Subgroups — C₂×C₁₁×D₄₄₅ #34086625

Order 19580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₄₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₈₉	—	5	1	no	maximal, Hall
5	C₂×C₁₁×C₈₉	D₅	1	1	yes	characteristic, complemented
6	C₁₁×D₈₉	—	5	2	no	—
7	C₂×D₄₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₈₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₈₉	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₄₄₅	C₂×C₁₁	1	2	yes	direct product factor
11	C₅×C₈₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×D₈₉	—	5	1	no	Hall
13	C₂×D₅×C₁₁	—	89	1	no	maximal, Hall
14	C₂×C₈₉	D₅×C₁₁	1	1	yes	characteristic, complemented
15	D₈₉	—	5	2	no	—
16	C₂×C₅×C₁₁	D₈₉	1	1	yes	characteristic, complemented
17	D₅×C₁₁	—	89	2	no	—
18	C₈₉	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₁₁	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₁	—	445	1	no	Hall
21	C₂×C₁₁	—	445	2	no	—
22	C₂×C₁₁	D₄₄₅	1	1	yes	characteristic, direct product factor
23	C₂×D₅	—	89	1	no	Hall
24	C₁₁	C₂×D₄₄₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₁₁×D₈₉	1	1	yes	characteristic, complemented
26	D₅	—	89	2	no	—
27	C₅	C₂×C₁₁×D₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	445	1	no	Sylow
29	C₂	—	445	2	no	—
30	C₂	C₁₁×D₄₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₄₅
commutator, cosocle, hypocenter	C₅×C₈₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₈₉	C₂
LCS	G ▷ C₅×C₈₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₄₄₅	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₈₉	C₂	semidirect
3. C₅×C₁₁×C₈₉	C₂²	semidirect
5. C₂×C₁₁×C₈₉	D₅	semidirect
7. C₂×D₄₄₅	C₁₁	direct (N × H)
8. C₁₁×C₈₉	C₂×D₅	semidirect
9. C₂×C₅×C₈₉	C₂×C₁₁	semidirect
10. D₄₄₅	C₂×C₁₁	direct (N × H)
11. C₅×C₈₉	C₂²×C₁₁	semidirect
14. C₂×C₈₉	D₅×C₁₁	semidirect
16. C₂×C₅×C₁₁	D₈₉	semidirect
18. C₈₉	C₂×D₅×C₁₁	semidirect
19. C₅×C₁₁	C₂×D₈₉	semidirect
22. C₂×C₁₁	D₄₄₅	direct (N × H)
24. C₁₁	C₂×D₄₄₅	direct (N × H)
25. C₂×C₅	C₁₁×D₈₉	semidirect
27. C₅	C₂×C₁₁×D₈₉	semidirect
30. C₂	C₁₁×D₄₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₄₄₅	2
C₂×C₅×C₁₁×C₈₉	2
C₂×C₁₁×D₈₉	5
C₂×D₄₄₅	11
C₂×D₅×C₁₁	89

Subgroups — C2×C11×D445 #34086625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₄₄₅ #34086625