Subgroups — C₄×C₁₁×Dic₅ #11724913

Order 880.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×Dic₅	C₂	1	2	yes	maximal
3	C₂²×C₅×C₁₁	C₂²	1	1	yes	characteristic
4	C₄×C₅×C₁₁	C₄	1	2	yes	complemented
5	C₁₁×Dic₅	C₄	1	4	yes	direct product factor
6	C₄²×C₁₁	—	5	1	no	maximal, Hall
7	C₂×C₅×C₁₁	C₂×C₄	1	2	yes	—
8	C₂×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₁	—	5	2	no	—
10	C₂×C₄×C₁₁	D₅	1	1	yes	characteristic
11	C₄×Dic₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₁₁	C₄²	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₁₁	C₂×D₅	1	1	yes	characteristic
14	C₄×C₁₁	—	5	4	no	—
15	C₄×C₁₁	Dic₅	1	2	yes	direct product factor
16	C₂×C₄×C₅	C₂×C₁₁	1	1	yes	characteristic
17	C₂×Dic₅	C₂×C₁₁	1	2	yes	—
18	C₂×C₁₁	C₄×D₅	1	2	yes	—
19	C₂×C₁₁	C₂×Dic₅	1	1	yes	characteristic
20	C₂²×C₅	C₂²×C₁₁	1	1	yes	characteristic
21	C₄×C₅	C₄×C₁₁	1	2	yes	complemented
22	Dic₅	C₄×C₁₁	1	4	yes	direct product factor
23	C₄²	—	5	1	no	Sylow
24	C₁₁	C₄×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₂×C₄×C₁₁	1	2	yes	—
26	C₂×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
27	C₂×C₄	—	5	2	no	—
28	C₂×C₄	D₅×C₁₁	1	1	yes	characteristic
29	C₅	C₄²×C₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂²	C₂×D₅×C₁₁	1	1	yes	characteristic
31	C₄	—	5	4	no	—
32	C₄	C₁₁×Dic₅	1	2	yes	direct product factor
33	C₂	C₄×D₅×C₁₁	1	2	yes	—
34	C₂	C₂×C₁₁×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₁	D₅
commutator, hypocenter	C₅	C₄²×C₁₁
Frattini	C₂²	C₂×D₅×C₁₁
Fitting	C₂×C₄×C₅×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	C₂²
cosocle	C₂²×C₅	C₂²×C₁₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
4. C₄×C₅×C₁₁	C₄	semidirect
5. C₁₁×Dic₅	C₄	direct (N × H)
11. C₄×Dic₅	C₁₁	direct (N × H)
12. C₅×C₁₁	C₄²	semidirect
15. C₄×C₁₁	Dic₅	direct (N × H)
21. C₄×C₅	C₄×C₁₁	semidirect
22. Dic₅	C₄×C₁₁	direct (N × H)
24. C₁₁	C₄×Dic₅	direct (N × H)
29. C₅	C₄²×C₁₁	semidirect
32. C₄	C₁₁×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₁	2
C₂×C₁₁×Dic₅	2
C₄²×C₁₁	5
C₄×Dic₅	11

Subgroups — C4×C11×Dic5 #11724913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×Dic₅ #11724913