Subgroups — C₅×D₅×C₂₁₁⋊C₃ #44539561

Order 31650.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₁₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅×C₂₁₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₅×C₂₁₁⋊C₃	—	5	1	no	maximal
5	C₅²×C₂₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂₁₁⋊C₃	—	2	2	no	—
7	C₅×C₂₁₁⋊C₃	D₅	1	1	yes	characteristic, direct product factor
8	C₅×C₂₁₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₅×C₂₁₁	—	5	1	no	—
10	D₅×C₂₁₁	C₃×C₅	1	1	yes	characteristic, complemented
11	C₂×C₂₁₁⋊C₃	—	5	1	no	Hall
12	C₅×C₂₁₁	—	2	2	no	—
13	C₅×C₂₁₁	C₃×D₅	1	1	yes	characteristic, complemented
14	C₅×C₂₁₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₂₁₁⋊C₃	C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₂₁₁	—	5	1	no	Hall
17	C₂₁₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₅	—	211	1	no	maximal, Hall
19	C₃×C₅²	—	211	1	no	Hall
20	C₅×D₅	C₂₁₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₅	—	1055	1	no	—
22	C₃×D₅	—	211	1	no	—
23	C₅²	C₂×C₂₁₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₅	—	422	2	no	—
25	C₃×C₅	—	211	1	no	—
26	C₃×C₅	—	211	1	no	—
27	C₂×C₅	—	5	1	no	—
28	D₅	C₅×C₂₁₁⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃	—	1055	1	no	Hall
30	C₅	—	2	2	no	—
31	C₅	C₂×C₅×C₂₁₁⋊C₃	1	1	yes	characteristic, complemented
32	C₅	D₅×C₂₁₁⋊C₃	1	1	yes	characteristic, direct product factor
33	C₃	—	211	1	no	Sylow
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₅×C₂₁₁⋊C₃
commutator, cosocle, hypocenter	C₅×C₂₁₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₂₁₁	C₂×C₃
LCS	G ▷ C₅×C₂₁₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×C₂₁₁⋊C₃	C₂	semidirect
2. C₅×D₅×C₂₁₁	C₃	semidirect
3. D₅×C₂₁₁⋊C₃	C₅	direct (N × H)
5. C₅²×C₂₁₁	C₂×C₃	semidirect
7. C₅×C₂₁₁⋊C₃	D₅	direct (N × H)
8. C₅×C₂₁₁⋊C₃	C₂×C₅	semidirect
10. D₅×C₂₁₁	C₃×C₅	semidirect
13. C₅×C₂₁₁	C₃×D₅	semidirect
14. C₅×C₂₁₁	C₂×C₃×C₅	semidirect
15. C₂₁₁⋊C₃	C₅×D₅	direct (N × H)
17. C₂₁₁	C₃×C₅×D₅	semidirect
20. C₅×D₅	C₂₁₁⋊C₃	direct (N × H)
23. C₅²	C₂×C₂₁₁⋊C₃	semidirect
28. D₅	C₅×C₂₁₁⋊C₃	direct (N × H)
31. C₅	C₂×C₅×C₂₁₁⋊C₃	semidirect
32. C₅	D₅×C₂₁₁⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₂₁₁⋊C₃	2
C₅×D₅×C₂₁₁	3
D₅×C₂₁₁⋊C₃	5
C₂×C₅×C₂₁₁⋊C₃	5
C₃×C₅×D₅	211

Subgroups — C5×D5×C211⋊C3 #44539561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×C₂₁₁⋊C₃ #44539561