Subgroups — C₄₇×#13813 #26053511

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#386	C₂	1	2	yes	maximal
3	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	2	yes	maximal, complemented
5	C₂²×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1437	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1436	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₇	—	2	8	no	—
17	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#386	C₄	1	16	yes	complemented
28	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
29	C₄×C₂²⋊C₄×C₄₇	—	2	8	no	—
30	C₂×#95×C₄₇	—	2	4	no	—
31	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#95×C₄₇	C₂²	1	2	yes	—
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#95×C₄₇	C₂²	1	2	yes	—
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
41	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
42	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	—	2	4	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	—	2	2	no	—
46	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
48	C₂³×C₄×C₄₇	—	2	4	no	—
49	C₂³×C₄×C₄₇	—	2	4	no	—
50	C₂³×C₄×C₄₇	—	2	4	no	—
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	2	no	—
53	C₂³×C₄×C₄₇	—	2	4	no	—
54	C₂³×C₄×C₄₇	—	2	2	no	—
55	C₂³×C₄×C₄₇	—	2	2	no	—
56	C₂³×C₄×C₄₇	—	2	2	no	—
57	C₂³×C₄×C₄₇	—	2	4	no	—
58	C₂³×C₄×C₄₇	—	4	2	no	—
59	C₂³×C₄×C₄₇	—	4	2	no	—
60	C₂³×C₄×C₄₇	—	4	2	no	—
61	C₂³×C₄×C₄₇	—	4	2	no	—
62	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
63	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
64	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
65	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₄₇	—	2	32	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
77	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
85	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
86	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
88	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
89	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	—
90	C₂×C₄²×C₄₇	—	2	4	no	—
91	C₂×C₄²×C₄₇	—	2	4	no	—
92	C₂×C₄²×C₄₇	—	2	4	no	—
93	C₂×C₄²×C₄₇	—	2	4	no	—
94	C₂×C₄²×C₄₇	—	2	4	no	—
95	C₂×C₄²×C₄₇	—	4	2	no	—
96	C₂×C₄²×C₄₇	—	4	2	no	—
97	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
98	#95×C₄₇	—	2	2	no	—
99	#95×C₄₇	—	2	4	no	—
100	#95×C₄₇	—	2	2	no	—
101	#95×C₄₇	—	2	4	no	—
102	#95×C₄₇	—	2	4	no	—
103	#95×C₄₇	—	2	2	no	—
104	#95×C₄₇	—	4	2	no	—
105	#95×C₄₇	C₂×C₄	1	8	yes	complemented
106	#95×C₄₇	C₂×C₄	1	8	yes	complemented
107	#95×C₄₇	D₄	1	4	yes	complemented
108	C₂⁴×C₄₇	—	2	1	no	—
109	C₂⁴×C₄₇	—	2	1	no	—
110	C₂⁴×C₄₇	—	2	2	no	—
111	C₂⁴×C₄₇	—	2	2	no	—
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂⁴×C₄₇	—	2	1	no	—
115	C₂⁴×C₄₇	—	2	2	no	—
116	C₂⁴×C₄₇	—	2	2	no	—
117	C₂⁴×C₄₇	—	2	1	no	—
118	C₂⁴×C₄₇	—	2	1	no	—
119	C₂⁴×C₄₇	—	2	1	no	—
120	C₂⁴×C₄₇	—	2	1	no	—
121	C₂⁴×C₄₇	—	2	2	no	—
122	C₂⁴×C₄₇	—	2	1	no	—
123	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
128	C₂⁴×C₄₇	#41	1	2	yes	—
129	C₂⁴×C₄₇	#41	1	2	yes	—
130	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂×D₄×C₄₇	—	2	8	no	—
132	C₂×D₄×C₄₇	—	2	8	no	—
133	C₂×D₄×C₄₇	—	2	16	no	—
134	C₂×D₄×C₄₇	—	2	16	no	—
135	C₂×D₄×C₄₇	C₄²	1	16	yes	complemented
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	1	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	1	no	—
145	C₂²×C₄×C₄₇	—	2	1	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	8	no	—
152	C₂²×C₄×C₄₇	—	2	16	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	1	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	2	2	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	2	2	no	—
171	C₂²×C₄×C₄₇	—	2	2	no	—
172	C₂²×C₄×C₄₇	—	2	2	no	—
173	C₂²×C₄×C₄₇	—	2	2	no	—
174	C₂²×C₄×C₄₇	—	2	2	no	—
175	C₂²×C₄×C₄₇	—	2	8	no	—
176	C₂²×C₄×C₄₇	—	2	8	no	—
177	C₂²×C₄×C₄₇	—	2	8	no	—
178	C₂²×C₄×C₄₇	—	2	16	no	—
179	C₂²×C₄×C₄₇	—	4	4	no	—
180	C₂²×C₄×C₄₇	—	4	4	no	—
181	C₂²×C₄×C₄₇	—	4	8	no	—
182	C₂²×C₄×C₄₇	—	4	8	no	—
183	C₂²×C₄×C₄₇	—	4	8	no	—
184	C₂²×C₄×C₄₇	—	4	8	no	—
185	C₂²×C₄×C₄₇	—	4	8	no	—
186	C₂²×C₄×C₄₇	—	4	8	no	—
187	C₂²×C₄×C₄₇	—	4	8	no	—
188	C₂²×C₄×C₄₇	—	4	8	no	—
189	C₂²×C₄×C₄₇	—	4	8	no	—
190	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
193	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
197	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
199	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
201	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₄₇	#41	1	2	yes	—
205	C₂²×C₄×C₄₇	#41	1	4	yes	—
206	C₄⋊C₄×C₄₇	—	2	8	no	—
207	C₂²⋊C₄×C₄₇	—	2	16	no	—
208	C₂²⋊C₄×C₄₇	—	2	8	no	—
209	C₂²⋊C₄×C₄₇	—	2	16	no	—
210	C₂²⋊C₄×C₄₇	—	4	8	no	—
211	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	16	yes	complemented
212	C₄²×C₄₇	—	2	8	no	—
213	C₄²×C₄₇	—	4	8	no	—
214	C₄²×C₄₇	—	4	8	no	—
215	C₂³×C₄₇	—	2	2	no	—
216	C₂³×C₄₇	—	2	4	no	—
217	C₂³×C₄₇	—	2	2	no	—
218	C₂³×C₄₇	—	2	4	no	—
219	C₂³×C₄₇	—	2	2	no	—
220	C₂³×C₄₇	—	2	4	no	—
221	C₂³×C₄₇	—	2	2	no	—
222	C₂³×C₄₇	—	2	4	no	—
223	C₂³×C₄₇	—	2	4	no	—
224	C₂³×C₄₇	—	2	2	no	—
225	C₂³×C₄₇	—	2	4	no	—
226	C₂³×C₄₇	—	2	4	no	—
227	C₂³×C₄₇	—	2	4	no	—
228	C₂³×C₄₇	—	2	2	no	—
229	C₂³×C₄₇	—	2	4	no	—
230	C₂³×C₄₇	—	2	2	no	—
231	C₂³×C₄₇	—	2	2	no	—
232	C₂³×C₄₇	—	2	4	no	—
233	C₂³×C₄₇	—	2	2	no	—
234	C₂³×C₄₇	—	2	2	no	—
235	C₂³×C₄₇	—	2	4	no	—
236	C₂³×C₄₇	—	2	2	no	—
237	C₂³×C₄₇	—	2	4	no	—
238	C₂³×C₄₇	—	2	4	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	2	4	no	—
241	C₂³×C₄₇	—	2	4	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	2	no	—
244	C₂³×C₄₇	—	2	4	no	—
245	C₂³×C₄₇	—	4	2	no	—
246	C₂³×C₄₇	—	4	2	no	—
247	C₂³×C₄₇	—	4	2	no	—
248	C₂³×C₄₇	—	4	1	no	—
249	C₂³×C₄₇	—	4	2	no	—
250	C₂³×C₄₇	—	4	1	no	—
251	C₂³×C₄₇	—	4	2	no	—
252	C₂³×C₄₇	—	4	1	no	—
253	C₂³×C₄₇	—	4	1	no	—
254	C₂³×C₄₇	—	4	2	no	—
255	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
256	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
257	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
258	C₂³×C₄₇	#117	1	4	yes	—
259	C₂³×C₄₇	C₄×D₄	1	8	yes	—
260	C₂³×C₄₇	C₄×D₄	1	8	yes	—
261	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
262	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
263	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
264	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
265	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
266	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
267	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
268	C₂³×C₄₇	C₂×#41	1	2	yes	—
269	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
270	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
271	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
272	D₄×C₄₇	—	2	32	no	—
273	C₂×C₄×C₄₇	—	2	2	no	—
274	C₂×C₄×C₄₇	—	2	2	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	2	no	—
277	C₂×C₄×C₄₇	—	2	4	no	—
278	C₂×C₄×C₄₇	—	2	4	no	—
279	C₂×C₄×C₄₇	—	2	4	no	—
280	C₂×C₄×C₄₇	—	2	2	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	4	no	—
284	C₂×C₄×C₄₇	—	2	2	no	—
285	C₂×C₄×C₄₇	—	2	4	no	—
286	C₂×C₄×C₄₇	—	2	4	no	—
287	C₂×C₄×C₄₇	—	2	4	no	—
288	C₂×C₄×C₄₇	—	2	4	no	—
289	C₂×C₄×C₄₇	—	2	4	no	—
290	C₂×C₄×C₄₇	—	2	4	no	—
291	C₂×C₄×C₄₇	—	2	4	no	—
292	C₂×C₄×C₄₇	—	2	4	no	—
293	C₂×C₄×C₄₇	—	2	4	no	—
294	C₂×C₄×C₄₇	—	2	4	no	—
295	C₂×C₄×C₄₇	—	2	2	no	—
296	C₂×C₄×C₄₇	—	2	4	no	—
297	C₂×C₄×C₄₇	—	2	4	no	—
298	C₂×C₄×C₄₇	—	2	4	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	4	no	—
301	C₂×C₄×C₄₇	—	2	4	no	—
302	C₂×C₄×C₄₇	—	2	4	no	—
303	C₂×C₄×C₄₇	—	2	4	no	—
304	C₂×C₄×C₄₇	—	2	4	no	—
305	C₂×C₄×C₄₇	—	2	2	no	—
306	C₂×C₄×C₄₇	—	2	4	no	—
307	C₂×C₄×C₄₇	—	4	16	no	—
308	C₂×C₄×C₄₇	—	4	16	no	—
309	C₂×C₄×C₄₇	—	4	32	no	—
310	C₂×C₄×C₄₇	—	4	2	no	—
311	C₂×C₄×C₄₇	—	4	2	no	—
312	C₂×C₄×C₄₇	—	4	2	no	—
313	C₂×C₄×C₄₇	—	4	2	no	—
314	C₂×C₄×C₄₇	—	4	2	no	—
315	C₂×C₄×C₄₇	—	4	2	no	—
316	C₂×C₄×C₄₇	—	4	2	no	—
317	C₂×C₄×C₄₇	—	4	2	no	—
318	C₂×C₄×C₄₇	—	4	2	no	—
319	C₂×C₄×C₄₇	—	4	2	no	—
320	C₂×C₄×C₄₇	—	4	2	no	—
321	C₂×C₄×C₄₇	—	4	2	no	—
322	C₂×C₄×C₄₇	—	4	2	no	—
323	C₂×C₄×C₄₇	—	4	2	no	—
324	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
325	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
326	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
327	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
328	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	complemented
329	#13813	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂²×C₄₇	—	2	4	no	—
331	C₂²×C₄₇	—	2	4	no	—
332	C₂²×C₄₇	—	2	4	no	—
333	C₂²×C₄₇	—	2	4	no	—
334	C₂²×C₄₇	—	2	8	no	—
335	C₂²×C₄₇	—	2	8	no	—
336	C₂²×C₄₇	—	2	8	no	—
337	C₂²×C₄₇	—	2	8	no	—
338	C₂²×C₄₇	—	2	4	no	—
339	C₂²×C₄₇	—	2	4	no	—
340	C₂²×C₄₇	—	2	4	no	—
341	C₂²×C₄₇	—	2	4	no	—
342	C₂²×C₄₇	—	2	4	no	—
343	C₂²×C₄₇	—	4	2	no	—
344	C₂²×C₄₇	—	4	2	no	—
345	C₂²×C₄₇	—	4	2	no	—
346	C₂²×C₄₇	—	4	2	no	—
347	C₂²×C₄₇	—	4	4	no	—
348	C₂²×C₄₇	—	4	4	no	—
349	C₂²×C₄₇	—	4	4	no	—
350	C₂²×C₄₇	—	4	4	no	—
351	C₂²×C₄₇	C₄×C₂²⋊C₄	1	8	yes	complemented
352	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
353	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
355	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
357	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
358	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
359	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
360	C₂²×C₄₇	C₄×#41	1	2	yes	—
361	C₂²×C₄₇	#518	1	1	yes	characteristic
362	C₂²×C₄₇	#518	1	2	yes	—
363	C₂²×C₄₇	#520	1	1	yes	characteristic
364	C₂²×C₄₇	#520	1	2	yes	—
365	C₂²×C₄₇	D₄²	1	2	yes	—
366	C₂²×C₄₇	#546	1	2	yes	—
367	C₂²×C₄₇	#546	1	2	yes	—
368	C₂²×C₄₇	#546	1	1	yes	characteristic
369	C₂²×C₄₇	#547	1	2	yes	—
370	C₂²×C₄₇	#548	1	1	yes	characteristic
371	C₂²×C₄₇	#551	1	2	yes	—
372	C₂²×C₄₇	#552	1	1	yes	characteristic
373	C₂²×C₄₇	#553	1	1	yes	characteristic
374	C₂²×C₄₇	#553	1	2	yes	—
375	C₄×C₄₇	—	2	4	no	—
376	C₄×C₄₇	—	2	4	no	—
377	C₄×C₄₇	—	2	4	no	—
378	C₄×C₄₇	—	2	8	no	—
379	C₄×C₄₇	—	2	4	no	—
380	C₄×C₄₇	—	4	2	no	—
381	C₄×C₄₇	—	4	4	no	—
382	C₄×C₄₇	—	4	4	no	—
383	C₄×C₄₇	—	4	4	no	—
384	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
385	C₂×#386	C₂×C₄₇	1	2	yes	—
386	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	2	yes	complemented
387	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
388	C₂²×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
389	#1437	C₂×C₄₇	1	2	yes	complemented
390	#1436	C₂×C₄₇	1	2	yes	complemented
391	#1434	C₂×C₄₇	1	1	yes	characteristic, complemented
392	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
393	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
394	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
395	C₂×C₄₇	—	2	8	no	—
396	C₂×C₄₇	—	4	4	no	—
397	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
399	C₂×C₄₇	#2275	1	1	yes	characteristic
400	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×C₄₇	#2339	1	1	yes	characteristic
402	C₂×C₄₇	#2352	1	1	yes	characteristic
403	C₂×C₄₇	#2353	1	1	yes	characteristic
404	C₂×C₄₇	#2358	1	2	yes	—
405	C₂×C₄₇	#2359	1	2	yes	—
406	C₂×C₄₇	#2361	1	2	yes	—
407	C₂×C₄₇	#2364	1	2	yes	—
408	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
409	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
410	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
411	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
412	C₂×C₄×D₄	—	2	8	no	—
413	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
414	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
418	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
419	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
420	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
421	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
422	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
423	#386	C₄×C₄₇	1	16	yes	complemented
424	C₄×C₂²⋊C₄	—	2	8	no	—
425	C₄×C₂²⋊C₄	—	2	4	no	—
426	C₂×#95	—	2	4	no	—
427	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
428	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
429	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
430	C₂×#95	C₂²×C₄₇	1	2	yes	—
431	C₂×#95	C₂²×C₄₇	1	2	yes	—
432	C₂×#95	C₂²×C₄₇	1	2	yes	—
433	C₂×#95	C₂²×C₄₇	1	2	yes	—
434	C₂×#95	C₂²×C₄₇	1	2	yes	—
435	C₂×#95	C₂²×C₄₇	1	2	yes	—
436	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
437	C₄₇	#13813	1	1	yes	characteristic, direct product factor, Sylow
438	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
439	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
440	C₂²×D₄	—	2	4	no	—
441	C₂²×D₄	—	2	2	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
444	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
445	C₂³×C₄	—	2	4	no	—
446	C₂³×C₄	—	2	4	no	—
447	C₂³×C₄	—	2	4	no	—
448	C₂³×C₄	—	2	4	no	—
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	2	2	no	—
452	C₂³×C₄	—	2	2	no	—
453	C₂³×C₄	—	2	2	no	—
454	C₂³×C₄	—	2	4	no	—
455	C₂³×C₄	—	4	2	no	—
456	C₂³×C₄	—	4	2	no	—
457	C₂³×C₄	—	4	2	no	—
458	C₂³×C₄	—	4	2	no	—
459	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
460	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	complemented
461	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	complemented
462	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
463	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
464	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
466	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
470	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
471	C₄×D₄	—	2	32	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
474	C₂×C₂²⋊C₄	—	2	4	no	—
475	C₂×C₂²⋊C₄	—	2	4	no	—
476	C₂×C₂²⋊C₄	—	2	4	no	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₂²⋊C₄	—	2	4	no	—
479	C₂×C₂²⋊C₄	—	4	2	no	—
480	C₂×C₂²⋊C₄	—	4	2	no	—
481	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
483	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
484	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
485	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
486	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	—
487	C₂×C₄²	—	2	4	no	—
488	C₂×C₄²	—	2	4	no	—
489	C₂×C₄²	—	2	4	no	—
490	C₂×C₄²	—	2	4	no	—
491	C₂×C₄²	—	2	4	no	—
492	C₂×C₄²	—	4	2	no	—
493	C₂×C₄²	—	4	2	no	—
494	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
495	#95	—	2	2	no	—
496	#95	—	2	4	no	—
497	#95	—	2	4	no	—
498	#95	—	2	4	no	—
499	#95	—	2	2	no	—
500	#95	—	2	2	no	—
501	#95	—	4	2	no	—
502	#95	C₂×C₄×C₄₇	1	8	yes	complemented
503	#95	C₂×C₄×C₄₇	1	8	yes	complemented
504	#95	D₄×C₄₇	1	4	yes	complemented
505	C₂⁴	—	2	1	no	—
506	C₂⁴	—	2	1	no	—
507	C₂⁴	—	2	2	no	—
508	C₂⁴	—	2	2	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	1	no	—
515	C₂⁴	—	2	1	no	—
516	C₂⁴	—	2	1	no	—
517	C₂⁴	—	2	1	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
521	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
522	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
523	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
524	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
525	C₂⁴	#41×C₄₇	1	2	yes	—
526	C₂⁴	#41×C₄₇	1	2	yes	—
527	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	2	16	no	—
531	C₂×D₄	—	2	16	no	—
532	C₂×D₄	C₄²×C₄₇	1	16	yes	complemented
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	2	16	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	8	no	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	16	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	8	no	—
579	C₂²×C₄	—	4	8	no	—
580	C₂²×C₄	—	4	8	no	—
581	C₂²×C₄	—	4	8	no	—
582	C₂²×C₄	—	4	8	no	—
583	C₂²×C₄	—	4	8	no	—
584	C₂²×C₄	—	4	8	no	—
585	C₂²×C₄	—	4	8	no	—
586	C₂²×C₄	—	4	8	no	—
587	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
588	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
589	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
591	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
592	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
593	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
594	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
595	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
596	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
597	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
598	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
599	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
601	C₂²×C₄	#41×C₄₇	1	2	yes	—
602	C₂²×C₄	#41×C₄₇	1	4	yes	—
603	C₄⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	16	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	16	no	—
607	C₂²⋊C₄	—	4	8	no	—
608	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	16	yes	complemented
609	C₄²	—	2	8	no	—
610	C₄²	—	4	8	no	—
611	C₄²	—	4	8	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	2	no	—
652	C₂³	C₂×C₄²×C₄₇	1	4	yes	—
653	C₂³	C₂×C₄²×C₄₇	1	4	yes	—
654	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
655	C₂³	#117×C₄₇	1	4	yes	—
656	C₂³	C₄×D₄×C₄₇	1	8	yes	—
657	C₂³	C₄×D₄×C₄₇	1	8	yes	—
658	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
659	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
660	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
661	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
662	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
663	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
664	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
665	C₂³	C₂×#41×C₄₇	1	2	yes	—
666	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
667	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
668	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
669	D₄	—	2	32	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	16	no	—
705	C₂×C₄	—	4	16	no	—
706	C₂×C₄	—	4	32	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
722	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
723	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
724	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
725	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	complemented
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	2	8	no	—
735	C₂²	—	2	8	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	4	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	C₄×C₂²⋊C₄×C₄₇	1	8	yes	complemented
748	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
749	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
750	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
751	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
752	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
753	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
754	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
755	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
756	C₂²	C₄×#41×C₄₇	1	2	yes	—
757	C₂²	C₄₇×#518	1	1	yes	characteristic
758	C₂²	C₄₇×#518	1	2	yes	—
759	C₂²	C₄₇×#520	1	1	yes	characteristic
760	C₂²	C₄₇×#520	1	2	yes	—
761	C₂²	D₄²×C₄₇	1	2	yes	—
762	C₂²	C₄₇×#546	1	2	yes	—
763	C₂²	C₄₇×#546	1	2	yes	—
764	C₂²	C₄₇×#546	1	1	yes	characteristic
765	C₂²	C₄₇×#547	1	2	yes	—
766	C₂²	C₄₇×#548	1	1	yes	characteristic
767	C₂²	C₄₇×#551	1	2	yes	—
768	C₂²	C₄₇×#552	1	1	yes	characteristic
769	C₂²	C₄₇×#553	1	1	yes	characteristic
770	C₂²	C₄₇×#553	1	2	yes	—
771	C₄	—	2	4	no	—
772	C₄	—	2	4	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	4	no	—
775	C₄	—	2	8	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	4	no	—
778	C₄	—	4	4	no	—
779	C₄	—	4	4	no	—
780	C₂	—	2	8	no	—
781	C₂	—	4	4	no	—
782	C₂	C₂×C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
783	C₂	C₄²×D₄×C₄₇	1	1	yes	characteristic
784	C₂	C₄₇×#2275	1	1	yes	characteristic
785	C₂	D₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
786	C₂	C₄₇×#2339	1	1	yes	characteristic
787	C₂	C₄₇×#2352	1	1	yes	characteristic
788	C₂	C₄₇×#2353	1	1	yes	characteristic
789	C₂	C₄₇×#2358	1	2	yes	—
790	C₂	C₄₇×#2359	1	2	yes	—
791	C₂	C₄₇×#2361	1	2	yes	—
792	C₂	C₄₇×#2364	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
5. C₂²×#95×C₄₇	C₂	semidirect
6. C₄₇×#1437	C₂	semidirect
7. C₄₇×#1436	C₂	semidirect
8. C₄₇×#1434	C₂	semidirect
9. C₄₇×C₂²⋊#95	C₂	semidirect
10. C₄₇×C₂²⋊#95	C₂	semidirect
11. C₄×#95×C₄₇	C₂	semidirect
17. C₂×C₄×D₄×C₄₇	C₄	semidirect
27. C₄₇×#386	C₄	semidirect
63. C₂³×C₄×C₄₇	C₂×C₄	semidirect
64. C₂³×C₄×C₄₇	C₂×C₄	semidirect
76. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
85. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
86. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
87. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
88. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
97. C₂×C₄²×C₄₇	C₂×C₄	semidirect
105. #95×C₄₇	C₂×C₄	semidirect
106. #95×C₄₇	C₂×C₄	semidirect
107. #95×C₄₇	D₄	semidirect
135. C₂×D₄×C₄₇	C₄²	semidirect
211. C₂²⋊C₄×C₄₇	C₂²⋊C₄	semidirect
328. C₂×C₄×C₄₇	C₄×D₄	semidirect
329. #13813	C₄₇	direct (N × H)
351. C₂²×C₄₇	C₄×C₂²⋊C₄	semidirect
386. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
387. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
388. C₂²×#95	C₂×C₄₇	semidirect
389. #1437	C₂×C₄₇	semidirect
390. #1436	C₂×C₄₇	semidirect
391. #1434	C₂×C₄₇	semidirect
392. C₂²⋊#95	C₂×C₄₇	semidirect
393. C₂²⋊#95	C₂×C₄₇	semidirect
394. C₄×#95	C₂×C₄₇	semidirect
413. C₂×C₄×D₄	C₄×C₄₇	semidirect
423. #386	C₄×C₄₇	semidirect
437. C₄₇	#13813	direct (N × H)
460. C₂³×C₄	C₂×C₄×C₄₇	semidirect
461. C₂³×C₄	C₂×C₄×C₄₇	semidirect
473. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
482. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
483. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
484. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
485. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
494. C₂×C₄²	C₂×C₄×C₄₇	semidirect
502. #95	C₂×C₄×C₄₇	semidirect
503. #95	C₂×C₄×C₄₇	semidirect
504. #95	D₄×C₄₇	semidirect
532. C₂×D₄	C₄²×C₄₇	semidirect
608. C₂²⋊C₄	C₂²⋊C₄×C₄₇	semidirect
725. C₂×C₄	C₄×D₄×C₄₇	semidirect
747. C₂²	C₄×C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄₇×#386	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂²×#95×C₄₇	2
C₄₇×#1437	2
C₄₇×#1436	2
C₄₇×#1434	2
C₄₇×C₂²⋊#95	2
C₄×#95×C₄₇	2
#13813	47

Subgroups — C47×#13813 #26053511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13813 #26053511