Subgroups — #20257256

Order 6016.

1232 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689857	C₂	1	2	yes	maximal, complemented
2	#15689856	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689855	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689792	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689791	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689791	C₂	1	2	yes	maximal, complemented
7	#15689769	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689767	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689764	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689763	C₂	1	2	yes	maximal, complemented
11	#15689760	C₂	1	2	yes	maximal, complemented
12	#15689725	C₂	1	2	yes	maximal, complemented
13	#15689723	C₂	1	2	yes	maximal, complemented
14	#15689688	C₂	1	2	yes	maximal, complemented
15	#15689675	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689672	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689670	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689669	C₂	1	1	yes	maximal, characteristic, complemented
19	#15689668	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13094020	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689596	C₂	1	2	yes	maximal, complemented
22	C₄×#10625352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
25	C₂×#10625350	C₂²	1	2	yes	complemented
26	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
27	C₂×#10625352	C₂²	1	1	yes	characteristic
28	C₂×#10625352	C₂²	1	2	yes	complemented
29	C₂×#10625352	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	—
33	#13094023	C₂²	1	1	yes	characteristic, complemented
34	#13094022	C₂²	1	1	yes	characteristic, complemented
35	#13094020	C₂²	1	1	yes	characteristic
36	#13094020	C₂²	1	2	yes	—
37	#13094020	C₂²	1	1	yes	characteristic
38	#13094020	C₂²	1	1	yes	characteristic
39	#13094020	C₂²	1	1	yes	characteristic
40	#13094020	C₂²	1	2	yes	—
41	#13094020	C₂²	1	2	yes	complemented
42	#13094020	C₂²	1	2	yes	complemented
43	#13094014	C₂²	1	2	yes	complemented
44	#13094013	C₂²	1	1	yes	characteristic, complemented
45	#13094012	C₂²	1	1	yes	characteristic, complemented
46	#13094011	C₂²	1	1	yes	characteristic, complemented
47	#13094010	C₂²	1	2	yes	complemented
48	#13094010	C₂²	1	2	yes	complemented
49	#13094010	C₂²	1	2	yes	complemented
50	#13094010	C₂²	1	2	yes	complemented
51	#13094009	C₂²	1	2	yes	complemented
52	#13094009	C₂²	1	2	yes	complemented
53	#13094008	C₂²	1	2	yes	complemented
54	#13094007	C₂²	1	2	yes	complemented
55	#13094006	C₂²	1	2	yes	complemented
56	#13094006	C₂²	1	2	yes	complemented
57	#13094005	C₂²	1	2	yes	complemented
58	#13094003	C₂²	1	1	yes	characteristic
59	#13094001	C₂²	1	2	yes	—
60	#13093999	C₂²	1	1	yes	characteristic, complemented
61	#13093999	C₂²	1	2	yes	complemented
62	#13093998	C₂²	1	2	yes	complemented
63	#13093998	C₂²	1	1	yes	characteristic, complemented
64	#13093997	C₂²	1	2	yes	complemented
65	#13093997	C₂²	1	2	yes	complemented
66	#13093997	C₂²	1	2	yes	complemented
67	#13093997	C₂²	1	2	yes	complemented
68	#13093997	C₂²	1	2	yes	complemented
69	#13093996	C₂²	1	2	yes	complemented
70	#13093996	C₂²	1	2	yes	complemented
71	#13093996	C₂²	1	2	yes	complemented
72	#13093996	C₂²	1	2	yes	complemented
73	#13093996	C₂²	1	2	yes	complemented
74	#13093995	C₂²	1	2	yes	complemented
75	#13093995	C₂²	1	1	yes	characteristic, complemented
76	#13093994	C₂²	1	2	yes	—
77	#13093993	C₂²	1	2	yes	—
78	#13093992	C₂²	1	2	yes	—
79	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
81	#13093989	C₂²	1	1	yes	characteristic, complemented
82	#13093989	C₂²	1	2	yes	complemented
83	#13093989	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
86	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
87	#13093986	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
95	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
96	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
100	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
102	#13093982	C₂²	1	1	yes	characteristic, complemented
103	#13093980	C₂²	1	1	yes	characteristic
104	#13093980	C₂²	1	2	yes	—
105	#13093980	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
109	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
114	#124×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₄₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
117	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
118	#121×C₄₇	C₂²	1	2	yes	complemented
119	#120×C₄₇	C₂²	1	2	yes	—
120	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
123	C₂⁴×C₄₇	C₂³	1	2	yes	—
124	C₂³×D₄₇	C₂³	1	2	yes	—
125	#41×C₄₇	—	4	2	no	—
126	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₄₇	—	4	2	no	—
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	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₄₇	—	2	8	no	—
139	C₂×C₂²⋊D₄₇	—	4	4	no	—
140	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
154	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
155	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
156	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
157	C₂²×Dic₄₇	C₂³	1	2	yes	—
158	C₂²×Dic₄₇	C₂³	1	2	yes	—
159	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
160	#10625354	—	4	2	no	—
161	#10625352	—	2	4	no	—
162	#10625352	—	4	2	no	—
163	#10625352	—	4	4	no	—
164	#10625350	—	4	4	no	—
165	#10625350	—	4	2	no	—
166	C₂×D₁₈₈	—	4	2	no	—
167	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
168	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
169	C₂×D₁₈₈	C₂³	1	2	yes	—
170	C₂×D₁₈₈	C₂³	1	2	yes	—
171	C₂×D₁₈₈	C₂³	1	2	yes	—
172	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₄₇	C₂³	1	2	yes	—
176	C₂×C₄×D₄₇	C₂³	1	2	yes	—
177	C₂×C₄×D₄₇	C₂³	1	2	yes	—
178	C₂×C₄×D₄₇	C₂³	1	2	yes	—
179	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
180	C₂×Dic₉₄	C₂³	1	2	yes	—
181	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
192	C₄²×C₄₇	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
195	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
196	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
197	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
199	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
200	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
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	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
210	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₄₇	C₂³	1	2	yes	—
213	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
220	Dic₄₇⋊C₄	C₂³	1	2	yes	—
221	Dic₄₇⋊C₄	C₂³	1	2	yes	—
222	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₄₇	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	1	yes	characteristic
230	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
231	C₄×Dic₄₇	C₂³	1	2	yes	—
232	C₄×Dic₄₇	C₂³	1	2	yes	—
233	C₂³×C₄₇	—	2	4	no	—
234	C₂³×C₄₇	—	4	2	no	—
235	C₂³×C₄₇	—	4	2	no	—
236	C₂³×C₄₇	C₂⁴	1	2	yes	—
237	C₂³×C₄₇	C₂⁴	1	2	yes	—
238	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₄₇	—	2	4	no	—
241	C₂²×D₄₇	—	4	2	no	—
242	C₂²×D₄₇	—	4	2	no	—
243	C₂²×D₄₇	C₂⁴	1	2	yes	—
244	C₂²×D₄₇	C₂⁴	1	2	yes	—
245	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
246	Q₈×C₄₇	—	2	2	no	—
247	D₄×C₄₇	—	2	2	no	—
248	D₄×C₄₇	—	2	2	no	—
249	D₄×C₄₇	—	2	2	no	—
250	D₄×C₄₇	—	4	2	no	—
251	D₄×C₄₇	—	4	2	no	—
252	D₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	4	2	no	—
256	C₂×C₄×C₄₇	—	4	2	no	—
257	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
262	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
264	C₂²⋊D₄₇	—	2	2	no	—
265	C₂²⋊D₄₇	—	2	2	no	—
266	C₂²⋊D₄₇	—	2	4	no	—
267	C₂²⋊D₄₇	—	2	4	no	—
268	C₂²⋊D₄₇	—	2	4	no	—
269	C₂²⋊D₄₇	—	2	4	no	—
270	C₂²⋊D₄₇	—	2	4	no	—
271	C₂²⋊D₄₇	—	2	4	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	2	no	—
277	C₂²⋊D₄₇	—	4	2	no	—
278	C₂×Dic₄₇	—	2	2	no	—
279	C₂×Dic₄₇	—	2	2	no	—
280	C₂×Dic₄₇	—	2	2	no	—
281	C₂×Dic₄₇	—	4	2	no	—
282	C₂×Dic₄₇	—	4	2	no	—
283	C₂×Dic₄₇	#41	1	4	yes	complemented
284	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₄₇	C₂⁴	1	2	yes	—
289	C₂×Dic₄₇	C₂⁴	1	2	yes	—
290	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
293	D₁₈₈	—	2	2	no	—
294	D₁₈₈	—	2	2	no	—
295	D₁₈₈	—	4	2	no	—
296	D₁₈₈	—	4	2	no	—
297	D₁₈₈	—	4	2	no	—
298	C₄×D₄₇	—	2	2	no	—
299	C₄×D₄₇	—	2	2	no	—
300	C₄×D₄₇	—	2	2	no	—
301	C₄×D₄₇	—	4	2	no	—
302	C₄×D₄₇	—	4	2	no	—
303	C₄×D₄₇	—	4	2	no	—
304	C₄×D₄₇	—	4	2	no	—
305	Dic₉₄	—	2	2	no	—
306	Dic₉₄	—	2	2	no	—
307	Dic₉₄	—	2	4	no	—
308	C₂²×C₄₇	—	2	1	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	—	2	2	no	—
315	C₂²×C₄₇	—	2	2	no	—
316	C₂²×C₄₇	—	2	2	no	—
317	C₂²×C₄₇	—	2	1	no	—
318	C₂²×C₄₇	—	2	2	no	—
319	C₂²×C₄₇	—	8	4	no	—
320	C₂²×C₄₇	C₂×#41	1	2	yes	—
321	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
322	C₂×D₄₇	—	2	1	no	—
323	C₂×D₄₇	—	2	2	no	—
324	C₂×D₄₇	—	2	2	no	—
325	C₂×D₄₇	—	2	1	no	—
326	C₂×D₄₇	—	2	1	no	—
327	C₂×D₄₇	—	2	2	no	—
328	C₂×D₄₇	—	2	2	no	—
329	C₂×D₄₇	—	2	2	no	—
330	C₂×D₄₇	—	2	2	no	—
331	C₂×D₄₇	—	8	4	no	—
332	C₄×C₄₇	—	2	1	no	—
333	C₄×C₄₇	—	2	2	no	—
334	C₄×C₄₇	—	2	1	no	—
335	C₄×C₄₇	—	2	1	no	—
336	C₄×C₄₇	—	2	2	no	—
337	C₄×C₄₇	—	2	1	no	—
338	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
339	Dic₄₇	—	2	1	no	—
340	Dic₄₇	—	2	2	no	—
341	Dic₄₇	—	2	2	no	—
342	Dic₄₇	—	2	1	no	—
343	Dic₄₇	—	2	1	no	—
344	Dic₄₇	—	2	1	no	—
345	Dic₄₇	C₂×#41	1	2	yes	—
346	Dic₄₇	C₂×#41	1	2	yes	—
347	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
348	#3508	—	47	1	no	maximal, Sylow
349	C₂×C₄₇	—	2	2	no	—
350	C₂×C₄₇	—	4	1	no	—
351	C₂×C₄₇	—	4	2	no	—
352	C₂×C₄₇	—	4	2	no	—
353	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
354	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	D₄₇	—	4	1	no	—
357	D₄₇	—	4	2	no	—
358	D₄₇	—	4	2	no	—
359	#559	—	47	1	no	—
360	#559	—	47	2	no	—
361	#559	—	47	1	no	—
362	#550	—	47	1	no	—
363	#550	—	47	1	no	—
364	#550	—	47	2	no	—
365	#546	—	47	1	no	—
366	#546	—	47	1	no	—
367	#546	—	47	2	no	—
368	#546	—	47	1	no	—
369	#546	—	47	2	no	—
370	#546	D₄₇	1	1	yes	characteristic, complemented
371	#540	—	47	2	no	—
372	#540	—	47	2	no	—
373	#535	—	47	2	no	—
374	#533	—	47	1	no	—
375	#532	—	47	1	no	—
376	#532	—	47	1	no	—
377	#532	—	47	1	no	—
378	#532	—	47	1	no	—
379	C₂×#127	—	47	1	no	—
380	#518	—	47	2	no	—
381	C₄×#41	—	47	1	no	—
382	C₄₇	#3508	1	1	yes	characteristic, complemented, Sylow
383	C₂×#41	—	47	1	no	—
384	C₂×#41	—	47	1	no	—
385	C₂×#41	—	47	2	no	—
386	C₂×#41	—	47	1	no	—
387	C₂×#41	—	47	2	no	—
388	C₂×#41	—	47	1	no	—
389	C₂×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	47	2	no	—
391	C₂²×D₄	—	47	2	no	—
392	C₂²×D₄	—	47	1	no	—
393	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
394	C₄⋊Q₈	—	47	1	no	—
395	C₄⋊Q₈	—	47	1	no	—
396	#127	—	47	1	no	—
397	#127	—	47	1	no	—
398	#127	—	47	2	no	—
399	#127	—	47	2	no	—
400	#127	—	47	1	no	—
401	#127	—	47	1	no	—
402	#127	—	47	2	no	—
403	#127	—	47	2	no	—
404	#125	—	47	2	no	—
405	#124	—	47	1	no	—
406	#124	—	47	1	no	—
407	#124	—	47	2	no	—
408	#124	—	47	2	no	—
409	#124	—	47	2	no	—
410	#124	—	47	2	no	—
411	#124	—	47	1	no	—
412	#124	C₂×D₄₇	1	1	yes	characteristic, complemented
413	#123	—	47	2	no	—
414	#123	—	47	2	no	—
415	#123	—	47	2	no	—
416	#123	—	47	2	no	—
417	#123	—	47	2	no	—
418	#123	—	47	2	no	—
419	#123	—	47	2	no	—
420	#123	C₂×D₄₇	1	2	yes	complemented
421	C₂²⋊Q₈	—	47	1	no	—
422	C₂²⋊Q₈	—	47	2	no	—
423	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
424	#121	—	47	2	no	—
425	#121	—	47	2	no	—
426	#121	—	47	1	no	—
427	#121	—	47	2	no	—
428	#121	—	47	2	no	—
429	#121	—	47	2	no	—
430	#121	—	47	2	no	—
431	#121	—	47	1	no	—
432	#121	—	47	2	no	—
433	#121	—	47	1	no	—
434	#121	—	47	2	no	—
435	#121	—	47	2	no	—
436	#121	—	47	2	no	—
437	#121	—	47	2	no	—
438	#121	—	47	2	no	—
439	#121	—	47	2	no	—
440	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
441	#121	C₂×D₄₇	1	2	yes	complemented
442	#120	—	47	2	no	—
443	#120	—	47	2	no	—
444	#120	—	47	2	no	—
445	#120	C₂×D₄₇	1	2	yes	—
446	C₄×Q₈	—	47	1	no	—
447	C₄×Q₈	—	47	1	no	—
448	C₄×Q₈	—	47	2	no	—
449	C₄×Q₈	—	47	1	no	—
450	C₄×Q₈	—	47	1	no	—
451	C₄×D₄	—	47	1	no	—
452	C₄×D₄	—	47	1	no	—
453	C₄×D₄	—	47	1	no	—
454	C₄×D₄	—	47	1	no	—
455	C₄×D₄	—	47	2	no	—
456	C₄×D₄	—	47	2	no	—
457	C₄×D₄	—	47	2	no	—
458	C₄×D₄	—	47	2	no	—
459	C₄×D₄	—	47	2	no	—
460	C₄×D₄	—	47	1	no	—
461	C₄×D₄	—	47	1	no	—
462	C₄×D₄	—	47	1	no	—
463	C₄×D₄	—	47	2	no	—
464	C₄×D₄	—	47	2	no	—
465	C₄×D₄	—	47	2	no	—
466	C₄×D₄	—	47	2	no	—
467	C₄×D₄	—	47	2	no	—
468	C₄×D₄	—	47	1	no	—
469	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
470	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
471	#117	—	47	1	no	—
472	#117	—	47	1	no	—
473	#117	—	47	1	no	—
474	#117	—	47	2	no	—
475	C₂×C₂²⋊C₄	—	47	2	no	—
476	C₂×C₂²⋊C₄	—	47	2	no	—
477	C₂×C₂²⋊C₄	—	47	2	no	—
478	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
479	C₂×C₄²	—	47	1	no	—
480	C₂×C₄²	—	47	1	no	—
481	C₂×C₄²	—	47	1	no	—
482	C₂⁴	—	47	2	no	—
483	C₂⁴	C₂²×D₄₇	1	2	yes	—
484	#41	—	4	2	no	—
485	#41	—	94	4	no	—
486	#41	—	188	2	no	—
487	#41	—	188	4	no	—
488	#41	—	188	2	no	—
489	#41	—	188	4	no	—
490	#41	—	188	2	no	—
491	C₂×Q₈	—	47	1	no	—
492	C₂×Q₈	—	47	2	no	—
493	C₂×Q₈	—	47	1	no	—
494	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	47	1	no	—
497	C₂×D₄	—	47	2	no	—
498	C₂×D₄	—	47	2	no	—
499	C₂×D₄	—	47	2	no	—
500	C₂×D₄	—	47	2	no	—
501	C₂×D₄	—	47	1	no	—
502	C₂×D₄	—	47	2	no	—
503	C₂×D₄	—	47	2	no	—
504	C₂×D₄	—	47	2	no	—
505	C₂×D₄	—	47	2	no	—
506	C₂×D₄	—	47	2	no	—
507	C₂×D₄	—	47	2	no	—
508	C₂×D₄	—	47	2	no	—
509	C₂×D₄	—	47	2	no	—
510	C₂×D₄	—	47	1	no	—
511	C₂×D₄	—	47	1	no	—
512	C₂×D₄	—	47	2	no	—
513	C₂×D₄	—	47	2	no	—
514	C₂×D₄	—	47	2	no	—
515	C₂×D₄	—	94	8	no	—
516	C₂×D₄	—	188	2	no	—
517	C₂×D₄	—	188	4	no	—
518	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₄₇	1	2	yes	—
522	C₂×D₄	C₂²×D₄₇	1	2	yes	—
523	C₂×D₄	C₂²×D₄₇	1	2	yes	—
524	C₂²×C₄	—	47	1	no	—
525	C₂²×C₄	—	47	1	no	—
526	C₂²×C₄	—	47	1	no	—
527	C₂²×C₄	—	47	1	no	—
528	C₂²×C₄	—	47	2	no	—
529	C₂²×C₄	—	47	2	no	—
530	C₂²×C₄	—	47	1	no	—
531	C₂²×C₄	—	47	1	no	—
532	C₂²×C₄	—	47	1	no	—
533	C₂²×C₄	—	47	2	no	—
534	C₂²×C₄	—	47	2	no	—
535	C₂²×C₄	—	47	2	no	—
536	C₂²×C₄	—	47	2	no	—
537	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
540	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
541	C₄⋊C₄	—	47	1	no	—
542	C₄⋊C₄	—	47	1	no	—
543	C₄⋊C₄	—	47	2	no	—
544	C₄⋊C₄	—	47	2	no	—
545	C₄⋊C₄	—	47	1	no	—
546	C₄⋊C₄	—	47	1	no	—
547	C₄⋊C₄	—	47	2	no	—
548	C₄⋊C₄	—	47	2	no	—
549	C₄⋊C₄	—	47	2	no	—
550	C₄⋊C₄	—	47	1	no	—
551	C₄⋊C₄	—	47	1	no	—
552	C₄⋊C₄	—	47	2	no	—
553	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
556	C₂²⋊C₄	—	47	1	no	—
557	C₂²⋊C₄	—	47	2	no	—
558	C₂²⋊C₄	—	47	2	no	—
559	C₂²⋊C₄	—	47	2	no	—
560	C₂²⋊C₄	—	47	1	no	—
561	C₂²⋊C₄	—	47	2	no	—
562	C₂²⋊C₄	—	47	2	no	—
563	C₂²⋊C₄	—	47	2	no	—
564	C₂²⋊C₄	—	47	2	no	—
565	C₂²⋊C₄	—	47	2	no	—
566	C₂²⋊C₄	—	47	2	no	—
567	C₂²⋊C₄	—	47	1	no	—
568	C₂²⋊C₄	—	47	1	no	—
569	C₂²⋊C₄	—	47	2	no	—
570	C₂²⋊C₄	—	47	2	no	—
571	C₂²⋊C₄	—	47	2	no	—
572	C₂²⋊C₄	—	47	2	no	—
573	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
580	C₄²	—	47	1	no	—
581	C₄²	—	47	1	no	—
582	C₄²	—	47	1	no	—
583	C₄²	—	47	1	no	—
584	C₄²	—	47	1	no	—
585	C₄²	—	47	1	no	—
586	C₄²	—	47	1	no	—
587	C₄²	—	47	1	no	—
588	C₄²	—	47	1	no	—
589	C₄²	—	47	2	no	—
590	C₄²	—	47	2	no	—
591	C₄²	C₂²×D₄₇	1	1	yes	characteristic
592	C₂³	—	2	4	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	47	2	no	—
596	C₂³	—	47	2	no	—
597	C₂³	—	47	1	no	—
598	C₂³	—	94	4	no	—
599	C₂³	—	188	2	no	—
600	C₂³	—	188	2	no	—
601	C₂³	C₂³×D₄₇	1	2	yes	—
602	C₂³	C₂³×D₄₇	1	2	yes	—
603	C₂³	C₂³×D₄₇	1	1	yes	characteristic
604	C₂³	C₂³×D₄₇	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	94	2	no	—
607	Q₈	—	94	4	no	—
608	Q₈	—	94	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	94	4	no	—
616	D₄	—	94	4	no	—
617	D₄	—	94	4	no	—
618	D₄	—	94	4	no	—
619	D₄	—	94	4	no	—
620	D₄	—	94	4	no	—
621	D₄	—	94	2	no	—
622	D₄	—	94	2	no	—
623	D₄	—	94	2	no	—
624	D₄	—	94	2	no	—
625	D₄	—	188	2	no	—
626	D₄	—	188	2	no	—
627	D₄	—	188	2	no	—
628	D₄	—	188	2	no	—
629	D₄	—	188	2	no	—
630	D₄	—	188	2	no	—
631	D₄	—	188	2	no	—
632	D₄	—	188	2	no	—
633	D₄	—	188	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	47	4	no	—
639	C₂×C₄	—	47	1	no	—
640	C₂×C₄	—	47	1	no	—
641	C₂×C₄	—	47	1	no	—
642	C₂×C₄	—	47	1	no	—
643	C₂×C₄	—	47	1	no	—
644	C₂×C₄	—	47	1	no	—
645	C₂×C₄	—	47	1	no	—
646	C₂×C₄	—	47	2	no	—
647	C₂×C₄	—	47	2	no	—
648	C₂×C₄	—	94	2	no	—
649	C₂×C₄	—	94	2	no	—
650	C₂×C₄	—	94	2	no	—
651	C₂×C₄	—	94	2	no	—
652	C₂×C₄	—	94	2	no	—
653	C₂×C₄	—	94	2	no	—
654	C₂×C₄	—	188	2	no	—
655	C₂×C₄	—	188	2	no	—
656	C₂×C₄	—	188	2	no	—
657	C₂×C₄	—	188	2	no	—
658	C₂×C₄	—	188	2	no	—
659	C₂×C₄	—	188	2	no	—
660	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₄₇	1	2	yes	—
665	C₂×C₄	C₂³×D₄₇	1	2	yes	—
666	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	8	4	no	—
679	C₂²	—	94	1	no	—
680	C₂²	—	94	2	no	—
681	C₂²	—	94	2	no	—
682	C₂²	—	94	1	no	—
683	C₂²	—	94	2	no	—
684	C₂²	—	94	2	no	—
685	C₂²	—	94	1	no	—
686	C₂²	—	94	2	no	—
687	C₂²	—	94	2	no	—
688	C₂²	—	376	4	no	—
689	C₂²	#41×D₄₇	1	2	yes	—
690	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	47	2	no	—
698	C₄	—	47	2	no	—
699	C₄	—	47	2	no	—
700	C₄	—	94	1	no	—
701	C₄	—	94	1	no	—
702	C₄	—	94	1	no	—
703	C₄	—	94	2	no	—
704	C₄	—	94	1	no	—
705	C₄	—	94	2	no	—
706	C₄	#13094069	1	2	yes	—
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	188	2	no	—
712	C₂	—	188	2	no	—
713	C₂	—	188	1	no	—
714	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
715	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
716	C₂	C₂×#13094069	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#546	C₂
hypercenter	#546	D₄₇
hypocenter	C₄₇	#3508
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #15689857	C₂	semidirect
2. #15689856	C₂	semidirect
3. #15689855	C₂	semidirect
4. #15689792	C₂	semidirect
5. #15689791	C₂	semidirect
6. #15689791	C₂	semidirect
7. #15689769	C₂	semidirect
8. #15689767	C₂	semidirect
9. #15689764	C₂	semidirect
10. #15689763	C₂	semidirect
11. #15689760	C₂	semidirect
12. #15689725	C₂	semidirect
13. #15689723	C₂	semidirect
14. #15689688	C₂	semidirect
15. #15689675	C₂	semidirect
16. #15689672	C₂	semidirect
17. #15689670	C₂	semidirect
18. #15689669	C₂	semidirect
19. #15689668	C₂	semidirect
20. C₂×#13094020	C₂	semidirect
21. #15689596	C₂	semidirect
22. C₄×#10625352	C₂	semidirect
23. C₄₇×#546	C₂	semidirect
24. C₂×#10625354	C₂²	semidirect
25. C₂×#10625350	C₂²	semidirect
26. C₂×#10625350	C₂²	semidirect
28. C₂×#10625352	C₂²	semidirect
29. C₂×#10625352	C₂²	semidirect
33. #13094023	C₂²	semidirect
34. #13094022	C₂²	semidirect
41. #13094020	C₂²	semidirect
42. #13094020	C₂²	semidirect
43. #13094014	C₂²	semidirect
44. #13094013	C₂²	semidirect
45. #13094012	C₂²	semidirect
46. #13094011	C₂²	semidirect
47. #13094010	C₂²	semidirect
48. #13094010	C₂²	semidirect
49. #13094010	C₂²	semidirect
50. #13094010	C₂²	semidirect
51. #13094009	C₂²	semidirect
52. #13094009	C₂²	semidirect
53. #13094008	C₂²	semidirect
54. #13094007	C₂²	semidirect
55. #13094006	C₂²	semidirect
56. #13094006	C₂²	semidirect
57. #13094005	C₂²	semidirect
60. #13093999	C₂²	semidirect
61. #13093999	C₂²	semidirect
62. #13093998	C₂²	semidirect
63. #13093998	C₂²	semidirect
64. #13093997	C₂²	semidirect
65. #13093997	C₂²	semidirect
66. #13093997	C₂²	semidirect
67. #13093997	C₂²	semidirect
68. #13093997	C₂²	semidirect
69. #13093996	C₂²	semidirect
70. #13093996	C₂²	semidirect
71. #13093996	C₂²	semidirect
72. #13093996	C₂²	semidirect
73. #13093996	C₂²	semidirect
74. #13093995	C₂²	semidirect
75. #13093995	C₂²	semidirect
79. Q₈×Dic₄₇	C₂²	semidirect
80. C₄×Dic₉₄	C₂²	semidirect
81. #13093989	C₂²	semidirect
82. #13093989	C₂²	semidirect
83. #13093989	C₂²	semidirect
84. C₄×D₁₈₈	C₂²	semidirect
86. D₄×Dic₄₇	C₂²	semidirect
87. #13093986	C₂²	semidirect
89. C₄×C₂²⋊D₄₇	C₂²	semidirect
90. C₄×C₂²⋊D₄₇	C₂²	semidirect
91. C₄×C₂²⋊D₄₇	C₂²	semidirect
92. C₄×C₂²⋊D₄₇	C₂²	semidirect
93. C₄×C₂²⋊D₄₇	C₂²	semidirect
94. C₄×C₂²⋊D₄₇	C₂²	semidirect
96. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
100. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
102. #13093982	C₂²	semidirect
105. #13093980	C₂²	semidirect
110. C₂×C₄×Dic₄₇	C₂²	semidirect
111. C₄²×D₄₇	C₂²	semidirect
112. C₂×#41×C₄₇	C₂²	semidirect
114. #124×C₄₇	C₂²	semidirect
115. #123×C₄₇	C₂²	semidirect
117. #121×C₄₇	C₂²	semidirect
118. #121×C₄₇	C₂²	semidirect
121. C₄×D₄×C₄₇	C₂²	semidirect
283. C₂×Dic₄₇	#41	semidirect
370. #546	D₄₇	semidirect
382. C₄₇	#3508	semidirect
389. C₂×#41	C₂×D₄₇	semidirect
412. #124	C₂×D₄₇	semidirect
420. #123	C₂×D₄₇	semidirect
440. #121	C₂×D₄₇	semidirect
441. #121	C₂×D₄₇	semidirect
470. C₄×D₄	C₂×D₄₇	semidirect