Subgroups — #20257330

Order 6016.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689858	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689832	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689822	C₂	1	2	yes	maximal, complemented
4	#15689821	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689814	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689797	C₂	1	2	yes	maximal, complemented
7	#15689797	C₂	1	2	yes	maximal, complemented
8	#15689774	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689769	C₂	1	2	yes	maximal, complemented
10	#15689761	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689761	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689745	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689728	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689720	C₂	1	2	yes	maximal, complemented
16	#15689706	C₂	1	2	yes	maximal, complemented
17	#15689660	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689651	C₂	1	1	yes	maximal, characteristic, complemented
19	#15689632	C₂	1	2	yes	maximal, complemented
20	C₂×#13094009	C₂	1	2	yes	maximal, complemented
21	#15689595	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#520	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625350	C₂²	1	2	yes	complemented
25	C₂²×D₁₈₈	C₂²	1	2	yes	—
26	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₄₇	C₂²	1	2	yes	complemented
29	#13094023	C₂²	1	1	yes	characteristic, complemented
30	#13094021	C₂²	1	1	yes	characteristic
31	#13094019	C₂²	1	1	yes	characteristic, complemented
32	#13094019	C₂²	1	2	yes	complemented
33	#13094019	C₂²	1	2	yes	complemented
34	#13094018	C₂²	1	2	yes	complemented
35	#13094018	C₂²	1	2	yes	complemented
36	#13094017	C₂²	1	1	yes	characteristic, complemented
37	#13094016	C₂²	1	1	yes	characteristic, complemented
38	#13094015	C₂²	1	1	yes	characteristic, complemented
39	#13094014	C₂²	1	2	yes	complemented
40	#13094014	C₂²	1	1	yes	characteristic, complemented
41	#13094013	C₂²	1	1	yes	characteristic, complemented
42	#13094013	C₂²	1	1	yes	characteristic, complemented
43	#13094012	C₂²	1	2	yes	complemented
44	#13094012	C₂²	1	2	yes	complemented
45	#13094010	C₂²	1	1	yes	characteristic, complemented
46	#13094009	C₂²	1	2	yes	—
47	#13094009	C₂²	1	1	yes	characteristic
48	#13094009	C₂²	1	2	yes	complemented
49	#13094009	C₂²	1	2	yes	complemented
50	#13094009	C₂²	1	2	yes	complemented
51	#13094009	C₂²	1	2	yes	complemented
52	#13094009	C₂²	1	2	yes	complemented
53	#13094009	C₂²	1	2	yes	complemented
54	#13094009	C₂²	1	2	yes	complemented
55	#13094009	C₂²	1	2	yes	complemented
56	#13094007	C₂²	1	2	yes	complemented
57	#13094007	C₂²	1	2	yes	complemented
58	#13094007	C₂²	1	2	yes	complemented
59	#13094006	C₂²	1	1	yes	characteristic, complemented
60	#13094003	C₂²	1	2	yes	complemented
61	#13094002	C₂²	1	2	yes	complemented
62	#13094002	C₂²	1	2	yes	complemented
63	#13094002	C₂²	1	1	yes	characteristic, complemented
64	#13094001	C₂²	1	2	yes	complemented
65	#13094001	C₂²	1	2	yes	complemented
66	#13094000	C₂²	1	1	yes	characteristic, complemented
67	#13094000	C₂²	1	1	yes	characteristic, complemented
68	#13093999	C₂²	1	1	yes	characteristic
69	#13093999	C₂²	1	1	yes	characteristic
70	#13093998	C₂²	1	2	yes	—
71	#13093998	C₂²	1	1	yes	characteristic, complemented
72	#13093998	C₂²	1	1	yes	characteristic, complemented
73	#13093998	C₂²	1	2	yes	complemented
74	#13093997	C₂²	1	1	yes	characteristic
75	#13093997	C₂²	1	2	yes	complemented
76	#13093997	C₂²	1	2	yes	complemented
77	#13093996	C₂²	1	2	yes	complemented
78	#13093996	C₂²	1	2	yes	complemented
79	#13093994	C₂²	1	2	yes	—
80	#13093994	C₂²	1	2	yes	—
81	#13093992	C₂²	1	2	yes	complemented
82	#13093992	C₂²	1	2	yes	complemented
83	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
85	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₁₈₈	C₂²	1	2	yes	complemented
88	C₄×D₁₈₈	C₂²	1	2	yes	complemented
89	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
90	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
91	#13093986	C₂²	1	1	yes	characteristic, complemented
92	#13093986	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
98	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
100	#13093982	C₂²	1	1	yes	characteristic, complemented
101	#13093981	C₂²	1	1	yes	characteristic, complemented
102	#13093981	C₂²	1	2	yes	complemented
103	#13093981	C₂²	1	2	yes	complemented
104	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
107	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
118	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
119	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
120	#117×C₄₇	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
123	C₂³×D₄₇	C₂³	1	2	yes	—
124	C₂³×D₄₇	C₂³	1	2	yes	—
125	#41×C₄₇	—	2	4	no	—
126	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₄₇	C₂³	1	2	yes	—
128	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₄₇	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	1	yes	characteristic
137	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
140	C₂²×Dic₄₇	C₂³	1	2	yes	—
141	C₂²×Dic₄₇	C₂³	1	2	yes	—
142	D₄×D₄₇	—	2	4	no	—
143	D₄×D₄₇	—	2	4	no	—
144	#10625350	—	4	4	no	—
145	C₂×D₁₈₈	—	4	4	no	—
146	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
147	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
148	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
149	C₂×D₁₈₈	C₂³	1	2	yes	—
150	C₂×D₁₈₈	C₂³	1	2	yes	—
151	C₂×D₁₈₈	C₂³	1	2	yes	—
152	C₂×D₁₈₈	C₂³	1	2	yes	—
153	C₂×C₄×D₄₇	—	4	4	no	—
154	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₄₇	C₂³	1	2	yes	—
157	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₄₇	C₂³	1	2	yes	—
160	C₂×C₄×D₄₇	C₂³	1	2	yes	—
161	C₂×C₄×D₄₇	C₂³	1	2	yes	—
162	C₂×C₄×D₄₇	C₂³	1	2	yes	—
163	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
164	C₂×Dic₉₄	C₂³	1	2	yes	—
165	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
170	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
171	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
176	C₄²×C₄₇	C₂³	1	1	yes	characteristic
177	C₄²×C₄₇	C₂³	1	1	yes	characteristic
178	C₄²×C₄₇	C₂³	1	2	yes	—
179	C₄²×C₄₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
184	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₄₇)⋊C₄	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	2	yes	—
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	2	yes	—
205	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₄₇	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	2	yes	—
211	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₄₇⋊C₄	C₂³	1	2	yes	—
213	Dic₄₇⋊C₄	C₂³	1	2	yes	—
214	Dic₄₇⋊C₄	C₂³	1	2	yes	—
215	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₄₇⋊C₄	C₂³	1	2	yes	—
218	Dic₄₇⋊C₄	C₂³	1	2	yes	—
219	Dic₄₇⋊C₄	C₂³	1	2	yes	—
220	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
222	Dic₄₇⋊C₄	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	2	yes	—
227	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
228	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₄₇	C₂⁴	1	2	yes	—
230	C₂²×D₄₇	—	2	4	no	—
231	C₂²×D₄₇	—	2	4	no	—
232	C₂²×D₄₇	—	2	4	no	—
233	C₂²×D₄₇	—	4	2	no	—
234	C₂²×D₄₇	—	4	2	no	—
235	C₂²×D₄₇	—	4	2	no	—
236	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₄₇	C₂⁴	1	2	yes	—
238	C₂²×D₄₇	C₂⁴	1	2	yes	—
239	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
240	Q₈×C₄₇	—	2	2	no	—
241	D₄×C₄₇	—	2	4	no	—
242	D₄×C₄₇	#41	1	4	yes	complemented
243	C₂×C₄×C₄₇	—	2	4	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
254	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₄₇	—	2	4	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂²⋊D₄₇	—	2	2	no	—
260	C₂²⋊D₄₇	—	4	2	no	—
261	C₂²⋊D₄₇	—	4	1	no	—
262	C₂²⋊D₄₇	—	4	2	no	—
263	C₂×Dic₄₇	—	4	2	no	—
264	C₂×Dic₄₇	—	4	2	no	—
265	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₄₇	C₂⁴	1	2	yes	—
270	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₄₇	C₂⁴	1	2	yes	—
273	D₁₈₈	—	2	2	no	—
274	D₁₈₈	—	2	4	no	—
275	D₁₈₈	—	2	2	no	—
276	D₁₈₈	—	2	2	no	—
277	D₁₈₈	—	4	2	no	—
278	D₁₈₈	—	4	2	no	—
279	D₁₈₈	—	4	2	no	—
280	C₄×D₄₇	—	2	2	no	—
281	C₄×D₄₇	—	2	4	no	—
282	C₄×D₄₇	—	2	2	no	—
283	C₄×D₄₇	—	2	2	no	—
284	C₄×D₄₇	—	4	2	no	—
285	C₄×D₄₇	—	4	2	no	—
286	C₄×D₄₇	—	4	1	no	—
287	C₄×D₄₇	—	4	2	no	—
288	C₄×D₄₇	—	4	2	no	—
289	Dic₉₄	—	4	1	no	—
290	Dic₉₄	—	4	2	no	—
291	C₂²×C₄₇	—	2	2	no	—
292	C₂²×C₄₇	—	2	2	no	—
293	C₂²×C₄₇	—	2	1	no	—
294	C₂²×C₄₇	—	2	1	no	—
295	C₂²×C₄₇	—	2	1	no	—
296	C₂²×C₄₇	C₂×#41	1	4	yes	—
297	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
298	C₂×D₄₇	—	2	1	no	—
299	C₂×D₄₇	—	2	1	no	—
300	C₂×D₄₇	—	2	1	no	—
301	C₂×D₄₇	—	2	2	no	—
302	C₂×D₄₇	—	2	2	no	—
303	C₂×D₄₇	—	2	2	no	—
304	C₂×D₄₇	—	2	2	no	—
305	C₂×D₄₇	—	2	1	no	—
306	C₂×D₄₇	—	2	2	no	—
307	C₂×D₄₇	—	2	2	no	—
308	C₂×D₄₇	—	2	1	no	—
309	C₂×D₄₇	—	4	8	no	—
310	C₂×D₄₇	—	8	4	no	—
311	C₂×D₄₇	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₄₇	—	2	1	no	—
313	C₄×C₄₇	—	2	2	no	—
314	C₄×C₄₇	—	2	2	no	—
315	C₄×C₄₇	—	2	1	no	—
316	C₄×C₄₇	—	2	2	no	—
317	C₄×C₄₇	—	2	1	no	—
318	C₄×C₄₇	—	2	1	no	—
319	C₄×C₄₇	—	2	1	no	—
320	C₄×C₄₇	C₂×#41	1	2	yes	—
321	Dic₄₇	—	2	1	no	—
322	Dic₄₇	—	2	1	no	—
323	Dic₄₇	—	2	1	no	—
324	Dic₄₇	—	2	2	no	—
325	Dic₄₇	—	2	1	no	—
326	Dic₄₇	—	2	1	no	—
327	Dic₄₇	—	2	1	no	—
328	Dic₄₇	—	2	2	no	—
329	#3513	—	47	1	no	maximal, Sylow
330	C₂×C₄₇	—	2	4	no	—
331	C₂×C₄₇	—	4	1	no	—
332	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
333	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄₇	#585	1	1	yes	characteristic
335	D₄₇	—	2	2	no	—
336	D₄₇	—	4	2	no	—
337	D₄₇	—	4	2	no	—
338	D₄₇	—	4	1	no	—
339	#559	—	47	1	no	—
340	#554	—	47	1	no	—
341	#553	—	47	2	no	—
342	#553	—	47	1	no	—
343	#552	—	47	1	no	—
344	#551	—	47	2	no	—
345	#551	—	47	2	no	—
346	#547	—	47	1	no	—
347	#546	—	47	1	no	—
348	#546	—	47	1	no	—
349	#546	—	47	2	no	—
350	D₄²	—	47	1	no	—
351	#542	—	47	1	no	—
352	#540	—	47	1	no	—
353	#539	—	47	2	no	—
354	#538	—	47	2	no	—
355	#529	—	47	1	no	—
356	#529	—	47	1	no	—
357	#525	—	47	2	no	—
358	C₂×#123	—	47	2	no	—
359	#520	D₄₇	1	1	yes	characteristic, complemented
360	#518	—	47	1	no	—
361	C₂×C₄×D₄	—	47	1	no	—
362	C₄₇	#3513	1	1	yes	characteristic, complemented, Sylow
363	C₂×#41	—	47	2	no	—
364	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
365	C₂²×D₄	—	47	1	no	—
366	C₂²×D₄	—	47	1	no	—
367	C₂²×D₄	—	47	2	no	—
368	C₂³×C₄	—	47	2	no	—
369	C₄⋊Q₈	—	47	1	no	—
370	#127	—	47	1	no	—
371	#126	—	47	2	no	—
372	#126	—	47	1	no	—
373	#126	—	47	2	no	—
374	#126	—	47	1	no	—
375	#126	—	47	2	no	—
376	#126	—	47	2	no	—
377	#125	—	47	1	no	—
378	#125	—	47	1	no	—
379	#125	—	47	2	no	—
380	#125	—	47	1	no	—
381	#124	—	47	1	no	—
382	#124	—	47	1	no	—
383	#124	—	47	1	no	—
384	#124	—	47	2	no	—
385	#124	—	47	2	no	—
386	#123	—	47	2	no	—
387	#123	—	47	2	no	—
388	#123	—	47	2	no	—
389	#123	—	47	1	no	—
390	#123	—	47	2	no	—
391	#123	—	47	2	no	—
392	#123	—	47	2	no	—
393	#123	—	47	2	no	—
394	#123	—	47	2	no	—
395	#123	—	47	2	no	—
396	#123	—	47	2	no	—
397	#123	—	47	2	no	—
398	#123	—	47	2	no	—
399	#123	—	47	1	no	—
400	C₂²⋊Q₈	—	47	1	no	—
401	C₂²⋊Q₈	—	47	1	no	—
402	C₂²⋊Q₈	—	47	2	no	—
403	C₂²⋊Q₈	—	47	2	no	—
404	C₂²⋊Q₈	—	47	1	no	—
405	C₂²⋊Q₈	—	47	2	no	—
406	C₂²⋊Q₈	—	47	2	no	—
407	C₂²⋊Q₈	—	47	2	no	—
408	#121	—	47	2	no	—
409	#121	—	47	2	no	—
410	#121	—	47	2	no	—
411	#121	—	47	2	no	—
412	#121	—	47	1	no	—
413	#121	—	47	1	no	—
414	#121	—	47	1	no	—
415	#121	—	47	1	no	—
416	#121	—	47	2	no	—
417	#121	—	47	1	no	—
418	#121	—	47	2	no	—
419	#120	—	47	2	no	—
420	#120	—	47	2	no	—
421	#120	—	47	2	no	—
422	#120	—	47	2	no	—
423	C₄×Q₈	—	47	1	no	—
424	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
425	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
426	C₄×D₄	—	47	1	no	—
427	C₄×D₄	—	47	1	no	—
428	C₄×D₄	—	47	2	no	—
429	C₄×D₄	—	47	2	no	—
430	C₄×D₄	—	47	2	no	—
431	C₄×D₄	—	47	1	no	—
432	C₄×D₄	—	47	1	no	—
433	C₄×D₄	—	47	1	no	—
434	C₄×D₄	—	47	1	no	—
435	C₄×D₄	—	47	2	no	—
436	C₄×D₄	—	47	2	no	—
437	C₄×D₄	—	47	1	no	—
438	C₄×D₄	—	47	1	no	—
439	C₄×D₄	—	47	2	no	—
440	C₄×D₄	—	47	1	no	—
441	C₄×D₄	—	47	2	no	—
442	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
443	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
444	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
445	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
446	#117	—	47	1	no	—
447	#117	—	47	1	no	—
448	#117	—	47	2	no	—
449	#117	—	47	2	no	—
450	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
451	#117	C₂×D₄₇	1	2	yes	complemented
452	C₂×C₄⋊C₄	—	47	2	no	—
453	C₂×C₄⋊C₄	—	47	1	no	—
454	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
455	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
456	C₂×C₂²⋊C₄	—	47	2	no	—
457	C₂×C₂²⋊C₄	—	47	2	no	—
458	C₂×C₂²⋊C₄	—	47	2	no	—
459	C₂×C₂²⋊C₄	—	47	2	no	—
460	C₂×C₂²⋊C₄	—	47	2	no	—
461	C₂×C₄²	—	47	1	no	—
462	C₂⁴	—	47	2	no	—
463	C₂⁴	—	47	2	no	—
464	#41	—	2	4	no	—
465	#41	—	188	4	no	—
466	C₂×Q₈	—	47	1	no	—
467	C₂×Q₈	—	47	2	no	—
468	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
469	C₂×D₄	—	47	2	no	—
470	C₂×D₄	—	47	2	no	—
471	C₂×D₄	—	47	1	no	—
472	C₂×D₄	—	47	1	no	—
473	C₂×D₄	—	47	2	no	—
474	C₂×D₄	—	47	2	no	—
475	C₂×D₄	—	47	1	no	—
476	C₂×D₄	—	47	1	no	—
477	C₂×D₄	—	47	2	no	—
478	C₂×D₄	—	47	1	no	—
479	C₂×D₄	—	47	2	no	—
480	C₂×D₄	—	47	2	no	—
481	C₂×D₄	—	47	2	no	—
482	C₂×D₄	—	94	4	no	—
483	C₂×D₄	—	94	4	no	—
484	C₂×D₄	—	188	4	no	—
485	C₂×D₄	C₂²×D₄₇	1	2	yes	—
486	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	—	47	2	no	—
488	C₂²×C₄	—	47	2	no	—
489	C₂²×C₄	—	47	1	no	—
490	C₂²×C₄	—	47	1	no	—
491	C₂²×C₄	—	47	2	no	—
492	C₂²×C₄	—	47	1	no	—
493	C₂²×C₄	—	47	1	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	—	188	4	no	—
499	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
500	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
502	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
503	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
504	C₄⋊C₄	—	47	1	no	—
505	C₄⋊C₄	—	47	2	no	—
506	C₄⋊C₄	—	47	2	no	—
507	C₄⋊C₄	—	47	2	no	—
508	C₄⋊C₄	—	47	2	no	—
509	C₄⋊C₄	—	47	1	no	—
510	C₄⋊C₄	—	47	1	no	—
511	C₄⋊C₄	—	47	2	no	—
512	C₄⋊C₄	—	47	2	no	—
513	C₄⋊C₄	—	47	2	no	—
514	C₄⋊C₄	—	47	1	no	—
515	C₄⋊C₄	—	47	1	no	—
516	C₄⋊C₄	—	47	1	no	—
517	C₄⋊C₄	—	47	1	no	—
518	C₄⋊C₄	—	47	1	no	—
519	C₄⋊C₄	—	47	1	no	—
520	C₄⋊C₄	—	47	1	no	—
521	C₄⋊C₄	—	47	2	no	—
522	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
527	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
528	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
529	C₂²⋊C₄	—	47	2	no	—
530	C₂²⋊C₄	—	47	2	no	—
531	C₂²⋊C₄	—	47	1	no	—
532	C₂²⋊C₄	—	47	1	no	—
533	C₂²⋊C₄	—	47	2	no	—
534	C₂²⋊C₄	—	47	1	no	—
535	C₂²⋊C₄	—	47	1	no	—
536	C₂²⋊C₄	—	47	1	no	—
537	C₂²⋊C₄	—	47	1	no	—
538	C₂²⋊C₄	—	47	2	no	—
539	C₂²⋊C₄	—	47	2	no	—
540	C₂²⋊C₄	—	47	2	no	—
541	C₂²⋊C₄	—	47	2	no	—
542	C₂²⋊C₄	—	47	2	no	—
543	C₂²⋊C₄	—	47	2	no	—
544	C₂²⋊C₄	—	47	2	no	—
545	C₂²⋊C₄	—	47	2	no	—
546	C₂²⋊C₄	—	47	2	no	—
547	C₂²⋊C₄	—	47	2	no	—
548	C₂²⋊C₄	—	47	1	no	—
549	C₂²⋊C₄	—	47	2	no	—
550	C₂²⋊C₄	—	47	1	no	—
551	C₂²⋊C₄	—	47	2	no	—
552	C₂²⋊C₄	—	47	2	no	—
553	C₂²⋊C₄	—	47	2	no	—
554	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
558	C₄²	—	47	1	no	—
559	C₄²	—	47	1	no	—
560	C₄²	—	47	1	no	—
561	C₄²	—	47	2	no	—
562	C₄²	—	47	1	no	—
563	C₄²	C₂²×D₄₇	1	1	yes	characteristic
564	C₄²	C₂²×D₄₇	1	2	yes	—
565	C₄²	C₂²×D₄₇	1	2	yes	—
566	C₄²	C₂²×D₄₇	1	1	yes	characteristic
567	C₂³	—	47	1	no	—
568	C₂³	—	47	1	no	—
569	C₂³	—	47	2	no	—
570	C₂³	—	47	2	no	—
571	C₂³	—	94	4	no	—
572	C₂³	—	94	4	no	—
573	C₂³	—	94	4	no	—
574	C₂³	—	188	2	no	—
575	C₂³	—	188	2	no	—
576	C₂³	—	188	2	no	—
577	C₂³	C₂³×D₄₇	1	1	yes	characteristic
578	C₂³	C₂³×D₄₇	1	2	yes	—
579	Q₈	—	2	2	no	—
580	Q₈	—	188	1	no	—
581	Q₈	—	188	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	94	2	no	—
584	D₄	—	94	4	no	—
585	D₄	—	94	2	no	—
586	D₄	—	94	4	no	—
587	D₄	—	94	4	no	—
588	D₄	—	94	2	no	—
589	D₄	—	94	2	no	—
590	D₄	—	188	2	no	—
591	D₄	—	188	2	no	—
592	D₄	—	188	2	no	—
593	D₄	—	188	2	no	—
594	D₄	—	188	1	no	—
595	D₄	—	188	2	no	—
596	D₄	#10625350	1	4	yes	complemented
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	47	1	no	—
603	C₂×C₄	—	47	1	no	—
604	C₂×C₄	—	47	1	no	—
605	C₂×C₄	—	47	1	no	—
606	C₂×C₄	—	47	1	no	—
607	C₂×C₄	—	47	2	no	—
608	C₂×C₄	—	47	1	no	—
609	C₂×C₄	—	47	2	no	—
610	C₂×C₄	—	94	2	no	—
611	C₂×C₄	—	94	4	no	—
612	C₂×C₄	—	94	2	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	188	2	no	—
615	C₂×C₄	—	188	1	no	—
616	C₂×C₄	—	188	2	no	—
617	C₂×C₄	—	188	2	no	—
618	C₂×C₄	—	188	2	no	—
619	C₂×C₄	—	188	2	no	—
620	C₂×C₄	—	188	2	no	—
621	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₄₇	1	2	yes	—
624	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₄₇	1	2	yes	—
626	C₂×C₄	C₂³×D₄₇	1	2	yes	—
627	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	47	2	no	—
636	C₂²	—	94	1	no	—
637	C₂²	—	94	1	no	—
638	C₂²	—	94	1	no	—
639	C₂²	—	94	2	no	—
640	C₂²	—	94	2	no	—
641	C₂²	—	94	2	no	—
642	C₂²	—	94	2	no	—
643	C₂²	—	94	1	no	—
644	C₂²	—	94	2	no	—
645	C₂²	—	94	2	no	—
646	C₂²	—	94	1	no	—
647	C₂²	—	376	4	no	—
648	C₂²	—	188	8	no	—
649	C₂²	C₂×#10625350	1	4	yes	—
650	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	94	1	no	—
660	C₄	—	94	1	no	—
661	C₄	—	94	1	no	—
662	C₄	—	94	2	no	—
663	C₄	—	94	1	no	—
664	C₄	—	94	2	no	—
665	C₄	—	94	1	no	—
666	C₄	—	94	1	no	—
667	C₄	C₂×#10625350	1	2	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	1	no	—
670	C₂	—	94	2	no	—
671	C₂	—	188	1	no	—
672	C₂	—	188	2	no	—
673	C₂	—	188	2	no	—
674	C₂	C₂²×#10625350	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
676	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#520	C₂
hypercenter	#520	D₄₇
hypocenter	C₄₇	#3513
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #15689858	C₂	semidirect
2. #15689832	C₂	semidirect
3. #15689822	C₂	semidirect
4. #15689821	C₂	semidirect
5. #15689814	C₂	semidirect
6. #15689797	C₂	semidirect
7. #15689797	C₂	semidirect
8. #15689774	C₂	semidirect
9. #15689769	C₂	semidirect
10. #15689761	C₂	semidirect
11. #15689761	C₂	semidirect
12. D₄×D₁₈₈	C₂	semidirect
13. #15689745	C₂	semidirect
14. #15689728	C₂	semidirect
15. #15689720	C₂	semidirect
16. #15689706	C₂	semidirect
17. #15689660	C₂	semidirect
18. #15689651	C₂	semidirect
19. #15689632	C₂	semidirect
20. C₂×#13094009	C₂	semidirect
21. #15689595	C₂	semidirect
22. C₄×D₄×D₄₇	C₂	semidirect
23. C₄₇×#520	C₂	semidirect
24. C₂×#10625350	C₂²	semidirect
28. C₂²×C₄×D₄₇	C₂²	semidirect
29. #13094023	C₂²	semidirect
31. #13094019	C₂²	semidirect
32. #13094019	C₂²	semidirect
33. #13094019	C₂²	semidirect
34. #13094018	C₂²	semidirect
35. #13094018	C₂²	semidirect
36. #13094017	C₂²	semidirect
37. #13094016	C₂²	semidirect
38. #13094015	C₂²	semidirect
39. #13094014	C₂²	semidirect
40. #13094014	C₂²	semidirect
41. #13094013	C₂²	semidirect
42. #13094013	C₂²	semidirect
43. #13094012	C₂²	semidirect
44. #13094012	C₂²	semidirect
45. #13094010	C₂²	semidirect
48. #13094009	C₂²	semidirect
49. #13094009	C₂²	semidirect
50. #13094009	C₂²	semidirect
51. #13094009	C₂²	semidirect
52. #13094009	C₂²	semidirect
53. #13094009	C₂²	semidirect
54. #13094009	C₂²	semidirect
55. #13094009	C₂²	semidirect
56. #13094007	C₂²	semidirect
57. #13094007	C₂²	semidirect
58. #13094007	C₂²	semidirect
59. #13094006	C₂²	semidirect
60. #13094003	C₂²	semidirect
61. #13094002	C₂²	semidirect
62. #13094002	C₂²	semidirect
63. #13094002	C₂²	semidirect
64. #13094001	C₂²	semidirect
65. #13094001	C₂²	semidirect
66. #13094000	C₂²	semidirect
67. #13094000	C₂²	semidirect
71. #13093998	C₂²	semidirect
72. #13093998	C₂²	semidirect
73. #13093998	C₂²	semidirect
75. #13093997	C₂²	semidirect
76. #13093997	C₂²	semidirect
77. #13093996	C₂²	semidirect
78. #13093996	C₂²	semidirect
81. #13093992	C₂²	semidirect
82. #13093992	C₂²	semidirect
83. C₄×Dic₉₄	C₂²	semidirect
85. C₄×D₁₈₈	C₂²	semidirect
86. C₄×D₁₈₈	C₂²	semidirect
87. C₄×D₁₈₈	C₂²	semidirect
88. C₄×D₁₈₈	C₂²	semidirect
91. #13093986	C₂²	semidirect
92. #13093986	C₂²	semidirect
93. C₄×C₂²⋊D₄₇	C₂²	semidirect
94. C₄×C₂²⋊D₄₇	C₂²	semidirect
95. C₄×C₂²⋊D₄₇	C₂²	semidirect
96. C₄×C₂²⋊D₄₇	C₂²	semidirect
97. C₄×C₂²⋊D₄₇	C₂²	semidirect
98. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
100. #13093982	C₂²	semidirect
101. #13093981	C₂²	semidirect
102. #13093981	C₂²	semidirect
103. #13093981	C₂²	semidirect
104. C₂×Dic₄₇⋊C₄	C₂²	semidirect
105. C₄⋊C₄×D₄₇	C₂²	semidirect
106. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
107. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
108. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
109. C₂²⋊C₄×D₄₇	C₂²	semidirect
110. C₂²⋊C₄×D₄₇	C₂²	semidirect
111. C₄²×D₄₇	C₂²	semidirect
113. C₄×Q₈×C₄₇	C₂²	semidirect
114. C₄×Q₈×C₄₇	C₂²	semidirect
117. C₄×D₄×C₄₇	C₂²	semidirect
118. C₄×D₄×C₄₇	C₂²	semidirect
119. #117×C₄₇	C₂²	semidirect
120. #117×C₄₇	C₂²	semidirect
121. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
242. D₄×C₄₇	#41	semidirect
359. #520	D₄₇	semidirect
362. C₄₇	#3513	semidirect
424. C₄×Q₈	C₂×D₄₇	semidirect
425. C₄×Q₈	C₂×D₄₇	semidirect
444. C₄×D₄	C₂×D₄₇	semidirect
445. C₄×D₄	C₂×D₄₇	semidirect
450. #117	C₂×D₄₇	semidirect
451. #117	C₂×D₄₇	semidirect
454. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
455. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
596. D₄	#10625350	semidirect