Subgroups — C₂×C₃×#64953 #14319874

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#685	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3963	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3963	C₂	1	2	yes	maximal, complemented
6	C₃×#64953	C₂	1	8	yes	maximal, direct product factor
7	C₂×#64953	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
12	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	—	2	8	no	—
14	C₂²×C₃×C₄×D₅	C₄	1	8	yes	complemented
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
16	C₂×C₃×#685	—	2	8	no	—
17	C₂×C₃×#685	C₂²	1	8	yes	—
18	C₃×C₅×#95	C₂²	1	4	yes	complemented
19	C₃×#3963	C₂²	1	4	yes	complemented
20	C₃×#3963	C₂²	1	8	yes	complemented
21	C₂×C₃×#381	—	5	1	no	maximal, Hall
22	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
23	C₂²×#685	C₂×C₃	1	2	yes	—
24	C₂×C₅×#95	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#3963	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#3963	C₂×C₃	1	2	yes	complemented
27	#64953	C₂×C₃	1	8	yes	direct product factor
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂³×C₃×D₅	—	2	4	no	—
30	C₂³×C₃×D₅	—	2	2	no	—
31	C₂³×C₃×D₅	—	2	2	no	—
32	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
33	C₂³×C₃×D₅	D₄	1	8	yes	—
34	C₂³×C₃×D₅	C₂³	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×Dic₅	—	2	4	no	—
43	C₂²×C₃×Dic₅	—	2	4	no	—
44	C₂²×C₃×Dic₅	—	2	4	no	—
45	C₂²×C₃×Dic₅	—	2	4	no	—
46	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
47	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₂×C₃×C₄×D₅	—	2	32	no	—
50	C₂×C₃×C₄×D₅	—	2	16	no	—
51	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
52	C₃×#685	—	2	16	no	—
53	C₂⁴×C₃×C₄	—	5	1	no	—
54	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
55	C₃×#381	—	5	8	no	—
56	C₂×C₃×#95	—	5	2	no	—
57	C₂×C₃×#95	—	5	1	no	—
58	C₂×C₃×#95	D₅	1	1	yes	characteristic, complemented
59	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
63	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₄×D₅	—	2	8	no	—
65	C₂²×C₄×D₅	C₃×C₄	1	8	yes	complemented
66	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
67	C₂×#685	—	2	8	no	—
68	C₂×#685	C₂²×C₃	1	8	yes	—
69	C₅×#95	C₂²×C₃	1	4	yes	complemented
70	#3963	C₂²×C₃	1	4	yes	complemented
71	#3963	C₂²×C₃	1	8	yes	complemented
72	C₂×#381	—	5	1	no	Sylow
73	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
75	C₂³×C₃×C₅	#41	1	4	yes	—
76	C₂³×C₃×C₅	#41	1	2	yes	—
77	C₂³×C₃×C₅	#41	1	2	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
79	C₂²×C₃×D₅	—	2	8	no	—
80	C₂²×C₃×D₅	—	2	8	no	—
81	C₂²×C₃×D₅	—	2	16	no	—
82	C₂²×C₃×D₅	—	2	16	no	—
83	C₂²×C₃×D₅	—	2	4	no	—
84	C₂²×C₃×D₅	—	2	2	no	—
85	C₂²×C₃×D₅	—	2	2	no	—
86	C₂²×C₃×D₅	C₂²⋊C₄	1	16	yes	—
87	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
88	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
89	C₂×C₃×C₄×C₅	—	2	8	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	4	8	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
96	C₂×C₃×Dic₅	—	2	8	no	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	—	2	4	no	—
99	C₂×C₃×Dic₅	—	2	4	no	—
100	C₂×C₃×Dic₅	—	2	4	no	—
101	C₂×C₃×Dic₅	—	4	8	no	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
103	C₃×C₄×D₅	—	2	32	no	—
104	C₂⁵×C₃	—	5	1	no	—
105	C₂³×C₃×C₄	—	5	1	no	—
106	C₂³×C₃×C₄	—	5	8	no	—
107	C₂³×C₃×C₄	—	5	4	no	—
108	C₂³×C₃×C₄	—	5	2	no	—
109	C₂³×C₃×C₄	—	10	8	no	—
110	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
111	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
112	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
113	C₂×C₃×C₂²⋊C₄	—	10	8	no	—
114	C₃×#95	—	5	8	no	—
115	C₃×#95	—	5	4	no	—
116	C₃×#95	C₂×D₅	1	4	yes	complemented
117	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂³×D₅	—	2	4	no	—
119	C₂³×D₅	—	2	2	no	—
120	C₂³×D₅	—	2	2	no	—
121	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
122	C₂³×D₅	C₃×D₄	1	8	yes	—
123	C₂³×D₅	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
131	C₂²×Dic₅	—	2	4	no	—
132	C₂²×Dic₅	—	2	4	no	—
133	C₂²×Dic₅	—	2	4	no	—
134	C₂²×Dic₅	—	2	4	no	—
135	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
136	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
137	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
138	C₂×C₄×D₅	—	2	32	no	—
139	C₂×C₄×D₅	—	2	16	no	—
140	C₂×C₄×D₅	C₂×C₃×C₄	1	16	yes	complemented
141	#685	—	2	16	no	—
142	C₂⁴×C₄	—	5	1	no	—
143	C₂²×C₂²⋊C₄	—	5	2	no	—
144	#381	—	5	8	no	—
145	C₂×#95	—	5	2	no	—
146	C₂×#95	—	5	1	no	—
147	C₂×#95	C₃×D₅	1	1	yes	characteristic, complemented
148	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂²×C₃×C₅	#117	1	4	yes	—
150	C₂²×C₃×C₅	#117	1	4	yes	—
151	C₂²×C₃×C₅	#123	1	8	yes	—
152	C₂²×C₃×C₅	#123	1	8	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
156	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
158	C₂×C₃×D₅	—	2	4	no	—
159	C₂×C₃×D₅	—	2	4	no	—
160	C₂×C₃×D₅	—	2	8	no	—
161	C₂×C₃×D₅	—	2	8	no	—
162	C₂×C₃×D₅	—	2	32	no	—
163	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	8	yes	—
164	C₃×C₄×C₅	—	2	4	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×Dic₅	—	2	4	no	—
167	C₃×Dic₅	—	4	4	no	—
168	C₂⁴×C₃	—	5	4	no	—
169	C₂⁴×C₃	—	5	8	no	—
170	C₂⁴×C₃	—	5	2	no	—
171	C₂⁴×C₃	—	10	4	no	—
172	C₂⁴×C₃	—	10	2	no	—
173	C₂⁴×C₃	—	10	2	no	—
174	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	5	4	no	—
180	C₂²×C₃×C₄	—	5	2	no	—
181	C₂²×C₃×C₄	—	5	16	no	—
182	C₂²×C₃×C₄	—	5	4	no	—
183	C₂²×C₃×C₄	—	10	16	no	—
184	C₂²×C₃×C₄	—	10	32	no	—
185	C₂²×C₃×C₄	—	10	4	no	—
186	C₂²×C₃×C₄	—	10	4	no	—
187	C₂²×C₃×C₄	—	10	4	no	—
188	C₂²×C₃×C₄	—	10	4	no	—
189	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
190	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
191	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
192	C₃×C₂²⋊C₄	—	10	16	no	—
193	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
194	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
195	C₂³×C₅	C₃×#41	1	4	yes	—
196	C₂³×C₅	C₃×#41	1	2	yes	—
197	C₂³×C₅	C₃×#41	1	2	yes	—
198	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
199	C₂²×D₅	—	2	8	no	—
200	C₂²×D₅	—	2	8	no	—
201	C₂²×D₅	—	2	16	no	—
202	C₂²×D₅	—	2	16	no	—
203	C₂²×D₅	—	2	4	no	—
204	C₂²×D₅	—	2	2	no	—
205	C₂²×D₅	—	2	2	no	—
206	C₂²×D₅	C₃×C₂²⋊C₄	1	16	yes	—
207	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
208	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
209	C₂×C₄×C₅	—	2	8	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	4	8	no	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
216	C₂×Dic₅	—	2	8	no	—
217	C₂×Dic₅	—	2	4	no	—
218	C₂×Dic₅	—	2	4	no	—
219	C₂×Dic₅	—	2	4	no	—
220	C₂×Dic₅	—	2	4	no	—
221	C₂×Dic₅	—	4	8	no	—
222	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
223	C₄×D₅	—	2	32	no	—
224	C₂⁵	—	5	1	no	—
225	C₂³×C₄	—	5	1	no	—
226	C₂³×C₄	—	5	8	no	—
227	C₂³×C₄	—	5	4	no	—
228	C₂³×C₄	—	5	2	no	—
229	C₂³×C₄	—	10	8	no	—
230	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
231	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	5	8	no	—
233	C₂×C₂²⋊C₄	—	10	8	no	—
234	#95	—	5	8	no	—
235	#95	—	5	4	no	—
236	#95	C₂×C₃×D₅	1	4	yes	complemented
237	C₂×C₃×C₅	#381	1	8	yes	complemented
238	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#123	1	2	yes	—
242	C₂×C₃×C₅	C₂×#123	1	2	yes	—
243	C₃×D₅	—	2	8	no	—
244	C₂³×C₃	—	5	4	no	—
245	C₂³×C₃	—	5	8	no	—
246	C₂³×C₃	—	5	16	no	—
247	C₂³×C₃	—	10	4	no	—
248	C₂³×C₃	—	10	2	no	—
249	C₂³×C₃	—	10	2	no	—
250	C₂³×C₃	—	10	8	no	—
251	C₂³×C₃	—	10	16	no	—
252	C₂³×C₃	—	10	8	no	—
253	C₂³×C₃	—	10	16	no	—
254	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
255	C₂³×C₃	#709	1	4	yes	—
256	C₂³×C₃	D₄×D₅	1	4	yes	—
257	C₂³×C₃	#711	1	2	yes	—
258	C₂³×C₃	#713	1	2	yes	—
259	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	8	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	4	8	no	—
266	C₂×C₃×C₄	—	5	4	no	—
267	C₂×C₃×C₄	—	10	32	no	—
268	C₂×C₃×C₄	—	10	4	no	—
269	C₂×C₃×C₄	—	10	8	no	—
270	C₂×C₃×C₄	—	10	4	no	—
271	C₂×C₃×C₄	—	10	4	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	—	20	8	no	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
275	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
276	C₂²×C₅	C₃×#117	1	4	yes	—
277	C₂²×C₅	C₃×#117	1	4	yes	—
278	C₂²×C₅	C₃×#123	1	8	yes	—
279	C₂²×C₅	C₃×#123	1	8	yes	—
280	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
281	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
282	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
283	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
284	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
285	C₂×D₅	—	2	32	no	—
286	C₂×D₅	—	2	4	no	—
287	C₂×D₅	—	2	4	no	—
288	C₂×D₅	—	2	8	no	—
289	C₂×D₅	—	2	8	no	—
290	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	8	yes	—
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	—	4	4	no	—
293	Dic₅	—	2	4	no	—
294	Dic₅	—	4	4	no	—
295	C₂⁴	—	5	4	no	—
296	C₂⁴	—	5	8	no	—
297	C₂⁴	—	5	2	no	—
298	C₂⁴	—	10	4	no	—
299	C₂⁴	—	10	2	no	—
300	C₂⁴	—	10	2	no	—
301	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	5	4	no	—
307	C₂²×C₄	—	5	2	no	—
308	C₂²×C₄	—	5	16	no	—
309	C₂²×C₄	—	5	4	no	—
310	C₂²×C₄	—	10	16	no	—
311	C₂²×C₄	—	10	32	no	—
312	C₂²×C₄	—	10	4	no	—
313	C₂²×C₄	—	10	4	no	—
314	C₂²×C₄	—	10	4	no	—
315	C₂²×C₄	—	10	4	no	—
316	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
317	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
318	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
319	C₂²⋊C₄	—	10	16	no	—
320	C₃×C₅	C₂×#381	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	5	8	no	—
322	C₂²×C₃	—	10	4	no	—
323	C₂²×C₃	—	10	8	no	—
324	C₂²×C₃	—	10	4	no	—
325	C₂²×C₃	—	10	8	no	—
326	C₂²×C₃	—	10	32	no	—
327	C₂²×C₃	#4018	1	4	yes	—
328	C₂²×C₃	D₅×C₂²⋊C₄	1	4	yes	—
329	C₂²×C₃	#4029	1	8	yes	—
330	C₂²×C₃	#4038	1	4	yes	—
331	C₂²×C₃	#4040	1	8	yes	—
332	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
333	C₂²×C₃	C₂×#709	1	2	yes	—
334	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
335	C₂²×C₃	C₂×#711	1	1	yes	characteristic
336	C₂²×C₃	C₂×#713	1	1	yes	characteristic
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	—	10	4	no	—
340	C₃×C₄	—	20	4	no	—
341	C₂×C₅	C₃×#381	1	8	yes	complemented
342	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
344	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
345	C₂×C₅	C₂×C₃×#123	1	2	yes	—
346	C₂×C₅	C₂×C₃×#123	1	2	yes	—
347	D₅	—	2	8	no	—
348	C₂³	—	5	4	no	—
349	C₂³	—	5	8	no	—
350	C₂³	—	5	16	no	—
351	C₂³	—	10	4	no	—
352	C₂³	—	10	2	no	—
353	C₂³	—	10	2	no	—
354	C₂³	—	10	8	no	—
355	C₂³	—	10	16	no	—
356	C₂³	—	10	8	no	—
357	C₂³	—	10	16	no	—
358	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
359	C₂³	C₃×#709	1	4	yes	—
360	C₂³	C₃×D₄×D₅	1	4	yes	—
361	C₂³	C₃×#711	1	2	yes	—
362	C₂³	C₃×#713	1	2	yes	—
363	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	5	4	no	—
371	C₂×C₄	—	10	32	no	—
372	C₂×C₄	—	10	4	no	—
373	C₂×C₄	—	10	8	no	—
374	C₂×C₄	—	10	4	no	—
375	C₂×C₄	—	10	4	no	—
376	C₂×C₄	—	10	4	no	—
377	C₂×C₄	—	20	8	no	—
378	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
379	C₂×C₃	—	10	8	no	—
380	C₂×C₃	#64953	1	8	yes	direct product factor
381	C₂×C₃	C₂×#4018	1	1	yes	characteristic
382	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₃	C₂×#4029	1	2	yes	—
384	C₂×C₃	C₂×#4038	1	1	yes	characteristic
385	C₂×C₃	C₂×#4040	1	2	yes	—
386	C₅	C₂×C₃×#381	1	1	yes	characteristic, complemented, Sylow
387	C₂²	—	5	8	no	—
388	C₂²	—	10	32	no	—
389	C₂²	—	10	4	no	—
390	C₂²	—	10	8	no	—
391	C₂²	—	10	4	no	—
392	C₂²	—	10	8	no	—
393	C₂²	C₃×#4018	1	4	yes	—
394	C₂²	C₃×D₅×C₂²⋊C₄	1	4	yes	—
395	C₂²	C₃×#4029	1	8	yes	—
396	C₂²	C₃×#4038	1	4	yes	—
397	C₂²	C₃×#4040	1	8	yes	—
398	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
399	C₂²	C₂×C₃×#709	1	2	yes	—
400	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
401	C₂²	C₂×C₃×#711	1	1	yes	characteristic
402	C₂²	C₂×C₃×#713	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	10	4	no	—
406	C₄	—	20	4	no	—
407	C₃	C₂×#64953	1	1	yes	characteristic, direct product factor, Sylow
408	C₂	—	10	8	no	—
409	C₂	C₃×#64953	1	8	yes	direct product factor
410	C₂	C₂×C₃×#4018	1	1	yes	characteristic
411	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₂	C₂×C₃×#4029	1	2	yes	—
413	C₂	C₂×C₃×#4038	1	1	yes	characteristic
414	C₂	C₂×C₃×#4040	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#95	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₃×D₅	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#95	D₅
hypocenter	C₅	C₂×C₃×#381
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂×C₃×#95

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×#95	C₂	semidirect
4. C₂×C₃×#3963	C₂	semidirect
5. C₂×C₃×#3963	C₂	semidirect
6. C₃×#64953	C₂	direct (N × H)
7. C₂×#64953	C₃	direct (N × H)
14. C₂²×C₃×C₄×D₅	C₄	semidirect
18. C₃×C₅×#95	C₂²	semidirect
19. C₃×#3963	C₂²	semidirect
20. C₃×#3963	C₂²	semidirect
24. C₂×C₅×#95	C₂×C₃	semidirect
25. C₂×#3963	C₂×C₃	semidirect
26. C₂×#3963	C₂×C₃	semidirect
27. #64953	C₂×C₃	direct (N × H)
51. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
58. C₂×C₃×#95	D₅	semidirect
65. C₂²×C₄×D₅	C₃×C₄	semidirect
69. C₅×#95	C₂²×C₃	semidirect
70. #3963	C₂²×C₃	semidirect
71. #3963	C₂²×C₃	semidirect
116. C₃×#95	C₂×D₅	semidirect
140. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
147. C₂×#95	C₃×D₅	semidirect
236. #95	C₂×C₃×D₅	semidirect
237. C₂×C₃×C₅	#381	semidirect
320. C₃×C₅	C₂×#381	semidirect
341. C₂×C₅	C₃×#381	semidirect
380. C₂×C₃	#64953	direct (N × H)
386. C₅	C₂×C₃×#381	semidirect
407. C₃	C₂×#64953	direct (N × H)
409. C₂	C₃×#64953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×D₅	2
C₂²×C₃×#685	2
C₂×C₃×C₅×#95	2
C₂×C₃×#3963	2
C₃×#64953	2
C₂×#64953	3
C₂×C₃×#381	5

Subgroups — C2×C3×#64953 #14319874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64953 #14319874