Subgroups — #20257225

Order 6016.

1152 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689825	C₂	1	2	yes	maximal, complemented
2	#15689816	C₂	1	2	yes	maximal, complemented
3	#15689816	C₂	1	2	yes	maximal, complemented
4	#15689810	C₂	1	2	yes	maximal, complemented
5	#15689804	C₂	1	2	yes	maximal, complemented
6	#15689796	C₂	1	2	yes	maximal, complemented
7	#15689779	C₂	1	2	yes	maximal, complemented
8	#15689760	C₂	1	2	yes	maximal, complemented
9	#15689717	C₂	1	2	yes	maximal, complemented
10	#15689708	C₂	1	2	yes	maximal, complemented
11	#15689682	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689650	C₂	1	2	yes	maximal, complemented
13	#15689629	C₂	1	2	yes	maximal, complemented
14	C₂×#13094001	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13093996	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689598	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689596	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#534	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625352	C₂²	1	2	yes	complemented
21	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
26	#13094019	C₂²	1	2	yes	complemented
27	#13094019	C₂²	1	2	yes	complemented
28	#13094017	C₂²	1	2	yes	complemented
29	#13094017	C₂²	1	2	yes	complemented
30	#13094017	C₂²	1	2	yes	complemented
31	#13094017	C₂²	1	2	yes	complemented
32	#13094015	C₂²	1	2	yes	complemented
33	#13094014	C₂²	1	2	yes	complemented
34	#13094014	C₂²	1	2	yes	complemented
35	#13094011	C₂²	1	2	yes	complemented
36	#13094010	C₂²	1	2	yes	complemented
37	#13094010	C₂²	1	2	yes	complemented
38	#13094008	C₂²	1	2	yes	complemented
39	#13094008	C₂²	1	2	yes	complemented
40	#13094007	C₂²	1	2	yes	complemented
41	#13094006	C₂²	1	2	yes	complemented
42	#13094006	C₂²	1	2	yes	complemented
43	#13094005	C₂²	1	2	yes	—
44	#13094005	C₂²	1	2	yes	complemented
45	#13094005	C₂²	1	2	yes	complemented
46	#13094004	C₂²	1	2	yes	complemented
47	#13094001	C₂²	1	2	yes	complemented
48	#13094001	C₂²	1	2	yes	complemented
49	#13094001	C₂²	1	2	yes	complemented
50	#13094001	C₂²	1	2	yes	complemented
51	#13094001	C₂²	1	2	yes	complemented
52	#13094001	C₂²	1	2	yes	complemented
53	#13093996	C₂²	1	2	yes	—
54	#13093996	C₂²	1	2	yes	—
55	#13093996	C₂²	1	2	yes	complemented
56	#13093996	C₂²	1	2	yes	complemented
57	#13093996	C₂²	1	2	yes	complemented
58	#13093996	C₂²	1	2	yes	complemented
59	#13093996	C₂²	1	2	yes	complemented
60	#13093996	C₂²	1	2	yes	complemented
61	#13093995	C₂²	1	2	yes	complemented
62	#13093993	C₂²	1	2	yes	complemented
63	#13093992	C₂²	1	2	yes	—
64	#13093989	C₂²	1	2	yes	complemented
65	D₄×Dic₄₇	C₂²	1	2	yes	—
66	D₄×Dic₄₇	C₂²	1	2	yes	—
67	D₄×Dic₄₇	C₂²	1	2	yes	complemented
68	D₄×Dic₄₇	C₂²	1	2	yes	complemented
69	D₄×Dic₄₇	C₂²	1	2	yes	complemented
70	D₄×Dic₄₇	C₂²	1	2	yes	complemented
71	D₄×Dic₄₇	C₂²	1	2	yes	complemented
72	D₄×Dic₄₇	C₂²	1	2	yes	complemented
73	D₄×Dic₄₇	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
76	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
77	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
78	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
79	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
80	#13093983	C₂²	1	2	yes	complemented
81	#13093982	C₂²	1	2	yes	complemented
82	#13093980	C₂²	1	2	yes	complemented
83	#13093980	C₂²	1	2	yes	complemented
84	#13093980	C₂²	1	2	yes	complemented
85	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
92	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
97	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
99	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
100	#123×C₄₇	C₂²	1	2	yes	—
101	#123×C₄₇	C₂²	1	2	yes	complemented
102	#121×C₄₇	C₂²	1	2	yes	complemented
103	#121×C₄₇	C₂²	1	2	yes	complemented
104	#120×C₄₇	C₂²	1	2	yes	—
105	#120×C₄₇	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
109	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
110	C₂³×D₄₇	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	4	no	—
113	C₂×D₄×C₄₇	C₂³	1	2	yes	—
114	C₂×D₄×C₄₇	C₂³	1	2	yes	—
115	C₂×D₄×C₄₇	C₂³	1	2	yes	—
116	C₂×D₄×C₄₇	C₂³	1	2	yes	—
117	C₂×D₄×C₄₇	C₂³	1	2	yes	—
118	C₂×D₄×C₄₇	C₂³	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊D₄₇	—	2	4	no	—
124	C₂×C₂²⋊D₄₇	—	4	2	no	—
125	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
131	C₂²×Dic₄₇	—	4	2	no	—
132	C₂²×Dic₄₇	—	4	2	no	—
133	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₄₇	C₂³	1	2	yes	—
138	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
139	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
141	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂³	1	2	yes	—
145	C₂²×Dic₄₇	C₂³	1	2	yes	—
146	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
147	C₂²×Dic₄₇	C₂³	1	2	yes	—
148	#10625352	—	4	4	no	—
149	C₂×C₄×D₄₇	C₂³	1	2	yes	—
150	C₂×C₄×D₄₇	C₂³	1	2	yes	—
151	C₂×Dic₉₄	—	4	2	no	—
152	C₂×Dic₉₄	C₂³	1	2	yes	—
153	C₂×Dic₉₄	C₂³	1	2	yes	—
154	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
164	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
165	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
166	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
171	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
174	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	C₄⋊Dic₄₇	C₂³	1	2	yes	—
181	C₄⋊Dic₄₇	C₂³	1	2	yes	—
182	C₄⋊Dic₄₇	C₂³	1	2	yes	—
183	C₄⋊Dic₄₇	C₂³	1	2	yes	—
184	C₄⋊Dic₄₇	C₂³	1	2	yes	—
185	C₄⋊Dic₄₇	C₂³	1	2	yes	—
186	Dic₄₇⋊C₄	C₂³	1	2	yes	—
187	Dic₄₇⋊C₄	C₂³	1	2	yes	—
188	Dic₄₇⋊C₄	C₂³	1	2	yes	—
189	Dic₄₇⋊C₄	C₂³	1	2	yes	—
190	Dic₄₇⋊C₄	C₂³	1	2	yes	—
191	Dic₄₇⋊C₄	C₂³	1	2	yes	—
192	Dic₄₇⋊C₄	C₂³	1	2	yes	—
193	Dic₄₇⋊C₄	C₂³	1	2	yes	—
194	Dic₄₇⋊C₄	C₂³	1	2	yes	—
195	Dic₄₇⋊C₄	C₂³	1	2	yes	—
196	C₄×Dic₄₇	C₂³	1	2	yes	—
197	C₄×Dic₄₇	C₂³	1	2	yes	—
198	C₄×Dic₄₇	C₂³	1	2	yes	—
199	C₄×Dic₄₇	C₂³	1	2	yes	—
200	C₄×Dic₄₇	C₂³	1	2	yes	—
201	C₄×Dic₄₇	C₂³	1	2	yes	—
202	C₂³×C₄₇	—	2	2	no	—
203	C₂³×C₄₇	—	2	2	no	—
204	C₂³×C₄₇	—	4	1	no	—
205	C₂³×C₄₇	—	4	1	no	—
206	C₂³×C₄₇	—	4	1	no	—
207	C₂³×C₄₇	—	4	1	no	—
208	C₂³×C₄₇	—	4	1	no	—
209	C₂³×C₄₇	—	4	1	no	—
210	C₂³×C₄₇	#41	1	4	yes	complemented
211	C₂³×C₄₇	C₂⁴	1	2	yes	—
212	C₂³×C₄₇	C₂⁴	1	2	yes	—
213	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
214	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
215	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
216	C₂²×D₄₇	—	2	2	no	—
217	C₂²×D₄₇	—	4	1	no	—
218	C₂²×D₄₇	—	4	1	no	—
219	C₂²×D₄₇	C₂⁴	1	2	yes	—
220	D₄×C₄₇	—	2	4	no	—
221	D₄×C₄₇	—	2	4	no	—
222	D₄×C₄₇	—	2	4	no	—
223	D₄×C₄₇	—	2	4	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	4	1	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
231	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
232	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
233	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
234	C₂²⋊D₄₇	—	2	4	no	—
235	C₂²⋊D₄₇	—	2	4	no	—
236	C₂²⋊D₄₇	—	2	4	no	—
237	C₂²⋊D₄₇	—	4	2	no	—
238	C₂²⋊D₄₇	—	4	2	no	—
239	C₂²⋊D₄₇	—	4	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	—	2	2	no	—
242	C₂×Dic₄₇	—	2	4	no	—
243	C₂×Dic₄₇	—	2	2	no	—
244	C₂×Dic₄₇	—	2	2	no	—
245	C₂×Dic₄₇	—	4	1	no	—
246	C₂×Dic₄₇	—	4	2	no	—
247	C₂×Dic₄₇	—	4	1	no	—
248	C₂×Dic₄₇	—	4	1	no	—
249	C₂×Dic₄₇	—	4	1	no	—
250	C₂×Dic₄₇	—	4	2	no	—
251	C₂×Dic₄₇	—	4	1	no	—
252	C₂×Dic₄₇	—	4	1	no	—
253	C₂×Dic₄₇	—	4	2	no	—
254	C₂×Dic₄₇	—	4	1	no	—
255	C₂×Dic₄₇	C₂⁴	1	2	yes	—
256	C₂×Dic₄₇	C₂⁴	1	2	yes	—
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	2	yes	—
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	2	yes	—
261	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
264	C₄×D₄₇	—	4	2	no	—
265	C₄×D₄₇	—	4	2	no	—
266	Dic₉₄	—	2	4	no	—
267	Dic₉₄	—	4	2	no	—
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	2	no	—
275	C₂²×C₄₇	—	2	2	no	—
276	C₂²×C₄₇	—	2	2	no	—
277	C₂²×C₄₇	—	2	2	no	—
278	C₂²×C₄₇	—	2	2	no	—
279	C₂²×C₄₇	—	2	2	no	—
280	C₂²×C₄₇	—	4	4	no	—
281	C₂²×C₄₇	—	4	4	no	—
282	C₂²×C₄₇	—	8	2	no	—
283	C₂²×C₄₇	C₂×#41	1	2	yes	—
284	C₂²×C₄₇	C₂×#41	1	2	yes	—
285	C₂²×C₄₇	C₂×#41	1	2	yes	—
286	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
287	C₂×D₄₇	—	2	2	no	—
288	C₂×D₄₇	—	2	2	no	—
289	C₂×D₄₇	—	2	2	no	—
290	C₂×D₄₇	—	8	2	no	—
291	C₄×C₄₇	—	2	2	no	—
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	2	no	—
294	C₄×C₄₇	—	2	2	no	—
295	Dic₄₇	—	2	2	no	—
296	Dic₄₇	—	2	2	no	—
297	Dic₄₇	—	2	1	no	—
298	Dic₄₇	—	2	2	no	—
299	Dic₄₇	—	2	1	no	—
300	Dic₄₇	—	2	1	no	—
301	Dic₄₇	—	2	2	no	—
302	Dic₄₇	—	2	2	no	—
303	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
304	#3505	—	47	1	no	maximal, Sylow
305	C₂×C₄₇	—	2	2	no	—
306	C₂×C₄₇	—	2	2	no	—
307	C₂×C₄₇	—	2	2	no	—
308	C₂×C₄₇	—	4	2	no	—
309	C₂×C₄₇	—	4	2	no	—
310	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
311	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄₇	#585	1	1	yes	characteristic
313	D₄₇	—	4	2	no	—
314	#553	—	47	2	no	—
315	#553	—	47	2	no	—
316	#553	—	47	2	no	—
317	#552	—	47	2	no	—
318	#551	—	47	2	no	—
319	#551	—	47	2	no	—
320	#548	—	47	2	no	—
321	#546	—	47	2	no	—
322	#539	—	47	2	no	—
323	#538	—	47	2	no	—
324	#534	—	47	1	no	—
325	#534	D₄₇	1	1	yes	characteristic, complemented
326	#529	—	47	2	no	—
327	#525	—	47	2	no	—
328	C₂×C₂²⋊Q₈	—	47	1	no	—
329	C₂×#121	—	47	1	no	—
330	#518	—	47	1	no	—
331	#518	—	47	1	no	—
332	C₂×C₄×D₄	—	47	1	no	—
333	C₄₇	#3505	1	1	yes	characteristic, complemented, Sylow
334	C₂×#41	—	47	2	no	—
335	C₂²×Q₈	—	47	1	no	—
336	C₂²×D₄	—	47	1	no	—
337	C₂²×D₄	—	47	1	no	—
338	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
339	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
340	C₂³×C₄	—	47	1	no	—
341	C₂³×C₄	—	47	1	no	—
342	#126	—	47	2	no	—
343	#126	—	47	2	no	—
344	#126	—	47	2	no	—
345	#126	—	47	2	no	—
346	#126	—	47	2	no	—
347	#126	—	47	2	no	—
348	#125	—	47	2	no	—
349	#125	—	47	2	no	—
350	#125	—	47	2	no	—
351	#124	—	47	2	no	—
352	#124	—	47	2	no	—
353	#124	—	47	2	no	—
354	#123	—	47	2	no	—
355	#123	—	47	2	no	—
356	#123	—	47	2	no	—
357	#123	—	47	2	no	—
358	#123	—	47	2	no	—
359	#123	—	47	2	no	—
360	#123	—	47	2	no	—
361	#123	—	47	2	no	—
362	#123	C₂×D₄₇	1	2	yes	—
363	#123	C₂×D₄₇	1	2	yes	complemented
364	C₂²⋊Q₈	—	47	2	no	—
365	C₂²⋊Q₈	—	47	2	no	—
366	C₂²⋊Q₈	—	47	2	no	—
367	C₂²⋊Q₈	—	47	2	no	—
368	C₂²⋊Q₈	—	47	2	no	—
369	C₂²⋊Q₈	—	47	2	no	—
370	C₂²⋊Q₈	—	47	2	no	—
371	#121	—	47	2	no	—
372	#121	—	47	2	no	—
373	#121	—	47	2	no	—
374	#121	—	47	2	no	—
375	#121	—	47	2	no	—
376	#121	—	47	2	no	—
377	#121	—	47	2	no	—
378	#121	—	47	2	no	—
379	#121	—	47	2	no	—
380	#121	C₂×D₄₇	1	2	yes	complemented
381	#121	C₂×D₄₇	1	2	yes	complemented
382	#120	—	47	2	no	—
383	#120	—	47	2	no	—
384	#120	C₂×D₄₇	1	2	yes	—
385	#120	C₂×D₄₇	1	2	yes	complemented
386	C₄×Q₈	—	47	2	no	—
387	C₄×D₄	—	47	2	no	—
388	C₄×D₄	—	47	2	no	—
389	C₄×D₄	—	47	2	no	—
390	C₄×D₄	—	47	2	no	—
391	C₄×D₄	—	47	2	no	—
392	C₄×D₄	—	47	2	no	—
393	C₄×D₄	—	47	2	no	—
394	C₄×D₄	—	47	2	no	—
395	C₄×D₄	—	47	2	no	—
396	C₄×D₄	—	47	2	no	—
397	C₄×D₄	—	47	2	no	—
398	C₄×D₄	—	47	2	no	—
399	C₄×D₄	—	47	2	no	—
400	C₄×D₄	—	47	2	no	—
401	C₄×D₄	—	47	2	no	—
402	#117	—	47	2	no	—
403	#117	—	47	2	no	—
404	#117	—	47	2	no	—
405	#117	—	47	2	no	—
406	#117	—	47	2	no	—
407	C₂×C₄⋊C₄	—	47	1	no	—
408	C₂×C₄⋊C₄	—	47	1	no	—
409	C₂×C₄⋊C₄	—	47	1	no	—
410	C₂×C₄⋊C₄	—	47	1	no	—
411	C₂×C₄⋊C₄	—	47	1	no	—
412	C₂×C₂²⋊C₄	—	47	1	no	—
413	C₂×C₂²⋊C₄	—	47	1	no	—
414	C₂×C₂²⋊C₄	—	47	1	no	—
415	C₂×C₂²⋊C₄	—	47	2	no	—
416	C₂×C₂²⋊C₄	—	47	1	no	—
417	C₂×C₂²⋊C₄	—	47	1	no	—
418	C₂×C₂²⋊C₄	—	47	2	no	—
419	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
420	C₂×C₄²	—	47	1	no	—
421	C₂⁴	—	47	1	no	—
422	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
423	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
424	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
425	#41	—	188	4	no	—
426	C₂×Q₈	—	47	2	no	—
427	C₂×Q₈	—	47	2	no	—
428	C₂×Q₈	—	188	2	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	47	2	no	—
432	C₂×D₄	—	47	2	no	—
433	C₂×D₄	—	47	2	no	—
434	C₂×D₄	—	47	2	no	—
435	C₂×D₄	—	47	2	no	—
436	C₂×D₄	—	47	2	no	—
437	C₂×D₄	—	94	4	no	—
438	C₂×D₄	—	188	2	no	—
439	C₂×D₄	C₂²×D₄₇	1	2	yes	—
440	C₂×D₄	C₂²×D₄₇	1	2	yes	—
441	C₂×D₄	C₂²×D₄₇	1	2	yes	—
442	C₂×D₄	C₂²×D₄₇	1	2	yes	—
443	C₂×D₄	C₂²×D₄₇	1	2	yes	—
444	C₂×D₄	C₂²×D₄₇	1	2	yes	—
445	C₂²×C₄	—	47	1	no	—
446	C₂²×C₄	—	47	1	no	—
447	C₂²×C₄	—	47	1	no	—
448	C₂²×C₄	—	47	1	no	—
449	C₂²×C₄	—	47	2	no	—
450	C₂²×C₄	—	47	1	no	—
451	C₂²×C₄	—	47	1	no	—
452	C₂²×C₄	—	47	1	no	—
453	C₂²×C₄	—	47	1	no	—
454	C₂²×C₄	—	47	1	no	—
455	C₂²×C₄	—	47	1	no	—
456	C₂²×C₄	—	47	2	no	—
457	C₂²×C₄	—	47	2	no	—
458	C₂²×C₄	—	47	1	no	—
459	C₂²×C₄	—	47	2	no	—
460	C₂²×C₄	—	47	2	no	—
461	C₂²×C₄	—	47	2	no	—
462	C₂²×C₄	—	188	2	no	—
463	C₂²×C₄	—	188	2	no	—
464	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
468	C₄⋊C₄	—	47	2	no	—
469	C₄⋊C₄	—	47	2	no	—
470	C₄⋊C₄	—	47	2	no	—
471	C₄⋊C₄	—	47	2	no	—
472	C₄⋊C₄	—	47	2	no	—
473	C₄⋊C₄	—	47	2	no	—
474	C₄⋊C₄	—	47	2	no	—
475	C₄⋊C₄	—	47	2	no	—
476	C₄⋊C₄	—	47	2	no	—
477	C₄⋊C₄	—	47	2	no	—
478	C₄⋊C₄	—	47	2	no	—
479	C₄⋊C₄	—	47	2	no	—
480	C₄⋊C₄	—	47	2	no	—
481	C₄⋊C₄	—	47	2	no	—
482	C₄⋊C₄	—	47	2	no	—
483	C₄⋊C₄	—	47	2	no	—
484	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
485	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
486	C₂²⋊C₄	—	47	2	no	—
487	C₂²⋊C₄	—	47	2	no	—
488	C₂²⋊C₄	—	47	2	no	—
489	C₂²⋊C₄	—	47	2	no	—
490	C₂²⋊C₄	—	47	2	no	—
491	C₂²⋊C₄	—	47	2	no	—
492	C₂²⋊C₄	—	47	2	no	—
493	C₂²⋊C₄	—	47	2	no	—
494	C₂²⋊C₄	—	47	2	no	—
495	C₂²⋊C₄	—	47	2	no	—
496	C₂²⋊C₄	—	47	2	no	—
497	C₂²⋊C₄	—	47	2	no	—
498	C₂²⋊C₄	—	47	2	no	—
499	C₂²⋊C₄	—	47	2	no	—
500	C₂²⋊C₄	—	47	2	no	—
501	C₂²⋊C₄	—	47	2	no	—
502	C₂²⋊C₄	—	47	2	no	—
503	C₂²⋊C₄	—	47	2	no	—
504	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
510	C₄²	—	47	2	no	—
511	C₄²	—	47	2	no	—
512	C₄²	—	47	2	no	—
513	C₄²	—	47	2	no	—
514	C₄²	—	47	2	no	—
515	C₄²	—	47	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	47	2	no	—
525	C₂³	—	94	2	no	—
526	C₂³	—	188	1	no	—
527	C₂³	—	188	1	no	—
528	C₂³	#10625352	1	4	yes	complemented
529	C₂³	C₂³×D₄₇	1	2	yes	—
530	C₂³	C₂³×D₄₇	1	2	yes	—
531	C₂³	C₂³×D₄₇	1	1	yes	characteristic
532	C₂³	C₂³×D₄₇	1	1	yes	characteristic
533	C₂³	C₂³×D₄₇	1	1	yes	characteristic
534	Q₈	—	94	4	no	—
535	Q₈	—	188	2	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	94	4	no	—
543	D₄	—	94	4	no	—
544	D₄	—	94	4	no	—
545	D₄	—	188	2	no	—
546	D₄	—	188	2	no	—
547	D₄	—	188	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	47	1	no	—
553	C₂×C₄	—	47	2	no	—
554	C₂×C₄	—	47	2	no	—
555	C₂×C₄	—	47	1	no	—
556	C₂×C₄	—	47	2	no	—
557	C₂×C₄	—	47	2	no	—
558	C₂×C₄	—	47	2	no	—
559	C₂×C₄	—	47	1	no	—
560	C₂×C₄	—	47	1	no	—
561	C₂×C₄	—	94	2	no	—
562	C₂×C₄	—	94	2	no	—
563	C₂×C₄	—	94	2	no	—
564	C₂×C₄	—	94	4	no	—
565	C₂×C₄	—	94	2	no	—
566	C₂×C₄	—	188	2	no	—
567	C₂×C₄	—	188	2	no	—
568	C₂×C₄	—	188	1	no	—
569	C₂×C₄	—	188	2	no	—
570	C₂×C₄	—	188	1	no	—
571	C₂×C₄	—	188	1	no	—
572	C₂×C₄	—	188	2	no	—
573	C₂×C₄	—	188	1	no	—
574	C₂×C₄	—	188	1	no	—
575	C₂×C₄	—	188	1	no	—
576	C₂×C₄	—	188	1	no	—
577	C₂×C₄	—	188	2	no	—
578	C₂×C₄	C₂³×D₄₇	1	2	yes	—
579	C₂×C₄	C₂³×D₄₇	1	2	yes	—
580	C₂×C₄	C₂³×D₄₇	1	2	yes	—
581	C₂×C₄	C₂³×D₄₇	1	2	yes	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	8	2	no	—
597	C₂²	—	94	2	no	—
598	C₂²	—	94	2	no	—
599	C₂²	—	94	2	no	—
600	C₂²	—	376	2	no	—
601	C₂²	C₂×#10625352	1	2	yes	—
602	C₂²	C₂×#10625352	1	2	yes	—
603	C₂²	C₂×#10625352	1	2	yes	—
604	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	47	2	no	—
610	C₄	—	94	2	no	—
611	C₄	—	94	1	no	—
612	C₄	—	94	2	no	—
613	C₄	—	94	1	no	—
614	C₄	—	94	1	no	—
615	C₄	—	94	2	no	—
616	C₄	—	94	2	no	—
617	C₄	—	94	2	no	—
618	C₂	—	2	2	no	—
619	C₂	—	2	2	no	—
620	C₂	—	2	2	no	—
621	C₂	—	4	2	no	—
622	C₂	—	4	2	no	—
623	C₂	—	188	2	no	—
624	C₂	C₂²×#10625352	1	1	yes	characteristic
625	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
626	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#534	C₂
hypercenter	#534	D₄₇
hypocenter	C₄₇	#3505
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. #15689825	C₂	semidirect
2. #15689816	C₂	semidirect
3. #15689816	C₂	semidirect
4. #15689810	C₂	semidirect
5. #15689804	C₂	semidirect
6. #15689796	C₂	semidirect
7. #15689779	C₂	semidirect
8. #15689760	C₂	semidirect
9. #15689717	C₂	semidirect
10. #15689708	C₂	semidirect
11. #15689682	C₂	semidirect
12. #15689650	C₂	semidirect
13. #15689629	C₂	semidirect
14. C₂×#13094001	C₂	semidirect
15. C₂×#13093996	C₂	semidirect
16. #15689598	C₂	semidirect
17. #15689596	C₂	semidirect
18. C₂×D₄×Dic₄₇	C₂	semidirect
19. C₄₇×#534	C₂	semidirect
20. C₂×#10625352	C₂²	semidirect
21. C₂²×Dic₉₄	C₂²	semidirect
23. C₂²×C₂²⋊D₄₇	C₂²	semidirect
25. C₂³×Dic₄₇	C₂²	semidirect
26. #13094019	C₂²	semidirect
27. #13094019	C₂²	semidirect
28. #13094017	C₂²	semidirect
29. #13094017	C₂²	semidirect
30. #13094017	C₂²	semidirect
31. #13094017	C₂²	semidirect
32. #13094015	C₂²	semidirect
33. #13094014	C₂²	semidirect
34. #13094014	C₂²	semidirect
35. #13094011	C₂²	semidirect
36. #13094010	C₂²	semidirect
37. #13094010	C₂²	semidirect
38. #13094008	C₂²	semidirect
39. #13094008	C₂²	semidirect
40. #13094007	C₂²	semidirect
41. #13094006	C₂²	semidirect
42. #13094006	C₂²	semidirect
44. #13094005	C₂²	semidirect
45. #13094005	C₂²	semidirect
46. #13094004	C₂²	semidirect
47. #13094001	C₂²	semidirect
48. #13094001	C₂²	semidirect
49. #13094001	C₂²	semidirect
50. #13094001	C₂²	semidirect
51. #13094001	C₂²	semidirect
52. #13094001	C₂²	semidirect
55. #13093996	C₂²	semidirect
56. #13093996	C₂²	semidirect
57. #13093996	C₂²	semidirect
58. #13093996	C₂²	semidirect
59. #13093996	C₂²	semidirect
60. #13093996	C₂²	semidirect
61. #13093995	C₂²	semidirect
62. #13093993	C₂²	semidirect
64. #13093989	C₂²	semidirect
67. D₄×Dic₄₇	C₂²	semidirect
68. D₄×Dic₄₇	C₂²	semidirect
69. D₄×Dic₄₇	C₂²	semidirect
70. D₄×Dic₄₇	C₂²	semidirect
71. D₄×Dic₄₇	C₂²	semidirect
72. D₄×Dic₄₇	C₂²	semidirect
73. D₄×Dic₄₇	C₂²	semidirect
74. C₄×C₂²⋊D₄₇	C₂²	semidirect
75. C₄×C₂²⋊D₄₇	C₂²	semidirect
76. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
77. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
78. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
79. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
80. #13093983	C₂²	semidirect
81. #13093982	C₂²	semidirect
82. #13093980	C₂²	semidirect
83. #13093980	C₂²	semidirect
84. #13093980	C₂²	semidirect
85. C₂×C₄⋊Dic₄₇	C₂²	semidirect
86. C₂×C₄⋊Dic₄₇	C₂²	semidirect
87. C₂×Dic₄₇⋊C₄	C₂²	semidirect
88. C₂×Dic₄₇⋊C₄	C₂²	semidirect
89. C₂×Dic₄₇⋊C₄	C₂²	semidirect
92. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
93. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
94. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
95. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
96. C₂²⋊C₄×D₄₇	C₂²	semidirect
97. C₂×C₄×Dic₄₇	C₂²	semidirect
101. #123×C₄₇	C₂²	semidirect
102. #121×C₄₇	C₂²	semidirect
103. #121×C₄₇	C₂²	semidirect
105. #120×C₄₇	C₂²	semidirect
210. C₂³×C₄₇	#41	semidirect
325. #534	D₄₇	semidirect
333. C₄₇	#3505	semidirect
363. #123	C₂×D₄₇	semidirect
380. #121	C₂×D₄₇	semidirect
381. #121	C₂×D₄₇	semidirect
385. #120	C₂×D₄₇	semidirect
528. C₂³	#10625352	semidirect