Subgroups — C₁₁×#1203 #13050366

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×C₅×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₂²⋊D₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×D₁₅	—	2	1	no	—
7	C₅×D₃×C₁₁	—	2	1	no	—
8	C₁₁×D₁₂	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	—	3	1	no	—
10	C₂×D₅×C₁₁	—	3	1	no	—
11	C₁₁×Dic₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₅×C₁₁	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃×C₁₁	—	5	1	no	—
14	C₂×D₃×C₁₁	D₅	1	1	yes	characteristic, complemented
15	C₃×C₄×C₁₁	—	5	1	no	—
16	#1203	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	—	6	1	no	—
18	C₂×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
19	D₅×C₁₁	—	6	1	no	—
20	D₄×C₁₁	—	15	1	no	Hall
21	C₂×C₃×C₁₁	C₂×D₅	1	1	yes	characteristic
22	D₃×C₁₁	—	2	1	no	—
23	D₃×C₁₁	—	10	1	no	—
24	C₂×D₁₅	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₂×C₅×D₃	C₂×C₁₁	1	1	yes	characteristic, complemented
26	C₃×Dic₅	C₂×C₁₁	1	1	yes	characteristic, complemented
27	C₅×C₁₁	D₁₂	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	—	3	1	no	—
29	C₂²×C₁₁	—	15	1	no	—
30	C₄×C₁₁	—	5	1	no	—
31	C₂²⋊D₅	—	3	1	no	Hall
32	C₃×C₁₁	C₂²⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	C₂²×C₁₁	1	1	yes	characteristic
34	D₁₅	—	2	1	no	—
35	C₅×D₃	—	2	1	no	—
36	D₁₂	—	5	1	no	Hall
37	C₂×C₁₁	—	6	1	no	—
38	C₂×C₁₁	—	30	1	no	—
39	C₂×C₁₁	D₃×D₅	1	1	yes	characteristic
40	C₂²×C₅	—	3	1	no	—
41	C₂×D₅	—	3	1	no	—
42	Dic₅	D₃×C₁₁	1	1	yes	characteristic, complemented
43	C₃×C₅	D₄×C₁₁	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃	—	5	1	no	—
45	C₂×D₃	D₅×C₁₁	1	1	yes	characteristic, complemented
46	C₃×C₄	—	5	1	no	—
47	C₁₁	#1203	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₅	—	6	1	no	—
49	C₂×C₅	C₂×D₃×C₁₁	1	1	yes	characteristic
50	D₅	—	6	1	no	—
51	D₄	—	15	1	no	Sylow
52	C₂×C₃	C₂×D₅×C₁₁	1	1	yes	characteristic
53	D₃	—	2	1	no	—
54	D₃	—	10	1	no	—
55	C₅	C₁₁×D₁₂	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	3	1	no	—
57	C₂²	—	15	1	no	—
58	C₄	—	5	1	no	—
59	C₃	C₁₁×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
60	C₂	—	6	1	no	—
61	C₂	—	30	1	no	—
62	C₂	D₃×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂²×C₁₁
Frattini	C₂	D₃×D₅×C₁₁
Fitting, socle	C₂×C₃×C₅×C₁₁	C₂²
hypocenter	C₃×C₅	D₄×C₁₁
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×D₁₅	C₂	semidirect
2. C₂×C₅×D₃×C₁₁	C₂	semidirect
3. C₃×C₁₁×Dic₅	C₂	semidirect
11. C₁₁×Dic₅	D₃	semidirect
12. C₃×C₅×C₁₁	D₄	semidirect
14. C₂×D₃×C₁₁	D₅	semidirect
16. #1203	C₁₁	direct (N × H)
24. C₂×D₁₅	C₂×C₁₁	semidirect
25. C₂×C₅×D₃	C₂×C₁₁	semidirect
26. C₃×Dic₅	C₂×C₁₁	semidirect
27. C₅×C₁₁	D₁₂	semidirect
32. C₃×C₁₁	C₂²⋊D₅	semidirect
42. Dic₅	D₃×C₁₁	semidirect
43. C₃×C₅	D₄×C₁₁	semidirect
45. C₂×D₃	D₅×C₁₁	semidirect
47. C₁₁	#1203	direct (N × H)
55. C₅	C₁₁×D₁₂	semidirect
59. C₃	C₁₁×C₂²⋊D₅	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×C₅×D₃×C₁₁	2
C₃×C₁₁×Dic₅	2
C₁₁×C₂²⋊D₅	3
C₁₁×D₁₂	5
#1203	11

Subgroups — C11×#1203 #13050366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1203 #13050366