Subgroups — #87839

Order 400.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6039	C₂	1	2	yes	maximal
2	#6034	C₂	1	1	yes	maximal, characteristic
3	#1039	C₂²	1	1	yes	characteristic
4	C₅×Dic₅	—	2	2	no	—
5	C₂×C₅²	D₄	1	1	yes	characteristic
6	Dic₁₀	—	10	2	no	—
7	#170	—	10	1	no	—
8	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
9	C₄×C₅	—	10	2	no	—
10	Dic₅	—	2	2	no	—
11	Dic₅	—	10	1	no	—
12	Dic₅	—	10	2	no	—
13	Q₁₆	—	25	1	no	maximal, Sylow
14	C₂×C₅	—	2	2	no	—
15	C₂×C₅	—	2	1	no	—
16	Q₈	—	25	2	no	—
17	C₈	—	25	1	no	—
18	C₅	—	2	2	no	—
19	C₅	—	2	1	no	—
20	C₄	—	10	2	no	—
21	C₄	—	25	1	no	—
22	C₂	D₅²⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²⋊C₂
commutator, cosocle	#1039	C₂²
Fitting, socle, prime radical	C₂×C₅²	D₄
hypocenter	C₅²	Q₁₆
LCS	G ▷ #1039 ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
8. C₅²	Q₁₆	semidirect

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