Subgroups — #20257813

Order 6016.

1050 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689872	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689864	C₂	1	2	yes	maximal, complemented
3	#15689839	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689835	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689824	C₂	1	2	yes	maximal, complemented
6	#15689805	C₂	1	2	yes	maximal, complemented
7	#15689800	C₂	1	2	yes	maximal, complemented
8	#15689783	C₂	1	2	yes	maximal, complemented
9	#15689765	C₂	1	2	yes	maximal, complemented
10	#15689729	C₂	1	2	yes	maximal, complemented
11	#15689725	C₂	1	2	yes	maximal, complemented
12	#15689713	C₂	1	2	yes	maximal, complemented
13	#15689712	C₂	1	2	yes	maximal, complemented
14	#15689703	C₂	1	2	yes	maximal, complemented
15	#15689698	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689691	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689674	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689656	C₂	1	2	yes	maximal, complemented
19	C₄₇×#563	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10625354	C₂²	1	1	yes	characteristic
21	C₂×#10625354	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10625350	C₂²	1	2	yes	—
23	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
25	#13094022	C₂²	1	1	yes	characteristic, complemented
26	#13094021	C₂²	1	1	yes	characteristic
27	#13094021	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	complemented
32	#13094018	C₂²	1	2	yes	complemented
33	#13094014	C₂²	1	2	yes	complemented
34	#13094014	C₂²	1	2	yes	complemented
35	#13094013	C₂²	1	1	yes	characteristic
36	#13094013	C₂²	1	1	yes	characteristic
37	#13094013	C₂²	1	1	yes	characteristic
38	#13094013	C₂²	1	2	yes	complemented
39	#13094013	C₂²	1	1	yes	characteristic, complemented
40	#13094012	C₂²	1	1	yes	characteristic
41	#13094010	C₂²	1	2	yes	—
42	#13094010	C₂²	1	2	yes	complemented
43	#13094009	C₂²	1	2	yes	—
44	#13094009	C₂²	1	2	yes	—
45	#13094009	C₂²	1	2	yes	—
46	#13094009	C₂²	1	2	yes	—
47	#13094009	C₂²	1	2	yes	complemented
48	#13094009	C₂²	1	2	yes	complemented
49	#13094009	C₂²	1	2	yes	complemented
50	#13094008	C₂²	1	2	yes	complemented
51	#13094006	C₂²	1	2	yes	complemented
52	#13094002	C₂²	1	2	yes	—
53	#13094002	C₂²	1	2	yes	complemented
54	#13094002	C₂²	1	2	yes	complemented
55	#13094002	C₂²	1	2	yes	complemented
56	#13094000	C₂²	1	2	yes	complemented
57	#13093999	C₂²	1	2	yes	—
58	#13093999	C₂²	1	2	yes	—
59	#13093999	C₂²	1	2	yes	complemented
60	#13093999	C₂²	1	2	yes	complemented
61	#13093999	C₂²	1	2	yes	complemented
62	#13093999	C₂²	1	2	yes	complemented
63	#13093999	C₂²	1	2	yes	complemented
64	#13093999	C₂²	1	2	yes	complemented
65	#13093998	C₂²	1	2	yes	complemented
66	#13093997	C₂²	1	2	yes	—
67	#13093997	C₂²	1	2	yes	—
68	#13093997	C₂²	1	2	yes	—
69	#13093997	C₂²	1	2	yes	complemented
70	#13093997	C₂²	1	2	yes	complemented
71	#13093997	C₂²	1	2	yes	complemented
72	#13093997	C₂²	1	2	yes	complemented
73	#13093996	C₂²	1	2	yes	—
74	#13093994	C₂²	1	2	yes	—
75	#13093994	C₂²	1	2	yes	—
76	#13093994	C₂²	1	2	yes	—
77	#13093994	C₂²	1	2	yes	—
78	#13093989	C₂²	1	2	yes	complemented
79	C₄×D₁₈₈	C₂²	1	2	yes	complemented
80	#13093986	C₂²	1	2	yes	—
81	#13093986	C₂²	1	2	yes	complemented
82	#13093986	C₂²	1	2	yes	complemented
83	#13093986	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
85	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
86	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
87	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
88	#13093982	C₂²	1	2	yes	complemented
89	#13093982	C₂²	1	2	yes	complemented
90	#13093981	C₂²	1	1	yes	characteristic
91	#13093981	C₂²	1	2	yes	complemented
92	#13093981	C₂²	1	1	yes	characteristic, complemented
93	#13093980	C₂²	1	2	yes	complemented
94	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
95	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
97	C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
99	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
100	#126×C₄₇	C₂²	1	2	yes	complemented
101	#126×C₄₇	C₂²	1	2	yes	complemented
102	#125×C₄₇	C₂²	1	2	yes	complemented
103	#124×C₄₇	C₂²	1	1	yes	characteristic
104	#123×C₄₇	C₂²	1	2	yes	—
105	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
106	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
107	C₂³×D₄₇	C₂³	1	2	yes	—
108	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
118	C₂²×Dic₄₇	C₂³	1	2	yes	—
119	#10625354	—	4	2	no	—
120	#10625354	—	4	2	no	—
121	Q₈×D₄₇	—	4	2	no	—
122	D₄×D₄₇	—	4	2	no	—
123	#10625350	—	4	4	no	—
124	C₂×D₁₈₈	C₂³	1	2	yes	—
125	C₂×D₁₈₈	C₂³	1	2	yes	—
126	C₂×D₁₈₈	C₂³	1	2	yes	—
127	C₂×D₁₈₈	C₂³	1	2	yes	—
128	C₂×D₁₈₈	C₂³	1	2	yes	—
129	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
130	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
131	C₂×D₁₈₈	C₂³	1	2	yes	—
132	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
133	C₂×D₁₈₈	C₂³	1	2	yes	—
134	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
135	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₄₇	C₂³	1	2	yes	—
138	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₄₇	C₂³	1	2	yes	—
141	C₂×C₄×D₄₇	C₂³	1	2	yes	—
142	C₂×C₄×D₄₇	C₂³	1	2	yes	—
143	C₂×C₄×D₄₇	C₂³	1	2	yes	—
144	C₂×C₄×D₄₇	C₂³	1	2	yes	—
145	C₂×C₄×D₄₇	C₂³	1	2	yes	—
146	C₂×Dic₉₄	C₂³	1	2	yes	—
147	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
151	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
152	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₄⋊C₄×C₄₇	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	C₄²×C₄₇	C₂³	1	1	yes	characteristic
162	C₄²×C₄₇	C₂³	1	1	yes	characteristic
163	C₄²×C₄₇	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
165	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₇)⋊C₄	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	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
183	C₄⋊Dic₄₇	C₂³	1	2	yes	—
184	C₄⋊Dic₄₇	C₂³	1	2	yes	—
185	Dic₄₇⋊C₄	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	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
194	C₄×Dic₄₇	C₂³	1	2	yes	—
195	C₄×Dic₄₇	C₂³	1	2	yes	—
196	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₄₇	C₂³	1	2	yes	—
199	C₂³×C₄₇	C₂⁴	1	2	yes	—
200	C₂²×D₄₇	—	4	2	no	—
201	C₂²×D₄₇	—	4	2	no	—
202	C₂²×D₄₇	—	4	2	no	—
203	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
204	C₂²×D₄₇	C₂⁴	1	2	yes	—
205	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
206	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
207	C₂²×D₄₇	C₂⁴	1	2	yes	—
208	Q₈×C₄₇	—	4	1	no	—
209	Q₈×C₄₇	—	4	1	no	—
210	Q₈×C₄₇	—	4	1	no	—
211	D₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
214	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
215	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
219	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
220	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
221	C₂²⋊D₄₇	—	2	4	no	—
222	C₂²⋊D₄₇	—	4	2	no	—
223	C₂²⋊D₄₇	—	4	2	no	—
224	C₂²⋊D₄₇	—	4	2	no	—
225	C₂²⋊D₄₇	—	4	2	no	—
226	C₂×Dic₄₇	—	4	2	no	—
227	C₂×Dic₄₇	C₂⁴	1	2	yes	—
228	C₂×Dic₄₇	C₂⁴	1	2	yes	—
229	C₂×Dic₄₇	C₂⁴	1	2	yes	—
230	C₂×Dic₄₇	C₂⁴	1	2	yes	—
231	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
232	D₁₈₈	—	4	2	no	—
233	D₁₈₈	—	4	2	no	—
234	D₁₈₈	—	4	2	no	—
235	D₁₈₈	—	4	2	no	—
236	D₁₈₈	—	4	2	no	—
237	D₁₈₈	—	4	2	no	—
238	D₁₈₈	—	4	1	no	—
239	D₁₈₈	—	4	1	no	—
240	D₁₈₈	—	4	2	no	—
241	D₁₈₈	—	4	1	no	—
242	D₁₈₈	—	4	1	no	—
243	D₁₈₈	—	4	1	no	—
244	C₄×D₄₇	—	2	4	no	—
245	C₄×D₄₇	—	2	2	no	—
246	C₄×D₄₇	—	2	2	no	—
247	C₄×D₄₇	—	2	2	no	—
248	C₄×D₄₇	—	4	2	no	—
249	C₄×D₄₇	—	4	2	no	—
250	C₄×D₄₇	—	4	2	no	—
251	C₄×D₄₇	—	4	2	no	—
252	C₄×D₄₇	—	4	2	no	—
253	C₄×D₄₇	—	4	2	no	—
254	Dic₉₄	—	2	4	no	—
255	Dic₉₄	—	4	1	no	—
256	C₂²×C₄₇	—	2	2	no	—
257	C₂²×C₄₇	—	2	2	no	—
258	C₂²×C₄₇	—	2	2	no	—
259	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
260	C₂×D₄₇	—	2	1	no	—
261	C₂×D₄₇	—	2	1	no	—
262	C₂×D₄₇	—	2	2	no	—
263	C₂×D₄₇	—	2	1	no	—
264	C₂×D₄₇	—	2	2	no	—
265	C₂×D₄₇	—	2	2	no	—
266	C₂×D₄₇	—	2	2	no	—
267	C₂×D₄₇	—	2	2	no	—
268	C₂×D₄₇	—	2	2	no	—
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	2	2	no	—
272	C₂×D₄₇	—	8	4	no	—
273	C₄×C₄₇	—	2	2	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	2	2	no	—
280	C₄×C₄₇	—	2	2	no	—
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	—	2	2	no	—
283	Dic₄₇	—	2	2	no	—
284	Dic₄₇	—	2	2	no	—
285	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
286	#3551	—	47	1	no	maximal, Sylow
287	C₂×C₄₇	—	4	2	no	—
288	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄₇	#585	1	2	yes	—
290	D₄₇	—	4	1	no	—
291	D₄₇	—	4	1	no	—
292	D₄₇	—	4	2	no	—
293	D₄₇	—	4	2	no	—
294	D₄₇	—	4	1	no	—
295	#563	—	47	1	no	—
296	#563	D₄₇	1	1	yes	characteristic, complemented
297	#560	—	47	2	no	—
298	#555	—	47	1	no	—
299	#555	—	47	1	no	—
300	#553	—	47	2	no	—
301	#552	—	47	2	no	—
302	#551	—	47	2	no	—
303	#548	—	47	2	no	—
304	#546	—	47	2	no	—
305	#540	—	47	2	no	—
306	#540	—	47	2	no	—
307	#538	—	47	2	no	—
308	#538	—	47	2	no	—
309	#537	—	47	2	no	—
310	#536	—	47	1	no	—
311	#535	—	47	1	no	—
312	#532	—	47	1	no	—
313	#529	—	47	2	no	—
314	C₄₇	#3551	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	47	1	no	—
316	C₂×#41	—	47	1	no	—
317	C₂×#41	—	47	2	no	—
318	C₂²×Q₈	—	47	1	no	—
319	C₂²×D₄	—	47	1	no	—
320	C₄⋊Q₈	—	47	1	no	—
321	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
322	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
323	#127	—	47	1	no	—
324	#127	—	47	1	no	—
325	#127	—	47	1	no	—
326	#126	—	47	2	no	—
327	#126	—	47	2	no	—
328	#126	—	47	2	no	—
329	#126	—	47	2	no	—
330	#126	C₂×D₄₇	1	2	yes	complemented
331	#126	C₂×D₄₇	1	2	yes	complemented
332	#125	—	47	2	no	—
333	#125	—	47	2	no	—
334	#125	C₂×D₄₇	1	2	yes	complemented
335	#124	—	47	1	no	—
336	#124	—	47	1	no	—
337	#124	—	47	1	no	—
338	#124	—	47	1	no	—
339	#124	—	47	2	no	—
340	#124	—	47	2	no	—
341	#124	—	47	2	no	—
342	#124	—	47	1	no	—
343	#124	C₂×D₄₇	1	1	yes	characteristic
344	#123	—	47	2	no	—
345	#123	—	47	2	no	—
346	#123	—	47	2	no	—
347	#123	—	47	2	no	—
348	#123	—	47	2	no	—
349	#123	—	47	2	no	—
350	#123	—	47	2	no	—
351	#123	—	47	2	no	—
352	#123	—	47	2	no	—
353	#123	C₂×D₄₇	1	2	yes	—
354	C₂²⋊Q₈	—	47	2	no	—
355	C₂²⋊Q₈	—	47	2	no	—
356	C₂²⋊Q₈	—	47	2	no	—
357	C₂²⋊Q₈	—	47	2	no	—
358	C₂²⋊Q₈	—	47	2	no	—
359	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
360	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
361	#121	—	47	2	no	—
362	#121	—	47	2	no	—
363	#121	—	47	2	no	—
364	#121	—	47	2	no	—
365	#121	—	47	2	no	—
366	#121	—	47	2	no	—
367	#121	—	47	2	no	—
368	#121	—	47	2	no	—
369	#121	—	47	2	no	—
370	#121	—	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	#120	—	47	2	no	—
379	#120	—	47	2	no	—
380	#120	—	47	2	no	—
381	#120	—	47	2	no	—
382	C₄×Q₈	—	47	2	no	—
383	C₄×D₄	—	47	2	no	—
384	C₄×D₄	—	47	2	no	—
385	C₄×D₄	—	47	2	no	—
386	C₄×D₄	—	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	#117	—	47	2	no	—
393	#117	—	47	2	no	—
394	#117	—	47	2	no	—
395	#117	—	47	1	no	—
396	#117	—	47	1	no	—
397	#117	—	47	2	no	—
398	C₂×C₄⋊C₄	—	47	2	no	—
399	C₂×C₂²⋊C₄	—	47	2	no	—
400	C₂×C₂²⋊C₄	—	47	2	no	—
401	C₂×C₄²	—	47	1	no	—
402	C₂⁴	—	47	2	no	—
403	#41	—	188	4	no	—
404	#41	—	188	2	no	—
405	#41	—	188	2	no	—
406	C₂×Q₈	—	47	2	no	—
407	C₂×Q₈	—	47	1	no	—
408	C₂×Q₈	—	188	2	no	—
409	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
410	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
412	C₂×D₄	—	47	2	no	—
413	C₂×D₄	—	47	2	no	—
414	C₂×D₄	—	47	2	no	—
415	C₂×D₄	—	47	2	no	—
416	C₂×D₄	—	47	2	no	—
417	C₂×D₄	—	47	2	no	—
418	C₂×D₄	—	47	2	no	—
419	C₂×D₄	—	47	2	no	—
420	C₂×D₄	—	47	2	no	—
421	C₂×D₄	—	47	2	no	—
422	C₂×D₄	—	47	1	no	—
423	C₂×D₄	—	47	1	no	—
424	C₂×D₄	—	47	2	no	—
425	C₂×D₄	—	47	2	no	—
426	C₂×D₄	—	47	1	no	—
427	C₂×D₄	—	47	1	no	—
428	C₂×D₄	—	47	1	no	—
429	C₂×D₄	—	188	2	no	—
430	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
431	C₂²×C₄	—	47	2	no	—
432	C₂²×C₄	—	47	1	no	—
433	C₂²×C₄	—	47	2	no	—
434	C₂²×C₄	—	47	1	no	—
435	C₂²×C₄	—	47	1	no	—
436	C₂²×C₄	—	47	2	no	—
437	C₂²×C₄	—	47	2	no	—
438	C₂²×C₄	—	47	2	no	—
439	C₂²×C₄	—	47	2	no	—
440	C₂²×C₄	—	47	2	no	—
441	C₂²×C₄	—	47	2	no	—
442	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
443	C₄⋊C₄	—	47	2	no	—
444	C₄⋊C₄	—	47	2	no	—
445	C₄⋊C₄	—	47	2	no	—
446	C₄⋊C₄	—	47	2	no	—
447	C₄⋊C₄	—	47	2	no	—
448	C₄⋊C₄	—	47	2	no	—
449	C₄⋊C₄	—	47	2	no	—
450	C₄⋊C₄	—	47	2	no	—
451	C₄⋊C₄	—	47	2	no	—
452	C₄⋊C₄	—	47	2	no	—
453	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
454	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
455	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
456	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
457	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
458	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
459	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
460	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
461	C₂²⋊C₄	—	47	2	no	—
462	C₂²⋊C₄	—	47	2	no	—
463	C₂²⋊C₄	—	47	2	no	—
464	C₂²⋊C₄	—	47	2	no	—
465	C₂²⋊C₄	—	47	2	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	—	47	2	no	—
471	C₂²⋊C₄	—	47	2	no	—
472	C₂²⋊C₄	—	47	2	no	—
473	C₂²⋊C₄	—	47	2	no	—
474	C₂²⋊C₄	—	47	2	no	—
475	C₂²⋊C₄	—	47	2	no	—
476	C₂²⋊C₄	—	47	2	no	—
477	C₂²⋊C₄	—	47	2	no	—
478	C₂²⋊C₄	—	47	2	no	—
479	C₂²⋊C₄	—	47	2	no	—
480	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
485	C₄²	—	47	1	no	—
486	C₄²	—	47	2	no	—
487	C₄²	—	47	1	no	—
488	C₄²	—	47	2	no	—
489	C₄²	—	47	2	no	—
490	C₄²	—	47	1	no	—
491	C₄²	C₂²×D₄₇	1	1	yes	characteristic
492	C₄²	C₂²×D₄₇	1	1	yes	characteristic
493	C₄²	C₂²×D₄₇	1	1	yes	characteristic
494	C₂³	—	47	1	no	—
495	C₂³	—	47	2	no	—
496	C₂³	—	47	1	no	—
497	C₂³	—	47	2	no	—
498	C₂³	—	47	1	no	—
499	C₂³	—	188	2	no	—
500	C₂³	—	188	2	no	—
501	C₂³	—	188	2	no	—
502	C₂³	C₂³×D₄₇	1	2	yes	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	94	4	no	—
507	Q₈	—	188	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	94	4	no	—
510	D₄	—	188	2	no	—
511	D₄	—	188	2	no	—
512	D₄	—	188	2	no	—
513	D₄	—	188	2	no	—
514	D₄	—	188	2	no	—
515	D₄	—	188	1	no	—
516	D₄	—	188	2	no	—
517	D₄	—	188	2	no	—
518	D₄	—	188	1	no	—
519	D₄	—	188	1	no	—
520	D₄	—	188	1	no	—
521	D₄	—	188	1	no	—
522	D₄	—	188	2	no	—
523	D₄	—	188	2	no	—
524	D₄	—	188	2	no	—
525	D₄	—	188	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	47	1	no	—
528	C₂×C₄	—	47	2	no	—
529	C₂×C₄	—	47	2	no	—
530	C₂×C₄	—	47	2	no	—
531	C₂×C₄	—	47	2	no	—
532	C₂×C₄	—	94	2	no	—
533	C₂×C₄	—	94	2	no	—
534	C₂×C₄	—	94	4	no	—
535	C₂×C₄	—	94	2	no	—
536	C₂×C₄	—	188	2	no	—
537	C₂×C₄	—	188	2	no	—
538	C₂×C₄	—	188	2	no	—
539	C₂×C₄	—	188	2	no	—
540	C₂×C₄	—	188	2	no	—
541	C₂×C₄	—	188	2	no	—
542	C₂×C₄	—	188	2	no	—
543	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₄₇	1	2	yes	—
545	C₂×C₄	C₂³×D₄₇	1	2	yes	—
546	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₄₇	1	2	yes	—
549	C₂×C₄	C₂³×D₄₇	1	2	yes	—
550	C₂×C₄	C₂³×D₄₇	1	2	yes	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	94	1	no	—
555	C₂²	—	94	1	no	—
556	C₂²	—	94	2	no	—
557	C₂²	—	94	1	no	—
558	C₂²	—	94	2	no	—
559	C₂²	—	94	2	no	—
560	C₂²	—	94	2	no	—
561	C₂²	—	94	2	no	—
562	C₂²	—	94	2	no	—
563	C₂²	—	94	2	no	—
564	C₂²	—	94	2	no	—
565	C₂²	—	94	2	no	—
566	C₂²	—	376	4	no	—
567	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	47	2	no	—
577	C₄	—	94	2	no	—
578	C₄	—	94	2	no	—
579	C₄	—	94	2	no	—
580	C₄	—	94	2	no	—
581	C₂	—	4	2	no	—
582	C₂	—	188	1	no	—
583	C₂	—	188	2	no	—
584	C₂	—	188	1	no	—
585	C₂	—	188	2	no	—
586	C₂	—	188	1	no	—
587	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
588	C₂	#15689960	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#563	C₂
hypercenter	#563	D₄₇
hypocenter	C₄₇	#3551
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #15689872	C₂	semidirect
2. #15689864	C₂	semidirect
3. #15689839	C₂	semidirect
4. #15689835	C₂	semidirect
5. #15689824	C₂	semidirect
6. #15689805	C₂	semidirect
7. #15689800	C₂	semidirect
8. #15689783	C₂	semidirect
9. #15689765	C₂	semidirect
10. #15689729	C₂	semidirect
11. #15689725	C₂	semidirect
12. #15689713	C₂	semidirect
13. #15689712	C₂	semidirect
14. #15689703	C₂	semidirect
15. #15689698	C₂	semidirect
16. #15689691	C₂	semidirect
17. #15689674	C₂	semidirect
18. #15689656	C₂	semidirect
19. C₄₇×#563	C₂	semidirect
21. C₂×#10625354	C₂²	semidirect
23. C₂×Q₈×D₄₇	C₂²	semidirect
25. #13094022	C₂²	semidirect
31. #13094019	C₂²	semidirect
32. #13094018	C₂²	semidirect
33. #13094014	C₂²	semidirect
34. #13094014	C₂²	semidirect
38. #13094013	C₂²	semidirect
39. #13094013	C₂²	semidirect
42. #13094010	C₂²	semidirect
47. #13094009	C₂²	semidirect
48. #13094009	C₂²	semidirect
49. #13094009	C₂²	semidirect
50. #13094008	C₂²	semidirect
51. #13094006	C₂²	semidirect
53. #13094002	C₂²	semidirect
54. #13094002	C₂²	semidirect
55. #13094002	C₂²	semidirect
56. #13094000	C₂²	semidirect
59. #13093999	C₂²	semidirect
60. #13093999	C₂²	semidirect
61. #13093999	C₂²	semidirect
62. #13093999	C₂²	semidirect
63. #13093999	C₂²	semidirect
64. #13093999	C₂²	semidirect
65. #13093998	C₂²	semidirect
69. #13093997	C₂²	semidirect
70. #13093997	C₂²	semidirect
71. #13093997	C₂²	semidirect
72. #13093997	C₂²	semidirect
78. #13093989	C₂²	semidirect
79. C₄×D₁₈₈	C₂²	semidirect
81. #13093986	C₂²	semidirect
82. #13093986	C₂²	semidirect
83. #13093986	C₂²	semidirect
84. C₄×C₂²⋊D₄₇	C₂²	semidirect
86. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
88. #13093982	C₂²	semidirect
89. #13093982	C₂²	semidirect
91. #13093981	C₂²	semidirect
92. #13093981	C₂²	semidirect
93. #13093980	C₂²	semidirect
94. C₄⋊C₄×D₄₇	C₂²	semidirect
97. C₄²×D₄₇	C₂²	semidirect
98. C₄⋊Q₈×C₄₇	C₂²	semidirect
99. C₄⋊Q₈×C₄₇	C₂²	semidirect
100. #126×C₄₇	C₂²	semidirect
101. #126×C₄₇	C₂²	semidirect
102. #125×C₄₇	C₂²	semidirect
105. C₂²⋊Q₈×C₄₇	C₂²	semidirect
106. C₂²⋊Q₈×C₄₇	C₂²	semidirect
296. #563	D₄₇	semidirect
314. C₄₇	#3551	semidirect
321. C₄⋊Q₈	C₂×D₄₇	semidirect
322. C₄⋊Q₈	C₂×D₄₇	semidirect
330. #126	C₂×D₄₇	semidirect
331. #126	C₂×D₄₇	semidirect
334. #125	C₂×D₄₇	semidirect
359. C₂²⋊Q₈	C₂×D₄₇	semidirect
360. C₂²⋊Q₈	C₂×D₄₇	semidirect