Subgroups — #26236473

Order 12032.

1306 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689195	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244183	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244003	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243996	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243686	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243686	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243681	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243573	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243568	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	#15689201	—	2	4	no	—
22	#15689195	—	2	4	no	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
26	#15689087	—	2	4	no	—
27	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
28	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13093935	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	#15688878	C₂²	1	1	yes	characteristic, complemented
43	#15688878	C₂²	1	1	yes	characteristic, complemented
44	#15688878	C₂²	1	1	yes	characteristic, complemented
45	#15688878	C₂²	1	1	yes	characteristic, complemented
46	#15688878	C₂²	1	1	yes	characteristic, complemented
47	#15688878	C₂²	1	1	yes	characteristic, complemented
48	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#120×C₄₇	C₄	1	1	yes	characteristic
50	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
53	C₄₇×#386	C₄	1	1	yes	characteristic
54	C₄₇×#386	C₄	1	1	yes	characteristic
55	C₄₇×#386	C₄	1	1	yes	characteristic
56	C₄₇×#385	C₄	1	1	yes	characteristic
57	C₄₇×#385	C₄	1	1	yes	characteristic
58	C₄₇×#385	C₄	1	1	yes	characteristic
59	C₄₇×#379	C₄	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
63	C₂×#10625329	—	2	2	no	—
64	C₂×#10625329	—	2	2	no	—
65	C₂×#10625329	—	2	2	no	—
66	C₂×#10625329	—	2	2	no	—
67	C₂×#10625329	—	2	2	no	—
68	C₂×#10625329	—	2	2	no	—
69	C₂×#10625329	—	4	1	no	—
70	C₂×#10625329	—	4	1	no	—
71	C₂×#10625329	—	4	1	no	—
72	C₂²×C₄₇⋊C₈	—	2	2	no	—
73	C₂²×C₄₇⋊C₈	—	2	2	no	—
74	C₂²×C₄₇⋊C₈	—	2	2	no	—
75	C₂²×C₄₇⋊C₈	—	2	2	no	—
76	C₂²×C₄₇⋊C₈	—	4	1	no	—
77	C₂²×C₄₇⋊C₈	—	4	1	no	—
78	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
87	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
88	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
89	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
91	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
92	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
94	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
95	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
96	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
97	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
98	C₂²⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
99	C₂²⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
100	#13093935	—	2	2	no	—
101	C₄×C₄₇⋊C₈	—	2	2	no	—
102	C₄×C₄₇⋊C₈	—	4	1	no	—
103	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	—	2	2	no	—
108	C₂³×C₄×C₄₇	—	2	2	no	—
109	C₂³×C₄×C₄₇	—	2	2	no	—
110	C₂³×C₄×C₄₇	—	2	2	no	—
111	C₂³×C₄×C₄₇	—	4	1	no	—
112	C₂³×C₄×C₄₇	—	4	1	no	—
113	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
120	#120×C₄₇	—	2	4	no	—
121	C₄×D₄×C₄₇	—	2	2	no	—
122	C₄×D₄×C₄₇	—	2	2	no	—
123	C₄×D₄×C₄₇	—	2	2	no	—
124	C₄×D₄×C₄₇	—	2	2	no	—
125	C₄×D₄×C₄₇	—	4	1	no	—
126	C₄×D₄×C₄₇	—	4	1	no	—
127	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
145	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
146	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
147	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
148	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
149	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
150	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
151	C₂⁴×C₄₇	—	2	2	no	—
152	C₂⁴×C₄₇	—	2	2	no	—
153	C₂⁴×C₄₇	—	2	2	no	—
154	C₂⁴×C₄₇	—	2	2	no	—
155	C₂⁴×C₄₇	—	2	2	no	—
156	C₂⁴×C₄₇	—	4	1	no	—
157	C₂⁴×C₄₇	—	4	1	no	—
158	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₄₇	—	2	2	no	—
163	C₂×D₄×C₄₇	—	2	2	no	—
164	C₂×D₄×C₄₇	—	2	2	no	—
165	C₂×D₄×C₄₇	—	2	2	no	—
166	C₂×D₄×C₄₇	—	2	2	no	—
167	C₂×D₄×C₄₇	—	2	2	no	—
168	C₂×D₄×C₄₇	—	2	2	no	—
169	C₂×D₄×C₄₇	—	4	1	no	—
170	C₂×D₄×C₄₇	—	4	1	no	—
171	C₂²×C₄×C₄₇	—	2	1	no	—
172	C₂²×C₄×C₄₇	—	2	1	no	—
173	C₂²×C₄×C₄₇	—	2	1	no	—
174	C₂²×C₄×C₄₇	—	2	1	no	—
175	C₂²×C₄×C₄₇	—	2	1	no	—
176	C₂²×C₄×C₄₇	—	2	1	no	—
177	C₂²×C₄×C₄₇	—	2	1	no	—
178	C₂²×C₄×C₄₇	—	2	1	no	—
179	C₂²×C₄×C₄₇	—	2	2	no	—
180	C₂²×C₄×C₄₇	—	2	2	no	—
181	C₂²×C₄×C₄₇	—	2	2	no	—
182	C₂²×C₄×C₄₇	—	2	2	no	—
183	C₂²×C₄×C₄₇	—	2	2	no	—
184	C₂²×C₄×C₄₇	—	2	2	no	—
185	C₂²×C₄×C₄₇	—	2	1	no	—
186	C₂²×C₄×C₄₇	—	2	1	no	—
187	C₂²×C₄×C₄₇	—	2	1	no	—
188	C₂²×C₄×C₄₇	—	2	1	no	—
189	C₂²×C₄×C₄₇	—	2	1	no	—
190	C₂²×C₄×C₄₇	—	2	1	no	—
191	C₂²×C₄×C₄₇	—	2	1	no	—
192	C₂²×C₄×C₄₇	—	2	1	no	—
193	C₂²×C₄×C₄₇	—	2	1	no	—
194	C₂²×C₄×C₄₇	—	2	1	no	—
195	C₂²×C₄×C₄₇	—	2	1	no	—
196	C₂²×C₄×C₄₇	—	2	1	no	—
197	C₂²×C₄×C₄₇	—	4	1	no	—
198	C₂²×C₄×C₄₇	—	4	1	no	—
199	C₂²×C₄×C₄₇	—	4	1	no	—
200	C₂²×C₄×C₄₇	—	4	4	no	—
201	C₂²×C₄×C₄₇	—	4	4	no	—
202	C₂²×C₄×C₄₇	—	4	4	no	—
203	C₂²×C₄×C₄₇	—	4	4	no	—
204	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₄₇	#41	1	2	yes	—
217	C₂²×C₄×C₄₇	#41	1	2	yes	—
218	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₄₇	—	2	2	no	—
220	C₄⋊C₄×C₄₇	—	2	2	no	—
221	C₄⋊C₄×C₄₇	—	4	1	no	—
222	C₂²⋊C₄×C₄₇	—	2	2	no	—
223	C₂²⋊C₄×C₄₇	—	2	2	no	—
224	C₂²⋊C₄×C₄₇	—	2	2	no	—
225	C₂²⋊C₄×C₄₇	—	2	2	no	—
226	C₂²⋊C₄×C₄₇	—	2	2	no	—
227	C₂²⋊C₄×C₄₇	—	2	2	no	—
228	C₂²⋊C₄×C₄₇	—	2	2	no	—
229	C₂²⋊C₄×C₄₇	—	2	2	no	—
230	C₂²⋊C₄×C₄₇	—	4	1	no	—
231	C₂²⋊C₄×C₄₇	—	4	1	no	—
232	C₂²⋊C₄×C₄₇	—	4	1	no	—
233	C₂²⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
234	C₄²×C₄₇	—	2	1	no	—
235	C₄²×C₄₇	—	2	1	no	—
236	C₄²×C₄₇	—	2	1	no	—
237	C₄²×C₄₇	—	2	1	no	—
238	C₄²×C₄₇	—	2	1	no	—
239	C₄²×C₄₇	—	2	1	no	—
240	#10625329	—	4	4	no	—
241	#10625329	—	4	4	no	—
242	#10625329	—	4	4	no	—
243	C₂×C₄₇⋊C₈	—	2	1	no	—
244	C₂×C₄₇⋊C₈	—	2	1	no	—
245	C₂×C₄₇⋊C₈	—	2	1	no	—
246	C₂×C₄₇⋊C₈	—	2	1	no	—
247	C₂×C₄₇⋊C₈	—	2	1	no	—
248	C₂×C₄₇⋊C₈	—	2	1	no	—
249	C₂×C₄₇⋊C₈	—	2	1	no	—
250	C₂×C₄₇⋊C₈	—	2	1	no	—
251	C₂×C₄₇⋊C₈	—	2	1	no	—
252	C₂×C₄₇⋊C₈	—	2	1	no	—
253	C₂×C₄₇⋊C₈	—	2	1	no	—
254	C₂×C₄₇⋊C₈	—	2	1	no	—
255	C₂×C₄₇⋊C₈	—	2	1	no	—
256	C₂×C₄₇⋊C₈	—	2	1	no	—
257	C₂×C₄₇⋊C₈	—	2	1	no	—
258	C₂×C₄₇⋊C₈	—	2	1	no	—
259	C₂×C₄₇⋊C₈	—	2	1	no	—
260	C₂×C₄₇⋊C₈	—	2	1	no	—
261	C₂×C₄₇⋊C₈	—	2	1	no	—
262	C₂×C₄₇⋊C₈	—	2	1	no	—
263	C₂×C₄₇⋊C₈	—	4	4	no	—
264	C₂×C₄₇⋊C₈	—	4	4	no	—
265	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
266	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
267	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
268	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
269	C₂³×C₄₇	—	2	1	no	—
270	C₂³×C₄₇	—	2	1	no	—
271	C₂³×C₄₇	—	2	1	no	—
272	C₂³×C₄₇	—	2	1	no	—
273	C₂³×C₄₇	—	2	8	no	—
274	C₂³×C₄₇	—	2	1	no	—
275	C₂³×C₄₇	—	2	1	no	—
276	C₂³×C₄₇	—	2	1	no	—
277	C₂³×C₄₇	—	2	1	no	—
278	C₂³×C₄₇	—	2	1	no	—
279	C₂³×C₄₇	—	2	1	no	—
280	C₂³×C₄₇	—	2	1	no	—
281	C₂³×C₄₇	—	2	1	no	—
282	C₂³×C₄₇	—	2	1	no	—
283	C₂³×C₄₇	—	2	1	no	—
284	C₂³×C₄₇	—	2	1	no	—
285	C₂³×C₄₇	—	2	1	no	—
286	C₂³×C₄₇	—	2	1	no	—
287	C₂³×C₄₇	—	2	1	no	—
288	C₂³×C₄₇	—	2	1	no	—
289	C₂³×C₄₇	—	2	1	no	—
290	C₂³×C₄₇	—	2	1	no	—
291	C₂³×C₄₇	—	2	1	no	—
292	C₂³×C₄₇	—	2	1	no	—
293	C₂³×C₄₇	—	4	4	no	—
294	C₂³×C₄₇	—	4	4	no	—
295	C₂³×C₄₇	—	4	4	no	—
296	C₂³×C₄₇	—	4	4	no	—
297	C₂³×C₄₇	—	4	4	no	—
298	C₂³×C₄₇	—	4	4	no	—
299	C₂³×C₄₇	C₄×D₄	1	2	yes	—
300	C₂³×C₄₇	C₄×D₄	1	2	yes	—
301	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
302	C₂³×C₄₇	#131	1	2	yes	—
303	C₂³×C₄₇	#131	1	2	yes	—
304	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
305	D₄×C₄₇	—	4	4	no	—
306	D₄×C₄₇	—	4	4	no	—
307	D₄×C₄₇	—	4	4	no	—
308	C₂×C₄×C₄₇	—	2	1	no	—
309	C₂×C₄×C₄₇	—	2	1	no	—
310	C₂×C₄×C₄₇	—	2	1	no	—
311	C₂×C₄×C₄₇	—	2	1	no	—
312	C₂×C₄×C₄₇	—	2	1	no	—
313	C₂×C₄×C₄₇	—	2	1	no	—
314	C₂×C₄×C₄₇	—	2	1	no	—
315	C₂×C₄×C₄₇	—	2	1	no	—
316	C₂×C₄×C₄₇	—	2	2	no	—
317	C₂×C₄×C₄₇	—	2	2	no	—
318	C₂×C₄×C₄₇	—	2	2	no	—
319	C₂×C₄×C₄₇	—	2	2	no	—
320	C₂×C₄×C₄₇	—	2	2	no	—
321	C₂×C₄×C₄₇	—	2	2	no	—
322	C₂×C₄×C₄₇	—	2	2	no	—
323	C₂×C₄×C₄₇	—	2	2	no	—
324	C₂×C₄×C₄₇	—	2	1	no	—
325	C₂×C₄×C₄₇	—	2	1	no	—
326	C₂×C₄×C₄₇	—	2	1	no	—
327	C₂×C₄×C₄₇	—	2	1	no	—
328	C₂×C₄×C₄₇	—	2	1	no	—
329	C₂×C₄×C₄₇	—	2	1	no	—
330	C₂×C₄×C₄₇	—	2	1	no	—
331	C₂×C₄×C₄₇	—	2	1	no	—
332	C₂×C₄×C₄₇	—	2	1	no	—
333	C₂×C₄×C₄₇	—	2	1	no	—
334	C₂×C₄×C₄₇	—	2	1	no	—
335	C₂×C₄×C₄₇	—	2	1	no	—
336	C₂×C₄×C₄₇	—	2	1	no	—
337	C₂×C₄×C₄₇	—	2	1	no	—
338	C₂×C₄×C₄₇	—	2	1	no	—
339	C₂×C₄×C₄₇	—	2	1	no	—
340	C₂×C₄×C₄₇	—	2	1	no	—
341	C₂×C₄×C₄₇	—	2	1	no	—
342	C₂×C₄×C₄₇	—	4	4	no	—
343	C₂×C₄×C₄₇	—	4	4	no	—
344	C₂×C₄×C₄₇	—	4	4	no	—
345	C₂×C₄×C₄₇	—	4	1	no	—
346	C₂×C₄×C₄₇	—	4	1	no	—
347	C₂×C₄×C₄₇	—	4	1	no	—
348	C₂×C₄×C₄₇	—	4	1	no	—
349	C₂×C₄×C₄₇	—	4	1	no	—
350	C₂×C₄×C₄₇	—	4	1	no	—
351	C₂×C₄×C₄₇	—	4	1	no	—
352	C₂×C₄×C₄₇	—	4	1	no	—
353	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
354	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
355	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
356	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
357	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
363	C₄₇⋊C₈	—	2	2	no	—
364	C₄₇⋊C₈	—	2	2	no	—
365	C₄₇⋊C₈	—	2	2	no	—
366	C₄₇⋊C₈	—	2	2	no	—
367	C₄₇⋊C₈	—	4	1	no	—
368	C₄₇⋊C₈	—	4	1	no	—
369	C₄₇⋊C₈	—	4	1	no	—
370	C₄₇⋊C₈	—	4	1	no	—
371	#22848	—	47	1	no	maximal, Sylow
372	C₂²×C₄₇	—	2	2	no	—
373	C₂²×C₄₇	—	2	2	no	—
374	C₂²×C₄₇	—	2	2	no	—
375	C₂²×C₄₇	—	2	2	no	—
376	C₂²×C₄₇	—	2	2	no	—
377	C₂²×C₄₇	—	2	2	no	—
378	C₂²×C₄₇	—	2	2	no	—
379	C₂²×C₄₇	—	2	2	no	—
380	C₂²×C₄₇	—	2	2	no	—
381	C₂²×C₄₇	—	2	2	no	—
382	C₂²×C₄₇	—	2	2	no	—
383	C₂²×C₄₇	—	2	2	no	—
384	C₂²×C₄₇	—	4	16	no	—
385	C₂²×C₄₇	—	4	1	no	—
386	C₂²×C₄₇	—	4	1	no	—
387	C₂²×C₄₇	—	4	1	no	—
388	C₂²×C₄₇	—	4	1	no	—
389	C₂²×C₄₇	—	4	1	no	—
390	C₂²×C₄₇	—	4	1	no	—
391	C₂²×C₄₇	—	4	1	no	—
392	C₂²×C₄₇	—	4	1	no	—
393	C₂²×C₄₇	—	4	1	no	—
394	C₂²×C₄₇	—	4	1	no	—
395	C₂²×C₄₇	—	4	1	no	—
396	C₂²×C₄₇	—	4	1	no	—
397	C₂²×C₄₇	—	4	1	no	—
398	C₂²×C₄₇	—	4	1	no	—
399	C₂²×C₄₇	—	4	1	no	—
400	C₂²×C₄₇	#436	1	4	yes	complemented
401	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
402	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
403	C₂²×C₄₇	#518	1	1	yes	characteristic
404	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
405	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
406	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
407	C₂²×C₄₇	#568	1	1	yes	characteristic
408	C₄×C₄₇	—	2	2	no	—
409	C₄×C₄₇	—	2	2	no	—
410	C₄×C₄₇	—	2	2	no	—
411	C₄×C₄₇	—	2	2	no	—
412	C₄×C₄₇	—	4	1	no	—
413	C₄×C₄₇	—	4	1	no	—
414	C₄×C₄₇	—	4	1	no	—
415	C₄×C₄₇	—	4	1	no	—
416	C₄×C₄₇	—	4	1	no	—
417	C₄×C₄₇	—	4	1	no	—
418	C₄×C₄₇	D₄²	1	1	yes	characteristic
419	C₄×C₄₇	#546	1	1	yes	characteristic
420	C₄×C₄₇	#546	1	1	yes	characteristic
421	C₄×C₄₇	#551	1	1	yes	characteristic
422	C₂×#436	—	47	1	no	—
423	C₂×#435	—	47	1	no	—
424	C₂×#407	—	47	1	no	—
425	C₂²×C₂²⋊C₈	—	47	1	no	—
426	C₄×#120	D₄₇	1	1	yes	characteristic
427	#1954	—	47	1	no	—
428	#1924	—	47	1	no	—
429	#1923	—	47	1	no	—
430	#1870	—	47	1	no	—
431	#1870	—	47	1	no	—
432	#1869	—	47	1	no	—
433	#1851	—	47	1	no	—
434	#1850	—	47	1	no	—
435	#1753	—	47	1	no	—
436	C₈×C₂²⋊C₄	—	47	1	no	—
437	C₂×C₄₇	—	2	4	no	—
438	C₂×C₄₇	—	4	2	no	—
439	C₂×C₄₇	—	4	2	no	—
440	C₂×C₄₇	—	8	1	no	—
441	C₂×C₄₇	#2358	1	1	yes	characteristic
442	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
443	C₂×C₄₇	#2929	1	1	yes	characteristic
444	C₂×C₄₇	#2933	1	1	yes	characteristic
445	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
446	C₂×C₄₇	#2974	1	1	yes	characteristic
447	C₂×C₄₇	#2976	1	1	yes	characteristic
448	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
449	C₂²×M₁₆	—	47	1	no	—
450	C₂²×M₁₆	—	47	1	no	—
451	C₂²×M₁₆	—	47	1	no	—
452	C₂³×C₈	—	47	1	no	—
453	C₂³×C₈	—	47	1	no	—
454	C₂×#120	Dic₄₇	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
458	#436	—	94	4	no	—
459	#435	—	94	4	no	—
460	C₂×C₄⋊C₈	—	47	1	no	—
461	C₂×C₄⋊C₈	—	47	1	no	—
462	C₂×C₄⋊C₈	—	47	1	no	—
463	#407	—	94	4	no	—
464	C₂×C₂²⋊C₈	—	47	1	no	—
465	C₂×C₂²⋊C₈	—	47	1	no	—
466	C₂×C₂²⋊C₈	—	47	1	no	—
467	C₂×C₂²⋊C₈	—	47	1	no	—
468	C₂×C₂²⋊C₈	—	47	1	no	—
469	C₂×C₂²⋊C₈	—	47	1	no	—
470	C₂×C₂²⋊C₈	—	47	1	no	—
471	C₂×C₂²⋊C₈	—	47	1	no	—
472	C₂×C₂²⋊C₈	—	47	1	no	—
473	C₂×C₂²⋊C₈	—	47	1	no	—
474	C₂×C₂²⋊C₈	—	47	1	no	—
475	C₂×C₂²⋊C₈	—	94	4	no	—
476	C₂×#97	—	47	1	no	—
477	C₂×C₄×C₈	—	47	1	no	—
478	C₂×C₄×C₈	—	47	1	no	—
479	#386	Dic₄₇	1	1	yes	characteristic
480	#386	Dic₄₇	1	1	yes	characteristic
481	#386	Dic₄₇	1	1	yes	characteristic
482	#385	Dic₄₇	1	1	yes	characteristic
483	#385	Dic₄₇	1	1	yes	characteristic
484	#385	Dic₄₇	1	1	yes	characteristic
485	#379	Dic₄₇	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
489	#336	—	47	1	no	—
490	#336	—	47	1	no	—
491	#336	—	47	1	no	—
492	#336	—	47	1	no	—
493	#336	—	47	1	no	—
494	#336	—	47	1	no	—
495	C₄₇	#22848	1	1	yes	characteristic, complemented, Sylow
496	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
497	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
498	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
499	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
500	C₂³×C₄	—	2	2	no	—
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	2	no	—
503	C₂³×C₄	—	2	2	no	—
504	C₂³×C₄	—	4	1	no	—
505	C₂³×C₄	—	4	1	no	—
506	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
507	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
508	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
509	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
510	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
511	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
512	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
513	C₂×M₁₆	—	94	2	no	—
514	C₂×M₁₆	—	94	2	no	—
515	C₂×M₁₆	—	94	2	no	—
516	C₂×M₁₆	—	94	2	no	—
517	C₂×M₁₆	—	94	2	no	—
518	C₂×M₁₆	—	94	2	no	—
519	C₂×M₁₆	—	188	1	no	—
520	C₂×M₁₆	—	188	1	no	—
521	C₂×M₁₆	—	188	1	no	—
522	C₂²×C₈	—	47	1	no	—
523	C₂²×C₈	—	47	1	no	—
524	C₂²×C₈	—	47	1	no	—
525	C₂²×C₈	—	47	1	no	—
526	C₂²×C₈	—	47	1	no	—
527	C₂²×C₈	—	47	1	no	—
528	C₂²×C₈	—	47	1	no	—
529	C₂²×C₈	—	47	1	no	—
530	C₂²×C₈	—	94	2	no	—
531	C₂²×C₈	—	94	2	no	—
532	C₂²×C₈	—	94	2	no	—
533	C₂²×C₈	—	94	2	no	—
534	C₂²×C₈	—	188	1	no	—
535	C₂²×C₈	—	188	1	no	—
536	#120	—	2	4	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	4	1	no	—
542	C₄×D₄	—	4	1	no	—
543	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
558	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
559	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
560	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
561	C₄⋊C₈	—	94	2	no	—
562	C₄⋊C₈	—	94	2	no	—
563	C₄⋊C₈	—	188	1	no	—
564	C₂²⋊C₈	—	47	4	no	—
565	C₂²⋊C₈	—	47	4	no	—
566	C₂²⋊C₈	—	94	2	no	—
567	C₂²⋊C₈	—	94	2	no	—
568	C₂²⋊C₈	—	94	2	no	—
569	C₂²⋊C₈	—	94	2	no	—
570	C₂²⋊C₈	—	94	2	no	—
571	C₂²⋊C₈	—	94	2	no	—
572	C₂²⋊C₈	—	94	2	no	—
573	C₂²⋊C₈	—	94	2	no	—
574	C₂²⋊C₈	—	188	1	no	—
575	#97	—	94	2	no	—
576	C₄×C₈	—	94	2	no	—
577	C₄×C₈	—	188	1	no	—
578	#95	C₂×Dic₄₇	1	1	yes	characteristic
579	#95	C₂×Dic₄₇	1	1	yes	characteristic
580	#95	C₂×Dic₄₇	1	1	yes	characteristic
581	#95	C₂×Dic₄₇	1	1	yes	characteristic
582	#95	C₂×Dic₄₇	1	1	yes	characteristic
583	#95	C₂×Dic₄₇	1	1	yes	characteristic
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	4	1	no	—
590	C₂⁴	—	4	1	no	—
591	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
592	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
593	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
594	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	4	no	—
634	C₂²×C₄	—	4	4	no	—
635	C₂²×C₄	—	4	4	no	—
636	C₂²×C₄	—	4	4	no	—
637	C₂²×C₄	D₄×D₄₇	1	2	yes	—
638	C₂²×C₄	D₄×D₄₇	1	2	yes	—
639	C₂²×C₄	#10625352	1	2	yes	—
640	C₂²×C₄	#10625352	1	2	yes	—
641	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
642	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
643	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
644	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
645	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
646	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
647	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
648	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
649	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
650	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
651	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
652	M₁₆	—	188	4	no	—
653	M₁₆	—	188	4	no	—
654	M₁₆	—	188	4	no	—
655	C₂×C₈	—	47	2	no	—
656	C₂×C₈	—	47	2	no	—
657	C₂×C₈	—	47	2	no	—
658	C₂×C₈	—	47	2	no	—
659	C₂×C₈	—	94	1	no	—
660	C₂×C₈	—	94	1	no	—
661	C₂×C₈	—	94	1	no	—
662	C₂×C₈	—	94	1	no	—
663	C₂×C₈	—	94	1	no	—
664	C₂×C₈	—	94	1	no	—
665	C₂×C₈	—	94	1	no	—
666	C₂×C₈	—	94	1	no	—
667	C₂×C₈	—	94	1	no	—
668	C₂×C₈	—	94	1	no	—
669	C₂×C₈	—	94	1	no	—
670	C₂×C₈	—	94	1	no	—
671	C₂×C₈	—	94	1	no	—
672	C₂×C₈	—	94	1	no	—
673	C₂×C₈	—	94	1	no	—
674	C₂×C₈	—	94	1	no	—
675	C₂×C₈	—	94	1	no	—
676	C₂×C₈	—	94	1	no	—
677	C₂×C₈	—	94	1	no	—
678	C₂×C₈	—	94	1	no	—
679	C₂×C₈	—	188	4	no	—
680	C₂×C₈	—	188	4	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	4	1	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	#10625329	1	4	yes	complemented
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	4	4	no	—
727	C₂³	—	4	4	no	—
728	C₂³	—	4	4	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	4	no	—
732	C₂³	D₄×Dic₄₇	1	2	yes	—
733	C₂³	D₄×Dic₄₇	1	2	yes	—
734	C₂³	C₂×#10625329	1	2	yes	—
735	C₂³	#13094031	1	2	yes	—
736	C₂³	#13094031	1	2	yes	—
737	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	D₄	—	4	4	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	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	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
787	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
788	C₂×C₄	C₂×#10625329	1	2	yes	—
789	C₂×C₄	C₂×#10625329	1	2	yes	—
790	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
791	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
792	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
793	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
794	C₂×C₄	#13094069	1	1	yes	characteristic
795	C₂×C₄	#13094069	1	1	yes	characteristic
796	C₈	—	94	2	no	—
797	C₈	—	94	2	no	—
798	C₈	—	94	2	no	—
799	C₈	—	94	2	no	—
800	C₈	—	188	1	no	—
801	C₈	—	188	1	no	—
802	C₈	—	188	1	no	—
803	C₈	—	188	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	4	16	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	#15689201	1	4	yes	complemented
833	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
834	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
835	C₂²	#15689598	1	1	yes	characteristic
836	C₂²	C₂²×#10625329	1	1	yes	characteristic
837	C₂²	C₂×#13094031	1	1	yes	characteristic
838	C₂²	C₂×#13094031	1	1	yes	characteristic
839	C₂²	#15689890	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	1	no	—
850	C₄	#15689755	1	1	yes	characteristic
851	C₄	#15689760	1	1	yes	characteristic
852	C₄	#15689760	1	1	yes	characteristic
853	C₄	#15689804	1	1	yes	characteristic
854	C₂	—	2	4	no	—
855	C₂	—	4	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	1	no	—
858	C₂	#20246372	1	1	yes	characteristic
859	C₂	C₂×#15689201	1	1	yes	characteristic
860	C₂	#20252083	1	1	yes	characteristic
861	C₂	#20252115	1	1	yes	characteristic
862	C₂	D₄×#10625329	1	1	yes	characteristic
863	C₂	#20252423	1	1	yes	characteristic
864	C₂	#20252436	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄×#120×C₄₇	C₂
prime radical	C₂×#120×C₄₇	C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#120	D₄₇
hypocenter	C₄₇	#22848
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#120

Complements

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

N	H ≅ G/N	type
1. C₂×#15689201	C₂	semidirect
2. C₂×#15689195	C₂	semidirect
3. C₂×#15689087	C₂	semidirect
4. C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
5. #20244183	C₂	semidirect
6. #20244003	C₂	semidirect
7. #20243996	C₂	semidirect
8. #20243686	C₂	semidirect
9. #20243686	C₂	semidirect
10. #20243681	C₂	semidirect
11. #20243573	C₂	semidirect
12. #20243568	C₂	semidirect
13. #20243172	C₂	semidirect
14. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
18. C₂²×#10625329	C₂²	semidirect
23. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
24. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
25. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
37. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
38. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
39. C₂×#13093935	C₂²	semidirect
40. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
41. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
42. #15688878	C₂²	semidirect
43. #15688878	C₂²	semidirect
44. #15688878	C₂²	semidirect
45. #15688878	C₂²	semidirect
46. #15688878	C₂²	semidirect
47. #15688878	C₂²	semidirect
98. C₂²⋊(C₄₇⋊C₈)	D₄	semidirect
99. C₂²⋊(C₄₇⋊C₈)	D₄	semidirect
233. C₂²⋊C₄×C₄₇	M₁₆	semidirect
400. C₂²×C₄₇	#436	semidirect
495. C₄₇	#22848	semidirect
695. C₂²⋊C₄	#10625329	semidirect
832. C₂²	#15689201	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689201	2
C₂×#15689195	2
C₂×#15689087	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
#20244183	2
#20244003	2
#20243996	2
#20243686	2
#20243681	2
#20243573	2
#20243568	2
#20243172	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₄×#120×C₄₇	2
#22848	47