Subgroups — #13050381

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₅₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	D₁₆₅	—	2	1	no	—
7	C₅×D₃×C₁₁	—	2	1	no	—
8	#63142	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	—	3	1	no	—
10	C₂×D₅₅	—	3	1	no	—
11	Dic₅₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₅×C₁₁	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃₃	—	5	1	no	—
14	C₂×D₃×C₁₁	D₅	1	1	yes	characteristic, complemented
15	C₃×Dic₁₁	—	5	1	no	—
16	#1203	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	—	6	1	no	—
18	C₂×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
19	D₅₅	—	6	1	no	—
20	C₂²⋊D₁₁	—	15	1	no	Hall
21	C₂×C₃×C₁₁	C₂×D₅	1	1	yes	characteristic
22	D₃₃	—	10	1	no	—
23	D₃×C₁₁	—	2	1	no	—
24	C₂×D₁₅	—	11	1	no	—
25	C₂×C₅×D₃	D₁₁	1	1	yes	characteristic, complemented
26	C₃×Dic₅	—	11	1	no	—
27	C₅×C₁₁	D₁₂	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	—	3	1	no	—
29	C₂×D₁₁	—	15	1	no	—
30	Dic₁₁	—	5	1	no	—
31	C₂²⋊D₅	—	33	1	no	Hall
32	C₃×C₁₁	C₂²⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	C₂×D₁₁	1	1	yes	characteristic
34	D₁₅	—	22	1	no	—
35	C₅×D₃	—	2	1	no	—
36	D₁₂	—	55	1	no	Hall
37	C₂×C₁₁	—	6	1	no	—
38	C₂×C₁₁	D₃×D₅	1	1	yes	characteristic
39	D₁₁	—	30	1	no	—
40	C₂²×C₅	—	3	1	no	—
41	C₂×D₅	—	33	1	no	—
42	Dic₅	—	11	1	no	—
43	C₃×C₅	C₂²⋊D₁₁	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃	—	55	1	no	—
45	C₂×D₃	D₅₅	1	1	yes	characteristic, complemented
46	C₃×C₄	—	55	1	no	—
47	C₁₁	#1203	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	—	6	1	no	—
49	C₂×C₅	D₃×D₁₁	1	1	yes	characteristic
50	D₅	—	66	1	no	—
51	D₄	—	165	1	no	Sylow
52	C₂×C₃	C₂×D₅₅	1	1	yes	characteristic
53	D₃	—	2	1	no	—
54	D₃	—	110	1	no	—
55	C₅	#63142	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	3	1	no	—
57	C₂²	—	165	1	no	—
58	C₄	—	55	1	no	—
59	C₃	C₂²⋊D₅₅	1	1	yes	characteristic, complemented, Sylow
60	C₂	—	6	1	no	—
61	C₂	—	330	1	no	—
62	C₂	D₃×D₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₅₅
commutator, Fitting, socle, cosocle	C₂×C₃×C₅×C₁₁	C₂²
hypocenter	C₃×C₅×C₁₁	D₄
LCS	G ▷ C₂×C₃×C₅×C₁₁ ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆₅	C₂	semidirect
2. C₂×C₅×D₃×C₁₁	C₂	semidirect
3. C₃×Dic₅₅	C₂	semidirect
11. Dic₅₅	D₃	semidirect
12. C₃×C₅×C₁₁	D₄	semidirect
14. C₂×D₃×C₁₁	D₅	semidirect
25. C₂×C₅×D₃	D₁₁	semidirect
27. C₅×C₁₁	D₁₂	semidirect
32. C₃×C₁₁	C₂²⋊D₅	semidirect
43. C₃×C₅	C₂²⋊D₁₁	semidirect
45. C₂×D₃	D₅₅	semidirect
47. C₁₁	#1203	semidirect
55. C₅	#63142	semidirect
59. C₃	C₂²⋊D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆₅	2
C₂×C₅×D₃×C₁₁	2
C₃×Dic₅₅	2
C₂²⋊D₅₅	3
#63142	5
#1203	11