Subgroups — #87781

Order 400.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1039	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₅	C₂	1	2	yes	maximal
3	C₂²×C₅²	C₂²	1	1	yes	characteristic
4	#1039	C₄	1	2	yes	complemented
5	C₅×Dic₅	—	2	2	no	—
6	#683	—	5	2	no	maximal
7	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
8	C₂×C₅²	D₄	1	1	yes	characteristic
9	C₂×C₅²	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅	—	5	2	no	—
11	C₂×Dic₅	—	5	2	no	—
12	C₂×Dic₅	—	10	2	no	—
13	C₂×Dic₅	D₅	1	2	yes	—
14	C₅²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	2	2	no	—
16	C₂²×C₅	C₂×D₅	1	2	yes	—
17	C₄×C₅	—	10	2	no	—
18	Dic₅	—	2	2	no	—
19	Dic₅	—	5	4	no	—
20	Dic₅	—	10	4	no	—
21	C₄⋊C₄	—	25	1	no	Sylow
22	C₂×C₅	—	2	2	no	—
23	C₂×C₅	—	2	2	no	—
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	Dic₁₀	1	2	yes	—
26	C₂×C₅	C₄×D₅	1	2	yes	—
27	C₂×C₅	C₂²⋊D₅	1	2	yes	—
28	C₂×C₄	—	5	2	no	—
29	C₂×C₄	—	25	1	no	—
30	C₅	—	2	2	no	—
31	C₅	#683	1	2	yes	complemented
32	C₂²	D₅²	1	1	yes	characteristic
33	C₄	—	10	2	no	—
34	C₄	—	25	2	no	—
35	C₂	#6036	1	1	yes	characteristic
36	C₂	#6037	1	1	yes	characteristic
37	C₂	#6039	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₅²
commutator	C₂×C₅²	C₂×C₄
Fitting, socle, prime radical, cosocle	C₂²×C₅²	C₂²
hypocenter	C₅²	C₄⋊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.