Subgroups — #13050358

Order 1320.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#89167	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×D₁₅	—	2	1	no	—
7	C₃×C₅×D₁₁	—	2	1	no	—
8	#63140	—	5	1	no	maximal, Hall
9	C₂×D₅×C₁₁	—	3	1	no	—
10	C₂×C₅×D₁₁	D₃	1	1	yes	characteristic, complemented
11	Dic₅₅	—	3	1	no	—
12	C₃×C₅×C₁₁	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃×C₁₁	—	5	1	no	—
14	C₂×C₃×D₁₁	D₅	1	1	yes	characteristic, complemented
15	Dic₃₃	—	5	1	no	—
16	#1220	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
18	C₅×D₁₁	—	2	1	no	—
19	D₅×C₁₁	—	6	1	no	—
20	C₂²⋊D₁₁	—	15	1	no	Hall
21	C₂×C₃×C₁₁	C₂×D₅	1	1	yes	characteristic
22	C₃×D₁₁	—	2	1	no	—
23	D₃×C₁₁	—	10	1	no	—
24	C₂²×C₃×C₅	—	11	1	no	—
25	C₂×D₁₅	D₁₁	1	1	yes	characteristic, complemented
26	Dic₁₅	—	11	1	no	—
27	C₅×C₁₁	#67	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	—	15	1	no	—
29	C₂×D₁₁	D₁₅	1	1	yes	characteristic, complemented
30	Dic₁₁	—	15	1	no	—
31	C₂²⋊D₅	—	33	1	no	Hall
32	C₃×C₁₁	C₂²⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	22	1	no	—
34	C₂×C₃×C₅	C₂×D₁₁	1	1	yes	characteristic
35	D₁₅	—	2	1	no	—
36	#67	—	55	1	no	Hall
37	C₂×C₁₁	—	30	1	no	—
38	C₂×C₁₁	C₂×D₁₅	1	1	yes	characteristic
39	D₁₁	—	2	1	no	—
40	C₂²×C₅	—	11	1	no	—
41	C₂×D₅	—	3	1	no	—
42	Dic₅	—	33	1	no	—
43	C₃×C₅	C₂²⋊D₁₁	1	1	yes	characteristic, complemented, Hall
44	C₂²×C₃	—	11	1	no	—
45	C₂×D₃	—	5	1	no	—
46	Dic₃	—	55	1	no	—
47	C₁₁	#1220	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	—	22	1	no	—
49	C₂×C₅	D₃×D₁₁	1	1	yes	characteristic
50	D₅	—	6	1	no	—
51	D₄	—	165	1	no	Sylow
52	C₂×C₃	—	22	1	no	—
53	C₂×C₃	D₅×D₁₁	1	1	yes	characteristic
54	D₃	—	10	1	no	—
55	C₅	#63140	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	11	1	no	—
57	C₂²	—	15	1	no	—
58	C₄	—	165	1	no	—
59	C₃	#89167	1	1	yes	characteristic, complemented, Sylow
60	C₂	—	22	1	no	—
61	C₂	—	30	1	no	—
62	C₂	D₁₁×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₁×D₁₅
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×C₁₁×D₁₅	C₂	semidirect
2. C₂×C₃×C₅×D₁₁	C₂	semidirect
3. Dic₁₆₅	C₂	semidirect
10. C₂×C₅×D₁₁	D₃	semidirect
12. C₃×C₅×C₁₁	D₄	semidirect
14. C₂×C₃×D₁₁	D₅	semidirect
25. C₂×D₁₅	D₁₁	semidirect
27. C₅×C₁₁	#67	semidirect
29. C₂×D₁₁	D₁₅	semidirect
32. C₃×C₁₁	C₂²⋊D₅	semidirect
43. C₃×C₅	C₂²⋊D₁₁	semidirect
47. C₁₁	#1220	semidirect
55. C₅	#63140	semidirect
59. C₃	#89167	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×D₁₅	2
C₂×C₃×C₅×D₁₁	2
Dic₁₆₅	2
#89167	3
#63140	5
#1220	11