Subgroups — C₇×#60233 #13237449

Order 1792.

2298 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₇×#2977	C₂	1	4	yes	maximal, complemented
3	C₇×#2976	C₂	1	4	yes	maximal, complemented
4	C₇×#2974	C₂	1	4	yes	maximal, complemented
5	C₇×#2973	C₂	1	2	yes	maximal, complemented
6	C₇×#2972	C₂	1	2	yes	maximal, complemented
7	C₇×#2933	C₂	1	4	yes	maximal, complemented
8	C₇×#2929	C₂	1	4	yes	maximal, complemented
9	C₇×#2924	C₂	1	2	yes	maximal, complemented
10	C₇×#2880	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#407	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂×C₇×#131	C₂²	1	4	yes	complemented
16	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
17	C₂³×C₇×C₈	C₂²	1	2	yes	complemented
18	C₇×#525	C₄	1	2	yes	—
19	C₇×#525	C₄	1	2	yes	—
20	C₇×#525	C₄	1	2	yes	—
21	C₇×#525	C₄	1	2	yes	—
22	C₇×#525	C₂²	1	2	yes	—
23	C₇×#525	C₂²	1	2	yes	—
24	C₇×#525	C₂²	1	2	yes	—
25	C₇×#525	C₂²	1	2	yes	—
26	C₂×C₇×#123	C₄	1	2	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
29	C₂×C₇×#121	C₄	1	1	yes	characteristic
30	C₂×C₇×#121	C₄	1	1	yes	characteristic
31	C₂×C₇×#120	C₄	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₂×C₇×#117	C₂²	1	1	yes	characteristic
35	C₇×#436	C₂²	1	8	yes	complemented
36	C₇×#435	C₂²	1	8	yes	complemented
37	C₇×#435	C₂²	1	8	yes	complemented
38	C₇×#435	C₂²	1	8	yes	complemented
39	C₇×#435	C₂²	1	8	yes	complemented
40	C₇×C₈×D₄	C₂²	1	8	yes	complemented
41	C₇×C₈×D₄	C₂²	1	8	yes	complemented
42	C₇×C₈×D₄	C₂²	1	8	yes	complemented
43	C₇×#433	C₂²	1	8	yes	complemented
44	C₇×#432	C₂²	1	4	yes	complemented
45	C₇×#431	C₂²	1	4	yes	complemented
46	C₇×#424	C₂²	1	4	yes	complemented
47	C₇×#408	C₂²	1	8	yes	complemented
48	C₇×#408	C₂²	1	4	yes	complemented
49	C₇×#407	C₂²	1	2	yes	—
50	C₇×#407	C₂²	1	2	yes	—
51	C₇×#407	C₂²	1	2	yes	complemented
52	C₇×#407	C₂²	1	2	yes	complemented
53	C₇×#407	C₂²	1	4	yes	complemented
54	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
59	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
60	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
61	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
62	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
63	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	complemented
64	C₇×#405	C₂²	1	4	yes	complemented
65	#60233	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁵×C₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₇×#41	—	4	4	no	—
68	C₂×C₇×#41	C₂×C₄	1	2	yes	—
69	C₂×C₇×#41	C₂×C₄	1	2	yes	—
70	C₂×C₇×#41	C₂³	1	2	yes	—
71	C₂×C₇×#41	C₂³	1	2	yes	—
72	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
74	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
75	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
77	C₂³×C₄×C₇	—	4	4	no	—
78	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
85	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₇×#131	—	4	8	no	—
94	C₂×C₇×M₁₆	—	4	4	no	—
95	C₂×C₇×M₁₆	C₂³	1	4	yes	—
96	C₂×C₇×M₁₆	C₂³	1	4	yes	—
97	C₂×C₇×M₁₆	C₂³	1	8	yes	complemented
98	C₂²×C₇×C₈	—	4	4	no	—
99	C₂²×C₇×C₈	C₂³	1	4	yes	—
100	C₂²×C₇×C₈	C₂³	1	2	yes	—
101	C₂²×C₇×C₈	C₂³	1	4	yes	—
102	C₂²×C₇×C₈	C₂³	1	2	yes	—
103	C₂²×C₇×C₈	C₂³	1	4	yes	—
104	C₂²×C₇×C₈	C₂³	1	8	yes	complemented
105	C₇×#123	C₂×C₄	1	4	yes	—
106	C₇×#123	C₂×C₄	1	4	yes	—
107	C₇×#123	C₂×C₄	1	4	yes	—
108	C₇×#123	C₂×C₄	1	4	yes	—
109	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
110	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
111	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
112	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
113	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
114	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
115	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
116	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
117	C₇×#121	C₂×C₄	1	2	yes	—
118	C₇×#121	C₂×C₄	1	2	yes	—
119	C₇×#121	C₂×C₄	1	2	yes	—
120	C₇×#121	C₂×C₄	1	2	yes	—
121	C₇×#121	C₂×C₄	1	2	yes	—
122	C₇×#121	C₂×C₄	1	2	yes	—
123	C₇×#121	C₂×C₄	1	2	yes	—
124	C₇×#121	C₂×C₄	1	2	yes	—
125	C₇×#120	C₂×C₄	1	4	yes	—
126	C₇×#120	C₂×C₄	1	4	yes	—
127	C₇×#120	C₂×C₄	1	4	yes	—
128	C₇×#120	C₂×C₄	1	4	yes	—
129	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
130	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
131	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
132	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
133	C₄×C₇×D₄	C₂³	1	4	yes	—
134	C₄×C₇×D₄	C₂³	1	4	yes	—
135	C₄×C₇×D₄	C₂³	1	4	yes	—
136	C₄×C₇×D₄	C₂³	1	4	yes	—
137	C₇×#117	C₂×C₄	1	2	yes	—
138	C₇×#117	C₂×C₄	1	2	yes	—
139	C₇×#117	C₂³	1	2	yes	—
140	C₇×#117	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
145	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
146	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
147	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
148	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
150	C₂×C₄²×C₇	C₂³	1	2	yes	—
151	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
152	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
153	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
154	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
155	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
156	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
157	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
158	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
160	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
161	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
162	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
164	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
165	C₇×#97	C₂³	1	8	yes	complemented
166	C₄×C₇×C₈	C₂³	1	8	yes	complemented
167	C₂×#525	C₂×C₇	1	1	yes	characteristic
168	#2977	C₂×C₇	1	4	yes	complemented
169	#2976	C₂×C₇	1	4	yes	complemented
170	#2974	C₂×C₇	1	4	yes	complemented
171	#2973	C₂×C₇	1	2	yes	complemented
172	#2972	C₂×C₇	1	2	yes	complemented
173	#2933	C₂×C₇	1	4	yes	complemented
174	#2929	C₂×C₇	1	4	yes	complemented
175	#2924	C₂×C₇	1	2	yes	complemented
176	#2880	C₂×C₇	1	2	yes	complemented
177	C₂×#407	C₂×C₇	1	1	yes	characteristic, complemented
178	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
179	C₂⁴×C₇	—	2	4	no	—
180	C₂⁴×C₇	—	4	2	no	—
181	C₂⁴×C₇	—	4	2	no	—
182	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
183	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
184	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
185	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
186	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
187	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
188	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
189	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
190	C₇×#41	—	2	8	no	—
191	C₇×#41	—	4	4	no	—
192	C₇×#41	—	4	4	no	—
193	C₇×#41	—	4	4	no	—
194	C₂×C₇×Q₈	—	4	2	no	—
195	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
196	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
197	C₂×C₇×D₄	—	2	8	no	—
198	C₂×C₇×D₄	—	4	2	no	—
199	C₂×C₇×D₄	—	4	4	no	—
200	C₂×C₇×D₄	—	4	4	no	—
201	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
202	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
203	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
204	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
205	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
206	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
207	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
208	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
209	C₂²×C₄×C₇	—	2	4	no	—
210	C₂²×C₄×C₇	—	2	4	no	—
211	C₂²×C₄×C₇	—	2	4	no	—
212	C₂²×C₄×C₇	—	4	2	no	—
213	C₂²×C₄×C₇	—	4	2	no	—
214	C₂²×C₄×C₇	—	4	2	no	—
215	C₂²×C₄×C₇	—	4	2	no	—
216	C₂²×C₄×C₇	—	4	2	no	—
217	C₂²×C₄×C₇	—	4	2	no	—
218	C₂²×C₄×C₇	—	4	2	no	—
219	C₂²×C₄×C₇	—	4	2	no	—
220	C₂²×C₄×C₇	—	4	4	no	—
221	C₂²×C₄×C₇	—	4	2	no	—
222	C₂²×C₄×C₇	—	4	2	no	—
223	C₂²×C₄×C₇	—	4	2	no	—
224	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
225	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
235	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
236	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
238	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
240	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
241	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
243	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
257	C₇×M₁₆	—	2	8	no	—
258	C₇×M₁₆	—	4	4	no	—
259	C₇×M₁₆	—	4	8	no	—
260	C₂×C₇×C₈	—	2	8	no	—
261	C₂×C₇×C₈	—	4	2	no	—
262	C₂×C₇×C₈	—	4	4	no	—
263	C₂×C₇×C₈	—	4	2	no	—
264	C₂×C₇×C₈	—	4	4	no	—
265	C₂×C₇×C₈	—	4	8	no	—
266	C₂×C₇×C₈	C₂⁴	1	4	yes	—
267	C₂×C₇×C₈	C₂⁴	1	8	yes	—
268	C₂×C₇×C₈	C₂⁴	1	4	yes	—
269	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
270	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
271	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
272	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
273	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
274	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
275	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
276	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
277	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
278	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
279	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
280	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
281	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
282	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
283	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
284	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
285	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
286	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
287	C₄²×C₇	C₂²×C₄	1	4	yes	—
288	C₄²×C₇	C₂⁴	1	4	yes	—
289	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
291	C₂×#131	C₂²×C₇	1	4	yes	complemented
292	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
293	C₂³×C₈	C₂²×C₇	1	2	yes	complemented
294	#525	C₄×C₇	1	2	yes	—
295	#525	C₄×C₇	1	2	yes	—
296	#525	C₄×C₇	1	2	yes	—
297	#525	C₄×C₇	1	2	yes	—
298	#525	C₂²×C₇	1	2	yes	—
299	#525	C₂²×C₇	1	2	yes	—
300	#525	C₂²×C₇	1	2	yes	—
301	#525	C₂²×C₇	1	2	yes	—
302	C₂×#123	C₄×C₇	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
304	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
305	C₂×#121	C₄×C₇	1	1	yes	characteristic
306	C₂×#121	C₄×C₇	1	1	yes	characteristic
307	C₂×#120	C₄×C₇	1	2	yes	—
308	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
310	C₂×#117	C₂²×C₇	1	1	yes	characteristic
311	#436	C₂²×C₇	1	8	yes	complemented
312	#435	C₂²×C₇	1	8	yes	complemented
313	#435	C₂²×C₇	1	8	yes	complemented
314	#435	C₂²×C₇	1	8	yes	complemented
315	#435	C₂²×C₇	1	8	yes	complemented
316	C₈×D₄	C₂²×C₇	1	8	yes	complemented
317	C₈×D₄	C₂²×C₇	1	8	yes	complemented
318	C₈×D₄	C₂²×C₇	1	8	yes	complemented
319	#433	C₂²×C₇	1	8	yes	complemented
320	#432	C₂²×C₇	1	4	yes	complemented
321	#431	C₂²×C₇	1	4	yes	complemented
322	#424	C₂²×C₇	1	4	yes	complemented
323	#408	C₂²×C₇	1	8	yes	complemented
324	#408	C₂²×C₇	1	4	yes	complemented
325	#407	C₂²×C₇	1	2	yes	—
326	#407	C₂²×C₇	1	2	yes	—
327	#407	C₂²×C₇	1	2	yes	complemented
328	#407	C₂²×C₇	1	2	yes	complemented
329	#407	C₂²×C₇	1	4	yes	complemented
330	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
331	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
334	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
335	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
336	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
337	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
338	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
339	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	complemented
340	#405	C₂²×C₇	1	4	yes	complemented
341	C₂³×C₇	—	2	2	no	—
342	C₂³×C₇	—	2	2	no	—
343	C₂³×C₇	—	2	2	no	—
344	C₂³×C₇	—	2	2	no	—
345	C₂³×C₇	—	2	2	no	—
346	C₂³×C₇	—	2	2	no	—
347	C₂³×C₇	—	2	2	no	—
348	C₂³×C₇	—	2	2	no	—
349	C₂³×C₇	—	2	2	no	—
350	C₂³×C₇	—	2	2	no	—
351	C₂³×C₇	—	2	2	no	—
352	C₂³×C₇	—	2	2	no	—
353	C₂³×C₇	—	2	4	no	—
354	C₂³×C₇	—	4	1	no	—
355	C₂³×C₇	—	4	1	no	—
356	C₂³×C₇	—	4	1	no	—
357	C₂³×C₇	—	4	1	no	—
358	C₂³×C₇	—	4	1	no	—
359	C₂³×C₇	—	4	1	no	—
360	C₂³×C₇	—	4	1	no	—
361	C₂³×C₇	—	4	1	no	—
362	C₂³×C₇	—	4	2	no	—
363	C₂³×C₇	—	4	2	no	—
364	C₂³×C₇	—	4	16	no	—
365	C₂³×C₇	#131	1	4	yes	complemented
366	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
367	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
368	C₂³×C₇	C₂³×C₄	1	4	yes	—
369	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
370	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
371	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
372	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
373	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
374	C₇×Q₈	—	2	4	no	—
375	C₇×Q₈	—	4	2	no	—
376	C₇×D₄	—	2	8	no	—
377	C₇×D₄	—	2	8	no	—
378	C₇×D₄	—	2	8	no	—
379	C₇×D₄	—	2	8	no	—
380	C₇×D₄	—	2	4	no	—
381	C₇×D₄	—	4	4	no	—
382	C₇×D₄	—	4	2	no	—
383	C₇×D₄	—	4	4	no	—
384	C₂×C₄×C₇	—	2	2	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	2	no	—
387	C₂×C₄×C₇	—	2	4	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	no	—
392	C₂×C₄×C₇	—	2	2	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	8	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	4	1	no	—
402	C₂×C₄×C₇	—	4	1	no	—
403	C₂×C₄×C₇	—	4	1	no	—
404	C₂×C₄×C₇	—	4	1	no	—
405	C₂×C₄×C₇	—	4	1	no	—
406	C₂×C₄×C₇	—	4	1	no	—
407	C₂×C₄×C₇	—	4	1	no	—
408	C₂×C₄×C₇	—	4	1	no	—
409	C₂×C₄×C₇	—	4	1	no	—
410	C₂×C₄×C₇	—	4	1	no	—
411	C₂×C₄×C₇	—	4	1	no	—
412	C₂×C₄×C₇	—	4	1	no	—
413	C₂×C₄×C₇	—	4	2	no	—
414	C₂×C₄×C₇	—	4	4	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
418	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
419	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
420	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
421	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
422	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
423	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
424	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
426	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
427	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
428	C₇×C₈	—	2	4	no	—
429	C₇×C₈	—	2	4	no	—
430	C₇×C₈	—	2	8	no	—
431	C₂⁵	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂×#41	—	4	4	no	—
433	C₂×#41	C₂×C₄×C₇	1	2	yes	—
434	C₂×#41	C₂×C₄×C₇	1	2	yes	—
435	C₂×#41	C₂³×C₇	1	2	yes	—
436	C₂×#41	C₂³×C₇	1	2	yes	—
437	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
438	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
439	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
440	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
441	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
442	C₂³×C₄	—	4	4	no	—
443	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
444	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
445	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
446	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
447	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
448	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
449	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₇	1	2	yes	—
456	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
458	#131	—	4	8	no	—
459	C₂×M₁₆	—	4	4	no	—
460	C₂×M₁₆	C₂³×C₇	1	4	yes	—
461	C₂×M₁₆	C₂³×C₇	1	4	yes	—
462	C₂×M₁₆	C₂³×C₇	1	8	yes	complemented
463	C₂²×C₈	—	4	4	no	—
464	C₂²×C₈	C₂³×C₇	1	4	yes	—
465	C₂²×C₈	C₂³×C₇	1	2	yes	—
466	C₂²×C₈	C₂³×C₇	1	4	yes	—
467	C₂²×C₈	C₂³×C₇	1	2	yes	—
468	C₂²×C₈	C₂³×C₇	1	4	yes	—
469	C₂²×C₈	C₂³×C₇	1	8	yes	complemented
470	#123	C₂×C₄×C₇	1	4	yes	—
471	#123	C₂×C₄×C₇	1	4	yes	—
472	#123	C₂×C₄×C₇	1	4	yes	—
473	#123	C₂×C₄×C₇	1	4	yes	—
474	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
475	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
476	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
477	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
478	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
479	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
480	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
481	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
482	#121	C₂×C₄×C₇	1	2	yes	—
483	#121	C₂×C₄×C₇	1	2	yes	—
484	#121	C₂×C₄×C₇	1	2	yes	—
485	#121	C₂×C₄×C₇	1	2	yes	—
486	#121	C₂×C₄×C₇	1	2	yes	—
487	#121	C₂×C₄×C₇	1	2	yes	—
488	#121	C₂×C₄×C₇	1	2	yes	—
489	#121	C₂×C₄×C₇	1	2	yes	—
490	#120	C₂×C₄×C₇	1	4	yes	—
491	#120	C₂×C₄×C₇	1	4	yes	—
492	#120	C₂×C₄×C₇	1	4	yes	—
493	#120	C₂×C₄×C₇	1	4	yes	—
494	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
495	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
496	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
497	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
498	C₄×D₄	C₂³×C₇	1	4	yes	—
499	C₄×D₄	C₂³×C₇	1	4	yes	—
500	C₄×D₄	C₂³×C₇	1	4	yes	—
501	C₄×D₄	C₂³×C₇	1	4	yes	—
502	#117	C₂×C₄×C₇	1	2	yes	—
503	#117	C₂×C₄×C₇	1	2	yes	—
504	#117	C₂³×C₇	1	2	yes	—
505	#117	C₂³×C₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
509	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
515	C₂×C₄²	C₂³×C₇	1	2	yes	—
516	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
517	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
518	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
519	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
520	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
521	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
522	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
523	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
524	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
526	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
527	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
528	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
529	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
530	#97	C₂³×C₇	1	8	yes	complemented
531	C₄×C₈	C₂³×C₇	1	8	yes	complemented
532	C₂²×C₇	—	2	8	no	—
533	C₂²×C₇	—	2	1	no	—
534	C₂²×C₇	—	2	1	no	—
535	C₂²×C₇	—	2	1	no	—
536	C₂²×C₇	—	2	1	no	—
537	C₂²×C₇	—	2	1	no	—
538	C₂²×C₇	—	2	1	no	—
539	C₂²×C₇	—	2	1	no	—
540	C₂²×C₇	—	2	1	no	—
541	C₂²×C₇	—	2	1	no	—
542	C₂²×C₇	—	2	1	no	—
543	C₂²×C₇	—	2	1	no	—
544	C₂²×C₇	—	2	1	no	—
545	C₂²×C₇	—	2	4	no	—
546	C₂²×C₇	—	2	4	no	—
547	C₂²×C₇	—	2	1	no	—
548	C₂²×C₇	—	2	1	no	—
549	C₂²×C₇	—	2	4	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	1	no	—
552	C₂²×C₇	—	4	4	no	—
553	C₂²×C₇	—	4	4	no	—
554	C₂²×C₇	—	4	4	no	—
555	C₂²×C₇	—	4	4	no	—
556	C₂²×C₇	—	4	4	no	—
557	C₂²×C₇	—	4	4	no	—
558	C₂²×C₇	—	8	4	no	—
559	C₂²×C₇	#518	1	2	yes	—
560	C₂²×C₇	C₂×#131	1	2	yes	—
561	C₂²×C₇	C₂×#131	1	2	yes	—
562	C₂²×C₇	C₂×#131	1	2	yes	—
563	C₂²×C₇	#568	1	2	yes	—
564	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
565	C₄×C₇	—	2	1	no	—
566	C₄×C₇	—	2	1	no	—
567	C₄×C₇	—	2	1	no	—
568	C₄×C₇	—	2	1	no	—
569	C₄×C₇	—	2	1	no	—
570	C₄×C₇	—	2	1	no	—
571	C₄×C₇	—	2	4	no	—
572	C₄×C₇	—	2	4	no	—
573	C₄×C₇	—	2	4	no	—
574	C₄×C₇	#518	1	2	yes	—
575	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
576	C₂⁴	—	2	4	no	—
577	C₂⁴	—	4	2	no	—
578	C₂⁴	—	4	2	no	—
579	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
580	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
581	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
582	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
583	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
584	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
585	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
586	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
587	#41	—	2	8	no	—
588	#41	—	4	4	no	—
589	#41	—	4	4	no	—
590	#41	—	4	4	no	—
591	C₂×Q₈	—	4	2	no	—
592	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
593	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
599	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
600	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
601	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
602	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
603	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
604	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
605	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
622	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
624	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
625	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
626	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
628	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
629	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
630	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
631	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
632	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
633	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
634	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
635	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
636	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
640	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
642	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
643	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
644	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
653	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
654	M₁₆	—	2	8	no	—
655	M₁₆	—	4	4	no	—
656	M₁₆	—	4	8	no	—
657	C₂×C₈	—	2	8	no	—
658	C₂×C₈	—	4	2	no	—
659	C₂×C₈	—	4	4	no	—
660	C₂×C₈	—	4	2	no	—
661	C₂×C₈	—	4	4	no	—
662	C₂×C₈	—	4	8	no	—
663	C₂×C₈	C₂⁴×C₇	1	4	yes	—
664	C₂×C₈	C₂⁴×C₇	1	8	yes	—
665	C₂×C₈	C₂⁴×C₇	1	4	yes	—
666	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
667	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
668	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
669	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
670	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
671	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
672	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
673	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
680	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
681	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
682	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
683	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
684	C₄²	C₂²×C₄×C₇	1	4	yes	—
685	C₄²	C₂⁴×C₇	1	4	yes	—
686	C₂×C₇	—	2	2	no	—
687	C₂×C₇	—	2	2	no	—
688	C₂×C₇	—	2	2	no	—
689	C₂×C₇	—	2	2	no	—
690	C₂×C₇	—	2	2	no	—
691	C₂×C₇	—	4	1	no	—
692	C₂×C₇	—	4	1	no	—
693	C₂×C₇	—	4	4	no	—
694	C₂×C₇	C₂×#518	1	1	yes	characteristic
695	C₂×C₇	C₂²×#131	1	1	yes	characteristic
696	C₂×C₇	C₂×#568	1	1	yes	characteristic
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	4	2	no	—
720	C₂³	—	4	16	no	—
721	C₂³	C₇×#131	1	4	yes	complemented
722	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
723	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
724	C₂³	C₂³×C₄×C₇	1	4	yes	—
725	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
726	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
727	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
728	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
729	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
730	Q₈	—	2	4	no	—
731	Q₈	—	4	2	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	8	no	—
734	D₄	—	2	8	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	4	no	—
737	D₄	—	4	4	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	4	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
773	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
774	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
775	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
776	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
777	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
778	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
779	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
780	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
781	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
782	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
783	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
784	C₈	—	2	4	no	—
785	C₈	—	2	4	no	—
786	C₈	—	2	8	no	—
787	C₇	#60233	1	1	yes	characteristic, direct product factor, Sylow
788	C₂²	—	2	8	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	4	no	—
808	C₂²	—	4	4	no	—
809	C₂²	—	4	4	no	—
810	C₂²	—	4	4	no	—
811	C₂²	—	4	4	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	4	no	—
814	C₂²	—	8	4	no	—
815	C₂²	C₇×#518	1	2	yes	—
816	C₂²	C₂×C₇×#131	1	2	yes	—
817	C₂²	C₂×C₇×#131	1	2	yes	—
818	C₂²	C₂×C₇×#131	1	2	yes	—
819	C₂²	C₇×#568	1	2	yes	—
820	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
821	C₄	—	2	4	no	—
822	C₄	—	2	4	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	4	no	—
830	C₄	C₇×#518	1	2	yes	—
831	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
832	C₂	—	2	2	no	—
833	C₂	—	2	2	no	—
834	C₂	—	2	2	no	—
835	C₂	—	2	2	no	—
836	C₂	—	2	2	no	—
837	C₂	—	4	1	no	—
838	C₂	—	4	1	no	—
839	C₂	—	4	4	no	—
840	C₂	C₂×C₇×#518	1	1	yes	characteristic
841	C₂	C₂²×C₇×#131	1	1	yes	characteristic
842	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₂×C₇×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2977	C₂	semidirect
3. C₇×#2976	C₂	semidirect
4. C₇×#2974	C₂	semidirect
5. C₇×#2973	C₂	semidirect
6. C₇×#2972	C₂	semidirect
7. C₇×#2933	C₂	semidirect
8. C₇×#2929	C₂	semidirect
9. C₇×#2924	C₂	semidirect
10. C₇×#2880	C₂	semidirect
11. C₂×C₇×#407	C₂	semidirect
12. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
15. C₂×C₇×#131	C₂²	semidirect
16. C₂²×C₇×M₁₆	C₂²	semidirect
17. C₂³×C₇×C₈	C₂²	semidirect
35. C₇×#436	C₂²	semidirect
36. C₇×#435	C₂²	semidirect
37. C₇×#435	C₂²	semidirect
38. C₇×#435	C₂²	semidirect
39. C₇×#435	C₂²	semidirect
40. C₇×C₈×D₄	C₂²	semidirect
41. C₇×C₈×D₄	C₂²	semidirect
42. C₇×C₈×D₄	C₂²	semidirect
43. C₇×#433	C₂²	semidirect
44. C₇×#432	C₂²	semidirect
45. C₇×#431	C₂²	semidirect
46. C₇×#424	C₂²	semidirect
47. C₇×#408	C₂²	semidirect
48. C₇×#408	C₂²	semidirect
51. C₇×#407	C₂²	semidirect
52. C₇×#407	C₂²	semidirect
53. C₇×#407	C₂²	semidirect
59. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
60. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
61. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
62. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
63. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
64. C₇×#405	C₂²	semidirect
65. #60233	C₇	direct (N × H)
97. C₂×C₇×M₁₆	C₂³	semidirect
104. C₂²×C₇×C₈	C₂³	semidirect
151. C₇×C₄⋊C₈	C₂³	semidirect
152. C₇×C₄⋊C₈	C₂³	semidirect
163. C₇×C₂²⋊C₈	C₂³	semidirect
164. C₇×C₂²⋊C₈	C₂³	semidirect
165. C₇×#97	C₂³	semidirect
166. C₄×C₇×C₈	C₂³	semidirect
168. #2977	C₂×C₇	semidirect
169. #2976	C₂×C₇	semidirect
170. #2974	C₂×C₇	semidirect
171. #2973	C₂×C₇	semidirect
172. #2972	C₂×C₇	semidirect
173. #2933	C₂×C₇	semidirect
174. #2929	C₂×C₇	semidirect
175. #2924	C₂×C₇	semidirect
176. #2880	C₂×C₇	semidirect
177. C₂×#407	C₂×C₇	semidirect
178. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
291. C₂×#131	C₂²×C₇	semidirect
292. C₂²×M₁₆	C₂²×C₇	semidirect
293. C₂³×C₈	C₂²×C₇	semidirect
311. #436	C₂²×C₇	semidirect
312. #435	C₂²×C₇	semidirect
313. #435	C₂²×C₇	semidirect
314. #435	C₂²×C₇	semidirect
315. #435	C₂²×C₇	semidirect
316. C₈×D₄	C₂²×C₇	semidirect
317. C₈×D₄	C₂²×C₇	semidirect
318. C₈×D₄	C₂²×C₇	semidirect
319. #433	C₂²×C₇	semidirect
320. #432	C₂²×C₇	semidirect
321. #431	C₂²×C₇	semidirect
322. #424	C₂²×C₇	semidirect
323. #408	C₂²×C₇	semidirect
324. #408	C₂²×C₇	semidirect
327. #407	C₂²×C₇	semidirect
328. #407	C₂²×C₇	semidirect
329. #407	C₂²×C₇	semidirect
335. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
336. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
337. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
338. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
339. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
340. #405	C₂²×C₇	semidirect
365. C₂³×C₇	#131	semidirect
462. C₂×M₁₆	C₂³×C₇	semidirect
469. C₂²×C₈	C₂³×C₇	semidirect
516. C₄⋊C₈	C₂³×C₇	semidirect
517. C₄⋊C₈	C₂³×C₇	semidirect
528. C₂²⋊C₈	C₂³×C₇	semidirect
529. C₂²⋊C₈	C₂³×C₇	semidirect
530. #97	C₂³×C₇	semidirect
531. C₄×C₈	C₂³×C₇	semidirect
721. C₂³	C₇×#131	semidirect
787. C₇	#60233	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×#525	2
C₇×#2977	2
C₇×#2976	2
C₇×#2974	2
C₇×#2973	2
C₇×#2972	2
C₇×#2933	2
C₇×#2929	2
C₇×#2924	2
C₇×#2880	2
C₂×C₇×#407	2
C₂²×C₇×C₂²⋊C₈	2
#60233	7

Subgroups — C7×#60233 #13237449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60233 #13237449