Subgroups — #20257610

Order 6016.

1134 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689868	C₂	1	4	yes	maximal, complemented
2	#15689828	C₂	1	2	yes	maximal, complemented
3	#15689779	C₂	1	2	yes	maximal, complemented
4	#15689773	C₂	1	2	yes	maximal, complemented
5	#15689767	C₂	1	2	yes	maximal, complemented
6	#15689767	C₂	1	4	yes	maximal, complemented
7	#15689749	C₂	1	2	yes	maximal, complemented
8	#15689740	C₂	1	2	yes	maximal, complemented
9	#15689718	C₂	1	2	yes	maximal, complemented
10	#15689711	C₂	1	2	yes	maximal, complemented
11	#15689702	C₂	1	2	yes	maximal, complemented
12	#15689700	C₂	1	2	yes	maximal, complemented
13	#15689634	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13094003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
17	C₂×#10625352	C₂²	1	4	yes	complemented
18	C₂×#10625352	C₂²	1	2	yes	complemented
19	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
20	#13094023	C₂²	1	2	yes	complemented
21	#13094017	C₂²	1	4	yes	complemented
22	#13094014	C₂²	1	4	yes	complemented
23	#13094011	C₂²	1	2	yes	complemented
24	#13094011	C₂²	1	4	yes	complemented
25	#13094010	C₂²	1	4	yes	complemented
26	#13094007	C₂²	1	2	yes	complemented
27	#13094006	C₂²	1	4	yes	complemented
28	#13094005	C₂²	1	4	yes	complemented
29	#13094005	C₂²	1	4	yes	complemented
30	#13094005	C₂²	1	4	yes	complemented
31	#13094004	C₂²	1	2	yes	complemented
32	#13094003	C₂²	1	1	yes	characteristic
33	#13094003	C₂²	1	4	yes	—
34	#13094003	C₂²	1	2	yes	—
35	#13094003	C₂²	1	2	yes	—
36	#13094003	C₂²	1	2	yes	complemented
37	#13094003	C₂²	1	2	yes	complemented
38	#13094003	C₂²	1	1	yes	characteristic, complemented
39	#13094002	C₂²	1	4	yes	complemented
40	#13094001	C₂²	1	4	yes	complemented
41	#13094001	C₂²	1	4	yes	complemented
42	#13094001	C₂²	1	4	yes	complemented
43	#13094001	C₂²	1	4	yes	complemented
44	#13093998	C₂²	1	1	yes	characteristic
45	#13093998	C₂²	1	1	yes	characteristic, complemented
46	#13093997	C₂²	1	4	yes	complemented
47	#13093996	C₂²	1	4	yes	complemented
48	#13093996	C₂²	1	4	yes	complemented
49	#13093996	C₂²	1	4	yes	complemented
50	#13093995	C₂²	1	2	yes	complemented
51	#13093995	C₂²	1	4	yes	complemented
52	#13093993	C₂²	1	2	yes	—
53	#13093993	C₂²	1	4	yes	—
54	#13093989	C₂²	1	2	yes	complemented
55	D₄×Dic₄₇	C₂²	1	2	yes	complemented
56	D₄×Dic₄₇	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
59	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
60	#13093983	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
62	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
63	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
65	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
66	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
68	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
69	#121×C₄₇	C₂²	1	2	yes	—
70	#121×C₄₇	C₂²	1	2	yes	—
71	#121×C₄₇	C₂²	1	2	yes	—
72	#121×C₄₇	C₂²	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
75	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
76	C₂⁴×C₄₇	C₂³	1	2	yes	—
77	C₂×D₄×C₄₇	—	4	2	no	—
78	C₂×D₄×C₄₇	—	4	4	no	—
79	C₂×D₄×C₄₇	C₂³	1	2	yes	—
80	C₂×D₄×C₄₇	C₂³	1	4	yes	—
81	C₂×D₄×C₄₇	C₂³	1	4	yes	—
82	C₂×D₄×C₄₇	C₂³	1	2	yes	—
83	C₂²×C₄×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
96	C₂²×Dic₄₇	C₂³	1	2	yes	—
97	C₂²×Dic₄₇	C₂³	1	2	yes	—
98	C₂²×Dic₄₇	C₂³	1	4	yes	—
99	C₂²×Dic₄₇	C₂³	1	4	yes	—
100	#10625352	—	4	4	no	—
101	#10625352	—	4	8	no	—
102	#10625350	—	4	2	no	—
103	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂³	1	2	yes	—
105	C₂×C₄×D₄₇	C₂³	1	4	yes	—
106	C₂×Dic₉₄	—	4	2	no	—
107	C₂×Dic₉₄	C₂³	1	2	yes	—
108	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
109	C₂×Dic₉₄	C₂³	1	4	yes	—
110	C₂×Dic₉₄	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
116	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
117	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
118	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
119	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
127	C₄⋊Dic₄₇	C₂³	1	2	yes	—
128	C₄⋊Dic₄₇	C₂³	1	2	yes	—
129	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₄₇	C₂³	1	4	yes	—
132	Dic₄₇⋊C₄	C₂³	1	4	yes	—
133	Dic₄₇⋊C₄	C₂³	1	4	yes	—
134	Dic₄₇⋊C₄	C₂³	1	4	yes	—
135	Dic₄₇⋊C₄	C₂³	1	2	yes	—
136	Dic₄₇⋊C₄	C₂³	1	4	yes	—
137	Dic₄₇⋊C₄	C₂³	1	2	yes	—
138	Dic₄₇⋊C₄	C₂³	1	4	yes	—
139	C₄×Dic₄₇	C₂³	1	2	yes	—
140	C₄×Dic₄₇	C₂³	1	4	yes	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	—	4	1	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂³×C₄₇	C₂⁴	1	4	yes	—
149	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂²×D₄₇	C₂⁴	1	2	yes	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	4	4	no	—
155	D₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
164	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₄₇	—	2	4	no	—
169	C₂²⋊D₄₇	—	2	4	no	—
170	C₂²⋊D₄₇	—	4	2	no	—
171	C₂²⋊D₄₇	—	4	4	no	—
172	C₂²⋊D₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	4	4	no	—
177	C₂×Dic₄₇	C₂⁴	1	2	yes	—
178	C₂×Dic₄₇	C₂⁴	1	4	yes	—
179	C₂×Dic₄₇	C₂⁴	1	2	yes	—
180	C₂×Dic₄₇	C₂⁴	1	2	yes	—
181	C₂×Dic₄₇	C₂⁴	1	4	yes	—
182	D₁₈₈	—	4	1	no	—
183	C₄×D₄₇	—	2	4	no	—
184	C₄×D₄₇	—	4	4	no	—
185	Dic₉₄	—	2	4	no	—
186	Dic₉₄	—	4	2	no	—
187	Dic₉₄	—	4	1	no	—
188	Dic₉₄	—	4	4	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	2	4	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	4	4	no	—
200	C₂²×C₄₇	—	8	4	no	—
201	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
202	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
203	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	4	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
212	Dic₄₇	—	2	4	no	—
213	Dic₄₇	—	2	2	no	—
214	Dic₄₇	—	2	2	no	—
215	Dic₄₇	—	2	4	no	—
216	Dic₄₇	—	2	2	no	—
217	#3536	—	47	1	no	maximal, Sylow
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	—	4	1	no	—
221	C₂×C₄₇	—	4	4	no	—
222	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
225	D₄₇	—	4	2	no	—
226	#562	—	47	4	no	—
227	#554	—	47	2	no	—
228	#548	—	47	2	no	—
229	#547	—	47	2	no	—
230	#546	—	47	4	no	—
231	#546	—	47	2	no	—
232	#543	—	47	2	no	—
233	#542	—	47	2	no	—
234	#539	—	47	2	no	—
235	#538	—	47	2	no	—
236	#537	—	47	2	no	—
237	#537	—	47	2	no	—
238	#525	—	47	1	no	—
239	C₂×C₂²⋊Q₈	—	47	1	no	—
240	C₂×#121	D₄₇	1	1	yes	characteristic, complemented
241	C₄₇	#3536	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	47	4	no	—
243	C₂×#41	—	47	2	no	—
244	C₂×#41	—	47	1	no	—
245	C₂²×Q₈	—	47	1	no	—
246	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
247	C₂²×D₄	C₂×D₄₇	1	2	yes	—
248	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
249	C₄⋊Q₈	—	47	2	no	—
250	#126	—	47	4	no	—
251	#125	—	47	4	no	—
252	#124	—	47	2	no	—
253	#124	—	47	4	no	—
254	#124	—	47	4	no	—
255	#123	—	47	4	no	—
256	#123	—	47	4	no	—
257	#123	—	47	4	no	—
258	#123	—	47	2	no	—
259	#123	—	47	4	no	—
260	C₂²⋊Q₈	—	47	2	no	—
261	C₂²⋊Q₈	—	47	2	no	—
262	C₂²⋊Q₈	—	47	2	no	—
263	C₂²⋊Q₈	—	47	2	no	—
264	C₂²⋊Q₈	—	47	1	no	—
265	C₂²⋊Q₈	—	47	1	no	—
266	C₂²⋊Q₈	—	47	4	no	—
267	C₂²⋊Q₈	—	47	2	no	—
268	C₂²⋊Q₈	—	47	4	no	—
269	C₂²⋊Q₈	—	47	4	no	—
270	C₂²⋊Q₈	—	47	4	no	—
271	C₂²⋊Q₈	—	47	4	no	—
272	C₂²⋊Q₈	—	47	4	no	—
273	#121	—	47	2	no	—
274	#121	—	47	4	no	—
275	#121	—	47	4	no	—
276	#121	—	47	4	no	—
277	#121	—	47	4	no	—
278	#121	—	47	1	no	—
279	#121	—	47	1	no	—
280	#121	—	47	4	no	—
281	#121	C₂×D₄₇	1	2	yes	—
282	#121	C₂×D₄₇	1	2	yes	—
283	#121	C₂×D₄₇	1	2	yes	—
284	#121	C₂×D₄₇	1	2	yes	—
285	#120	—	47	2	no	—
286	#120	—	47	4	no	—
287	C₄×Q₈	—	47	2	no	—
288	C₄×D₄	—	47	4	no	—
289	C₄×D₄	—	47	2	no	—
290	C₄×D₄	—	47	2	no	—
291	C₄×D₄	—	47	2	no	—
292	C₄×D₄	—	47	4	no	—
293	#117	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	2	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	47	2	no	—
299	C₂×C₂²⋊C₄	—	47	4	no	—
300	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
301	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
302	C₂⁴	C₂²×D₄₇	1	2	yes	—
303	#41	—	188	2	no	—
304	#41	—	188	8	no	—
305	#41	—	188	4	no	—
306	C₂×Q₈	—	47	2	no	—
307	C₂×Q₈	—	47	1	no	—
308	C₂×Q₈	—	47	2	no	—
309	C₂×Q₈	—	47	4	no	—
310	C₂×Q₈	—	188	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	47	2	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	47	2	no	—
316	C₂×D₄	—	47	4	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	47	1	no	—
319	C₂×D₄	C₂²×D₄₇	1	4	yes	—
320	C₂×D₄	C₂²×D₄₇	1	2	yes	—
321	C₂×D₄	C₂²×D₄₇	1	2	yes	—
322	C₂×D₄	C₂²×D₄₇	1	4	yes	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	47	4	no	—
327	C₂²×C₄	—	47	4	no	—
328	C₂²×C₄	—	47	2	no	—
329	C₂²×C₄	—	47	4	no	—
330	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
335	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
337	C₄⋊C₄	—	47	4	no	—
338	C₄⋊C₄	—	47	4	no	—
339	C₄⋊C₄	—	47	4	no	—
340	C₄⋊C₄	—	47	2	no	—
341	C₄⋊C₄	—	47	2	no	—
342	C₄⋊C₄	—	47	4	no	—
343	C₄⋊C₄	—	47	4	no	—
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	1	no	—
347	C₄⋊C₄	—	47	1	no	—
348	C₄⋊C₄	—	47	4	no	—
349	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
350	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
351	C₂²⋊C₄	—	47	4	no	—
352	C₂²⋊C₄	—	47	2	no	—
353	C₂²⋊C₄	—	47	4	no	—
354	C₂²⋊C₄	—	47	4	no	—
355	C₂²⋊C₄	—	47	4	no	—
356	C₂²⋊C₄	—	47	2	no	—
357	C₂²⋊C₄	—	47	2	no	—
358	C₂²⋊C₄	—	47	4	no	—
359	C₂²⋊C₄	—	47	4	no	—
360	C₂²⋊C₄	—	47	2	no	—
361	C₂²⋊C₄	—	47	4	no	—
362	C₂²⋊C₄	—	47	2	no	—
363	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
364	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
365	C₄²	—	47	2	no	—
366	C₄²	—	47	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	47	2	no	—
374	C₂³	C₂³×D₄₇	1	1	yes	characteristic
375	C₂³	C₂³×D₄₇	1	4	yes	—
376	C₂³	C₂³×D₄₇	1	1	yes	characteristic
377	C₂³	C₂³×D₄₇	1	1	yes	characteristic
378	Q₈	—	94	4	no	—
379	Q₈	—	188	2	no	—
380	Q₈	—	188	1	no	—
381	Q₈	—	188	4	no	—
382	D₄	—	2	8	no	—
383	D₄	—	2	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	94	4	no	—
387	D₄	—	94	4	no	—
388	D₄	—	188	1	no	—
389	D₄	—	188	2	no	—
390	D₄	—	188	4	no	—
391	D₄	—	188	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	47	2	no	—
400	C₂×C₄	—	47	2	no	—
401	C₂×C₄	—	47	4	no	—
402	C₂×C₄	—	47	2	no	—
403	C₂×C₄	—	47	4	no	—
404	C₂×C₄	—	94	4	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	4	no	—
409	C₂×C₄	—	188	4	no	—
410	C₂×C₄	C₂³×D₄₇	1	4	yes	—
411	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	94	2	no	—
428	C₂²	—	94	2	no	—
429	C₂²	—	94	2	no	—
430	C₂²	#13094069	1	2	yes	—
431	C₂²	#13094071	1	2	yes	—
432	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	4	no	—
437	C₄	—	94	4	no	—
438	C₄	—	94	2	no	—
439	C₄	—	94	2	no	—
440	C₄	—	94	4	no	—
441	C₄	—	94	2	no	—
442	C₄	#13094069	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	4	1	no	—
446	C₂	—	4	4	no	—
447	C₂	—	188	2	no	—
448	C₂	C₂×#13094069	1	1	yes	characteristic
449	C₂	C₂×#13094069	1	1	yes	characteristic
450	C₂	C₂×#13094071	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	#3536
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. #15689828	C₂	semidirect
3. #15689779	C₂	semidirect
4. #15689773	C₂	semidirect
5. #15689767	C₂	semidirect
6. #15689767	C₂	semidirect
7. #15689749	C₂	semidirect
8. #15689740	C₂	semidirect
9. #15689718	C₂	semidirect
10. #15689711	C₂	semidirect
11. #15689702	C₂	semidirect
12. #15689700	C₂	semidirect
13. #15689634	C₂	semidirect
14. C₂×#13094003	C₂	semidirect
15. C₂×#121×C₄₇	C₂	semidirect
16. C₂×#10625350	C₂²	semidirect
17. C₂×#10625352	C₂²	semidirect
18. C₂×#10625352	C₂²	semidirect
19. C₂²×Dic₉₄	C₂²	semidirect
20. #13094023	C₂²	semidirect
21. #13094017	C₂²	semidirect
22. #13094014	C₂²	semidirect
23. #13094011	C₂²	semidirect
24. #13094011	C₂²	semidirect
25. #13094010	C₂²	semidirect
26. #13094007	C₂²	semidirect
27. #13094006	C₂²	semidirect
28. #13094005	C₂²	semidirect
29. #13094005	C₂²	semidirect
30. #13094005	C₂²	semidirect
31. #13094004	C₂²	semidirect
36. #13094003	C₂²	semidirect
37. #13094003	C₂²	semidirect
38. #13094003	C₂²	semidirect
39. #13094002	C₂²	semidirect
40. #13094001	C₂²	semidirect
41. #13094001	C₂²	semidirect
42. #13094001	C₂²	semidirect
43. #13094001	C₂²	semidirect
45. #13093998	C₂²	semidirect
46. #13093997	C₂²	semidirect
47. #13093996	C₂²	semidirect
48. #13093996	C₂²	semidirect
49. #13093996	C₂²	semidirect
50. #13093995	C₂²	semidirect
51. #13093995	C₂²	semidirect
54. #13093989	C₂²	semidirect
55. D₄×Dic₄₇	C₂²	semidirect
56. D₄×Dic₄₇	C₂²	semidirect
59. C₄×C₂²⋊D₄₇	C₂²	semidirect
60. #13093983	C₂²	semidirect
61. C₂×C₄⋊Dic₄₇	C₂²	semidirect
62. C₂×Dic₄₇⋊C₄	C₂²	semidirect
63. C₄⋊C₄×D₄₇	C₂²	semidirect
240. C₂×#121	D₄₇	semidirect
241. C₄₇	#3536	semidirect