Subgroups — #20257578

Order 6016.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689868	C₂	1	2	yes	maximal, complemented
2	#15689861	C₂	1	2	yes	maximal, complemented
3	#15689816	C₂	1	2	yes	maximal, complemented
4	#15689799	C₂	1	2	yes	maximal, complemented
5	#15689767	C₂	1	2	yes	maximal, complemented
6	#15689763	C₂	1	2	yes	maximal, complemented
7	#15689762	C₂	1	2	yes	maximal, complemented
8	D₄×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
9	#15689723	C₂	1	2	yes	maximal, complemented
10	#15689720	C₂	1	2	yes	maximal, complemented
11	#15689718	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689710	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689705	C₂	1	2	yes	maximal, complemented
14	#15689700	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689682	C₂	1	2	yes	maximal, complemented
16	#15689681	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10625352	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
24	C₂×D₄×D₄₇	C₂²	1	2	yes	complemented
25	#13094020	C₂²	1	2	yes	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	#13094014	C₂²	1	2	yes	complemented
31	#13094014	C₂²	1	2	yes	complemented
32	#13094011	C₂²	1	2	yes	complemented
33	#13094010	C₂²	1	2	yes	complemented
34	#13094010	C₂²	1	2	yes	complemented
35	#13094009	C₂²	1	2	yes	complemented
36	#13094009	C₂²	1	2	yes	complemented
37	#13094008	C₂²	1	2	yes	complemented
38	#13094007	C₂²	1	2	yes	complemented
39	#13094007	C₂²	1	2	yes	complemented
40	#13094007	C₂²	1	2	yes	complemented
41	#13094007	C₂²	1	2	yes	complemented
42	#13094007	C₂²	1	2	yes	complemented
43	#13094006	C₂²	1	2	yes	complemented
44	#13094006	C₂²	1	2	yes	complemented
45	#13094005	C₂²	1	2	yes	complemented
46	#13094005	C₂²	1	2	yes	complemented
47	#13094005	C₂²	1	2	yes	complemented
48	#13094005	C₂²	1	2	yes	complemented
49	#13094003	C₂²	1	2	yes	complemented
50	#13094003	C₂²	1	1	yes	characteristic, complemented
51	#13094003	C₂²	1	1	yes	characteristic, complemented
52	#13094002	C₂²	1	2	yes	complemented
53	#13094002	C₂²	1	2	yes	complemented
54	#13094001	C₂²	1	2	yes	complemented
55	#13094001	C₂²	1	2	yes	complemented
56	#13093998	C₂²	1	2	yes	—
57	#13093998	C₂²	1	1	yes	characteristic, complemented
58	#13093998	C₂²	1	1	yes	characteristic, complemented
59	#13093997	C₂²	1	2	yes	complemented
60	#13093997	C₂²	1	2	yes	complemented
61	#13093996	C₂²	1	2	yes	complemented
62	#13093996	C₂²	1	2	yes	complemented
63	#13093996	C₂²	1	2	yes	complemented
64	#13093996	C₂²	1	2	yes	complemented
65	#13093996	C₂²	1	2	yes	complemented
66	#13093996	C₂²	1	2	yes	complemented
67	#13093996	C₂²	1	2	yes	complemented
68	#13093996	C₂²	1	2	yes	complemented
69	#13093995	C₂²	1	2	yes	complemented
70	#13093995	C₂²	1	2	yes	complemented
71	#13093994	C₂²	1	2	yes	complemented
72	#13093993	C₂²	1	2	yes	—
73	#13093993	C₂²	1	2	yes	complemented
74	#13093993	C₂²	1	2	yes	complemented
75	#13093992	C₂²	1	2	yes	complemented
76	#13093992	C₂²	1	2	yes	complemented
77	#13093992	C₂²	1	2	yes	complemented
78	#13093992	C₂²	1	2	yes	complemented
79	D₄×Dic₄₇	C₂²	1	2	yes	complemented
80	D₄×Dic₄₇	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
85	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
86	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
87	#13093983	C₂²	1	1	yes	characteristic, complemented
88	#13093980	C₂²	1	2	yes	complemented
89	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
96	C₂²×D₄×C₄₇	C₂²	1	2	yes	complemented
97	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
99	#121×C₄₇	C₂²	1	1	yes	characteristic
100	#121×C₄₇	C₂²	1	2	yes	complemented
101	#121×C₄₇	C₂²	1	2	yes	complemented
102	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
103	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
104	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂⁴×C₄₇	C₂³	1	2	yes	—
109	C₂³×D₄₇	C₂³	1	1	yes	characteristic
110	C₂³×D₄₇	C₂³	1	2	yes	—
111	C₂×D₄×C₄₇	—	4	2	no	—
112	C₂×D₄×C₄₇	—	4	4	no	—
113	C₂×D₄×C₄₇	C₂³	1	2	yes	—
114	C₂×D₄×C₄₇	C₂³	1	2	yes	—
115	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₄₇	—	4	2	no	—
129	C₂×C₂²⋊D₄₇	—	4	4	no	—
130	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
141	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂³	1	2	yes	—
144	C₂²×Dic₄₇	C₂³	1	2	yes	—
145	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₄₇	C₂³	1	2	yes	—
147	#10625352	—	4	4	no	—
148	D₄×D₄₇	—	4	4	no	—
149	#10625350	—	4	2	no	—
150	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
151	C₂×D₁₈₈	C₂³	1	2	yes	—
152	C₂×C₄×D₄₇	C₂³	1	2	yes	—
153	C₂×C₄×D₄₇	C₂³	1	2	yes	—
154	C₂×C₄×D₄₇	C₂³	1	2	yes	—
155	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
156	C₂×Dic₉₄	C₂³	1	2	yes	—
157	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₄₇	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	C₂²⋊Dic₄₇	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	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₄₇	C₂³	1	2	yes	—
188	C₄⋊Dic₄₇	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	Dic₄₇⋊C₄	C₂³	1	2	yes	—
197	Dic₄₇⋊C₄	C₂³	1	2	yes	—
198	Dic₄₇⋊C₄	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	—	2	4	no	—
205	C₂³×C₄₇	—	4	1	no	—
206	C₂³×C₄₇	—	4	2	no	—
207	C₂³×C₄₇	—	4	2	no	—
208	C₂³×C₄₇	C₂⁴	1	2	yes	—
209	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂³×C₄₇	C₂⁴	1	2	yes	—
211	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
212	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂²×D₄₇	—	2	2	no	—
214	C₂²×D₄₇	—	4	2	no	—
215	C₂²×D₄₇	—	4	2	no	—
216	C₂²×D₄₇	—	4	1	no	—
217	C₂²×D₄₇	—	4	2	no	—
218	C₂²×D₄₇	—	4	1	no	—
219	C₂²×D₄₇	C₂⁴	1	2	yes	—
220	C₂²×D₄₇	C₂⁴	1	2	yes	—
221	D₄×C₄₇	—	2	4	no	—
222	D₄×C₄₇	—	2	4	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	1	no	—
226	D₄×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	1	no	—
233	C₂×C₄×C₄₇	—	4	1	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
237	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
238	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₄₇	—	2	4	no	—
242	C₂²⋊D₄₇	—	2	4	no	—
243	C₂²⋊D₄₇	—	2	4	no	—
244	C₂²⋊D₄₇	—	4	2	no	—
245	C₂²⋊D₄₇	—	4	2	no	—
246	C₂²⋊D₄₇	—	4	2	no	—
247	C₂²⋊D₄₇	—	4	2	no	—
248	C₂²⋊D₄₇	—	4	2	no	—
249	C₂²⋊D₄₇	—	4	2	no	—
250	C₂²⋊D₄₇	—	4	2	no	—
251	C₂²⋊D₄₇	—	4	2	no	—
252	C₂×Dic₄₇	—	2	2	no	—
253	C₂×Dic₄₇	—	4	2	no	—
254	C₂×Dic₄₇	—	4	1	no	—
255	C₂×Dic₄₇	—	4	2	no	—
256	C₂×Dic₄₇	—	4	2	no	—
257	C₂×Dic₄₇	—	4	1	no	—
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	2	yes	—
262	C₂×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂×Dic₄₇	C₂⁴	1	2	yes	—
264	D₁₈₈	—	4	1	no	—
265	D₁₈₈	—	4	2	no	—
266	C₄×D₄₇	—	4	2	no	—
267	C₄×D₄₇	—	4	2	no	—
268	C₄×D₄₇	—	4	2	no	—
269	Dic₉₄	—	4	1	no	—
270	Dic₉₄	—	4	2	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	2	no	—
276	C₂²×C₄₇	—	2	2	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	2	no	—
279	C₂²×C₄₇	—	2	2	no	—
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	1	no	—
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	4	4	no	—
285	C₂²×C₄₇	—	8	4	no	—
286	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
288	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
289	C₂×D₄₇	—	2	2	no	—
290	C₂×D₄₇	—	2	2	no	—
291	C₂×D₄₇	—	2	2	no	—
292	C₂×D₄₇	—	2	2	no	—
293	C₂×D₄₇	—	2	2	no	—
294	C₂×D₄₇	—	2	2	no	—
295	C₂×D₄₇	—	8	2	no	—
296	C₂×D₄₇	—	8	4	no	—
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	2	1	no	—
300	C₄×C₄₇	—	2	2	no	—
301	C₄×C₄₇	—	2	1	no	—
302	C₄×C₄₇	—	2	1	no	—
303	Dic₄₇	—	2	2	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	—	2	2	no	—
306	Dic₄₇	—	2	2	no	—
307	Dic₄₇	—	2	2	no	—
308	Dic₄₇	—	2	2	no	—
309	#3534	—	47	1	no	maximal, Sylow
310	C₂×C₄₇	—	2	2	no	—
311	C₂×C₄₇	—	2	2	no	—
312	C₂×C₄₇	—	4	2	no	—
313	C₂×C₄₇	—	4	1	no	—
314	C₂×C₄₇	—	4	2	no	—
315	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₄₇	#585	1	1	yes	characteristic
318	D₄₇	—	4	2	no	—
319	D₄₇	—	4	2	no	—
320	#562	—	47	2	no	—
321	#560	—	47	2	no	—
322	#553	—	47	2	no	—
323	#551	—	47	2	no	—
324	#546	—	47	2	no	—
325	#546	—	47	2	no	—
326	#546	—	47	2	no	—
327	D₄²	—	47	2	no	—
328	#540	—	47	2	no	—
329	#539	—	47	1	no	—
330	#539	—	47	2	no	—
331	#538	—	47	2	no	—
332	#538	—	47	1	no	—
333	#537	—	47	1	no	—
334	#534	—	47	2	no	—
335	#534	—	47	1	no	—
336	#525	—	47	1	no	—
337	C₂×#123	—	47	1	no	—
338	C₂×#121	D₄₇	1	1	yes	characteristic, complemented
339	C₄₇	#3534	1	1	yes	characteristic, complemented, Sylow
340	C₂×#41	—	47	2	no	—
341	C₂×#41	—	47	1	no	—
342	C₂²×D₄	—	47	1	no	—
343	C₂²×D₄	—	47	2	no	—
344	C₂²×D₄	—	47	2	no	—
345	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
346	C₂²×D₄	C₂×D₄₇	1	2	yes	complemented
347	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
348	#127	—	47	2	no	—
349	#126	—	47	2	no	—
350	#126	—	47	2	no	—
351	#126	—	47	2	no	—
352	#126	—	47	2	no	—
353	#125	—	47	2	no	—
354	#125	—	47	2	no	—
355	#124	—	47	2	no	—
356	#124	—	47	2	no	—
357	#124	—	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	—	47	2	no	—
363	#123	—	47	2	no	—
364	#123	—	47	2	no	—
365	#123	—	47	2	no	—
366	#123	—	47	2	no	—
367	#123	—	47	2	no	—
368	#123	—	47	2	no	—
369	#123	—	47	2	no	—
370	#123	—	47	2	no	—
371	#123	—	47	2	no	—
372	C₂²⋊Q₈	—	47	1	no	—
373	C₂²⋊Q₈	—	47	1	no	—
374	C₂²⋊Q₈	—	47	2	no	—
375	C₂²⋊Q₈	—	47	2	no	—
376	C₂²⋊Q₈	—	47	2	no	—
377	C₂²⋊Q₈	—	47	2	no	—
378	C₂²⋊Q₈	—	47	2	no	—
379	#121	—	47	2	no	—
380	#121	—	47	2	no	—
381	#121	—	47	2	no	—
382	#121	—	47	2	no	—
383	#121	—	47	2	no	—
384	#121	—	47	2	no	—
385	#121	—	47	2	no	—
386	#121	—	47	2	no	—
387	#121	—	47	2	no	—
388	#121	—	47	2	no	—
389	#121	—	47	1	no	—
390	#121	—	47	1	no	—
391	#121	—	47	2	no	—
392	#121	—	47	2	no	—
393	#121	—	47	2	no	—
394	#121	C₂×D₄₇	1	1	yes	characteristic
395	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
396	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
397	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
398	#121	C₂×D₄₇	1	2	yes	complemented
399	#121	C₂×D₄₇	1	2	yes	complemented
400	#120	—	47	2	no	—
401	#120	—	47	2	no	—
402	#120	—	47	2	no	—
403	#120	—	47	2	no	—
404	#120	—	47	2	no	—
405	#120	—	47	2	no	—
406	#120	—	47	2	no	—
407	#120	—	47	2	no	—
408	C₄×D₄	—	47	2	no	—
409	C₄×D₄	—	47	2	no	—
410	C₄×D₄	—	47	2	no	—
411	C₄×D₄	—	47	2	no	—
412	C₄×D₄	—	47	2	no	—
413	C₄×D₄	—	47	2	no	—
414	C₄×D₄	—	47	2	no	—
415	C₄×D₄	—	47	2	no	—
416	#117	—	47	1	no	—
417	#117	—	47	2	no	—
418	C₂×C₄⋊C₄	—	47	1	no	—
419	C₂×C₄⋊C₄	—	47	1	no	—
420	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	47	1	no	—
422	C₂×C₂²⋊C₄	—	47	2	no	—
423	C₂×C₂²⋊C₄	—	47	1	no	—
424	C₂×C₂²⋊C₄	—	47	1	no	—
425	C₂×C₂²⋊C₄	—	47	2	no	—
426	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	complemented
427	C₂⁴	—	47	1	no	—
428	C₂⁴	—	47	2	no	—
429	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
430	C₂⁴	C₂²×D₄₇	1	2	yes	—
431	#41	—	188	2	no	—
432	#41	—	188	4	no	—
433	C₂×Q₈	—	47	1	no	—
434	C₂×Q₈	—	47	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	47	2	no	—
438	C₂×D₄	—	47	2	no	—
439	C₂×D₄	—	47	2	no	—
440	C₂×D₄	—	47	2	no	—
441	C₂×D₄	—	47	2	no	—
442	C₂×D₄	—	47	2	no	—
443	C₂×D₄	—	47	2	no	—
444	C₂×D₄	—	47	2	no	—
445	C₂×D₄	—	47	2	no	—
446	C₂×D₄	—	47	2	no	—
447	C₂×D₄	—	47	2	no	—
448	C₂×D₄	—	47	1	no	—
449	C₂×D₄	—	47	2	no	—
450	C₂×D₄	—	188	4	no	—
451	C₂×D₄	—	188	2	no	—
452	C₂×D₄	—	188	4	no	—
453	C₂×D₄	C₂²×D₄₇	1	2	yes	—
454	C₂×D₄	C₂²×D₄₇	1	2	yes	—
455	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
456	C₂×D₄	C₂²×D₄₇	1	2	yes	—
457	C₂×D₄	C₂²×D₄₇	1	2	yes	—
458	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
459	C₂×D₄	C₂²×D₄₇	1	2	yes	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	47	1	no	—
462	C₂²×C₄	—	47	1	no	—
463	C₂²×C₄	—	47	2	no	—
464	C₂²×C₄	—	47	2	no	—
465	C₂²×C₄	—	47	1	no	—
466	C₂²×C₄	—	47	2	no	—
467	C₂²×C₄	—	47	2	no	—
468	C₂²×C₄	—	47	2	no	—
469	C₂²×C₄	—	47	2	no	—
470	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
475	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
485	C₄⋊C₄	—	47	2	no	—
486	C₄⋊C₄	—	47	2	no	—
487	C₄⋊C₄	—	47	1	no	—
488	C₄⋊C₄	—	47	1	no	—
489	C₄⋊C₄	—	47	2	no	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
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	—	47	2	no	—
505	C₂²⋊C₄	—	47	2	no	—
506	C₂²⋊C₄	—	47	2	no	—
507	C₂²⋊C₄	—	47	2	no	—
508	C₂²⋊C₄	—	47	2	no	—
509	C₂²⋊C₄	—	47	2	no	—
510	C₂²⋊C₄	—	47	2	no	—
511	C₂²⋊C₄	—	47	2	no	—
512	C₂²⋊C₄	—	47	2	no	—
513	C₂²⋊C₄	—	47	2	no	—
514	C₂²⋊C₄	—	47	2	no	—
515	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
519	C₄²	—	47	2	no	—
520	C₄²	—	47	2	no	—
521	C₄²	—	47	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	47	2	no	—
529	C₂³	—	47	2	no	—
530	C₂³	—	94	2	no	—
531	C₂³	—	188	1	no	—
532	C₂³	—	188	2	no	—
533	C₂³	—	188	2	no	—
534	C₂³	—	188	1	no	—
535	C₂³	—	188	2	no	—
536	C₂³	C₂³×D₄₇	1	2	yes	—
537	C₂³	C₂³×D₄₇	1	1	yes	characteristic
538	C₂³	C₂³×D₄₇	1	2	yes	—
539	C₂³	C₂³×D₄₇	1	1	yes	characteristic
540	C₂³	C₂³×D₄₇	1	1	yes	characteristic
541	Q₈	—	188	1	no	—
542	Q₈	—	188	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	94	4	no	—
551	D₄	—	94	4	no	—
552	D₄	—	94	4	no	—
553	D₄	—	188	2	no	—
554	D₄	—	188	1	no	—
555	D₄	—	188	2	no	—
556	D₄	—	188	2	no	—
557	D₄	—	188	2	no	—
558	D₄	—	188	2	no	—
559	D₄	—	188	2	no	—
560	D₄	—	188	2	no	—
561	D₄	—	188	2	no	—
562	D₄	—	188	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	47	2	no	—
571	C₂×C₄	—	47	2	no	—
572	C₂×C₄	—	47	2	no	—
573	C₂×C₄	—	47	2	no	—
574	C₂×C₄	—	47	2	no	—
575	C₂×C₄	—	47	2	no	—
576	C₂×C₄	—	94	2	no	—
577	C₂×C₄	—	188	2	no	—
578	C₂×C₄	—	188	2	no	—
579	C₂×C₄	—	188	2	no	—
580	C₂×C₄	—	188	1	no	—
581	C₂×C₄	—	188	2	no	—
582	C₂×C₄	—	188	1	no	—
583	C₂×C₄	—	188	2	no	—
584	C₂×C₄	—	188	2	no	—
585	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₄₇	1	2	yes	—
587	C₂×C₄	C₂³×D₄₇	1	2	yes	—
588	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	94	2	no	—
607	C₂²	—	94	2	no	—
608	C₂²	—	94	2	no	—
609	C₂²	—	94	2	no	—
610	C₂²	—	94	2	no	—
611	C₂²	—	94	2	no	—
612	C₂²	—	376	2	no	—
613	C₂²	—	376	4	no	—
614	C₂²	#13094069	1	2	yes	—
615	C₂²	#13094069	1	2	yes	—
616	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	94	2	no	—
624	C₄	—	94	2	no	—
625	C₄	—	94	2	no	—
626	C₄	—	94	2	no	—
627	C₄	—	94	2	no	—
628	C₄	—	94	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	188	2	no	—
635	C₂	—	188	2	no	—
636	C₂	C₂×#13094069	1	1	yes	characteristic
637	C₂	C₂×#13094069	1	1	yes	characteristic
638	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×#121×C₄₇	C₂
hypercenter	C₂×#121	D₄₇
hypocenter	C₄₇	#3534
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #15689868	C₂	semidirect
2. #15689861	C₂	semidirect
3. #15689816	C₂	semidirect
4. #15689799	C₂	semidirect
5. #15689767	C₂	semidirect
6. #15689763	C₂	semidirect
7. #15689762	C₂	semidirect
8. D₄×C₂²⋊D₄₇	C₂	semidirect
9. #15689723	C₂	semidirect
10. #15689720	C₂	semidirect
11. #15689718	C₂	semidirect
12. #15689710	C₂	semidirect
13. #15689705	C₂	semidirect
14. #15689700	C₂	semidirect
15. #15689682	C₂	semidirect
16. #15689681	C₂	semidirect
17. #15689634	C₂	semidirect
18. C₂×#13094007	C₂	semidirect
19. C₂×#121×C₄₇	C₂	semidirect
20. C₂×#10625350	C₂²	semidirect
21. C₂×#10625352	C₂²	semidirect
23. C₂²×C₂²⋊D₄₇	C₂²	semidirect
24. C₂×D₄×D₄₇	C₂²	semidirect
25. #13094020	C₂²	semidirect
26. #13094019	C₂²	semidirect
27. #13094019	C₂²	semidirect
28. #13094017	C₂²	semidirect
29. #13094017	C₂²	semidirect
30. #13094014	C₂²	semidirect
31. #13094014	C₂²	semidirect
32. #13094011	C₂²	semidirect
33. #13094010	C₂²	semidirect
34. #13094010	C₂²	semidirect
35. #13094009	C₂²	semidirect
36. #13094009	C₂²	semidirect
37. #13094008	C₂²	semidirect
38. #13094007	C₂²	semidirect
39. #13094007	C₂²	semidirect
40. #13094007	C₂²	semidirect
41. #13094007	C₂²	semidirect
42. #13094007	C₂²	semidirect
43. #13094006	C₂²	semidirect
44. #13094006	C₂²	semidirect
45. #13094005	C₂²	semidirect
46. #13094005	C₂²	semidirect
47. #13094005	C₂²	semidirect
48. #13094005	C₂²	semidirect
49. #13094003	C₂²	semidirect
50. #13094003	C₂²	semidirect
51. #13094003	C₂²	semidirect
52. #13094002	C₂²	semidirect
53. #13094002	C₂²	semidirect
54. #13094001	C₂²	semidirect
55. #13094001	C₂²	semidirect
57. #13093998	C₂²	semidirect
58. #13093998	C₂²	semidirect
59. #13093997	C₂²	semidirect
60. #13093997	C₂²	semidirect
61. #13093996	C₂²	semidirect
62. #13093996	C₂²	semidirect
63. #13093996	C₂²	semidirect
64. #13093996	C₂²	semidirect
65. #13093996	C₂²	semidirect
66. #13093996	C₂²	semidirect
67. #13093996	C₂²	semidirect
68. #13093996	C₂²	semidirect
69. #13093995	C₂²	semidirect
70. #13093995	C₂²	semidirect
71. #13093994	C₂²	semidirect
73. #13093993	C₂²	semidirect
74. #13093993	C₂²	semidirect
75. #13093992	C₂²	semidirect
76. #13093992	C₂²	semidirect
77. #13093992	C₂²	semidirect
78. #13093992	C₂²	semidirect
79. D₄×Dic₄₇	C₂²	semidirect
80. D₄×Dic₄₇	C₂²	semidirect
81. C₄×C₂²⋊D₄₇	C₂²	semidirect
82. C₄×C₂²⋊D₄₇	C₂²	semidirect
83. C₄×C₂²⋊D₄₇	C₂²	semidirect
84. C₄×C₂²⋊D₄₇	C₂²	semidirect
85. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
87. #13093983	C₂²	semidirect
88. #13093980	C₂²	semidirect
89. C₂×Dic₄₇⋊C₄	C₂²	semidirect
90. C₂×Dic₄₇⋊C₄	C₂²	semidirect
91. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
92. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
93. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
94. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
95. C₂²⋊C₄×D₄₇	C₂²	semidirect
96. C₂²×D₄×C₄₇	C₂²	semidirect
97. C₂²×D₄×C₄₇	C₂²	semidirect
98. C₂³×C₄×C₄₇	C₂²	semidirect
100. #121×C₄₇	C₂²	semidirect
101. #121×C₄₇	C₂²	semidirect
102. #121×C₄₇	C₂²	semidirect
103. #121×C₄₇	C₂²	semidirect
104. #121×C₄₇	C₂²	semidirect
105. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₄₇	C₂²	semidirect
338. C₂×#121	D₄₇	semidirect
339. C₄₇	#3534	semidirect
345. C₂²×D₄	C₂×D₄₇	semidirect
346. C₂²×D₄	C₂×D₄₇	semidirect
347. C₂³×C₄	C₂×D₄₇	semidirect
395. #121	C₂×D₄₇	semidirect
396. #121	C₂×D₄₇	semidirect
397. #121	C₂×D₄₇	semidirect
398. #121	C₂×D₄₇	semidirect
399. #121	C₂×D₄₇	semidirect
420. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
426. C₂×C₂²⋊C₄	C₂×D₄₇	semidirect