Subgroups — C₂×(C₅⋊D₅)⋊C₅ #92544

Order 500.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	H(3,𝔽₅)	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₅⋊D₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×D₅	—	5	1	no	maximal
6	C₂×C₅²	—	2	2	no	—
7	C₂×C₅²	D₅	1	1	yes	characteristic, complemented
8	C₂×C₅²	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅⋊D₅	C₂×C₅	1	2	yes	complemented
10	C₅×D₅	—	5	2	no	—
11	C₅²	—	2	2	no	—
12	C₅²	C₂×D₅	1	1	yes	characteristic, complemented
13	C₅²	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂²×C₅	—	25	1	no	—
15	C₂×D₅	—	5	1	no	—
16	C₂×D₅	—	25	1	no	—
17	C₂×C₅	—	5	1	no	—
18	C₂×C₅	—	5	1	no	—
19	C₂×C₅	—	10	2	no	—
20	C₂×C₅	—	25	2	no	—
21	C₂×C₅	C₅×D₅	1	1	yes	characteristic
22	D₅	—	5	2	no	—
23	D₅	—	25	2	no	—
24	C₅	—	5	1	no	—
25	C₅	—	5	1	no	—
26	C₅	—	10	2	no	—
27	C₅	C₂×C₅×D₅	1	1	yes	characteristic
28	C₂²	—	25	1	no	Sylow
29	C₂	—	25	2	no	—
30	C₂	(C₅⋊D₅)⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₅⋊D₅)⋊C₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₅
Frattini	C₅	C₂×C₅×D₅
Fitting	C₂×H(3,𝔽₅)	C₂
socle	C₂×C₅	C₅×D₅
LCS	G ▷ C₅²
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.