Subgroups — #87768

Order 400.

48 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	#6029	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	C₄	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	C₄	1	1	yes	characteristic
7	#681	—	5	1	no	maximal
8	#676	—	5	1	no	maximal
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₅×D₅	—	2	1	no	—
11	C₂×C₄×C₅	—	5	1	no	—
12	C₄×D₅	D₅	1	1	yes	characteristic
13	C₅×C₈	—	5	1	no	—
14	#168	—	5	1	no	—
15	#168	—	5	1	no	—
16	#168	—	10	2	no	—
17	#168	D₅	1	1	yes	characteristic, complemented
18	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	5	1	no	—
20	C₂×D₅	Dic₅	1	1	yes	characteristic
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	—	5	1	no	—
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂×D₅	1	1	yes	characteristic
25	Dic₅	Dic₅	1	1	yes	characteristic
26	M₁₆	—	25	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	—	10	1	no	—
29	C₂×C₅	C₄×D₅	1	1	yes	characteristic
30	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
31	D₅	—	2	1	no	—
32	C₂×C₄	—	5	1	no	—
33	C₈	—	5	1	no	—
34	C₈	—	25	1	no	—
35	C₅	—	2	2	no	—
36	C₅	#676	1	1	yes	characteristic, complemented
37	C₅	#681	1	1	yes	characteristic, complemented
38	C₂²	—	5	1	no	—
39	C₄	—	5	1	no	—
40	C₄	D₅²	1	1	yes	characteristic
41	C₂	—	10	1	no	—
42	C₂	D₅×Dic₅	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.