Subgroups — C₂²×C₂₉×C₁₁⋊C₂₅ #44541985

Order 31900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×C₁₁⋊C₂₅	C₂	1	3	yes	maximal, direct product factor
2	C₂₉×C₁₁⋊C₂₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅×C₁₁×C₂₉	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₁×C₂₉	C₂×C₅	1	3	yes	—
5	C₂²×C₂₅×C₂₉	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₉	C₂²×C₅	1	1	yes	characteristic
7	C₂×C₂₅×C₂₉	—	11	3	no	—
8	C₂²×C₁₁×C₂₉	C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₁⋊C₂₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂₅×C₂₉	—	11	1	no	Hall
11	C₂×C₁₁×C₂₉	C₂×C₂₅	1	3	yes	complemented
12	C₂²×C₅×C₂₉	C₁₁⋊C₅	1	1	yes	characteristic
13	C₂×C₁₁⋊C₂₅	C₂×C₂₉	1	3	yes	direct product factor
14	C₁₁×C₂₉	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₂₉	C₂×C₁₁⋊C₅	1	3	yes	—
16	C₁₁⋊C₂₅	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₅×C₁₁	C₅×C₂₉	1	1	yes	characteristic
18	C₅×C₂₉	C₂²×C₁₁⋊C₅	1	1	yes	characteristic
19	C₂²×C₂₉	C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	C₂×C₅×C₂₉	1	3	yes	—
21	C₂²×C₂₅	—	11	1	no	Hall
22	C₂×C₂₉	C₂×C₁₁⋊C₂₅	1	3	yes	direct product factor
23	C₅×C₁₁	C₂²×C₅×C₂₉	1	1	yes	characteristic
24	C₂×C₂₅	—	11	3	no	—
25	C₂²×C₁₁	C₂₅×C₂₉	1	1	yes	characteristic, complemented, Hall
26	C₂₉	C₂²×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂₅	—	11	1	no	Sylow
28	C₂×C₁₁	C₂×C₂₅×C₂₉	1	3	yes	complemented
29	C₂²×C₅	C₂₉×C₁₁⋊C₅	1	1	yes	characteristic
30	C₁₁	C₂²×C₂₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	C₂×C₂₉×C₁₁⋊C₅	1	3	yes	—
32	C₅	C₂²×C₂₉×C₁₁⋊C₅	1	1	yes	characteristic
33	C₂²	C₂₉×C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₂₉×C₁₁⋊C₂₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₂₉	C₁₁⋊C₅
commutator, hypocenter	C₁₁	C₂²×C₂₅×C₂₉
Frattini	C₅	C₂²×C₂₉×C₁₁⋊C₅
Fitting, socle, prime radical	C₂²×C₅×C₁₁×C₂₉	C₅
cosocle	C₅×C₁₁	C₂²×C₅×C₂₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×C₁₁⋊C₂₅	C₂	direct (N × H)
2. C₂₉×C₁₁⋊C₂₅	C₂²	direct (N × H)
8. C₂²×C₁₁×C₂₉	C₂₅	semidirect
9. C₂²×C₁₁⋊C₂₅	C₂₉	direct (N × H)
11. C₂×C₁₁×C₂₉	C₂×C₂₅	semidirect
13. C₂×C₁₁⋊C₂₅	C₂×C₂₉	direct (N × H)
14. C₁₁×C₂₉	C₂²×C₂₅	semidirect
16. C₁₁⋊C₂₅	C₂²×C₂₉	direct (N × H)
19. C₂²×C₂₉	C₁₁⋊C₂₅	direct (N × H)
22. C₂×C₂₉	C₂×C₁₁⋊C₂₅	direct (N × H)
25. C₂²×C₁₁	C₂₅×C₂₉	semidirect
26. C₂₉	C₂²×C₁₁⋊C₂₅	direct (N × H)
28. C₂×C₁₁	C₂×C₂₅×C₂₉	semidirect
30. C₁₁	C₂²×C₂₅×C₂₉	semidirect
33. C₂²	C₂₉×C₁₁⋊C₂₅	direct (N × H)
34. C₂	C₂×C₂₉×C₁₁⋊C₂₅	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×C₂₉×C₁₁⋊C₂₅	2
C₂²×C₅×C₁₁×C₂₉	5
C₂²×C₂₅×C₂₉	11
C₂²×C₁₁⋊C₂₅	29

Subgroups — C22×C29×C11⋊C25 #44541985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₉×C₁₁⋊C₂₅ #44541985