Subgroups — #20257747

Order 6016.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689861	C₂	1	2	yes	maximal, complemented
2	#15689860	C₂	1	2	yes	maximal, complemented
3	#15689845	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689822	C₂	1	2	yes	maximal, complemented
5	#15689793	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689791	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689772	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689769	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689762	C₂	1	2	yes	maximal, complemented
10	#15689761	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689757	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689745	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689740	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689706	C₂	1	2	yes	maximal, complemented
15	#15689705	C₂	1	2	yes	maximal, complemented
16	#15689700	C₂	1	2	yes	maximal, complemented
17	#15689687	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689686	C₂	1	2	yes	maximal, complemented
19	#15689686	C₂	1	1	yes	maximal, characteristic, complemented
20	#15689669	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689668	C₂	1	1	yes	maximal, characteristic, complemented
22	#15689653	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
25	C₂×#10625352	C₂²	1	2	yes	complemented
26	C₂×#10625352	C₂²	1	1	yes	characteristic, complemented
27	C₂×#10625352	C₂²	1	2	yes	complemented
28	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₄₇	C₂²	1	2	yes	—
31	#13094023	C₂²	1	1	yes	characteristic, complemented
32	#13094022	C₂²	1	1	yes	characteristic, complemented
33	#13094020	C₂²	1	1	yes	characteristic
34	#13094020	C₂²	1	1	yes	characteristic
35	#13094020	C₂²	1	1	yes	characteristic, complemented
36	#13094020	C₂²	1	2	yes	complemented
37	#13094019	C₂²	1	2	yes	complemented
38	#13094019	C₂²	1	1	yes	characteristic, complemented
39	#13094018	C₂²	1	2	yes	complemented
40	#13094018	C₂²	1	2	yes	complemented
41	#13094017	C₂²	1	2	yes	complemented
42	#13094017	C₂²	1	1	yes	characteristic, complemented
43	#13094014	C₂²	1	1	yes	characteristic, complemented
44	#13094013	C₂²	1	1	yes	characteristic
45	#13094013	C₂²	1	1	yes	characteristic, complemented
46	#13094012	C₂²	1	1	yes	characteristic
47	#13094012	C₂²	1	2	yes	complemented
48	#13094011	C₂²	1	1	yes	characteristic, complemented
49	#13094011	C₂²	1	2	yes	complemented
50	#13094010	C₂²	1	1	yes	characteristic
51	#13094010	C₂²	1	2	yes	complemented
52	#13094009	C₂²	1	2	yes	complemented
53	#13094009	C₂²	1	2	yes	complemented
54	#13094008	C₂²	1	1	yes	characteristic, complemented
55	#13094007	C₂²	1	2	yes	complemented
56	#13094007	C₂²	1	2	yes	complemented
57	#13094005	C₂²	1	2	yes	complemented
58	#13094005	C₂²	1	2	yes	complemented
59	#13094005	C₂²	1	1	yes	characteristic, complemented
60	#13094003	C₂²	1	1	yes	characteristic, complemented
61	#13094002	C₂²	1	2	yes	complemented
62	#13094002	C₂²	1	2	yes	complemented
63	#13094001	C₂²	1	2	yes	complemented
64	#13094001	C₂²	1	1	yes	characteristic, complemented
65	#13094000	C₂²	1	1	yes	characteristic, complemented
66	#13093999	C₂²	1	1	yes	characteristic
67	#13093998	C₂²	1	1	yes	characteristic
68	#13093998	C₂²	1	2	yes	complemented
69	#13093998	C₂²	1	2	yes	complemented
70	#13093997	C₂²	1	2	yes	—
71	#13093997	C₂²	1	2	yes	complemented
72	#13093997	C₂²	1	2	yes	complemented
73	#13093996	C₂²	1	2	yes	—
74	#13093996	C₂²	1	1	yes	characteristic
75	#13093996	C₂²	1	2	yes	complemented
76	#13093996	C₂²	1	2	yes	complemented
77	#13093996	C₂²	1	2	yes	complemented
78	#13093996	C₂²	1	2	yes	complemented
79	#13093996	C₂²	1	2	yes	complemented
80	#13093996	C₂²	1	2	yes	complemented
81	#13093996	C₂²	1	2	yes	complemented
82	#13093996	C₂²	1	2	yes	complemented
83	#13093996	C₂²	1	2	yes	complemented
84	#13093995	C₂²	1	2	yes	complemented
85	#13093994	C₂²	1	2	yes	—
86	#13093992	C₂²	1	2	yes	—
87	#13093992	C₂²	1	2	yes	complemented
88	#13093992	C₂²	1	2	yes	complemented
89	#13093992	C₂²	1	2	yes	complemented
90	#13093992	C₂²	1	2	yes	complemented
91	#13093992	C₂²	1	2	yes	complemented
92	#13093992	C₂²	1	2	yes	complemented
93	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
94	#13093989	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
98	#13093986	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
103	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
105	#13093983	C₂²	1	1	yes	characteristic, complemented
106	#13093981	C₂²	1	1	yes	characteristic, complemented
107	#13093981	C₂²	1	2	yes	complemented
108	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
109	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
114	#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	#127×C₄₇	C₂²	1	2	yes	complemented
116	#121×C₄₇	C₂²	1	1	yes	characteristic
117	#121×C₄₇	C₂²	1	2	yes	complemented
118	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₄₇	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
123	C₂³×D₄₇	C₂³	1	2	yes	—
124	C₂³×D₄₇	C₂³	1	2	yes	—
125	#41×C₄₇	—	4	2	no	—
126	#41×C₄₇	—	4	2	no	—
127	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₄₇	C₂³	1	2	yes	—
132	C₂×D₄×C₄₇	C₂³	1	2	yes	—
133	C₂×D₄×C₄₇	C₂³	1	2	yes	—
134	C₂×D₄×C₄₇	C₂³	1	2	yes	—
135	C₂×D₄×C₄₇	C₂³	1	2	yes	—
136	C₂×D₄×C₄₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
153	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
154	C₂²×Dic₄₇	C₂³	1	2	yes	—
155	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
156	C₂²×Dic₄₇	C₂³	1	2	yes	—
157	C₂²×Dic₄₇	C₂³	1	2	yes	—
158	#10625352	—	4	2	no	—
159	#10625352	—	4	4	no	—
160	#10625352	—	4	4	no	—
161	D₄×D₄₇	—	4	2	no	—
162	D₄×D₄₇	—	4	4	no	—
163	#10625350	—	4	2	no	—
164	C₂×D₁₈₈	—	4	2	no	—
165	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
166	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
167	C₂×D₁₈₈	C₂³	1	2	yes	—
168	C₂×D₁₈₈	C₂³	1	2	yes	—
169	C₂×C₄×D₄₇	C₂³	1	2	yes	—
170	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₄₇	C₂³	1	2	yes	—
172	C₂×C₄×D₄₇	C₂³	1	2	yes	—
173	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
174	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
175	C₂×Dic₉₄	C₂³	1	2	yes	—
176	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
181	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
183	C₄²×C₄₇	C₂³	1	1	yes	characteristic
184	C₄²×C₄₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
190	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
191	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
193	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
194	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
209	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
213	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₄₇⋊C₄	C₂³	1	2	yes	—
215	Dic₄₇⋊C₄	C₂³	1	2	yes	—
216	Dic₄₇⋊C₄	C₂³	1	2	yes	—
217	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₄₇⋊C₄	C₂³	1	2	yes	—
222	Dic₄₇⋊C₄	C₂³	1	2	yes	—
223	Dic₄₇⋊C₄	C₂³	1	2	yes	—
224	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
225	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
229	C₄×Dic₄₇	C₂³	1	2	yes	—
230	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
231	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
232	C₂³×C₄₇	C₂⁴	1	2	yes	—
233	C₂³×C₄₇	C₂⁴	1	2	yes	—
234	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₄₇	—	4	2	no	—
236	C₂²×D₄₇	—	4	2	no	—
237	C₂²×D₄₇	—	4	2	no	—
238	C₂²×D₄₇	—	4	2	no	—
239	C₂²×D₄₇	—	4	2	no	—
240	C₂²×D₄₇	—	4	2	no	—
241	C₂²×D₄₇	C₂⁴	1	2	yes	—
242	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
243	C₂²×D₄₇	C₂⁴	1	2	yes	—
244	Q₈×C₄₇	—	2	2	no	—
245	D₄×C₄₇	—	2	2	no	—
246	D₄×C₄₇	—	2	2	no	—
247	D₄×C₄₇	—	4	2	no	—
248	D₄×C₄₇	—	4	2	no	—
249	D₄×C₄₇	—	4	2	no	—
250	D₄×C₄₇	—	4	1	no	—
251	D₄×C₄₇	—	4	2	no	—
252	D₄×C₄₇	—	4	2	no	—
253	D₄×C₄₇	—	4	2	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	2	no	—
256	C₂×C₄×C₄₇	—	4	2	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₄₇	—	2	2	no	—
266	C₂²⋊D₄₇	—	2	4	no	—
267	C₂²⋊D₄₇	—	4	2	no	—
268	C₂²⋊D₄₇	—	4	2	no	—
269	C₂²⋊D₄₇	—	4	2	no	—
270	C₂²⋊D₄₇	—	4	2	no	—
271	C₂²⋊D₄₇	—	4	2	no	—
272	C₂²⋊D₄₇	—	4	2	no	—
273	C₂²⋊D₄₇	—	4	2	no	—
274	C₂²⋊D₄₇	—	4	2	no	—
275	C₂²⋊D₄₇	—	4	2	no	—
276	C₂²⋊D₄₇	—	4	1	no	—
277	C₂×Dic₄₇	—	2	2	no	—
278	C₂×Dic₄₇	—	2	4	no	—
279	C₂×Dic₄₇	—	4	2	no	—
280	C₂×Dic₄₇	—	4	2	no	—
281	C₂×Dic₄₇	—	4	1	no	—
282	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₄₇	C₂⁴	1	2	yes	—
287	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₄₇	C₂⁴	1	2	yes	—
290	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
291	D₁₈₈	—	2	2	no	—
292	D₁₈₈	—	2	2	no	—
293	D₁₈₈	—	4	2	no	—
294	D₁₈₈	—	4	2	no	—
295	C₄×D₄₇	—	2	2	no	—
296	C₄×D₄₇	—	2	4	no	—
297	C₄×D₄₇	—	4	2	no	—
298	C₄×D₄₇	—	4	2	no	—
299	Dic₉₄	—	2	2	no	—
300	Dic₉₄	—	2	2	no	—
301	Dic₉₄	—	4	2	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	1	no	—
304	C₂²×C₄₇	—	2	2	no	—
305	C₂²×C₄₇	—	2	2	no	—
306	C₂²×C₄₇	—	2	1	no	—
307	C₂²×C₄₇	—	2	1	no	—
308	C₂²×C₄₇	—	2	2	no	—
309	C₂²×C₄₇	—	2	1	no	—
310	C₂²×C₄₇	—	2	1	no	—
311	C₂²×C₄₇	—	2	2	no	—
312	C₂²×C₄₇	—	2	2	no	—
313	C₂²×C₄₇	—	2	1	no	—
314	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
315	C₂×D₄₇	—	2	2	no	—
316	C₂×D₄₇	—	2	1	no	—
317	C₂×D₄₇	—	2	2	no	—
318	C₂×D₄₇	—	2	2	no	—
319	C₂×D₄₇	—	2	2	no	—
320	C₂×D₄₇	—	2	1	no	—
321	C₂×D₄₇	—	2	2	no	—
322	C₂×D₄₇	—	2	2	no	—
323	C₂×D₄₇	—	2	1	no	—
324	C₂×D₄₇	—	8	4	no	—
325	C₂×D₄₇	—	8	4	no	—
326	C₄×C₄₇	—	2	1	no	—
327	C₄×C₄₇	—	2	2	no	—
328	C₄×C₄₇	—	2	1	no	—
329	C₄×C₄₇	—	2	1	no	—
330	C₄×C₄₇	—	2	2	no	—
331	C₄×C₄₇	—	2	1	no	—
332	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
333	Dic₄₇	—	2	2	no	—
334	Dic₄₇	—	2	1	no	—
335	Dic₄₇	—	2	1	no	—
336	Dic₄₇	—	2	2	no	—
337	Dic₄₇	—	2	1	no	—
338	Dic₄₇	—	2	1	no	—
339	Dic₄₇	—	2	1	no	—
340	Dic₄₇	—	2	1	no	—
341	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
342	#3546	—	47	1	no	maximal, Sylow
343	C₂×C₄₇	—	4	1	no	—
344	C₂×C₄₇	—	4	2	no	—
345	C₂×C₄₇	—	4	2	no	—
346	C₂×C₄₇	—	4	1	no	—
347	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₄₇	#585	1	1	yes	characteristic
350	D₄₇	—	4	2	no	—
351	D₄₇	—	4	2	no	—
352	D₄₇	—	4	1	no	—
353	#560	—	47	2	no	—
354	#560	—	47	2	no	—
355	#556	—	47	1	no	—
356	#553	—	47	2	no	—
357	#550	—	47	1	no	—
358	#550	—	47	1	no	—
359	#550	D₄₇	1	1	yes	characteristic, complemented
360	#547	—	47	1	no	—
361	#546	—	47	1	no	—
362	#546	—	47	2	no	—
363	#546	—	47	1	no	—
364	D₄²	—	47	1	no	—
365	#542	—	47	1	no	—
366	#542	—	47	1	no	—
367	#538	—	47	2	no	—
368	#538	—	47	2	no	—
369	#537	—	47	2	no	—
370	#535	—	47	1	no	—
371	#535	—	47	1	no	—
372	#535	—	47	2	no	—
373	#532	—	47	1	no	—
374	#532	—	47	1	no	—
375	#529	—	47	1	no	—
376	C₄₇	#3546	1	1	yes	characteristic, complemented, Sylow
377	C₂×#41	—	47	2	no	—
378	C₂×#41	—	47	1	no	—
379	C₂×#41	—	47	2	no	—
380	C₂×#41	—	47	1	no	—
381	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
382	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
383	C₂²×D₄	—	47	2	no	—
384	C₂²×D₄	—	47	1	no	—
385	C₂²×D₄	—	47	1	no	—
386	C₄⋊Q₈	—	47	1	no	—
387	C₄⋊Q₈	—	47	1	no	—
388	#127	—	47	1	no	—
389	#127	—	47	1	no	—
390	#127	—	47	1	no	—
391	#127	—	47	2	no	—
392	#127	C₂×D₄₇	1	1	yes	characteristic, complemented
393	#127	C₂×D₄₇	1	2	yes	complemented
394	#126	—	47	1	no	—
395	#126	—	47	2	no	—
396	#126	—	47	1	no	—
397	#126	—	47	2	no	—
398	#126	—	47	2	no	—
399	#126	—	47	2	no	—
400	#125	—	47	1	no	—
401	#124	—	47	1	no	—
402	#124	—	47	1	no	—
403	#124	—	47	1	no	—
404	#124	—	47	2	no	—
405	#124	—	47	1	no	—
406	#124	—	47	2	no	—
407	#124	—	47	2	no	—
408	#124	—	47	1	no	—
409	#123	—	47	1	no	—
410	#123	—	47	2	no	—
411	#123	—	47	2	no	—
412	#123	—	47	2	no	—
413	#123	—	47	2	no	—
414	#123	—	47	2	no	—
415	#123	—	47	2	no	—
416	#123	—	47	1	no	—
417	C₂²⋊Q₈	—	47	1	no	—
418	C₂²⋊Q₈	—	47	1	no	—
419	C₂²⋊Q₈	—	47	2	no	—
420	C₂²⋊Q₈	—	47	2	no	—
421	C₂²⋊Q₈	—	47	1	no	—
422	C₂²⋊Q₈	—	47	2	no	—
423	#121	—	47	1	no	—
424	#121	—	47	2	no	—
425	#121	—	47	2	no	—
426	#121	—	47	2	no	—
427	#121	—	47	2	no	—
428	#121	—	47	2	no	—
429	#121	—	47	2	no	—
430	#121	—	47	2	no	—
431	#121	—	47	2	no	—
432	#121	—	47	2	no	—
433	#121	—	47	2	no	—
434	#121	—	47	2	no	—
435	#121	—	47	1	no	—
436	#121	—	47	2	no	—
437	#121	—	47	2	no	—
438	#121	—	47	1	no	—
439	#121	—	47	2	no	—
440	#121	—	47	2	no	—
441	#121	—	47	2	no	—
442	#121	C₂×D₄₇	1	1	yes	characteristic
443	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
444	#121	C₂×D₄₇	1	2	yes	complemented
445	#121	C₂×D₄₇	1	2	yes	complemented
446	#120	—	47	2	no	—
447	#120	—	47	2	no	—
448	#120	—	47	2	no	—
449	#120	—	47	2	no	—
450	#120	—	47	2	no	—
451	#120	—	47	2	no	—
452	#120	—	47	2	no	—
453	#120	—	47	2	no	—
454	C₄×Q₈	—	47	1	no	—
455	C₄×Q₈	—	47	1	no	—
456	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
457	C₄×D₄	—	47	1	no	—
458	C₄×D₄	—	47	1	no	—
459	C₄×D₄	—	47	1	no	—
460	C₄×D₄	—	47	1	no	—
461	C₄×D₄	—	47	2	no	—
462	C₄×D₄	—	47	2	no	—
463	C₄×D₄	—	47	1	no	—
464	C₄×D₄	—	47	2	no	—
465	C₄×D₄	—	47	2	no	—
466	C₄×D₄	—	47	1	no	—
467	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
469	#117	—	47	1	no	—
470	#117	—	47	1	no	—
471	#117	—	47	2	no	—
472	C₂×C₄⋊C₄	—	47	2	no	—
473	C₂×C₂²⋊C₄	—	47	2	no	—
474	C₂×C₂²⋊C₄	—	47	2	no	—
475	C₂×C₄²	—	47	1	no	—
476	C₂⁴	—	47	2	no	—
477	C₂⁴	—	47	2	no	—
478	#41	—	4	2	no	—
479	#41	—	4	2	no	—
480	#41	—	188	2	no	—
481	#41	—	188	4	no	—
482	#41	—	188	2	no	—
483	#41	—	188	4	no	—
484	C₂×Q₈	—	47	1	no	—
485	C₂×Q₈	—	47	1	no	—
486	C₂×Q₈	—	47	2	no	—
487	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
488	C₂×D₄	—	47	1	no	—
489	C₂×D₄	—	47	2	no	—
490	C₂×D₄	—	47	2	no	—
491	C₂×D₄	—	47	2	no	—
492	C₂×D₄	—	47	1	no	—
493	C₂×D₄	—	47	2	no	—
494	C₂×D₄	—	47	2	no	—
495	C₂×D₄	—	47	2	no	—
496	C₂×D₄	—	47	2	no	—
497	C₂×D₄	—	47	2	no	—
498	C₂×D₄	—	47	2	no	—
499	C₂×D₄	—	47	2	no	—
500	C₂×D₄	—	47	1	no	—
501	C₂×D₄	—	47	1	no	—
502	C₂×D₄	—	47	2	no	—
503	C₂×D₄	—	47	2	no	—
504	C₂×D₄	—	188	2	no	—
505	C₂×D₄	—	188	2	no	—
506	C₂×D₄	—	188	4	no	—
507	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₄₇	1	2	yes	—
511	C₂×D₄	C₂²×D₄₇	1	2	yes	—
512	C₂×D₄	C₂²×D₄₇	1	2	yes	—
513	C₂×D₄	C₂²×D₄₇	1	2	yes	—
514	C₂×D₄	C₂²×D₄₇	1	2	yes	—
515	C₂×D₄	C₂²×D₄₇	1	2	yes	—
516	C₂²×C₄	—	47	1	no	—
517	C₂²×C₄	—	47	2	no	—
518	C₂²×C₄	—	47	1	no	—
519	C₂²×C₄	—	47	2	no	—
520	C₂²×C₄	—	47	2	no	—
521	C₂²×C₄	—	47	2	no	—
522	C₂²×C₄	—	47	1	no	—
523	C₂²×C₄	—	47	2	no	—
524	C₂²×C₄	—	47	2	no	—
525	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
528	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
529	C₄⋊C₄	—	47	1	no	—
530	C₄⋊C₄	—	47	2	no	—
531	C₄⋊C₄	—	47	2	no	—
532	C₄⋊C₄	—	47	2	no	—
533	C₄⋊C₄	—	47	1	no	—
534	C₄⋊C₄	—	47	1	no	—
535	C₄⋊C₄	—	47	1	no	—
536	C₄⋊C₄	—	47	1	no	—
537	C₄⋊C₄	—	47	2	no	—
538	C₄⋊C₄	—	47	2	no	—
539	C₄⋊C₄	—	47	2	no	—
540	C₄⋊C₄	—	47	1	no	—
541	C₄⋊C₄	—	47	1	no	—
542	C₄⋊C₄	—	47	1	no	—
543	C₄⋊C₄	—	47	1	no	—
544	C₄⋊C₄	—	47	1	no	—
545	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
548	C₂²⋊C₄	—	47	2	no	—
549	C₂²⋊C₄	—	47	1	no	—
550	C₂²⋊C₄	—	47	1	no	—
551	C₂²⋊C₄	—	47	1	no	—
552	C₂²⋊C₄	—	47	2	no	—
553	C₂²⋊C₄	—	47	2	no	—
554	C₂²⋊C₄	—	47	2	no	—
555	C₂²⋊C₄	—	47	1	no	—
556	C₂²⋊C₄	—	47	2	no	—
557	C₂²⋊C₄	—	47	1	no	—
558	C₂²⋊C₄	—	47	2	no	—
559	C₂²⋊C₄	—	47	2	no	—
560	C₂²⋊C₄	—	47	2	no	—
561	C₂²⋊C₄	—	47	2	no	—
562	C₂²⋊C₄	—	47	2	no	—
563	C₂²⋊C₄	—	47	2	no	—
564	C₂²⋊C₄	—	47	1	no	—
565	C₂²⋊C₄	—	47	1	no	—
566	C₂²⋊C₄	—	47	2	no	—
567	C₂²⋊C₄	—	47	1	no	—
568	C₂²⋊C₄	—	47	2	no	—
569	C₂²⋊C₄	—	47	2	no	—
570	C₂²⋊C₄	—	47	2	no	—
571	C₂²⋊C₄	—	47	2	no	—
572	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
576	C₄²	—	47	1	no	—
577	C₄²	—	47	1	no	—
578	C₄²	—	47	1	no	—
579	C₄²	—	47	1	no	—
580	C₄²	—	47	1	no	—
581	C₄²	—	47	2	no	—
582	C₄²	C₂²×D₄₇	1	1	yes	characteristic
583	C₄²	C₂²×D₄₇	1	2	yes	—
584	C₂³	—	47	2	no	—
585	C₂³	—	47	1	no	—
586	C₂³	—	47	2	no	—
587	C₂³	—	188	2	no	—
588	C₂³	—	188	2	no	—
589	C₂³	—	188	2	no	—
590	C₂³	—	188	2	no	—
591	C₂³	—	188	2	no	—
592	C₂³	—	188	2	no	—
593	C₂³	C₂³×D₄₇	1	1	yes	characteristic
594	C₂³	C₂³×D₄₇	1	2	yes	—
595	C₂³	C₂³×D₄₇	1	1	yes	characteristic
596	C₂³	C₂³×D₄₇	1	2	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	94	2	no	—
599	Q₈	—	94	2	no	—
600	Q₈	—	188	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	94	2	no	—
611	D₄	—	94	4	no	—
612	D₄	—	94	2	no	—
613	D₄	—	94	2	no	—
614	D₄	—	188	2	no	—
615	D₄	—	188	2	no	—
616	D₄	—	188	2	no	—
617	D₄	—	188	2	no	—
618	D₄	—	188	1	no	—
619	D₄	—	188	2	no	—
620	D₄	—	188	2	no	—
621	D₄	—	188	2	no	—
622	D₄	—	188	2	no	—
623	D₄	—	188	2	no	—
624	D₄	—	188	2	no	—
625	D₄	—	188	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	47	1	no	—
631	C₂×C₄	—	47	1	no	—
632	C₂×C₄	—	47	1	no	—
633	C₂×C₄	—	47	1	no	—
634	C₂×C₄	—	47	1	no	—
635	C₂×C₄	—	47	1	no	—
636	C₂×C₄	—	47	2	no	—
637	C₂×C₄	—	47	2	no	—
638	C₂×C₄	—	47	1	no	—
639	C₂×C₄	—	94	4	no	—
640	C₂×C₄	—	94	4	no	—
641	C₂×C₄	—	94	2	no	—
642	C₂×C₄	—	94	2	no	—
643	C₂×C₄	—	188	2	no	—
644	C₂×C₄	—	188	2	no	—
645	C₂×C₄	—	188	1	no	—
646	C₂×C₄	—	188	2	no	—
647	C₂×C₄	—	188	2	no	—
648	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₄₇	1	2	yes	—
650	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₄₇	1	2	yes	—
652	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	94	2	no	—
668	C₂²	—	94	2	no	—
669	C₂²	—	94	1	no	—
670	C₂²	—	94	1	no	—
671	C₂²	—	94	2	no	—
672	C₂²	—	94	2	no	—
673	C₂²	—	94	2	no	—
674	C₂²	—	94	2	no	—
675	C₂²	—	94	1	no	—
676	C₂²	—	376	4	no	—
677	C₂²	—	376	4	no	—
678	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	47	2	no	—
686	C₄	—	94	2	no	—
687	C₄	—	94	1	no	—
688	C₄	—	94	1	no	—
689	C₄	—	94	1	no	—
690	C₄	—	94	2	no	—
691	C₄	—	94	1	no	—
692	C₄	—	94	1	no	—
693	C₄	—	94	1	no	—
694	C₄	#13094069	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	4	1	no	—
698	C₂	—	4	2	no	—
699	C₂	—	188	2	no	—
700	C₂	—	188	1	no	—
701	C₂	—	188	2	no	—
702	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
703	C₂	C₂×#13094069	1	1	yes	characteristic
704	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#550	C₂
hypercenter	#550	D₄₇
hypocenter	C₄₇	#3546
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #15689861	C₂	semidirect
2. #15689860	C₂	semidirect
3. #15689845	C₂	semidirect
4. #15689822	C₂	semidirect
5. #15689793	C₂	semidirect
6. #15689791	C₂	semidirect
7. #15689772	C₂	semidirect
8. #15689769	C₂	semidirect
9. #15689762	C₂	semidirect
10. #15689761	C₂	semidirect
11. #15689757	C₂	semidirect
12. #15689745	C₂	semidirect
13. #15689740	C₂	semidirect
14. #15689706	C₂	semidirect
15. #15689705	C₂	semidirect
16. #15689700	C₂	semidirect
17. #15689687	C₂	semidirect
18. #15689686	C₂	semidirect
19. #15689686	C₂	semidirect
20. #15689669	C₂	semidirect
21. #15689668	C₂	semidirect
22. #15689653	C₂	semidirect
23. C₄₇×#550	C₂	semidirect
24. C₂×#10625350	C₂²	semidirect
25. C₂×#10625352	C₂²	semidirect
26. C₂×#10625352	C₂²	semidirect
27. C₂×#10625352	C₂²	semidirect
31. #13094023	C₂²	semidirect
32. #13094022	C₂²	semidirect
35. #13094020	C₂²	semidirect
36. #13094020	C₂²	semidirect
37. #13094019	C₂²	semidirect
38. #13094019	C₂²	semidirect
39. #13094018	C₂²	semidirect
40. #13094018	C₂²	semidirect
41. #13094017	C₂²	semidirect
42. #13094017	C₂²	semidirect
43. #13094014	C₂²	semidirect
45. #13094013	C₂²	semidirect
47. #13094012	C₂²	semidirect
48. #13094011	C₂²	semidirect
49. #13094011	C₂²	semidirect
51. #13094010	C₂²	semidirect
52. #13094009	C₂²	semidirect
53. #13094009	C₂²	semidirect
54. #13094008	C₂²	semidirect
55. #13094007	C₂²	semidirect
56. #13094007	C₂²	semidirect
57. #13094005	C₂²	semidirect
58. #13094005	C₂²	semidirect
59. #13094005	C₂²	semidirect
60. #13094003	C₂²	semidirect
61. #13094002	C₂²	semidirect
62. #13094002	C₂²	semidirect
63. #13094001	C₂²	semidirect
64. #13094001	C₂²	semidirect
65. #13094000	C₂²	semidirect
68. #13093998	C₂²	semidirect
69. #13093998	C₂²	semidirect
71. #13093997	C₂²	semidirect
72. #13093997	C₂²	semidirect
75. #13093996	C₂²	semidirect
76. #13093996	C₂²	semidirect
77. #13093996	C₂²	semidirect
78. #13093996	C₂²	semidirect
79. #13093996	C₂²	semidirect
80. #13093996	C₂²	semidirect
81. #13093996	C₂²	semidirect
82. #13093996	C₂²	semidirect
83. #13093996	C₂²	semidirect
84. #13093995	C₂²	semidirect
87. #13093992	C₂²	semidirect
88. #13093992	C₂²	semidirect
89. #13093992	C₂²	semidirect
90. #13093992	C₂²	semidirect
91. #13093992	C₂²	semidirect
92. #13093992	C₂²	semidirect
93. C₄×Dic₉₄	C₂²	semidirect
94. #13093989	C₂²	semidirect
95. C₄×D₁₈₈	C₂²	semidirect
96. D₄×Dic₄₇	C₂²	semidirect
97. D₄×Dic₄₇	C₂²	semidirect
100. C₄×C₂²⋊D₄₇	C₂²	semidirect
101. C₄×C₂²⋊D₄₇	C₂²	semidirect
102. C₄×C₂²⋊D₄₇	C₂²	semidirect
103. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
105. #13093983	C₂²	semidirect
106. #13093981	C₂²	semidirect
107. #13093981	C₂²	semidirect
108. C₂×Dic₄₇⋊C₄	C₂²	semidirect
109. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₄₇	C₂²	semidirect
111. C₂×C₄×Dic₄₇	C₂²	semidirect
112. C₂×#41×C₄₇	C₂²	semidirect
113. C₂×#41×C₄₇	C₂²	semidirect
114. #127×C₄₇	C₂²	semidirect
115. #127×C₄₇	C₂²	semidirect
117. #121×C₄₇	C₂²	semidirect
118. #121×C₄₇	C₂²	semidirect
119. #121×C₄₇	C₂²	semidirect
120. C₄×Q₈×C₄₇	C₂²	semidirect
121. C₄×D₄×C₄₇	C₂²	semidirect
122. C₄×D₄×C₄₇	C₂²	semidirect
359. #550	D₄₇	semidirect
376. C₄₇	#3546	semidirect
381. C₂×#41	C₂×D₄₇	semidirect
382. C₂×#41	C₂×D₄₇	semidirect
392. #127	C₂×D₄₇	semidirect
393. #127	C₂×D₄₇	semidirect
443. #121	C₂×D₄₇	semidirect
444. #121	C₂×D₄₇	semidirect
445. #121	C₂×D₄₇	semidirect
456. C₄×Q₈	C₂×D₄₇	semidirect
467. C₄×D₄	C₂×D₄₇	semidirect
468. C₄×D₄	C₂×D₄₇	semidirect