Subgroups — #87779

Order 400.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅²	C₂²	1	1	yes	characteristic
4	C₂×C₅⋊D₅	—	2	2	no	—
5	C₂×C₅⋊D₅	C₄	1	2	yes	complemented
6	C₅×Dic₅	—	2	2	no	—
7	#685	—	5	2	no	maximal
8	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅²	D₄	1	2	yes	—
10	C₅⋊D₅	—	2	2	no	—
11	C₂²×D₅	—	5	2	no	—
12	C₂²×D₅	—	10	2	no	—
13	C₂×C₄×C₅	—	5	2	no	—
14	C₂×Dic₅	D₅	1	2	yes	complemented
15	C₅²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	—	2	2	no	—
17	C₂²×C₅	C₂×D₅	1	2	yes	—
18	C₂×D₅	—	5	4	no	—
19	C₂×D₅	—	10	4	no	—
20	C₂×D₅	—	10	8	no	—
21	C₂×D₅	—	10	2	no	—
22	C₂×D₅	—	10	2	no	—
23	C₄×C₅	—	10	2	no	—
24	Dic₅	—	2	2	no	—
25	C₂²⋊C₄	—	25	1	no	Sylow
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	—	2	4	no	—
28	C₂×C₅	C₄×D₅	1	2	yes	—
29	C₂×C₅	D₂₀	1	2	yes	—
30	C₂×C₅	C₂²⋊D₅	1	2	yes	—
31	D₅	—	10	8	no	—
32	D₅	—	10	4	no	—
33	C₂³	—	25	1	no	—
34	C₂×C₄	—	5	2	no	—
35	C₅	—	2	2	no	—
36	C₅	#685	1	2	yes	complemented
37	C₂²	—	25	2	no	—
38	C₂²	—	50	2	no	—
39	C₂²	D₅²	1	1	yes	characteristic
40	C₄	—	10	2	no	—
41	C₂	—	50	2	no	—
42	C₂	#6036	1	1	yes	characteristic
43	C₂	#6038	1	2	yes	—

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

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.