Subgroups — C₂×D₅×C₁₁×C₁₀₉ #37561870

Order 23980.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×C₁₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₁×C₁₀₉	—	5	1	no	maximal, Hall
5	C₂×C₁₁×C₁₀₉	—	5	2	no	—
6	C₂×C₁₁×C₁₀₉	D₅	1	1	yes	characteristic, direct product factor
7	C₂×D₅×C₁₀₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₁₀₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₁₀₉	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₅×C₁₀₉	C₂×C₁₁	1	2	yes	direct product factor
11	C₅×C₁₀₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₀₉	—	5	1	no	Hall
13	C₂×D₅×C₁₁	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₉	—	5	2	no	—
15	C₂×C₁₀₉	D₅×C₁₁	1	1	yes	characteristic, direct product factor
16	C₂×C₅×C₁₁	C₂×C₁₀₉	1	1	yes	characteristic, complemented
17	D₅×C₁₁	C₂×C₁₀₉	1	2	yes	direct product factor
18	C₁₀₉	C₂×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₅×C₁₁	C₂²×C₁₀₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₁₁	—	5	1	no	Hall
21	C₂×C₁₁	—	5	2	no	—
22	C₂×C₁₁	D₅×C₁₀₉	1	1	yes	characteristic, direct product factor
23	C₂×D₅	C₁₁×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
24	C₁₁	C₂×D₅×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₂×C₁₁×C₁₀₉	1	1	yes	characteristic, complemented
26	D₅	C₂×C₁₁×C₁₀₉	1	2	yes	direct product factor
27	C₅	C₂²×C₁₁×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	5	1	no	Sylow
29	C₂	—	5	2	no	—
30	C₂	D₅×C₁₁×C₁₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₀₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₁₁×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₀₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₁×C₁₀₉

Complements

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

N	H ≅ G/N	type
1. D₅×C₁₁×C₁₀₉	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₁₀₉	C₂	semidirect
3. C₅×C₁₁×C₁₀₉	C₂²	semidirect
6. C₂×C₁₁×C₁₀₉	D₅	direct (N × H)
7. C₂×D₅×C₁₀₉	C₁₁	direct (N × H)
8. C₁₁×C₁₀₉	C₂×D₅	direct (N × H)
9. C₂×C₅×C₁₀₉	C₂×C₁₁	semidirect
10. D₅×C₁₀₉	C₂×C₁₁	direct (N × H)
11. C₅×C₁₀₉	C₂²×C₁₁	semidirect
13. C₂×D₅×C₁₁	C₁₀₉	direct (N × H)
15. C₂×C₁₀₉	D₅×C₁₁	direct (N × H)
16. C₂×C₅×C₁₁	C₂×C₁₀₉	semidirect
17. D₅×C₁₁	C₂×C₁₀₉	direct (N × H)
18. C₁₀₉	C₂×D₅×C₁₁	direct (N × H)
19. C₅×C₁₁	C₂²×C₁₀₉	semidirect
22. C₂×C₁₁	D₅×C₁₀₉	direct (N × H)
23. C₂×D₅	C₁₁×C₁₀₉	direct (N × H)
24. C₁₁	C₂×D₅×C₁₀₉	direct (N × H)
25. C₂×C₅	C₂×C₁₁×C₁₀₉	semidirect
26. D₅	C₂×C₁₁×C₁₀₉	direct (N × H)
27. C₅	C₂²×C₁₁×C₁₀₉	semidirect
30. C₂	D₅×C₁₁×C₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
D₅×C₁₁×C₁₀₉	2
C₂×C₅×C₁₁×C₁₀₉	2
C₂²×C₁₁×C₁₀₉	5
C₂×D₅×C₁₀₉	11
C₂×D₅×C₁₁	109

Subgroups — C2×D5×C11×C109 #37561870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₁₁×C₁₀₉ #37561870