Subgroups — C₅×#4341 #11725013

Order 880.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂²⋊D₁₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×Dic₁₁	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₁	C₂²	1	2	yes	—
7	C₂×C₅×D₁₁	C₂²	1	1	yes	characteristic
8	C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₅×Dic₁₁	C₂²	1	2	yes	—
10	C₅×Dic₁₁	C₂²	1	1	yes	characteristic
11	#4341	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₁₁	—	2	2	no	—
13	C₂×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₅×D₁₁	—	2	1	no	—
15	D₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂²⋊D₁₁	C₂×C₅	1	2	yes	complemented
17	C₂×Dic₁₁	C₂×C₅	1	2	yes	complemented
18	C₄×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
19	Dic₂₂	C₂×C₅	1	1	yes	characteristic, complemented
20	C₅×#41	—	11	1	no	maximal, Hall
21	C₅×C₁₁	#41	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₁₁	C₂²×C₅	1	2	yes	—
23	C₂×D₁₁	C₂²×C₅	1	1	yes	characteristic
24	C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
25	Dic₁₁	C₂²×C₅	1	2	yes	—
26	Dic₁₁	C₂²×C₅	1	1	yes	characteristic
27	C₅×Q₈	—	11	1	no	—
28	C₅×D₄	—	11	2	no	—
29	C₅×D₄	D₁₁	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅	—	11	2	no	—
31	C₂×C₄×C₅	—	11	1	no	—
32	C₂×C₁₁	—	2	2	no	—
33	C₂×C₁₁	C₂³×C₅	1	1	yes	characteristic
34	D₁₁	—	2	1	no	—
35	C₂²×C₅	—	11	1	no	—
36	C₂²×C₅	C₂×D₁₁	1	2	yes	—
37	C₄×C₅	—	11	1	no	—
38	C₄×C₅	—	11	2	no	—
39	C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
40	#41	—	11	1	no	Sylow
41	C₁₁	C₅×#41	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	2	2	no	—
43	C₂×C₅	—	22	1	no	—
44	C₂×C₅	C₂²×D₁₁	1	1	yes	characteristic
45	Q₈	—	11	1	no	—
46	D₄	—	11	2	no	—
47	D₄	C₅×D₁₁	1	1	yes	characteristic, complemented
48	C₂×C₄	—	11	2	no	—
49	C₂×C₄	—	11	1	no	—
50	C₅	#4341	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²	—	11	1	no	—
52	C₂²	C₂×C₅×D₁₁	1	2	yes	—
53	C₄	—	11	1	no	—
54	C₄	—	11	2	no	—
55	C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
56	C₂	—	2	2	no	—
57	C₂	—	22	1	no	—
58	C₂	C₂²×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₁₁
commutator, cosocle	C₂×C₁₁	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₁₁
Fitting	C₅×D₄×C₁₁	C₂
socle	C₂×C₅×C₁₁	C₂³
hypercenter	C₅×D₄	D₁₁
hypocenter	C₁₁	C₅×#41
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×C₁₁	C₂	semidirect
2. C₅×C₂²⋊D₁₁	C₂	semidirect
3. C₂×C₅×Dic₁₁	C₂	semidirect
4. C₄×C₅×D₁₁	C₂	semidirect
5. C₅×Dic₂₂	C₂	semidirect
11. #4341	C₅	direct (N × H)
15. D₄×C₁₁	C₂×C₅	semidirect
16. C₂²⋊D₁₁	C₂×C₅	semidirect
17. C₂×Dic₁₁	C₂×C₅	semidirect
18. C₄×D₁₁	C₂×C₅	semidirect
19. Dic₂₂	C₂×C₅	semidirect
21. C₅×C₁₁	#41	semidirect
29. C₅×D₄	D₁₁	semidirect
41. C₁₁	C₅×#41	semidirect
47. D₄	C₅×D₁₁	semidirect
50. C₅	#4341	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₄×C₁₁	2
C₅×C₂²⋊D₁₁	2
C₂×C₅×Dic₁₁	2
C₄×C₅×D₁₁	2
C₅×Dic₂₂	2
#4341	5
C₅×#41	11

Subgroups — C5×#4341 #11725013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#4341 #11725013