Subgroups — C₅×#66929 #13183003

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×(C₂×D₁₁)⋊C₄	C₂	1	3	yes	maximal
3	C₅×Dic₁₁⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₂²×C₅×D₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂×C₅×Dic₁₁	C₂²	1	3	yes	—
7	#66929	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×C₅×D₁₁	—	2	3	no	—
10	C₄×C₅×C₁₁	—	2	3	no	—
11	C₅×Dic₁₁	—	2	3	no	—
12	C₄²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
13	(C₂×D₁₁)⋊C₄	C₂×C₅	1	3	yes	—
14	Dic₁₁⋊C₄	C₂×C₅	1	3	yes	complemented
15	C₅×#126	—	11	1	no	maximal, Hall
16	C₂×C₅×C₁₁	#41	1	3	yes	—
17	C₅×D₁₁	—	4	1	no	—
18	C₂²×D₁₁	C₂²×C₅	1	1	yes	characteristic
19	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
20	C₂×Dic₁₁	C₂²×C₅	1	3	yes	—
21	C₅×C₄⋊C₄	—	11	3	no	—
22	C₅×C₂²⋊C₄	—	11	3	no	—
23	C₄²×C₅	D₁₁	1	1	yes	characteristic, complemented
24	C₅×C₁₁	#126	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
26	C₂×D₁₁	—	2	3	no	—
27	C₄×C₁₁	—	2	3	no	—
28	Dic₁₁	—	2	3	no	—
29	C₂³×C₅	—	11	1	no	—
30	C₂×C₄×C₅	—	11	3	no	—
31	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
32	#126	—	11	1	no	Sylow
33	C₂×C₁₁	C₅×#41	1	3	yes	—
34	D₁₁	—	4	1	no	—
35	C₂²×C₅	—	22	3	no	—
36	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
37	C₄×C₅	—	2	3	no	—
38	C₄×C₅	—	22	3	no	—
39	C₄⋊C₄	—	11	3	no	—
40	C₂²⋊C₄	—	11	3	no	—
41	C₄²	C₅×D₁₁	1	1	yes	characteristic, complemented
42	C₁₁	C₅×#126	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₅	—	44	1	no	—
44	C₂×C₅	#4339	1	3	yes	—
45	C₂³	—	11	1	no	—
46	C₂×C₄	—	11	3	no	—
47	C₂×C₄	C₂×C₅×D₁₁	1	3	yes	—
48	C₅	#66929	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	—	22	3	no	—
50	C₂²	C₂²×C₅×D₁₁	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	22	3	no	—
53	C₂	—	44	1	no	—
54	C₂	C₅×#4339	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₁
commutator, cosocle	C₂²×C₁₁	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₁₁
Fitting	C₄²×C₅×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×C₅×D₁₁	C₂²
hypercenter	C₄²×C₅	D₁₁
hypocenter	C₁₁	C₅×#126
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
1. C₄²×C₅×C₁₁	C₂	semidirect
3. C₅×Dic₁₁⋊C₄	C₂	semidirect
7. #66929	C₅	direct (N × H)
12. C₄²×C₁₁	C₂×C₅	semidirect
14. Dic₁₁⋊C₄	C₂×C₅	semidirect
23. C₄²×C₅	D₁₁	semidirect
24. C₅×C₁₁	#126	semidirect
41. C₄²	C₅×D₁₁	semidirect
42. C₁₁	C₅×#126	semidirect
48. C₅	#66929	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₁₁	2
C₅×(C₂×D₁₁)⋊C₄	2
C₅×Dic₁₁⋊C₄	2
#66929	5
C₅×#126	11

Subgroups — C5×#66929 #13183003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66929 #13183003