Subgroups — #20257232

Order 6016.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689859	C₂	1	2	yes	maximal, complemented
2	#15689856	C₂	1	2	yes	maximal, complemented
3	#15689846	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689843	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689837	C₂	1	2	yes	maximal, complemented
6	#15689816	C₂	1	4	yes	maximal, complemented
7	#15689793	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689772	C₂	1	2	yes	maximal, complemented
9	#15689705	C₂	1	4	yes	maximal, complemented
10	#15689686	C₂	1	2	yes	maximal, complemented
11	#15689677	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689671	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689633	C₂	1	2	yes	maximal, complemented
14	#15689630	C₂	1	2	yes	maximal, complemented
15	#15689602	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10625352	C₂²	1	2	yes	—
19	C₂×#10625352	C₂²	1	2	yes	complemented
20	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₄₇	C₂²	1	2	yes	—
22	#13094024	C₂²	1	1	yes	characteristic, complemented
23	#13094023	C₂²	1	1	yes	characteristic, complemented
24	#13094022	C₂²	1	1	yes	characteristic, complemented
25	#13094020	C₂²	1	2	yes	—
26	#13094019	C₂²	1	4	yes	complemented
27	#13094017	C₂²	1	4	yes	complemented
28	#13094014	C₂²	1	2	yes	complemented
29	#13094012	C₂²	1	2	yes	—
30	#13094011	C₂²	1	2	yes	—
31	#13094011	C₂²	1	4	yes	complemented
32	#13094011	C₂²	1	2	yes	complemented
33	#13094010	C₂²	1	4	yes	complemented
34	#13094007	C₂²	1	4	yes	complemented
35	#13094006	C₂²	1	4	yes	complemented
36	#13094005	C₂²	1	4	yes	complemented
37	#13094005	C₂²	1	4	yes	complemented
38	#13094004	C₂²	1	1	yes	characteristic
39	#13094003	C₂²	1	2	yes	complemented
40	#13094002	C₂²	1	2	yes	—
41	#13094000	C₂²	1	1	yes	characteristic
42	#13094000	C₂²	1	2	yes	complemented
43	#13093996	C₂²	1	4	yes	—
44	#13093996	C₂²	1	4	yes	—
45	#13093996	C₂²	1	4	yes	complemented
46	#13093995	C₂²	1	2	yes	—
47	#13093995	C₂²	1	2	yes	—
48	#13093995	C₂²	1	2	yes	complemented
49	#13093992	C₂²	1	4	yes	—
50	#13093992	C₂²	1	4	yes	—
51	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
52	C₄×Dic₉₄	C₂²	1	2	yes	complemented
53	C₄×Dic₉₄	C₂²	1	2	yes	complemented
54	#13093989	C₂²	1	2	yes	complemented
55	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
56	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
57	D₄×Dic₄₇	C₂²	1	2	yes	complemented
58	D₄×Dic₄₇	C₂²	1	2	yes	complemented
59	D₄×Dic₄₇	C₂²	1	2	yes	complemented
60	D₄×Dic₄₇	C₂²	1	4	yes	complemented
61	#13093986	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
64	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
65	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
66	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
67	#13093983	C₂²	1	2	yes	complemented
68	#13093982	C₂²	1	2	yes	complemented
69	#13093981	C₂²	1	2	yes	—
70	#13093980	C₂²	1	4	yes	complemented
71	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
72	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
73	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
74	C₄²×D₄₇	C₂²	1	1	yes	characteristic
75	C₂×#41×C₄₇	C₂²	1	2	yes	complemented
76	#127×C₄₇	C₂²	1	2	yes	—
77	#127×C₄₇	C₂²	1	1	yes	characteristic, complemented
78	#121×C₄₇	C₂²	1	4	yes	complemented
79	#121×C₄₇	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
83	C₂³×D₄₇	C₂³	1	2	yes	—
84	#41×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₄₇	C₂³	1	2	yes	—
88	C₂×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×D₄×C₄₇	C₂³	1	4	yes	—
90	C₂×D₄×C₄₇	C₂³	1	2	yes	—
91	C₂×D₄×C₄₇	C₂³	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
98	C₂²×Dic₄₇	C₂³	1	4	yes	—
99	C₂²×Dic₄₇	C₂³	1	4	yes	—
100	C₂²×Dic₄₇	C₂³	1	2	yes	—
101	#10625352	—	2	8	no	—
102	#10625352	—	4	4	no	—
103	D₄×D₄₇	—	2	4	no	—
104	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₇	—	4	4	no	—
106	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₇	C₂³	1	2	yes	—
108	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₄₇	C₂³	1	2	yes	—
110	C₂×C₄×D₄₇	C₂³	1	2	yes	—
111	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
112	C₂×Dic₉₄	C₂³	1	2	yes	—
113	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
114	C₂×Dic₉₄	C₂³	1	2	yes	—
115	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
120	C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₄²×C₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
123	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
125	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
126	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
127	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
128	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
134	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₄₇	C₂³	1	2	yes	—
136	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₂³	1	2	yes	—
138	C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	Dic₄₇⋊C₄	C₂³	1	2	yes	—
140	Dic₄₇⋊C₄	C₂³	1	2	yes	—
141	Dic₄₇⋊C₄	C₂³	1	4	yes	—
142	Dic₄₇⋊C₄	C₂³	1	4	yes	—
143	Dic₄₇⋊C₄	C₂³	1	2	yes	—
144	Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	Dic₄₇⋊C₄	C₂³	1	2	yes	—
146	Dic₄₇⋊C₄	C₂³	1	2	yes	—
147	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
148	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
149	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
150	C₄×Dic₄₇	C₂³	1	4	yes	—
151	C₄×Dic₄₇	C₂³	1	4	yes	—
152	C₄×Dic₄₇	C₂³	1	2	yes	—
153	C₂³×C₄₇	C₂⁴	1	2	yes	—
154	C₂³×C₄₇	C₂⁴	1	4	yes	—
155	C₂²×D₄₇	—	2	4	no	—
156	C₂²×D₄₇	—	4	2	no	—
157	C₂²×D₄₇	—	4	2	no	—
158	C₂²×D₄₇	C₂⁴	1	2	yes	—
159	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	4	no	—
163	D₄×C₄₇	—	2	4	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
171	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
173	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂²⋊D₄₇	—	2	8	no	—
176	C₂²⋊D₄₇	—	2	4	no	—
177	C₂²⋊D₄₇	—	4	4	no	—
178	C₂²⋊D₄₇	—	4	4	no	—
179	C₂×Dic₄₇	—	2	8	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	4	no	—
182	C₂×Dic₄₇	C₂⁴	1	2	yes	—
183	C₂×Dic₄₇	C₂⁴	1	2	yes	—
184	C₂×Dic₄₇	C₂⁴	1	4	yes	—
185	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₄₇	C₂⁴	1	2	yes	—
188	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
189	D₁₈₈	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	4	no	—
192	C₄×D₄₇	—	4	2	no	—
193	C₄×D₄₇	—	4	2	no	—
194	C₄×D₄₇	—	4	1	no	—
195	C₄×D₄₇	#41	1	4	yes	complemented
196	Dic₉₄	—	2	4	no	—
197	Dic₉₄	—	2	2	no	—
198	Dic₉₄	—	4	2	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
206	C₂×D₄₇	—	2	1	no	—
207	C₂×D₄₇	—	2	1	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	4	8	no	—
212	C₂×D₄₇	C₂×#41	1	2	yes	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	C₂×#41	1	2	yes	—
218	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	2	1	no	—
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	2	1	no	—
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	C₂×#41	1	2	yes	—
226	#3506	—	47	1	no	maximal, Sylow
227	C₂×C₄₇	—	4	2	no	—
228	C₂×C₄₇	—	4	4	no	—
229	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄₇	#585	1	1	yes	characteristic
232	D₄₇	—	2	2	no	—
233	D₄₇	—	4	2	no	—
234	#559	—	47	2	no	—
235	#559	—	47	2	no	—
236	#556	—	47	1	no	—
237	#556	—	47	1	no	—
238	#555	—	47	2	no	—
239	#553	—	47	4	no	—
240	#550	—	47	1	no	—
241	#550	D₄₇	1	1	yes	characteristic, complemented
242	#547	—	47	2	no	—
243	#538	—	47	4	no	—
244	#535	—	47	2	no	—
245	#533	—	47	1	no	—
246	#532	—	47	1	no	—
247	#525	—	47	2	no	—
248	#525	—	47	2	no	—
249	#520	—	47	2	no	—
250	C₂×C₄×D₄	—	47	1	no	—
251	C₄₇	#3506	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	47	2	no	—
253	C₂×#41	—	47	2	no	—
254	C₂×#41	C₂×D₄₇	1	2	yes	complemented
255	C₂²×D₄	—	47	1	no	—
256	C₂³×C₄	—	47	2	no	—
257	C₄⋊Q₈	—	47	1	no	—
258	C₄⋊Q₈	—	47	1	no	—
259	C₄⋊Q₈	—	47	1	no	—
260	#127	—	47	2	no	—
261	#127	C₂×D₄₇	1	2	yes	—
262	#127	C₂×D₄₇	1	1	yes	characteristic, complemented
263	#126	—	47	4	no	—
264	#126	—	47	4	no	—
265	#125	—	47	2	no	—
266	#124	—	47	2	no	—
267	#124	—	47	2	no	—
268	#124	—	47	4	no	—
269	#124	—	47	4	no	—
270	#124	—	47	2	no	—
271	#123	—	47	4	no	—
272	#123	—	47	4	no	—
273	#123	—	47	4	no	—
274	#123	—	47	4	no	—
275	C₂²⋊Q₈	—	47	1	no	—
276	C₂²⋊Q₈	—	47	2	no	—
277	C₂²⋊Q₈	—	47	2	no	—
278	C₂²⋊Q₈	—	47	1	no	—
279	C₂²⋊Q₈	—	47	2	no	—
280	#121	—	47	2	no	—
281	#121	—	47	2	no	—
282	#121	—	47	2	no	—
283	#121	—	47	4	no	—
284	#121	—	47	4	no	—
285	#121	—	47	4	no	—
286	#121	C₂×D₄₇	1	2	yes	complemented
287	#121	C₂×D₄₇	1	4	yes	complemented
288	#120	—	47	4	no	—
289	#120	—	47	4	no	—
290	C₄×Q₈	—	47	2	no	—
291	C₄×Q₈	—	47	2	no	—
292	C₄×Q₈	—	47	1	no	—
293	C₄×Q₈	—	47	2	no	—
294	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
295	C₄×D₄	—	47	1	no	—
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	47	4	no	—
298	C₄×D₄	—	47	2	no	—
299	C₄×D₄	—	47	2	no	—
300	C₄×D₄	—	47	2	no	—
301	C₄×D₄	—	47	4	no	—
302	C₄×D₄	—	47	4	no	—
303	C₄×D₄	—	47	1	no	—
304	C₄×D₄	—	47	2	no	—
305	C₄×D₄	—	47	4	no	—
306	C₄×D₄	—	47	1	no	—
307	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
308	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
309	#117	—	47	2	no	—
310	#117	—	47	2	no	—
311	#117	—	47	4	no	—
312	#117	—	47	2	no	—
313	C₂×C₄⋊C₄	—	47	4	no	—
314	C₂×C₄⋊C₄	—	47	1	no	—
315	C₂×C₂²⋊C₄	—	47	2	no	—
316	C₂×C₄²	—	47	1	no	—
317	C₂⁴	—	47	2	no	—
318	#41	—	4	4	no	—
319	#41	—	94	8	no	—
320	#41	—	188	4	no	—
321	C₂×Q₈	—	47	2	no	—
322	C₂×Q₈	—	47	1	no	—
323	C₂×Q₈	—	47	2	no	—
324	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×D₄	—	47	4	no	—
326	C₂×D₄	—	47	2	no	—
327	C₂×D₄	—	47	4	no	—
328	C₂×D₄	—	47	4	no	—
329	C₂×D₄	—	47	1	no	—
330	C₂×D₄	—	94	4	no	—
331	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₄₇	1	2	yes	—
333	C₂×D₄	C₂²×D₄₇	1	2	yes	—
334	C₂×D₄	C₂²×D₄₇	1	4	yes	—
335	C₂×D₄	C₂²×D₄₇	1	2	yes	—
336	C₂×D₄	C₂²×D₄₇	1	4	yes	—
337	C₂²×C₄	—	47	1	no	—
338	C₂²×C₄	—	47	4	no	—
339	C₂²×C₄	—	47	4	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	47	2	no	—
346	C₂²×C₄	—	188	4	no	—
347	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
348	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
349	C₄⋊C₄	—	47	2	no	—
350	C₄⋊C₄	—	47	2	no	—
351	C₄⋊C₄	—	47	4	no	—
352	C₄⋊C₄	—	47	4	no	—
353	C₄⋊C₄	—	47	2	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	47	2	no	—
357	C₄⋊C₄	—	47	1	no	—
358	C₄⋊C₄	—	47	2	no	—
359	C₄⋊C₄	—	47	1	no	—
360	C₄⋊C₄	—	47	2	no	—
361	C₄⋊C₄	—	47	2	no	—
362	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
365	C₂²⋊C₄	—	47	2	no	—
366	C₂²⋊C₄	—	47	4	no	—
367	C₂²⋊C₄	—	47	4	no	—
368	C₂²⋊C₄	—	47	4	no	—
369	C₂²⋊C₄	—	47	4	no	—
370	C₂²⋊C₄	—	47	4	no	—
371	C₂²⋊C₄	—	47	2	no	—
372	C₂²⋊C₄	—	47	2	no	—
373	C₂²⋊C₄	—	47	2	no	—
374	C₂²⋊C₄	—	47	2	no	—
375	C₂²⋊C₄	—	47	4	no	—
376	C₂²⋊C₄	—	47	4	no	—
377	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
379	C₄²	—	47	1	no	—
380	C₄²	—	47	1	no	—
381	C₄²	—	47	1	no	—
382	C₄²	—	47	4	no	—
383	C₄²	—	47	4	no	—
384	C₄²	—	47	2	no	—
385	C₄²	C₂²×D₄₇	1	1	yes	characteristic
386	C₄²	C₂²×D₄₇	1	2	yes	—
387	C₂³	—	47	1	no	—
388	C₂³	—	47	2	no	—
389	C₂³	—	94	4	no	—
390	C₂³	—	188	2	no	—
391	C₂³	—	188	2	no	—
392	C₂³	C₂³×D₄₇	1	2	yes	—
393	C₂³	C₂³×D₄₇	1	4	yes	—
394	Q₈	—	2	2	no	—
395	Q₈	—	94	4	no	—
396	Q₈	—	94	2	no	—
397	Q₈	—	188	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	94	4	no	—
405	D₄	—	94	8	no	—
406	D₄	—	94	2	no	—
407	D₄	—	188	4	no	—
408	D₄	—	188	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	47	1	no	—
412	C₂×C₄	—	47	4	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	1	no	—
415	C₂×C₄	—	47	4	no	—
416	C₂×C₄	—	47	2	no	—
417	C₂×C₄	—	47	1	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	94	8	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	4	no	—
422	C₂×C₄	—	188	1	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	4	no	—
427	C₂×C₄	C₂³×D₄₇	1	2	yes	—
428	C₂×C₄	C₂³×D₄₇	1	2	yes	—
429	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₄₇	1	2	yes	—
431	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	47	2	no	—
440	C₂²	—	94	1	no	—
441	C₂²	—	94	1	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	94	2	no	—
444	C₂²	—	94	2	no	—
445	C₂²	—	188	8	no	—
446	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	47	2	no	—
452	C₄	—	94	4	no	—
453	C₄	—	94	1	no	—
454	C₄	—	94	2	no	—
455	C₄	—	94	2	no	—
456	C₄	—	94	1	no	—
457	C₄	—	94	2	no	—
458	C₄	#41×D₄₇	1	2	yes	—
459	C₄	#13094069	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	94	2	no	—
463	C₂	—	188	2	no	—
464	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
465	C₂	C₂×#13094069	1	1	yes	characteristic
466	C₂	#15689958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#550	C₂
hypercenter	#550	D₄₇
hypocenter	C₄₇	#3506
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #15689859	C₂	semidirect
2. #15689856	C₂	semidirect
3. #15689846	C₂	semidirect
4. #15689843	C₂	semidirect
5. #15689837	C₂	semidirect
6. #15689816	C₂	semidirect
7. #15689793	C₂	semidirect
8. #15689772	C₂	semidirect
9. #15689705	C₂	semidirect
10. #15689686	C₂	semidirect
11. #15689677	C₂	semidirect
12. #15689671	C₂	semidirect
13. #15689633	C₂	semidirect
14. #15689630	C₂	semidirect
15. #15689602	C₂	semidirect
16. C₄×D₄×D₄₇	C₂	semidirect
17. C₄₇×#550	C₂	semidirect
19. C₂×#10625352	C₂²	semidirect
22. #13094024	C₂²	semidirect
23. #13094023	C₂²	semidirect
24. #13094022	C₂²	semidirect
26. #13094019	C₂²	semidirect
27. #13094017	C₂²	semidirect
28. #13094014	C₂²	semidirect
31. #13094011	C₂²	semidirect
32. #13094011	C₂²	semidirect
33. #13094010	C₂²	semidirect
34. #13094007	C₂²	semidirect
35. #13094006	C₂²	semidirect
36. #13094005	C₂²	semidirect
37. #13094005	C₂²	semidirect
39. #13094003	C₂²	semidirect
42. #13094000	C₂²	semidirect
45. #13093996	C₂²	semidirect
48. #13093995	C₂²	semidirect
51. C₄×Dic₉₄	C₂²	semidirect
52. C₄×Dic₉₄	C₂²	semidirect
53. C₄×Dic₉₄	C₂²	semidirect
54. #13093989	C₂²	semidirect
57. D₄×Dic₄₇	C₂²	semidirect
58. D₄×Dic₄₇	C₂²	semidirect
59. D₄×Dic₄₇	C₂²	semidirect
60. D₄×Dic₄₇	C₂²	semidirect
64. C₄×C₂²⋊D₄₇	C₂²	semidirect
67. #13093983	C₂²	semidirect
68. #13093982	C₂²	semidirect
70. #13093980	C₂²	semidirect
71. C₂×Dic₄₇⋊C₄	C₂²	semidirect
75. C₂×#41×C₄₇	C₂²	semidirect
77. #127×C₄₇	C₂²	semidirect
78. #121×C₄₇	C₂²	semidirect
79. #121×C₄₇	C₂²	semidirect
80. C₄×Q₈×C₄₇	C₂²	semidirect
82. C₄×D₄×C₄₇	C₂²	semidirect
195. C₄×D₄₇	#41	semidirect
241. #550	D₄₇	semidirect
251. C₄₇	#3506	semidirect
254. C₂×#41	C₂×D₄₇	semidirect
262. #127	C₂×D₄₇	semidirect
286. #121	C₂×D₄₇	semidirect
287. #121	C₂×D₄₇	semidirect
294. C₄×Q₈	C₂×D₄₇	semidirect
308. C₄×D₄	C₂×D₄₇	semidirect