₂²	1	1	yes	characteristic, complemented
81	C₇×#447	C₂²	1	2	yes	—
82	C₇×#447	C₂²	1	2	yes	complemented
83	C₇×#447	C₂²	1	1	yes	characteristic, complemented
84	C₇×#433	C₂²	1	4	yes	complemented
85	C₇×#432	C₂²	1	2	yes	complemented
86	C₇×#431	C₂²	1	2	yes	complemented
87	C₇×#424	C₂²	1	2	yes	complemented
88	C₇×#418	C₂²	1	2	yes	complemented
89	C₇×#417	C₂²	1	2	yes	complemented
90	C₇×#416	C₂²	1	2	yes	complemented
91	C₂×C₇×#102	C₂²	1	2	yes	complemented
92	C₇×#407	C₂²	1	1	yes	characteristic
93	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₇×#405	C₂²	1	2	yes	complemented
95	#60812	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁵×C₇	—	2	1	no	—
97	C₂×C₇×#41	—	2	1	no	—
98	C₂×C₇×#41	—	2	1	no	—
99	C₂×C₇×#41	—	4	4	no	—
100	C₂×C₇×#41	C₂³	1	2	yes	—
101	C₂×C₇×#41	C₂³	1	1	yes	characteristic
102	C₂×C₇×#41	C₂³	1	2	yes	—
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×D₄	—	2	1	no	—
106	C₂²×C₇×D₄	—	2	1	no	—
107	C₂²×C₇×D₄	—	2	1	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	—	2	2	no	—
110	C₂²×C₇×D₄	—	2	2	no	—
111	C₂²×C₇×D₄	—	4	4	no	—
112	C₂²×C₇×D₄	C₂³	1	2	yes	—
113	C₂²×C₇×D₄	C₂³	1	2	yes	—
114	C₂²×C₇×D₄	C₂³	1	2	yes	—
115	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	—	2	1	no	—
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₇×#137	—	4	4	no	—
119	C₇×AGL(1,ℤ/8)	—	4	4	no	—
120	C₇×#135	—	4	4	no	—
121	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
122	C₂×C₇×Q₁₆	C₂³	1	2	yes	complemented
123	C₂×C₇×SD₁₆	—	4	4	no	—
124	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
126	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₇×SD₁₆	C₂³	1	2	yes	complemented
128	C₂×C₇×SD₁₆	C₂³	1	4	yes	complemented
129	C₂×C₇×SD₁₆	C₂³	1	2	yes	complemented
130	C₂×C₇×D₈	C₂³	1	4	yes	—
131	C₂×C₇×D₈	C₂³	1	2	yes	complemented
132	C₂×C₇×M₁₆	C₂³	1	2	yes	—
133	C₂²×C₇×C₈	C₂³	1	2	yes	—
134	C₇×C₄⋊Q₈	—	2	1	no	—
135	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
137	C₇×#127	—	2	2	no	—
138	C₇×#127	—	2	2	no	—
139	C₇×#127	C₂³	1	4	yes	—
140	C₇×#127	C₂³	1	4	yes	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#125	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	—	2	1	no	—
148	C₇×#125	—	2	2	no	—
149	C₇×#125	C₂³	1	2	yes	complemented
150	C₇×#124	—	2	2	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	—	2	2	no	—
153	C₇×#124	C₂³	1	4	yes	—
154	C₇×#124	C₂³	1	4	yes	—
155	C₇×#124	C₂³	1	2	yes	complemented
156	C₇×#123	—	2	1	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×#123	—	2	2	no	—
160	C₇×C₂²⋊Q₈	—	2	1	no	—
161	C₇×C₂²⋊Q₈	—	2	1	no	—
162	C₇×C₂²⋊Q₈	—	2	2	no	—
163	C₇×C₂²⋊Q₈	—	2	1	no	—
164	C₇×C₂²⋊Q₈	—	2	1	no	—
165	C₇×C₂²⋊Q₈	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	no	—
167	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×#121	—	2	2	no	—
172	C₇×#121	—	2	2	no	—
173	C₇×#121	—	2	4	no	—
174	C₇×#121	—	2	2	no	—
175	C₇×#121	—	2	2	no	—
176	C₇×#121	—	2	4	no	—
177	C₇×#121	C₂³	1	1	yes	characteristic
178	C₇×#121	C₂³	1	1	yes	characteristic
179	C₇×#120	—	2	1	no	—
180	C₇×#120	—	2	4	no	—
181	C₇×#120	—	2	4	no	—
182	C₇×#120	—	2	4	no	—
183	C₇×#120	—	2	4	no	—
184	C₄×C₇×Q₈	—	2	1	no	—
185	C₄×C₇×Q₈	—	2	1	no	—
186	C₄×C₇×Q₈	—	2	2	no	—
187	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
188	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
189	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
190	C₄×C₇×D₄	—	2	1	no	—
191	C₄×C₇×D₄	—	2	1	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	—	2	2	no	—
194	C₄×C₇×D₄	C₂³	1	2	yes	complemented
195	C₇×#117	—	2	2	no	—
196	C₇×#117	—	2	1	no	—
197	C₇×#117	—	2	2	no	—
198	C₇×#117	—	2	2	no	—
199	C₇×#117	D₄	1	1	yes	characteristic
200	C₇×#117	D₄	1	2	yes	—
201	C₇×#117	D₄	1	1	yes	characteristic
202	C₇×#117	C₂³	1	1	yes	characteristic
203	C₇×#117	C₂³	1	1	yes	characteristic
204	C₇×#117	C₂³	1	1	yes	characteristic
205	C₇×#117	C₂³	1	2	yes	—
206	C₂×C₇×C₄⋊C₄	—	2	1	no	—
207	C₂×C₇×C₄⋊C₄	—	2	1	no	—
208	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
209	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
210	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
214	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
218	C₇×#103	C₂³	1	2	yes	complemented
219	C₇×#103	C₂³	1	4	yes	complemented
220	C₇×#103	C₂³	1	2	yes	complemented
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	4	yes	—
225	C₇×#102	C₂³	1	2	yes	complemented
226	C₇×#102	C₂³	1	4	yes	complemented
227	C₇×#102	C₂³	1	2	yes	complemented
228	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
230	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₇×#97	C₂³	1	4	yes	complemented
234	C₄×C₇×C₈	C₂³	1	4	yes	complemented
235	#3495	C₂×C₇	1	1	yes	characteristic, complemented
236	C₂×#535	C₂×C₇	1	1	yes	characteristic, complemented
237	#3224	C₂×C₇	1	4	yes	complemented
238	#3222	C₂×C₇	1	4	yes	complemented
239	#3217	C₂×C₇	1	2	yes	complemented
240	#3215	C₂×C₇	1	2	yes	complemented
241	#3211	C₂×C₇	1	2	yes	complemented
242	#3208	C₂×C₇	1	2	yes	complemented
243	#3154	C₂×C₇	1	2	yes	complemented
244	#3136	C₂×C₇	1	2	yes	complemented
245	#3045	C₂×C₇	1	2	yes	complemented
246	#3043	C₂×C₇	1	2	yes	complemented
247	#3007	C₂×C₇	1	1	yes	characteristic, complemented
248	#3003	C₂×C₇	1	1	yes	characteristic, complemented
249	#3002	C₂×C₇	1	1	yes	characteristic, complemented
250	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
251	#2924	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂⁴×C₇	—	2	2	no	—
253	C₂⁴×C₇	—	2	1	no	—
254	C₂⁴×C₇	—	2	2	no	—
255	C₂⁴×C₇	—	2	2	no	—
256	C₂⁴×C₇	—	4	4	no	—
257	C₂⁴×C₇	—	8	2	no	—
258	C₂⁴×C₇	—	8	2	no	—
259	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
260	C₇×#41	—	2	4	no	—
261	C₇×#41	—	2	4	no	—
262	C₇×#41	—	2	4	no	—
263	C₇×#41	—	4	2	no	—
264	C₇×#41	—	4	2	no	—
265	C₇×#41	—	4	4	no	—
266	C₇×#41	—	4	4	no	—
267	C₂×C₇×Q₈	—	2	1	no	—
268	C₂×C₇×Q₈	—	2	1	no	—
269	C₂×C₇×Q₈	—	2	2	no	—
270	C₂×C₇×Q₈	—	2	4	no	—
271	C₂×C₇×Q₈	—	4	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	1	no	—
277	C₂×C₇×D₄	—	2	2	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	1	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	4	no	—
285	C₂×C₇×D₄	—	2	4	no	—
286	C₂×C₇×D₄	—	2	4	no	—
287	C₂×C₇×D₄	—	2	4	no	—
288	C₂×C₇×D₄	—	2	4	no	—
289	C₂×C₇×D₄	—	2	4	no	—
290	C₂×C₇×D₄	—	4	4	no	—
291	C₂×C₇×D₄	—	4	4	no	—
292	C₂×C₇×D₄	—	4	2	no	—
293	C₂×C₇×D₄	—	4	4	no	—
294	C₂×C₇×D₄	—	4	4	no	—
295	C₂×C₇×D₄	—	4	4	no	—
296	C₂×C₇×D₄	—	4	4	no	—
297	C₂×C₇×D₄	—	8	4	no	—
298	C₂×C₇×D₄	—	8	4	no	—
299	C₂×C₇×D₄	C₂⁴	1	4	yes	—
300	C₂×C₇×D₄	C₂⁴	1	2	yes	—
301	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₇	—	2	4	no	—
303	C₂²×C₄×C₇	—	2	1	no	—
304	C₂²×C₄×C₇	—	2	1	no	—
305	C₂²×C₄×C₇	—	2	1	no	—
306	C₂²×C₄×C₇	—	2	1	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	2	no	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	4	4	no	—
311	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
312	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₇×Q₁₆	—	4	2	no	—
320	C₇×Q₁₆	—	4	4	no	—
321	C₇×SD₁₆	—	4	4	no	—
322	C₇×SD₁₆	—	4	4	no	—
323	C₇×SD₁₆	—	4	4	no	—
324	C₇×SD₁₆	—	4	2	no	—
325	C₇×SD₁₆	—	4	2	no	—
326	C₇×SD₁₆	—	4	4	no	—
327	C₇×D₈	—	4	4	no	—
328	C₇×D₈	—	4	2	no	—
329	C₇×M₁₆	—	2	4	no	—
330	C₂×C₇×C₈	—	2	4	no	—
331	C₂×C₇×C₈	C₂⁴	1	2	yes	—
332	C₂×C₇×C₈	C₂⁴	1	4	yes	—
333	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	1	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	1	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
348	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
349	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
350	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
351	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
352	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
353	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
354	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
355	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	1	no	—
359	C₇×C₂²⋊C₄	—	2	1	no	—
360	C₇×C₂²⋊C₄	—	2	1	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	4	no	—
363	C₇×C₂²⋊C₄	—	2	4	no	—
364	C₇×C₂²⋊C₄	—	2	4	no	—
365	C₇×C₂²⋊C₄	—	2	1	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	1	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
371	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
372	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
373	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
374	C₄²×C₇	—	2	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	2	no	—
377	C₄²×C₇	—	2	1	no	—
378	C₄²×C₇	C₂×D₄	1	2	yes	—
379	C₄²×C₇	C₂×D₄	1	2	yes	—
380	C₄²×C₇	C₂⁴	1	2	yes	—
381	C₄²×C₇	C₂⁴	1	2	yes	—
382	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
383	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
384	C₂×#137	C₂²×C₇	1	2	yes	complemented
385	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
386	C₂×#135	C₂²×C₇	1	2	yes	complemented
387	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
388	#556	—	2	1	no	—
389	#554	—	2	1	no	—
390	#552	—	2	2	no	—
391	#552	—	2	1	no	—
392	#552	—	2	1	no	—
393	#551	—	2	2	no	—
394	#544	C₂²×C₇	1	1	yes	characteristic, complemented
395	#542	C₂²×C₇	1	2	yes	complemented
396	#541	C₂²×C₇	1	2	yes	complemented
397	#536	C₂²×C₇	1	1	yes	characteristic, complemented
398	#535	—	2	1	no	—
399	#535	—	2	2	no	—
400	#535	—	2	1	no	—
401	#535	C₂²×C₇	1	2	yes	—
402	#535	C₂²×C₇	1	4	yes	—
403	#535	C₂²×C₇	1	2	yes	—
404	#533	C₂²×C₇	1	2	yes	complemented
405	C₂×#127	C₂²×C₇	1	2	yes	—
406	#529	C₂²×C₇	1	2	yes	complemented
407	C₂×#124	C₂²×C₇	1	2	yes	—
408	#525	C₂²×C₇	1	1	yes	characteristic
409	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
410	C₂×#121	—	2	1	no	—
411	C₂×#121	—	2	1	no	—
412	C₂×#120	—	2	2	no	—
413	#520	C₂²×C₇	1	1	yes	characteristic, complemented
414	#519	C₂²×C₇	1	1	yes	characteristic, complemented
415	C₂×#117	C₂²×C₇	1	1	yes	characteristic
416	#497	C₂²×C₇	1	4	yes	complemented
417	#496	C₂²×C₇	1	4	yes	complemented
418	#495	C₂²×C₇	1	4	yes	complemented
419	#492	C₂²×C₇	1	4	yes	complemented
420	#490	C₂²×C₇	1	4	yes	complemented
421	#489	C₂²×C₇	1	4	yes	complemented
422	#488	C₂²×C₇	1	4	yes	complemented
423	#486	C₂²×C₇	1	4	yes	complemented
424	#464	C₂²×C₇	1	4	yes	complemented
425	#464	C₂²×C₇	1	4	yes	complemented
426	#464	C₂²×C₇	1	4	yes	complemented
427	#463	C₂²×C₇	1	4	yes	complemented
428	#460	C₂²×C₇	1	4	yes	complemented
429	#460	C₂²×C₇	1	4	yes	complemented
430	#460	C₂²×C₇	1	4	yes	complemented
431	#459	C₂²×C₇	1	4	yes	complemented
432	#452	C₂²×C₇	1	2	yes	complemented
433	#452	C₂²×C₇	1	4	yes	complemented
434	#451	C₂²×C₇	1	2	yes	complemented
435	#451	C₂²×C₇	1	1	yes	characteristic, complemented
436	#450	C₂²×C₇	1	2	yes	—
437	#450	C₂²×C₇	1	2	yes	—
438	#450	C₂²×C₇	1	2	yes	—
439	#450	C₂²×C₇	1	2	yes	complemented
440	#450	C₂²×C₇	1	4	yes	complemented
441	#450	C₂²×C₇	1	1	yes	characteristic, complemented
442	#450	C₂²×C₇	1	2	yes	complemented
443	#449	C₂²×C₇	1	2	yes	complemented
444	#448	C₂²×C₇	1	1	yes	characteristic, complemented
445	#447	C₂²×C₇	1	2	yes	—
446	#447	C₂²×C₇	1	2	yes	complemented
447	#447	C₂²×C₇	1	1	yes	characteristic, complemented
448	#433	C₂²×C₇	1	4	yes	complemented
449	#432	C₂²×C₇	1	2	yes	complemented
450	#431	C₂²×C₇	1	2	yes	complemented
451	#424	C₂²×C₇	1	2	yes	complemented
452	#418	C₂²×C₇	1	2	yes	complemented
453	#417	C₂²×C₇	1	2	yes	complemented
454	#416	C₂²×C₇	1	2	yes	complemented
455	C₂×#102	C₂²×C₇	1	2	yes	complemented
456	#407	C₂²×C₇	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
458	#405	C₂²×C₇	1	2	yes	complemented
459	C₂³×C₇	—	2	2	no	—
460	C₂³×C₇	—	2	2	no	—
461	C₂³×C₇	—	2	1	no	—
462	C₂³×C₇	—	2	4	no	—
463	C₂³×C₇	—	2	2	no	—
464	C₂³×C₇	—	4	1	no	—
465	C₂³×C₇	—	4	2	no	—
466	C₂³×C₇	—	4	4	no	—
467	C₂³×C₇	—	4	4	no	—
468	C₂³×C₇	—	4	2	no	—
469	C₂³×C₇	—	4	4	no	—
470	C₂³×C₇	—	4	4	no	—
471	C₂³×C₇	—	4	2	no	—
472	C₂³×C₇	—	4	4	no	—
473	C₂³×C₇	—	8	2	no	—
474	C₂³×C₇	—	8	2	no	—
475	C₂³×C₇	—	8	2	no	—
476	C₂³×C₇	—	8	2	no	—
477	C₂³×C₇	—	8	16	no	—
478	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
480	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₇×Q₈	—	2	4	no	—
482	C₇×Q₈	—	2	2	no	—
483	C₇×Q₈	—	2	2	no	—
484	C₇×Q₈	—	2	2	no	—
485	C₇×Q₈	—	4	2	no	—
486	C₇×Q₈	—	4	2	no	—
487	C₇×Q₈	—	8	2	no	—
488	C₇×D₄	—	2	2	no	—
489	C₇×D₄	—	2	4	no	—
490	C₇×D₄	—	2	2	no	—
491	C₇×D₄	—	2	4	no	—
492	C₇×D₄	—	2	2	no	—
493	C₇×D₄	—	4	4	no	—
494	C₇×D₄	—	4	4	no	—
495	C₇×D₄	—	4	2	no	—
496	C₇×D₄	—	4	4	no	—
497	C₇×D₄	—	4	4	no	—
498	C₇×D₄	—	4	2	no	—
499	C₇×D₄	—	4	2	no	—
500	C₇×D₄	—	4	4	no	—
501	C₇×D₄	—	8	4	no	—
502	C₇×D₄	—	8	4	no	—
503	C₇×D₄	—	8	4	no	—
504	C₇×D₄	—	8	4	no	—
505	C₇×D₄	—	8	1	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	2	4	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	4	2	no	—
519	C₂×C₄×C₇	—	4	4	no	—
520	C₂×C₄×C₇	—	4	2	no	—
521	C₂×C₄×C₇	—	4	2	no	—
522	C₂×C₄×C₇	—	4	4	no	—
523	C₂×C₄×C₇	—	4	2	no	—
524	C₂×C₄×C₇	—	8	2	no	—
525	C₂×C₄×C₇	—	8	1	no	—
526	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
534	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
535	C₇×C₈	—	2	2	no	—
536	C₇×C₈	—	2	2	no	—
537	C₇×C₈	—	2	4	no	—
538	C₂⁵	—	2	1	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	4	4	no	—
542	C₂×#41	C₂³×C₇	1	1	yes	characteristic
543	C₂×#41	C₂³×C₇	1	2	yes	—
544	C₂×#41	C₂³×C₇	1	2	yes	—
545	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	4	4	no	—
554	C₂²×D₄	C₂³×C₇	1	2	yes	—
555	C₂²×D₄	C₂³×C₇	1	2	yes	—
556	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₇	1	2	yes	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
560	#137	—	4	4	no	—
561	AGL(1,ℤ/8)	—	4	4	no	—
562	#135	—	4	4	no	—
563	C₂×Q₁₆	C₂³×C₇	1	2	yes	complemented
564	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
565	C₂×SD₁₆	—	4	4	no	—
566	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
568	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
569	C₂×SD₁₆	C₂³×C₇	1	2	yes	complemented
570	C₂×SD₁₆	C₂³×C₇	1	2	yes	complemented
571	C₂×SD₁₆	C₂³×C₇	1	4	yes	complemented
572	C₂×D₈	C₂³×C₇	1	4	yes	—
573	C₂×D₈	C₂³×C₇	1	2	yes	complemented
574	C₂×M₁₆	C₂³×C₇	1	2	yes	—
575	C₂²×C₈	C₂³×C₇	1	2	yes	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
578	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
579	#127	—	2	2	no	—
580	#127	—	2	2	no	—
581	#127	C₂³×C₇	1	4	yes	—
582	#127	C₂³×C₇	1	4	yes	—
583	#126	—	2	2	no	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#125	—	2	2	no	—
588	#125	—	2	2	no	—
589	#125	—	2	1	no	—
590	#125	—	2	2	no	—
591	#125	C₂³×C₇	1	2	yes	complemented
592	#124	—	2	2	no	—
593	#124	—	2	2	no	—
594	#124	—	2	2	no	—
595	#124	C₂³×C₇	1	4	yes	—
596	#124	C₂³×C₇	1	4	yes	—
597	#124	C₂³×C₇	1	2	yes	complemented
598	#123	—	2	1	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	1	no	—
604	C₂²⋊Q₈	—	2	2	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
612	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	2	no	—
616	#121	—	2	4	no	—
617	#121	—	2	2	no	—
618	#121	—	2	4	no	—
619	#121	C₂³×C₇	1	1	yes	characteristic
620	#121	C₂³×C₇	1	1	yes	characteristic
621	#120	—	2	1	no	—
622	#120	—	2	4	no	—
623	#120	—	2	4	no	—
624	#120	—	2	4	no	—
625	#120	—	2	4	no	—
626	C₄×Q₈	—	2	1	no	—
627	C₄×Q₈	—	2	1	no	—
628	C₄×Q₈	—	2	2	no	—
629	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
630	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
631	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	C₂³×C₇	1	2	yes	complemented
637	#117	—	2	2	no	—
638	#117	—	2	1	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	C₇×D₄	1	1	yes	characteristic
642	#117	C₇×D₄	1	2	yes	—
643	#117	C₇×D₄	1	1	yes	characteristic
644	#117	C₂³×C₇	1	1	yes	characteristic
645	#117	C₂³×C₇	1	1	yes	characteristic
646	#117	C₂³×C₇	1	1	yes	characteristic
647	#117	C₂³×C₇	1	2	yes	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	2	no	—
655	C₂×C₂²⋊C₄	—	2	2	no	—
656	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
657	C₂×C₄²	C₂³×C₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
659	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
660	#103	C₂³×C₇	1	2	yes	complemented
661	#103	C₂³×C₇	1	2	yes	complemented
662	#103	C₂³×C₇	1	4	yes	complemented
663	#102	C₂³×C₇	1	4	yes	—
664	#102	C₂³×C₇	1	4	yes	—
665	#102	C₂³×C₇	1	4	yes	—
666	#102	C₂³×C₇	1	4	yes	—
667	#102	C₂³×C₇	1	2	yes	complemented
668	#102	C₂³×C₇	1	2	yes	complemented
669	#102	C₂³×C₇	1	4	yes	complemented
670	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
671	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
672	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
675	#97	C₂³×C₇	1	4	yes	complemented
676	C₄×C₈	C₂³×C₇	1	4	yes	complemented
677	C₂²×C₇	—	2	1	no	—
678	C₂²×C₇	—	2	1	no	—
679	C₂²×C₇	—	2	1	no	—
680	C₂²×C₇	—	2	1	no	—
681	C₂²×C₇	—	2	1	no	—
682	C₂²×C₇	—	2	1	no	—
683	C₂²×C₇	—	2	1	no	—
684	C₂²×C₇	—	4	4	no	—
685	C₂²×C₇	—	4	1	no	—
686	C₂²×C₇	—	4	2	no	—
687	C₂²×C₇	—	4	4	no	—
688	C₂²×C₇	—	4	2	no	—
689	C₂²×C₇	—	4	1	no	—
690	C₂²×C₇	—	4	4	no	—
691	C₂²×C₇	—	4	1	no	—
692	C₂²×C₇	—	4	2	no	—
693	C₂²×C₇	—	4	4	no	—
694	C₂²×C₇	—	8	4	no	—
695	C₂²×C₇	—	8	8	no	—
696	C₂²×C₇	—	8	8	no	—
697	C₂²×C₇	—	8	8	no	—
698	C₂²×C₇	#535	1	2	yes	—
699	C₂²×C₇	#577	1	2	yes	—
700	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
701	C₄×C₇	—	2	2	no	—
702	C₄×C₇	—	2	2	no	—
703	C₄×C₇	—	2	1	no	—
704	C₄×C₇	—	2	1	no	—
705	C₄×C₇	—	2	2	no	—
706	C₄×C₇	—	2	2	no	—
707	C₄×C₇	—	4	2	no	—
708	C₄×C₇	—	4	1	no	—
709	C₄×C₇	—	4	2	no	—
710	C₄×C₇	—	4	1	no	—
711	C₄×C₇	—	4	2	no	—
712	C₄×C₇	—	4	1	no	—
713	C₄×C₇	#535	1	2	yes	—
714	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
715	C₂⁴	—	2	2	no	—
716	C₂⁴	—	2	1	no	—
717	C₂⁴	—	2	2	no	—
718	C₂⁴	—	2	2	no	—
719	C₂⁴	—	4	4	no	—
720	C₂⁴	—	8	2	no	—
721	C₂⁴	—	8	2	no	—
722	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
723	#41	—	2	4	no	—
724	#41	—	2	4	no	—
725	#41	—	2	4	no	—
726	#41	—	4	2	no	—
727	#41	—	4	2	no	—
728	#41	—	4	4	no	—
729	#41	—	4	4	no	—
730	C₂×Q₈	—	2	1	no	—
731	C₂×Q₈	—	2	1	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
736	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
737	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	2	4	no	—
750	C₂×D₄	—	2	4	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	4	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	4	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	4	4	no	—
760	C₂×D₄	—	8	4	no	—
761	C₂×D₄	—	8	4	no	—
762	C₂×D₄	C₂⁴×C₇	1	4	yes	—
763	C₂×D₄	C₂⁴×C₇	1	2	yes	—
764	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
765	C₂²×C₄	—	2	4	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	4	4	no	—
774	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
775	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
776	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
777	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
778	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
782	Q₁₆	—	4	2	no	—
783	Q₁₆	—	4	4	no	—
784	SD₁₆	—	4	4	no	—
785	SD₁₆	—	4	4	no	—
786	SD₁₆	—	4	4	no	—
787	SD₁₆	—	4	2	no	—
788	SD₁₆	—	4	2	no	—
789	SD₁₆	—	4	4	no	—
790	D₈	—	4	4	no	—
791	D₈	—	4	2	no	—
792	M₁₆	—	2	4	no	—
793	C₂×C₈	—	2	4	no	—
794	C₂×C₈	C₂⁴×C₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₇	1	4	yes	—
796	C₂×C₈	C₂⁴×C₇	1	2	yes	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
811	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
812	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
813	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
814	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
815	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
818	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	1	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	1	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
834	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
835	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
836	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	1	no	—
841	C₄²	C₂×C₇×D₄	1	2	yes	—
842	C₄²	C₂×C₇×D₄	1	2	yes	—
843	C₄²	C₂⁴×C₇	1	2	yes	—
844	C₄²	C₂⁴×C₇	1	2	yes	—
845	C₂×C₇	—	2	2	no	—
846	C₂×C₇	—	2	2	no	—
847	C₂×C₇	—	4	1	no	—
848	C₂×C₇	—	8	1	no	—
849	C₂×C₇	—	8	2	no	—
850	C₂×C₇	—	8	4	no	—
851	C₂×C₇	C₂×#535	1	1	yes	characteristic
852	C₂×C₇	C₂×#577	1	1	yes	characteristic
853	C₂×C₇	#3585	1	1	yes	characteristic
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	2	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	2	no	—
870	C₂³	—	8	2	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	16	no	—
873	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
874	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
875	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
876	Q₈	—	2	4	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	4	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	8	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	4	no	—
887	D₄	—	2	2	no	—
888	D₄	—	4	4	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	2	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	4	no	—
896	D₄	—	8	4	no	—
897	D₄	—	8	4	no	—
898	D₄	—	8	4	no	—
899	D₄	—	8	4	no	—
900	D₄	—	8	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	4	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	2	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	4	2	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
922	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
923	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
924	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
925	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
926	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
927	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
928	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
929	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	4	no	—
933	C₇	#60812	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	4	4	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	8	8	no	—
952	C₂²	—	8	4	no	—
953	C₂²	—	8	8	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₇×#535	1	2	yes	—
956	C₂²	C₇×#577	1	2	yes	—
957	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	C₇×#535	1	2	yes	—
971	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
972	C₂	—	2	2	no	—
973	C₂	—	2	2	no	—
974	C₂	—	4	1	no	—
975	C₂	—	8	4	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	1	no	—
978	C₂	C₂×C₇×#535	1	1	yes	characteristic
979	C₂	C₂×C₇×#577	1	1	yes	characteristic
980	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 ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
2. C₂×C₇×#535	C₂	semidirect
3. C₇×#3224	C₂	semidirect
4. C₇×#3222	C₂	semidirect
5. C₇×#3217	C₂	semidirect
6. C₇×#3215	C₂	semidirect
7. C₇×#3211	C₂	semidirect
8. C₇×#3208	C₂	semidirect
9. C₇×#3154	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3045	C₂	semidirect
12. C₇×#3043	C₂	semidirect
13. C₇×#3007	C₂	semidirect
14. C₇×#3003	C₂	semidirect
15. C₇×#3002	C₂	semidirect
16. C₂×C₇×#450	C₂	semidirect
17. C₇×#2924	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₇×#135	C₂²	semidirect
23. C₂²×C₇×SD₁₆	C₂²	semidirect
30. C₇×#544	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
32. C₇×#541	C₂²	semidirect
33. C₇×#536	C₂²	semidirect
40. C₇×#533	C₂²	semidirect
42. C₇×#529	C₂²	semidirect
49. C₇×#520	C₂²	semidirect
50. C₇×#519	C₂²	semidirect
52. C₇×#497	C₂²	semidirect
53. C₇×#496	C₂²	semidirect
54. C₇×#495	C₂²	semidirect
55. C₇×#492	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#489	C₂²	semidirect
58. C₇×#488	C₂²	semidirect
59. C₇×#486	C₂²	semidirect
60. C₇×#464	C₂²	semidirect
61. C₇×#464	C₂²	semidirect
62. C₇×#464	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#460	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#459	C₂²	semidirect
68. C₇×#452	C₂²	semidirect
69. C₇×#452	C₂²	semidirect
70. C₇×#451	C₂²	semidirect
71. C₇×#451	C₂²	semidirect
75. C₇×#450	C₂²	semidirect
76. C₇×#450	C₂²	semidirect
77. C₇×#450	C₂²	semidirect
78. C₇×#450	C₂²	semidirect
79. C₇×#449	C₂²	semidirect
80. C₇×#448	C₂²	semidirect
82. C₇×#447	C₂²	semidirect
83. C₇×#447	C₂²	semidirect
84. C₇×#433	C₂²	semidirect
85. C₇×#432	C₂²	semidirect
86. C₇×#431	C₂²	semidirect
87. C₇×#424	C₂²	semidirect
88. C₇×#418	C₂²	semidirect
89. C₇×#417	C₂²	semidirect
90. C₇×#416	C₂²	semidirect
91. C₂×C₇×#102	C₂²	semidirect
94. C₇×#405	C₂²	semidirect
95. #60812	C₇	direct (N × H)
121. C₂×C₇×Q₁₆	C₂³	semidirect
122. C₂×C₇×Q₁₆	C₂³	semidirect
127. C₂×C₇×SD₁₆	C₂³	semidirect
128. C₂×C₇×SD₁₆	C₂³	semidirect
129. C₂×C₇×SD₁₆	C₂³	semidirect
131. C₂×C₇×D₈	C₂³	semidirect
135. C₇×C₄⋊Q₈	C₂³	semidirect
136. C₇×C₄⋊Q₈	C₂³	semidirect
149. C₇×#125	C₂³	semidirect
155. C₇×#124	C₂³	semidirect
187. C₄×C₇×Q₈	C₂³	semidirect
188. C₄×C₇×Q₈	C₂³	semidirect
189. C₄×C₇×Q₈	C₂³	semidirect
194. C₄×C₇×D₄	C₂³	semidirect
216. C₇×C₄⋊C₈	C₂³	semidirect
217. C₇×C₄⋊C₈	C₂³	semidirect
218. C₇×#103	C₂³	semidirect
219. C₇×#103	C₂³	semidirect
220. C₇×#103	C₂³	semidirect
225. C₇×#102	C₂³	semidirect
226. C₇×#102	C₂³	semidirect
227. C₇×#102	C₂³	semidirect
233. C₇×#97	C₂³	semidirect
234. C₄×C₇×C₈	C₂³	semidirect
235. #3495	C₂×C₇	semidirect
236. C₂×#535	C₂×C₇	semidirect
237. #3224	C₂×C₇	semidirect
238. #3222	C₂×C₇	semidirect
239. #3217	C₂×C₇	semidirect
240. #3215	C₂×C₇	semidirect
241. #3211	C₂×C₇	semidirect
242. #3208	C₂×C₇	semidirect
243. #3154	C₂×C₇	semidirect
244. #3136	C₂×C₇	semidirect
245. #3045	C₂×C₇	semidirect
246. #3043	C₂×C₇	semidirect
247. #3007	C₂×C₇	semidirect
248. #3003	C₂×C₇	semidirect
249. #3002	C₂×C₇	semidirect
250. C₂×#450	C₂×C₇	semidirect
251. #2924	C₂×C₇	semidirect
384. C₂×#137	C₂²×C₇	semidirect
385. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
386. C₂×#135	C₂²×C₇	semidirect
387. C₂²×SD₁₆	C₂²×C₇	semidirect
394. #544	C₂²×C₇	semidirect
395. #542	C₂²×C₇	semidirect
396. #541	C₂²×C₇	semidirect
397. #536	C₂²×C₇	semidirect
404. #533	C₂²×C₇	semidirect
406. #529	C₂²×C₇	semidirect
413. #520	C₂²×C₇	semidirect
414. #519	C₂²×C₇	semidirect
416. #497	C₂²×C₇	semidirect
417. #496	C₂²×C₇	semidirect
418. #495	C₂²×C₇	semidirect
419. #492	C₂²×C₇	semidirect
420. #490	C₂²×C₇	semidirect
421. #489	C₂²×C₇	semidirect
422. #488	C₂²×C₇	semidirect
423. #486	C₂²×C₇	semidirect
424. #464	C₂²×C₇	semidirect
425. #464	C₂²×C₇	semidirect
426. #464	C₂²×C₇	semidirect
427. #463	C₂²×C₇	semidirect
428. #460	C₂²×C₇	semidirect
429. #460	C₂²×C₇	semidirect
430. #460	C₂²×C₇	semidirect
431. #459	C₂²×C₇	semidirect
432. #452	C₂²×C₇	semidirect
433. #452	C₂²×C₇	semidirect
434. #451	C₂²×C₇	semidirect
435. #451	C₂²×C₇	semidirect
439. #450	C₂²×C₇	semidirect
440. #450	C₂²×C₇	semidirect
441. #450	C₂²×C₇	semidirect
442. #450	C₂²×C₇	semidirect
443. #449	C₂²×C₇	semidirect
444. #448	C₂²×C₇	semidirect
446. #447	C₂²×C₇	semidirect
447. #447	C₂²×C₇	semidirect
448. #433	C₂²×C₇	semidirect
449. #432	C₂²×C₇	semidirect
450. #431	C₂²×C₇	semidirect
451. #424	C₂²×C₇	semidirect
452. #418	C₂²×C₇	semidirect
453. #417	C₂²×C₇	semidirect
454. #416	C₂²×C₇	semidirect
455. C₂×#102	C₂²×C₇	semidirect
458. #405	C₂²×C₇	semidirect
563. C₂×Q₁₆	C₂³×C₇	semidirect
564. C₂×Q₁₆	C₂³×C₇	semidirect
569. C₂×SD₁₆	C₂³×C₇	semidirect
570. C₂×SD₁₆	C₂³×C₇	semidirect
571. C₂×SD₁₆	C₂³×C₇	semidirect
573. C₂×D₈	C₂³×C₇	semidirect
577. C₄⋊Q₈	C₂³×C₇	semidirect
578. C₄⋊Q₈	C₂³×C₇	semidirect
591. #125	C₂³×C₇	semidirect
597. #124	C₂³×C₇	semidirect
629. C₄×Q₈	C₂³×C₇	semidirect
630. C₄×Q₈	C₂³×C₇	semidirect
631. C₄×Q₈	C₂³×C₇	semidirect
636. C₄×D₄	C₂³×C₇	semidirect
658. C₄⋊C₈	C₂³×C₇	semidirect
659. C₄⋊C₈	C₂³×C₇	semidirect
660. #103	C₂³×C₇	semidirect
661. #103	C₂³×C₇	semidirect
662. #103	C₂³×C₇	semidirect
667. #102	C₂³×C₇	semidirect
668. #102	C₂³×C₇	semidirect
669. #102	C₂³×C₇	semidirect
675. #97	C₂³×C₇	semidirect
676. C₄×C₈	C₂³×C₇	semidirect
933. C₇	#60812	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×#3495	2
C₂×C₇×#535	2
C₇×#3224	2
C₇×#3222	2
C₇×#3217	2
C₇×#3215	2
C₇×#3211	2
C₇×#3208	2
C₇×#3154	2
C₇×#3136	2
C₇×#3045	2
C₇×#3043	2
C₇×#3007	2
C₇×#3003	2
C₇×#3002	2
C₂×C₇×#450	2
C₇×#2924	2
#60812	7

Subgroups — C7×#60812 #13238028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60812 #13238028