Subgroups — (C₃₁⋊C₂₅)⋊C₂₅ #34084243

Order 19375.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic
2	C₅×C₃₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic
3	C₅×C₃₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic
4	C₅×C₃₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic
5	C₅×C₃₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic
6	C₅×C₂₅×C₃₁	C₅	1	1	yes	maximal, characteristic
7	C₅²×C₃₁	C₅²	1	1	yes	characteristic
8	C₂₅×C₃₁	—	5	1	no	—
9	C₃₁⋊C₂₅	—	5	1	no	—
10	C₃₁⋊C₂₅	—	5	1	no	—
11	C₃₁⋊C₂₅	—	5	1	no	—
12	C₃₁⋊C₂₅	—	5	1	no	—
13	C₃₁⋊C₂₅	C₂₅	1	5	yes	complemented
14	C₂₅⋊C₂₅	—	31	1	no	maximal, Sylow
15	C₅×C₃₁	C₅×C₂₅	1	1	yes	characteristic
16	C₅×C₃₁	5₋¹⁺²	1	1	yes	characteristic
17	C₅×C₃₁	5₋¹⁺²	1	1	yes	characteristic
18	C₅×C₃₁	5₋¹⁺²	1	1	yes	characteristic
19	C₅×C₃₁	5₋¹⁺²	1	1	yes	characteristic
20	C₅×C₃₁	5₋¹⁺²	1	1	yes	characteristic
21	C₅×C₂₅	—	31	1	no	—
22	C₅×C₂₅	—	31	1	no	—
23	C₅×C₂₅	—	31	1	no	—
24	C₅×C₂₅	—	31	1	no	—
25	C₅×C₂₅	—	31	1	no	—
26	C₅×C₂₅	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
27	C₃₁	C₂₅⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
28	C₅²	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
29	C₂₅	—	5	1	no	—
30	C₂₅	—	31	5	no	—
31	C₂₅	—	155	1	no	—
32	C₂₅	—	155	1	no	—
33	C₂₅	—	155	1	no	—
34	C₂₅	—	155	1	no	—
35	C₅	C₂₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
36	C₅	#16838870	1	1	yes	characteristic
37	C₅	#16838871	1	1	yes	characteristic
38	C₅	#16838872	1	1	yes	characteristic
39	C₅	#16838873	1	1	yes	characteristic
40	C₅	#16838874	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₅²	C₅×ΓL(1,𝔽₃₂)
commutator	C₅×C₃₁	C₅×C₂₅
Fitting	C₅×C₂₅×C₃₁	C₅
socle, prime radical, cosocle	C₅²×C₃₁	C₅²
hypercenter	C₅×C₂₅	ΓL(1,𝔽₃₂)
hypocenter	C₃₁	C₂₅⋊C₂₅
LCS	G ▷ C₅×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₅² ◁ C₅×C₂₅

Complements

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

N	H ≅ G/N	type
13. C₃₁⋊C₂₅	C₂₅	semidirect
27. C₃₁	C₂₅⋊C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₁⋊C₂₅	5
C₅×C₂₅×C₃₁	5
C₂₅⋊C₂₅	31

Subgroups — (C31⋊C25)⋊C25 #34084243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃₁⋊C₂₅)⋊C₂₅ #34084243