Subgroups — (C₃₁₁⋊C₅)⋊Dic₅ #44527352

Order 31100.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₅₅₅	C₅	1	1	yes	maximal, characteristic, complemented
4	Dic₃₁₁⋊C₅	—	5	1	no	maximal
5	C₂×C₅×C₃₁₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₃₁₁⋊C₅	—	2	2	no	—
7	C₂×C₃₁₁⋊C₅	D₅	1	1	yes	characteristic
8	C₅×C₃₁₁	C₄×C₅	1	1	yes	characteristic, complemented
9	C₃₁₁⋊C₅	—	2	2	no	—
10	C₃₁₁⋊C₅	Dic₅	1	1	yes	characteristic, complemented
11	Dic₃₁₁	—	5	1	no	Hall
12	C₂×C₃₁₁	C₅×D₅	1	1	yes	characteristic
13	C₃₁₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
14	C₅×Dic₅	—	311	1	no	maximal, Hall
15	C₂×C₅²	—	311	1	no	—
16	C₅²	—	311	1	no	Sylow
17	C₄×C₅	—	1555	1	no	—
18	Dic₅	—	311	1	no	—
19	C₂×C₅	—	311	1	no	—
20	C₂×C₅	—	622	2	no	—
21	C₂×C₅	D₃₁₁⋊C₅	1	1	yes	characteristic
22	C₅	—	311	1	no	—
23	C₅	—	622	2	no	—
24	C₅	Dic₃₁₁⋊C₅	1	1	yes	characteristic, complemented
25	C₄	—	1555	1	no	Sylow
26	C₂	C₅⋊(D₃₁₁⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(D₃₁₁⋊C₅)
commutator, hypocenter	C₅×C₃₁₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₅×C₃₁₁	C₂×C₅
prime radical	C₂×C₅×C₃₁₁⋊C₅	C₂
LCS	G ▷ C₅×C₃₁₁
UCS	C₁ ◁ C₂

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

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