Subgroups — #1181×C₁₁⋊C₂₅ #44541981

Order 31900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₁₁⋊C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₁×#1181	C₅	1	1	yes	maximal, characteristic
4	C₅×C₁₁×D₂₉	C₂×C₅	1	1	yes	characteristic
5	C₂₅×#1181	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₉	C₄×C₅	1	1	yes	characteristic
7	C₂₅×D₂₉	—	11	1	no	—
8	C₁₁×#1181	C₂₅	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₁⋊C₂₅	—	29	1	no	maximal, Hall
10	C₂₅×C₂₉	—	11	1	no	Hall
11	C₁₁×D₂₉	C₂×C₂₅	1	1	yes	characteristic
12	C₅×#1181	C₁₁⋊C₅	1	1	yes	characteristic
13	C₂×C₁₁⋊C₂₅	—	29	1	no	—
14	C₁₁×C₂₉	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
15	C₅×D₂₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic
16	C₁₁⋊C₂₅	#1181	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₅×C₁₁	—	29	1	no	—
18	C₅×C₂₉	C₄×C₁₁⋊C₅	1	1	yes	characteristic
19	#1181	C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	—	29	1	no	—
21	C₄×C₂₅	—	319	1	no	Hall
22	D₂₉	C₂×C₁₁⋊C₂₅	1	1	yes	characteristic
23	C₅×C₁₁	C₅×#1181	1	1	yes	characteristic
24	C₂×C₂₅	—	319	1	no	—
25	C₄×C₁₁	—	29	1	no	Hall
26	C₂₉	C₄×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
27	C₂₅	—	11	1	no	Sylow
28	C₂×C₁₁	—	29	1	no	—
29	C₄×C₅	—	29	1	no	—
30	C₁₁	C₂₅×#1181	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	29	1	no	—
32	C₅	C₁₁⋊C₅×#1181	1	1	yes	characteristic
33	C₄	—	29	1	no	Sylow
34	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₁₁⋊C₅×#1181
commutator, hypocenter	C₁₁×C₂₉	C₄×C₂₅
Fitting, socle	C₅×C₁₁×C₂₉	C₄×C₅
prime radical, cosocle	C₅×C₁₁×D₂₉	C₂×C₅
LCS	G ▷ C₁₁×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₁₁⋊C₂₅	C₄	semidirect
8. C₁₁×#1181	C₂₅	semidirect
14. C₁₁×C₂₉	C₄×C₂₅	semidirect
16. C₁₁⋊C₂₅	#1181	direct (N × H)
19. #1181	C₁₁⋊C₂₅	direct (N × H)
26. C₂₉	C₄×C₁₁⋊C₂₅	semidirect
30. C₁₁	C₂₅×#1181	semidirect

Maximal subgroups

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

subgroup	index
D₂₉×C₁₁⋊C₂₅	2
C₅×C₁₁×#1181	5
C₂₅×#1181	11
C₄×C₁₁⋊C₂₅	29

Subgroups — #1181×C11⋊C25 #44541981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1181×C₁₁⋊C₂₅ #44541981