Subgroups — #87769

Order 400.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#168	C₂	1	2	yes	maximal, complemented
3	C₂×C₅⋊D₅	C₄	1	1	yes	characteristic
4	C₄×C₅²	C₂²	1	1	yes	characteristic
5	#1039	C₄	1	1	yes	characteristic
6	#676	—	5	2	no	maximal
7	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
8	C₅⋊D₅	—	2	1	no	—
9	C₄×D₅	—	5	2	no	—
10	C₄×D₅	—	10	2	no	—
11	C₅×C₈	—	5	2	no	—
12	#168	D₅	1	2	yes	complemented
13	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	5	2	no	—
15	C₂×D₅	—	10	2	no	—
16	C₄×C₅	—	2	2	no	—
17	C₄×C₅	C₂×D₅	1	2	yes	—
18	Dic₅	—	5	2	no	—
19	Dic₅	—	10	2	no	—
20	M₁₆	—	25	1	no	Sylow
21	C₂×C₅	—	2	2	no	—
22	C₂×C₅	C₄×D₅	1	2	yes	—
23	D₅	—	10	4	no	—
24	D₅	—	10	2	no	—
25	C₂×C₄	—	25	1	no	—
26	C₈	—	5	2	no	—
27	C₅	—	2	2	no	—
28	C₅	#676	1	2	yes	complemented
29	C₂²	—	25	1	no	—
30	C₄	—	25	1	no	—
31	C₄	D₅²	1	1	yes	characteristic
32	C₂	—	50	1	no	—
33	C₂	#6036	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅²
commutator, socle	C₂×C₅²	C₂×C₄
Fitting, cosocle	C₄×C₅²	C₂²
prime radical	C₂×C₅⋊D₅	C₄
hypocenter	C₅²	M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄

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.