Subgroups — #20257302

Order 6016.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689826	C₂	1	2	yes	maximal, complemented
2	#15689826	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689824	C₂	1	2	yes	maximal, complemented
4	#15689821	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689819	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689818	C₂	1	2	yes	maximal, complemented
7	#15689817	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689817	C₂	1	2	yes	maximal, complemented
9	#15689815	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689814	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689807	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689732	C₂	1	2	yes	maximal, complemented
13	#15689725	C₂	1	2	yes	maximal, complemented
14	#15689703	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689703	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689670	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689656	C₂	1	2	yes	maximal, complemented
18	#15689651	C₂	1	2	yes	maximal, complemented
19	#125×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#15689604	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689603	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#10625354	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625354	C₂²	1	1	yes	characteristic
25	C₂×#10625350	C₂²	1	1	yes	characteristic
26	C₂×#10625350	C₂²	1	1	yes	characteristic
27	#13094023	C₂²	1	1	yes	characteristic
28	#13094020	C₂²	1	1	yes	characteristic
29	#13094019	C₂²	1	2	yes	—
30	#13094019	C₂²	1	2	yes	—
31	#13094019	C₂²	1	2	yes	—
32	#13094019	C₂²	1	2	yes	—
33	#13094018	C₂²	1	2	yes	—
34	#13094018	C₂²	1	2	yes	—
35	#13094017	C₂²	1	2	yes	—
36	#13094016	C₂²	1	1	yes	characteristic
37	#13094015	C₂²	1	2	yes	—
38	#13094015	C₂²	1	1	yes	characteristic
39	#13094015	C₂²	1	1	yes	characteristic
40	#13094014	C₂²	1	2	yes	—
41	#13094014	C₂²	1	2	yes	—
42	#13094014	C₂²	1	2	yes	—
43	#13094014	C₂²	1	2	yes	—
44	#13094010	C₂²	1	1	yes	characteristic
45	#13094010	C₂²	1	1	yes	characteristic
46	#13094009	C₂²	1	2	yes	—
47	#13094009	C₂²	1	2	yes	—
48	#13094009	C₂²	1	2	yes	—
49	#13094008	C₂²	1	2	yes	—
50	#13094006	C₂²	1	2	yes	—
51	#13094006	C₂²	1	2	yes	—
52	#13094006	C₂²	1	2	yes	—
53	#13094002	C₂²	1	2	yes	—
54	#13094002	C₂²	1	2	yes	—
55	#13094000	C₂²	1	1	yes	characteristic
56	#13094000	C₂²	1	1	yes	characteristic
57	#13093999	C₂²	1	2	yes	—
58	#13093999	C₂²	1	1	yes	characteristic
59	#13093999	C₂²	1	1	yes	characteristic
60	#13093999	C₂²	1	2	yes	—
61	#13093999	C₂²	1	1	yes	characteristic
62	#13093999	C₂²	1	2	yes	—
63	#13093998	C₂²	1	1	yes	characteristic
64	#13093998	C₂²	1	2	yes	—
65	#13093998	C₂²	1	1	yes	characteristic
66	#13093997	C₂²	1	1	yes	characteristic
67	#13093997	C₂²	1	2	yes	—
68	#13093997	C₂²	1	2	yes	—
69	#13093997	C₂²	1	2	yes	—
70	#13093997	C₂²	1	1	yes	characteristic
71	#13093997	C₂²	1	2	yes	—
72	#13093997	C₂²	1	2	yes	—
73	#13093996	C₂²	1	2	yes	—
74	#13093995	C₂²	1	1	yes	characteristic
75	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
76	C₄×Dic₉₄	C₂²	1	2	yes	—
77	#13093989	C₂²	1	2	yes	—
78	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
79	C₄×D₁₈₈	C₂²	1	2	yes	—
80	C₄×D₁₈₈	C₂²	1	2	yes	—
81	C₄×D₁₈₈	C₂²	1	2	yes	—
82	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
83	#13093986	C₂²	1	1	yes	characteristic
84	#13093986	C₂²	1	2	yes	—
85	#13093986	C₂²	1	2	yes	—
86	#13093986	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
92	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
93	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
95	#13093983	C₂²	1	1	yes	characteristic
96	#13093982	C₂²	1	2	yes	—
97	#13093982	C₂²	1	2	yes	—
98	#13093982	C₂²	1	1	yes	characteristic
99	#13093982	C₂²	1	1	yes	characteristic
100	#13093982	C₂²	1	1	yes	characteristic
101	#13093981	C₂²	1	2	yes	—
102	#13093980	C₂²	1	2	yes	—
103	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
107	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
108	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
110	C₄²×D₄₇	C₂²	1	1	yes	characteristic
111	C₄²×D₄₇	C₂²	1	2	yes	—
112	#126×C₄₇	C₂²	1	2	yes	—
113	#125×C₄₇	C₂²	1	2	yes	—
114	#125×C₄₇	C₂²	1	1	yes	characteristic
115	#123×C₄₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
120	#117×C₄₇	C₂²	1	1	yes	characteristic
121	#117×C₄₇	C₂²	1	2	yes	—
122	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×D₄×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	2	yes	—
128	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂³	1	2	yes	—
137	#10625354	—	2	4	no	—
138	#10625350	—	2	4	no	—
139	#10625350	—	2	4	no	—
140	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
141	C₂×D₁₈₈	C₂³	1	2	yes	—
142	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
143	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
144	C₂×D₁₈₈	C₂³	1	2	yes	—
145	C₂×D₁₈₈	C₂³	1	2	yes	—
146	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₄₇	C₂³	1	2	yes	—
148	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
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×C₄×D₄₇	C₂³	1	2	yes	—
156	C₂×C₄×D₄₇	C₂³	1	2	yes	—
157	C₂×C₄×D₄₇	C₂³	1	2	yes	—
158	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
160	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
169	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
170	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
171	C₂²⋊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	2	yes	—
176	C₄²×C₄₇	C₂³	1	2	yes	—
177	C₄²×C₄₇	C₂³	1	2	yes	—
178	C₄²×C₄₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
182	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
189	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₄₇	C₂³	1	2	yes	—
201	C₄⋊Dic₄₇	C₂³	1	2	yes	—
202	C₄⋊Dic₄₇	C₂³	1	2	yes	—
203	C₄⋊Dic₄₇	C₂³	1	2	yes	—
204	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
205	Dic₄₇⋊C₄	C₂³	1	2	yes	—
206	Dic₄₇⋊C₄	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	2	yes	—
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	2	yes	—
211	Dic₄₇⋊C₄	C₂³	1	2	yes	—
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	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₇	C₂³	1	2	yes	—
219	C₄×Dic₄₇	C₂³	1	2	yes	—
220	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂²×D₄₇	C₂⁴	1	2	yes	—
228	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
229	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
231	Q₈×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	4	1	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	4	2	no	—
236	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
237	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
243	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₄₇	—	2	2	no	—
246	C₂²⋊D₄₇	—	2	2	no	—
247	C₂²⋊D₄₇	—	2	2	no	—
248	C₂²⋊D₄₇	—	2	2	no	—
249	C₂²⋊D₄₇	—	4	2	no	—
250	C₂²⋊D₄₇	—	4	2	no	—
251	C₂²⋊D₄₇	—	4	1	no	—
252	C₂²⋊D₄₇	—	4	1	no	—
253	C₂×Dic₄₇	—	4	2	no	—
254	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₄₇	C₂⁴	1	2	yes	—
256	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	2	yes	—
261	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
262	D₁₈₈	—	2	2	no	—
263	D₁₈₈	—	2	2	no	—
264	D₁₈₈	—	2	4	no	—
265	D₁₈₈	—	2	2	no	—
266	D₁₈₈	—	4	2	no	—
267	D₁₈₈	—	4	2	no	—
268	D₁₈₈	—	4	1	no	—
269	C₄×D₄₇	—	2	2	no	—
270	C₄×D₄₇	—	2	2	no	—
271	C₄×D₄₇	—	2	4	no	—
272	C₄×D₄₇	—	4	2	no	—
273	C₄×D₄₇	—	4	1	no	—
274	C₄×D₄₇	—	4	2	no	—
275	C₄×D₄₇	—	4	2	no	—
276	C₄×D₄₇	—	4	2	no	—
277	C₄×D₄₇	—	4	2	no	—
278	C₄×D₄₇	—	4	2	no	—
279	C₄×D₄₇	—	4	1	no	—
280	C₄×D₄₇	#41	1	4	yes	—
281	Dic₉₄	—	2	2	no	—
282	Dic₉₄	—	2	2	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	1	no	—
285	C₂²×C₄₇	—	2	1	no	—
286	C₂²×C₄₇	—	2	1	no	—
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
290	C₂×D₄₇	—	2	1	no	—
291	C₂×D₄₇	—	2	1	no	—
292	C₂×D₄₇	—	2	2	no	—
293	C₂×D₄₇	—	2	1	no	—
294	C₂×D₄₇	—	2	1	no	—
295	C₂×D₄₇	—	2	1	no	—
296	C₂×D₄₇	—	2	1	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	2	2	no	—
299	C₂×D₄₇	—	2	1	no	—
300	C₂×D₄₇	—	2	1	no	—
301	C₂×D₄₇	C₂×#41	1	2	yes	—
302	C₄×C₄₇	—	2	1	no	—
303	C₄×C₄₇	—	2	1	no	—
304	C₄×C₄₇	—	2	2	no	—
305	C₄×C₄₇	—	2	1	no	—
306	C₄×C₄₇	—	2	2	no	—
307	C₄×C₄₇	—	2	2	no	—
308	C₄×C₄₇	—	2	2	no	—
309	C₄×C₄₇	—	2	1	no	—
310	C₄×C₄₇	C₂×#41	1	2	yes	—
311	Dic₄₇	—	2	1	no	—
312	Dic₄₇	—	2	1	no	—
313	Dic₄₇	—	2	1	no	—
314	Dic₄₇	—	2	2	no	—
315	Dic₄₇	—	2	2	no	—
316	Dic₄₇	—	2	2	no	—
317	Dic₄₇	—	2	1	no	—
318	Dic₄₇	C₂×#41	1	2	yes	—
319	#3512	—	47	1	no	maximal, Sylow
320	C₂×C₄₇	—	4	1	no	—
321	C₂×C₄₇	—	4	1	no	—
322	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
323	C₂×C₄₇	#585	1	1	yes	characteristic
324	C₂×C₄₇	#585	1	1	yes	characteristic
325	D₄₇	—	2	2	no	—
326	D₄₇	—	4	2	no	—
327	D₄₇	—	4	1	no	—
328	D₄₇	—	4	1	no	—
329	#553	—	47	2	no	—
330	#553	—	47	1	no	—
331	#553	—	47	2	no	—
332	#553	—	47	2	no	—
333	#553	—	47	1	no	—
334	#553	—	47	1	no	—
335	#553	—	47	2	no	—
336	#553	—	47	1	no	—
337	#552	—	47	1	no	—
338	#552	—	47	1	no	—
339	#552	—	47	1	no	—
340	#552	D₄₇	1	1	yes	characteristic, complemented
341	#541	—	47	2	no	—
342	#540	—	47	2	no	—
343	#537	—	47	1	no	—
344	#537	—	47	1	no	—
345	#532	—	47	1	no	—
346	#529	—	47	2	no	—
347	#529	—	47	2	no	—
348	C₂×#125	—	47	1	no	—
349	#520	—	47	1	no	—
350	#520	—	47	1	no	—
351	C₄×#41	—	47	1	no	—
352	C₄₇	#3512	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	47	1	no	—
354	C₂×#41	—	47	1	no	—
355	C₂×#41	—	47	1	no	—
356	C₄⋊Q₈	—	47	1	no	—
357	#127	—	47	1	no	—
358	#126	—	47	2	no	—
359	#126	—	47	2	no	—
360	#126	—	47	2	no	—
361	#126	—	47	2	no	—
362	#126	—	47	2	no	—
363	#126	—	47	2	no	—
364	#126	—	47	2	no	—
365	#126	C₂×D₄₇	1	2	yes	—
366	#125	—	47	2	no	—
367	#125	—	47	2	no	—
368	#125	—	47	1	no	—
369	#125	—	47	1	no	—
370	#125	—	47	2	no	—
371	#125	—	47	2	no	—
372	#125	—	47	2	no	—
373	#125	—	47	1	no	—
374	#125	C₂×D₄₇	1	1	yes	characteristic
375	#125	C₂×D₄₇	1	2	yes	—
376	#124	—	47	1	no	—
377	#124	—	47	1	no	—
378	#123	—	47	2	no	—
379	#123	—	47	2	no	—
380	#123	—	47	2	no	—
381	#123	—	47	2	no	—
382	#123	—	47	2	no	—
383	#123	—	47	2	no	—
384	#123	—	47	2	no	—
385	#123	C₂×D₄₇	1	2	yes	—
386	C₂²⋊Q₈	—	47	1	no	—
387	C₂²⋊Q₈	—	47	1	no	—
388	C₂²⋊Q₈	—	47	2	no	—
389	C₂²⋊Q₈	—	47	2	no	—
390	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
392	#121	—	47	1	no	—
393	#121	—	47	2	no	—
394	#121	—	47	1	no	—
395	#121	—	47	1	no	—
396	#121	—	47	2	no	—
397	#121	—	47	1	no	—
398	#121	—	47	2	no	—
399	#121	—	47	2	no	—
400	#121	—	47	1	no	—
401	#121	—	47	1	no	—
402	#121	—	47	2	no	—
403	#121	—	47	2	no	—
404	#121	—	47	2	no	—
405	#121	—	47	1	no	—
406	#121	—	47	1	no	—
407	#121	—	47	2	no	—
408	#121	—	47	2	no	—
409	#121	—	47	2	no	—
410	C₄×Q₈	—	47	1	no	—
411	C₄×Q₈	—	47	2	no	—
412	C₄×Q₈	—	47	2	no	—
413	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
414	C₄×D₄	—	47	2	no	—
415	C₄×D₄	—	47	2	no	—
416	C₄×D₄	—	47	2	no	—
417	C₄×D₄	—	47	1	no	—
418	C₄×D₄	—	47	1	no	—
419	C₄×D₄	—	47	2	no	—
420	C₄×D₄	—	47	1	no	—
421	C₄×D₄	—	47	2	no	—
422	C₄×D₄	—	47	2	no	—
423	C₄×D₄	—	47	2	no	—
424	C₄×D₄	—	47	2	no	—
425	C₄×D₄	—	47	2	no	—
426	C₄×D₄	—	47	2	no	—
427	C₄×D₄	—	47	1	no	—
428	C₄×D₄	—	47	2	no	—
429	C₄×D₄	—	47	2	no	—
430	C₄×D₄	—	47	1	no	—
431	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
432	#117	—	47	1	no	—
433	#117	—	47	1	no	—
434	#117	—	47	2	no	—
435	#117	—	47	1	no	—
436	#117	—	47	1	no	—
437	#117	—	47	2	no	—
438	#117	—	47	2	no	—
439	#117	—	47	2	no	—
440	#117	C₂×D₄₇	1	1	yes	characteristic
441	#117	C₂×D₄₇	1	2	yes	—
442	C₂×C₄⋊C₄	—	47	1	no	—
443	C₂×C₄⋊C₄	—	47	1	no	—
444	C₂×C₄⋊C₄	—	47	1	no	—
445	C₂×C₄⋊C₄	—	47	1	no	—
446	C₂×C₄⋊C₄	—	47	1	no	—
447	C₂×C₄⋊C₄	—	47	2	no	—
448	C₂×C₄⋊C₄	—	47	2	no	—
449	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
450	C₂×C₄²	—	47	1	no	—
451	C₂×C₄²	—	47	2	no	—
452	#41	—	94	4	no	—
453	#41	—	94	4	no	—
454	#41	—	94	4	no	—
455	C₂×Q₈	—	47	1	no	—
456	C₂×Q₈	—	47	1	no	—
457	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×D₄	—	47	1	no	—
459	C₂×D₄	—	47	1	no	—
460	C₂×D₄	—	47	1	no	—
461	C₂×D₄	—	47	1	no	—
462	C₂×D₄	—	47	2	no	—
463	C₂×D₄	—	47	2	no	—
464	C₂×D₄	—	47	1	no	—
465	C₂×D₄	—	47	1	no	—
466	C₂×D₄	—	47	1	no	—
467	C₂×D₄	—	47	2	no	—
468	C₂×D₄	—	47	1	no	—
469	C₂×D₄	—	47	1	no	—
470	C₂×D₄	—	47	2	no	—
471	C₂×D₄	—	47	2	no	—
472	C₂×D₄	—	47	1	no	—
473	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
474	C₂²×C₄	—	47	1	no	—
475	C₂²×C₄	—	47	2	no	—
476	C₂²×C₄	—	47	2	no	—
477	C₂²×C₄	—	47	1	no	—
478	C₂²×C₄	—	47	1	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	1	no	—
481	C₂²×C₄	—	47	2	no	—
482	C₂²×C₄	—	47	2	no	—
483	C₂²×C₄	—	47	2	no	—
484	C₂²×C₄	—	47	2	no	—
485	C₂²×C₄	—	47	2	no	—
486	C₂²×C₄	—	47	2	no	—
487	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	—	47	2	no	—
492	C₄⋊C₄	—	47	2	no	—
493	C₄⋊C₄	—	47	2	no	—
494	C₄⋊C₄	—	47	2	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	2	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	—	47	2	no	—
499	C₄⋊C₄	—	47	2	no	—
500	C₄⋊C₄	—	47	1	no	—
501	C₄⋊C₄	—	47	1	no	—
502	C₄⋊C₄	—	47	1	no	—
503	C₄⋊C₄	—	47	1	no	—
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	C₂²×D₄₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
517	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
518	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
519	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
520	C₂²⋊C₄	—	47	1	no	—
521	C₂²⋊C₄	—	47	2	no	—
522	C₂²⋊C₄	—	47	1	no	—
523	C₂²⋊C₄	—	47	1	no	—
524	C₂²⋊C₄	—	47	1	no	—
525	C₂²⋊C₄	—	47	2	no	—
526	C₂²⋊C₄	—	47	2	no	—
527	C₂²⋊C₄	—	47	2	no	—
528	C₂²⋊C₄	—	47	2	no	—
529	C₂²⋊C₄	—	47	2	no	—
530	C₂²⋊C₄	—	47	2	no	—
531	C₂²⋊C₄	—	47	2	no	—
532	C₂²⋊C₄	—	47	1	no	—
533	C₂²⋊C₄	—	47	1	no	—
534	C₂²⋊C₄	—	47	2	no	—
535	C₂²⋊C₄	—	47	2	no	—
536	C₂²⋊C₄	—	47	2	no	—
537	C₂²⋊C₄	—	47	2	no	—
538	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
543	C₄²	—	47	1	no	—
544	C₄²	—	47	2	no	—
545	C₄²	—	47	2	no	—
546	C₄²	—	47	1	no	—
547	C₄²	—	47	1	no	—
548	C₄²	—	47	2	no	—
549	C₄²	—	47	2	no	—
550	C₄²	—	47	2	no	—
551	C₄²	C₂²×D₄₇	1	2	yes	—
552	C₄²	C₂²×D₄₇	1	1	yes	characteristic
553	C₄²	C₂²×D₄₇	1	2	yes	—
554	C₂³	—	47	1	no	—
555	C₂³	—	47	1	no	—
556	C₂³	—	47	2	no	—
557	C₂³	—	47	1	no	—
558	C₂³	C₂³×D₄₇	1	1	yes	characteristic
559	C₂³	C₂³×D₄₇	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	94	2	no	—
562	Q₈	—	94	2	no	—
563	D₄	—	4	1	no	—
564	D₄	—	94	2	no	—
565	D₄	—	94	2	no	—
566	D₄	—	94	4	no	—
567	D₄	—	94	2	no	—
568	D₄	—	94	2	no	—
569	D₄	—	94	2	no	—
570	D₄	—	94	2	no	—
571	D₄	—	94	2	no	—
572	D₄	—	188	2	no	—
573	D₄	—	188	1	no	—
574	D₄	—	188	2	no	—
575	D₄	—	188	2	no	—
576	D₄	—	188	2	no	—
577	D₄	—	188	1	no	—
578	D₄	—	188	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	47	1	no	—
583	C₂×C₄	—	47	4	no	—
584	C₂×C₄	—	47	1	no	—
585	C₂×C₄	—	47	2	no	—
586	C₂×C₄	—	47	1	no	—
587	C₂×C₄	—	47	1	no	—
588	C₂×C₄	—	47	1	no	—
589	C₂×C₄	—	47	2	no	—
590	C₂×C₄	—	47	2	no	—
591	C₂×C₄	—	94	4	no	—
592	C₂×C₄	—	94	2	no	—
593	C₂×C₄	—	94	2	no	—
594	C₂×C₄	—	188	2	no	—
595	C₂×C₄	—	188	2	no	—
596	C₂×C₄	—	188	2	no	—
597	C₂×C₄	—	188	1	no	—
598	C₂×C₄	—	188	2	no	—
599	C₂×C₄	—	188	1	no	—
600	C₂×C₄	—	188	2	no	—
601	C₂×C₄	—	188	2	no	—
602	C₂×C₄	—	188	2	no	—
603	C₂×C₄	C₂³×D₄₇	1	2	yes	—
604	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₄₇	1	2	yes	—
607	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₄₇	1	2	yes	—
609	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₄₇	1	2	yes	—
611	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	47	2	no	—
619	C₂²	—	94	1	no	—
620	C₂²	—	94	1	no	—
621	C₂²	—	94	2	no	—
622	C₂²	—	94	1	no	—
623	C₂²	—	94	1	no	—
624	C₂²	—	94	1	no	—
625	C₂²	—	94	2	no	—
626	C₂²	—	94	1	no	—
627	C₂²	—	94	1	no	—
628	C₂²	—	94	2	no	—
629	C₂²	—	94	1	no	—
630	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	47	2	no	—
640	C₄	—	94	1	no	—
641	C₄	—	94	1	no	—
642	C₄	—	94	1	no	—
643	C₄	—	94	2	no	—
644	C₄	—	94	2	no	—
645	C₄	—	94	2	no	—
646	C₄	—	94	1	no	—
647	C₄	#41×D₄₇	1	2	yes	—
648	C₂	—	4	1	no	—
649	C₂	—	4	1	no	—
650	C₂	—	94	2	no	—
651	C₂	—	188	1	no	—
652	C₂	—	188	2	no	—
653	C₂	—	188	1	no	—
654	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
655	C₂	#15689959	1	1	yes	characteristic
656	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#552	C₂
hypercenter	#552	D₄₇
hypocenter	C₄₇	#3512
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #15689826	C₂	semidirect
2. #15689826	C₂	semidirect
3. #15689824	C₂	semidirect
4. #15689821	C₂	semidirect
5. #15689819	C₂	semidirect
6. #15689818	C₂	semidirect
7. #15689817	C₂	semidirect
8. #15689817	C₂	semidirect
9. #15689815	C₂	semidirect
10. #15689814	C₂	semidirect
11. #15689807	C₂	semidirect
12. #15689732	C₂	semidirect
13. #15689725	C₂	semidirect
14. #15689703	C₂	semidirect
15. #15689703	C₂	semidirect
16. #15689670	C₂	semidirect
17. #15689656	C₂	semidirect
18. #15689651	C₂	semidirect
19. #125×D₄₇	C₂	semidirect
20. #15689604	C₂	semidirect
21. #15689603	C₂	semidirect
22. C₄×#10625354	C₂	semidirect
23. C₄₇×#552	C₂	semidirect
340. #552	D₄₇	semidirect
352. C₄₇	#3512	semidirect