Subgroups — #14297921

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#91102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748786	C₂	1	2	yes	maximal
5	#11745980	C₂	1	2	yes	maximal, complemented
6	#10602764	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
10	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×D₃×C₈	—	2	2	no	—
12	C₂×C₅×D₃×C₈	—	2	2	no	—
13	C₂×C₅×D₃×C₈	C₄	1	4	yes	complemented
14	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
15	C₂×(C₂×D₃)⋊Dic₅	—	2	2	no	—
16	#91102	—	2	2	no	—
17	C₃×#3950	—	2	2	no	—
18	#90994	—	2	2	no	—
19	#70630	—	5	1	no	maximal, Hall
20	C₂³×C₅×C₈	—	3	1	no	—
21	#65501	—	3	2	no	—
22	C₂×#3950	—	3	1	no	—
23	C₂×#3950	D₃	1	1	yes	characteristic, complemented
24	#64771	—	3	2	no	—
25	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₅	—	2	2	no	—
28	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
29	C₂×C₄×C₅×D₃	—	2	1	no	—
30	C₂×C₄×C₅×D₃	—	2	1	no	—
31	C₂×C₄×C₅×D₃	—	2	1	no	—
32	C₂×C₄×C₅×D₃	—	2	1	no	—
33	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
35	C₂²×C₃×Dic₅	—	2	2	no	—
36	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
39	C₄⋊Dic₁₅	—	2	2	no	—
40	C₄⋊Dic₁₅	—	2	2	no	—
41	C₂×C₅×C₃⋊C₈	—	2	1	no	—
42	C₂×C₅×C₃⋊C₈	—	2	1	no	—
43	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₅×D₃×C₈	—	2	8	no	—
45	C₃×C₄⋊Dic₅	—	2	2	no	—
46	C₃×C₄⋊Dic₅	—	2	2	no	—
47	(C₂×D₃)⋊Dic₅	—	4	4	no	—
48	C₂²×D₃×C₈	D₅	1	1	yes	characteristic
49	C₂×C₃×#107	—	5	1	no	—
50	C₂×#818	—	5	1	no	—
51	#4987	—	5	2	no	—
52	#4529	—	5	2	no	—
53	C₂³×C₄×C₅	—	3	1	no	—
54	C₂²×C₅×C₈	—	3	1	no	—
55	C₂²×C₅×C₈	—	3	4	no	—
56	C₂²×C₅×C₈	—	6	2	no	—
57	C₂²×C₅×C₈	—	6	2	no	—
58	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₅	—	6	2	no	—
60	C₂×C₄⋊Dic₅	—	3	2	no	—
61	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	—
62	#3963	—	6	2	no	—
63	#3950	—	2	2	no	—
64	#3950	—	6	2	no	—
65	#1808	—	15	1	no	Sylow
66	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₅×D₃	—	2	1	no	—
68	C₂²×C₅×D₃	—	2	1	no	—
69	C₂²×C₅×D₃	—	2	1	no	—
70	C₂²×C₅×D₃	—	2	1	no	—
71	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
72	C₂²×C₅×D₃	D₈	1	2	yes	—
73	C₂²×C₅×D₃	Q₁₆	1	2	yes	—
74	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
80	C₂×Dic₁₅	—	4	2	no	—
81	C₂×Dic₁₅	—	4	2	no	—
82	C₂×Dic₁₅	—	4	2	no	—
83	C₂×C₅×Dic₃	—	2	1	no	—
84	C₂×C₅×Dic₃	—	2	1	no	—
85	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
86	C₄×C₅×D₃	—	2	2	no	—
87	C₄×C₅×D₃	—	2	2	no	—
88	C₄×C₅×D₃	—	2	2	no	—
89	C₄×C₅×D₃	—	2	2	no	—
90	C₂×C₃×Dic₅	—	4	2	no	—
91	C₂×C₃×Dic₅	—	4	2	no	—
92	C₂×C₃×Dic₅	—	4	2	no	—
93	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
94	C₅×C₃⋊C₈	—	2	2	no	—
95	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
96	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
97	C₂×C₃×C₄⋊C₄	—	5	2	no	—
98	C₂×(C₂×D₃)⋊C₄	—	10	2	no	—
99	C₂×C₄⋊Dic₃	—	5	2	no	—
100	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
101	C₂×D₃×C₈	—	2	2	no	—
102	C₂×D₃×C₈	—	2	2	no	—
103	C₂×D₃×C₈	Dic₅	1	4	yes	complemented
104	C₃×#107	—	10	2	no	—
105	C₃⋊#95	—	10	2	no	—
106	#818	—	10	2	no	—
107	C₂⁴×C₅	—	3	1	no	—
108	C₂²×C₄×C₅	—	3	1	no	—
109	C₂²×C₄×C₅	—	3	2	no	—
110	C₂²×C₄×C₅	—	3	2	no	—
111	C₂²×C₄×C₅	—	6	1	no	—
112	C₂²×C₄×C₅	—	6	1	no	—
113	C₂²×C₄×C₅	—	6	1	no	—
114	C₂²×C₄×C₅	—	6	1	no	—
115	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
116	C₂²×Dic₅	—	2	2	no	—
117	C₂²×Dic₅	—	6	2	no	—
118	C₂×C₅×C₈	—	3	2	no	—
119	C₂×C₅×C₈	—	6	1	no	—
120	C₂×C₅×C₈	—	6	1	no	—
121	C₂×C₅×C₈	—	6	8	no	—
122	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
123	C₂×C₅×C₈	D₁₂	1	2	yes	—
124	C₂×C₅×C₈	#67	1	2	yes	—
125	C₂²⋊Dic₅	—	12	4	no	—
126	C₄⋊Dic₅	—	2	2	no	—
127	C₄⋊Dic₅	—	2	2	no	—
128	C₄⋊Dic₅	—	6	2	no	—
129	C₄⋊Dic₅	—	6	2	no	—
130	C₂³×C₈	—	3	1	no	—
131	C₂×#107	—	5	1	no	—
132	C₂×#107	—	15	1	no	—
133	#380	—	15	2	no	—
134	#340	—	15	2	no	—
135	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂²×C₃×C₅	#121	1	1	yes	characteristic
137	C₂²×C₃×C₅	#121	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
140	C₂²×C₃×C₅	#135	1	1	yes	characteristic
141	C₂²×C₃×C₅	#135	1	1	yes	characteristic
142	C₂×C₅×D₃	—	2	2	no	—
143	C₂×C₅×D₃	—	2	2	no	—
144	C₂×C₅×D₃	—	2	2	no	—
145	C₂×C₅×D₃	—	2	2	no	—
146	C₂×C₅×D₃	—	2	2	no	—
147	C₂×C₅×D₃	—	2	2	no	—
148	C₂×C₅×D₃	#107	1	4	yes	complemented
149	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₃×C₄×C₅	#117	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
153	Dic₁₅	—	8	2	no	—
154	C₃×Dic₅	—	8	2	no	—
155	C₅×Dic₃	—	2	2	no	—
156	C₂³×D₃	D₂₀	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	10	2	no	—
158	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
159	C₂²×Dic₃	—	10	2	no	—
160	C₂²×Dic₃	D₂₀	1	1	yes	characteristic
161	C₂×C₄×D₃	—	2	1	no	—
162	C₂×C₄×D₃	—	2	1	no	—
163	C₂×C₄×D₃	—	2	1	no	—
164	C₂×C₄×D₃	—	2	1	no	—
165	C₂×C₄×D₃	Dic₁₀	1	2	yes	—
166	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
167	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
168	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
169	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
170	C₃×C₄⋊C₄	—	10	2	no	—
171	C₃×C₄⋊C₄	—	10	2	no	—
172	(C₂×D₃)⋊C₄	—	20	4	no	—
173	C₄⋊Dic₃	—	10	2	no	—
174	C₄⋊Dic₃	—	10	2	no	—
175	C₂×C₃⋊C₈	—	2	1	no	—
176	C₂×C₃⋊C₈	—	2	1	no	—
177	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
178	D₃×C₈	—	2	8	no	—
179	C₂³×C₅	—	3	2	no	—
180	C₂³×C₅	—	3	2	no	—
181	C₂³×C₅	—	3	2	no	—
182	C₂³×C₅	—	6	1	no	—
183	C₂³×C₅	—	6	1	no	—
184	C₂³×C₅	—	6	1	no	—
185	C₂³×C₅	—	6	1	no	—
186	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅	—	3	2	no	—
188	C₂×C₄×C₅	—	6	1	no	—
189	C₂×C₄×C₅	—	6	1	no	—
190	C₂×C₄×C₅	—	6	2	no	—
191	C₂×C₄×C₅	—	6	2	no	—
192	C₂×C₄×C₅	—	6	2	no	—
193	C₂×C₄×C₅	—	6	2	no	—
194	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
196	C₂×C₄×C₅	#237	1	1	yes	characteristic
197	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₅	#239	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
200	C₂×Dic₅	—	4	2	no	—
201	C₂×Dic₅	—	4	2	no	—
202	C₂×Dic₅	—	4	2	no	—
203	C₂×Dic₅	—	12	2	no	—
204	C₂×Dic₅	—	12	2	no	—
205	C₂×Dic₅	—	12	2	no	—
206	C₅×C₈	—	6	2	no	—
207	C₅×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
208	C₂³×C₄	—	3	1	no	—
209	C₂²×C₈	—	3	1	no	—
210	C₂²×C₈	—	3	4	no	—
211	C₂²×C₈	—	6	2	no	—
212	C₂²×C₈	—	6	2	no	—
213	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
214	C₂×C₄⋊C₄	—	5	2	no	—
215	C₂×C₄⋊C₄	—	15	2	no	—
216	C₂×C₂²⋊C₄	—	30	2	no	—
217	#107	—	10	2	no	—
218	#107	—	30	2	no	—
219	#95	—	30	2	no	—
220	C₂×C₃×C₅	#380	1	1	yes	characteristic
221	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
222	C₂×C₃×C₅	#427	1	1	yes	characteristic
223	C₂×C₃×C₅	#466	1	1	yes	characteristic
224	C₂×C₃×C₅	#466	1	1	yes	characteristic
225	C₂×C₃×C₅	#467	1	1	yes	characteristic
226	C₂×C₃×C₅	#467	1	1	yes	characteristic
227	C₅×D₃	—	2	4	no	—
228	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
229	C₂²×D₃	—	2	1	no	—
230	C₂²×D₃	—	2	1	no	—
231	C₂²×D₃	—	2	1	no	—
232	C₂²×D₃	—	2	1	no	—
233	C₂²×D₃	D₄₀	1	2	yes	—
234	C₂²×D₃	Dic₂₀	1	2	yes	—
235	C₂²×D₃	C₄⋊Dic₅	1	2	yes	—
236	C₂×C₃×C₄	—	20	2	no	—
237	C₂×C₃×C₄	—	20	2	no	—
238	C₂×C₃×C₄	—	20	2	no	—
239	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
240	C₂×C₃×C₄	#709	1	1	yes	characteristic
241	C₂×C₃×C₄	#709	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
245	C₂×Dic₃	—	2	1	no	—
246	C₂×Dic₃	—	2	1	no	—
247	C₂×Dic₃	—	20	2	no	—
248	C₂×Dic₃	—	20	2	no	—
249	C₂×Dic₃	—	20	2	no	—
250	C₂×Dic₃	C₄⋊Dic₅	1	2	yes	—
251	C₄×D₃	—	2	2	no	—
252	C₄×D₃	—	2	2	no	—
253	C₄×D₃	—	2	2	no	—
254	C₄×D₃	—	2	2	no	—
255	C₃×C₈	C₂²⋊Dic₅	1	4	yes	complemented
256	C₃⋊C₈	—	2	2	no	—
257	C₂²×C₅	—	3	4	no	—
258	C₂²×C₅	—	6	2	no	—
259	C₂²×C₅	—	6	2	no	—
260	C₂²×C₅	—	6	2	no	—
261	C₂²×C₅	—	6	2	no	—
262	C₂²×C₅	—	6	2	no	—
263	C₂²×C₅	—	6	2	no	—
264	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
265	C₂²×C₅	#895	1	1	yes	characteristic
266	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
267	C₂²×C₅	#912	1	1	yes	characteristic
268	C₂²×C₅	D₃×Q₁₆	1	1	yes	characteristic
269	C₂²×C₅	#919	1	1	yes	characteristic
270	C₂²×C₅	#938	1	1	yes	characteristic
271	C₄×C₅	—	6	2	no	—
272	C₄×C₅	#892	1	1	yes	characteristic
273	C₄×C₅	#897	1	1	yes	characteristic
274	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
275	C₄×C₅	#946	1	1	yes	characteristic
276	Dic₅	—	8	2	no	—
277	Dic₅	—	24	2	no	—
278	C₂⁴	—	3	1	no	—
279	C₂²×C₄	—	3	1	no	—
280	C₂²×C₄	—	3	2	no	—
281	C₂²×C₄	—	3	2	no	—
282	C₂²×C₄	—	6	1	no	—
283	C₂²×C₄	—	6	1	no	—
284	C₂²×C₄	—	6	1	no	—
285	C₂²×C₄	—	6	1	no	—
286	C₂²×C₄	—	10	2	no	—
287	C₂²×C₄	—	30	2	no	—
288	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
289	C₂×C₈	—	3	2	no	—
290	C₂×C₈	—	6	1	no	—
291	C₂×C₈	—	6	1	no	—
292	C₂×C₈	—	6	8	no	—
293	C₂×C₈	D₃×Dic₅	1	2	yes	—
294	C₂×C₈	#1201	1	2	yes	—
295	C₂×C₈	#1203	1	2	yes	—
296	C₄⋊C₄	—	10	2	no	—
297	C₄⋊C₄	—	10	2	no	—
298	C₄⋊C₄	—	30	2	no	—
299	C₄⋊C₄	—	30	2	no	—
300	C₂²⋊C₄	—	60	4	no	—
301	C₃×C₅	#1808	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	C₂×D₄₀	1	1	yes	characteristic
303	C₂²×C₃	#4050	1	1	yes	characteristic
304	C₂²×C₃	#4050	1	1	yes	characteristic
305	C₂²×C₃	C₂×Dic₂₀	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
307	C₂²×C₃	#4076	1	1	yes	characteristic
308	C₂²×C₃	#4076	1	1	yes	characteristic
309	C₂×D₃	—	2	2	no	—
310	C₂×D₃	—	2	2	no	—
311	C₂×D₃	—	2	2	no	—
312	C₂×D₃	—	2	2	no	—
313	C₂×D₃	—	2	2	no	—
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	#3950	1	4	yes	complemented
316	C₃×C₄	—	40	2	no	—
317	C₃×C₄	#4070	1	1	yes	characteristic
318	C₃×C₄	#4070	1	1	yes	characteristic
319	C₃×C₄	#4072	1	1	yes	characteristic
320	C₃×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
321	Dic₃	—	2	2	no	—
322	Dic₃	—	40	2	no	—
323	C₂×C₅	—	6	4	no	—
324	C₂×C₅	D₃×#107	1	1	yes	characteristic
325	C₂×C₅	#4880	1	1	yes	characteristic
326	C₂×C₅	#4883	1	1	yes	characteristic
327	C₂×C₅	#4887	1	1	yes	characteristic
328	C₂×C₅	#4987	1	1	yes	characteristic
329	C₂×C₅	#5157	1	1	yes	characteristic
330	C₂×C₅	#5188	1	1	yes	characteristic
331	C₂³	—	3	2	no	—
332	C₂³	—	3	2	no	—
333	C₂³	—	3	2	no	—
334	C₂³	—	6	1	no	—
335	C₂³	—	6	1	no	—
336	C₂³	—	6	1	no	—
337	C₂³	—	6	1	no	—
338	C₂³	D₃×D₂₀	1	1	yes	characteristic
339	C₂×C₄	—	3	2	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	6	2	no	—
346	C₂×C₄	—	20	2	no	—
347	C₂×C₄	—	20	2	no	—
348	C₂×C₄	—	20	2	no	—
349	C₂×C₄	—	60	2	no	—
350	C₂×C₄	—	60	2	no	—
351	C₂×C₄	—	60	2	no	—
352	C₂×C₄	#6765	1	1	yes	characteristic
353	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
354	C₂×C₄	#6769	1	1	yes	characteristic
355	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
356	C₂×C₄	C₂×#1201	1	1	yes	characteristic
357	C₂×C₄	C₂×#1203	1	1	yes	characteristic
358	C₈	—	6	2	no	—
359	C₈	(C₂×D₃)⋊Dic₅	1	4	yes	complemented
360	C₂×C₃	C₂×#3950	1	1	yes	characteristic
361	C₂×C₃	#65395	1	1	yes	characteristic
362	C₂×C₃	#65404	1	1	yes	characteristic
363	C₂×C₃	#65404	1	1	yes	characteristic
364	C₂×C₃	#65405	1	1	yes	characteristic
365	C₂×C₃	#65405	1	1	yes	characteristic
366	C₂×C₃	#65501	1	1	yes	characteristic
367	D₃	—	2	4	no	—
368	C₅	#70630	1	1	yes	characteristic, complemented, Sylow
369	C₂²	—	3	4	no	—
370	C₂²	—	6	2	no	—
371	C₂²	—	6	2	no	—
372	C₂²	—	6	2	no	—
373	C₂²	—	6	2	no	—
374	C₂²	—	6	2	no	—
375	C₂²	—	6	2	no	—
376	C₂²	D₃×D₄₀	1	1	yes	characteristic
377	C₂²	D₃×Dic₂₀	1	1	yes	characteristic
378	C₂²	#91273	1	1	yes	characteristic
379	C₂²	#91275	1	1	yes	characteristic
380	C₂²	D₃×C₄⋊Dic₅	1	1	yes	characteristic
381	C₂²	#91456	1	1	yes	characteristic
382	C₂²	#91460	1	1	yes	characteristic
383	C₄	—	6	2	no	—
384	C₄	—	40	2	no	—
385	C₄	—	120	2	no	—
386	C₄	#91338	1	1	yes	characteristic
387	C₄	#91365	1	1	yes	characteristic
388	C₄	#91369	1	1	yes	characteristic
389	C₄	C₂×(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
390	C₃	#10602764	1	1	yes	characteristic, complemented, Sylow
391	C₂	—	6	4	no	—
392	C₂	D₃×#3950	1	1	yes	characteristic
393	C₂	#11747682	1	1	yes	characteristic
394	C₂	#11747915	1	1	yes	characteristic
395	C₂	#11747917	1	1	yes	characteristic
396	C₂	#11747950	1	1	yes	characteristic
397	C₂	#11747952	1	1	yes	characteristic
398	C₂	#11748786	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×D₂₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1808
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#91102	C₂	semidirect
3. C₂×C₃×#3950	C₂	semidirect
5. #11745980	C₂	semidirect
13. C₂×C₅×D₃×C₈	C₄	semidirect
23. C₂×#3950	D₃	semidirect
93. C₃×C₅×C₈	C₂²⋊C₄	semidirect
103. C₂×D₃×C₈	Dic₅	semidirect
148. C₂×C₅×D₃	#107	semidirect
207. C₅×C₈	(C₂×D₃)⋊C₄	semidirect
255. C₃×C₈	C₂²⋊Dic₅	semidirect
301. C₃×C₅	#1808	semidirect
315. C₂×D₃	#3950	semidirect
359. C₈	(C₂×D₃)⋊Dic₅	semidirect
368. C₅	#70630	semidirect
390. C₃	#10602764	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×D₃×C₈	2
C₂×#91102	2
C₂×C₃×#3950	2
#11748786	2
#11745980	2
#10602764	3
#70630	5