Subgroups — D₅⋊#170 #87833

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×Dic₅	C₂	1	1	yes	maximal, characteristic
2	#6034	C₂	1	1	yes	maximal, characteristic, complemented
3	#6033	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	C₄	1	1	yes	characteristic
5	#1039	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	C₄	1	1	yes	characteristic
7	C₂×#170	—	5	1	no	maximal
8	D₅⋊C₈	—	5	1	no	maximal
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₅×D₅	C₈	1	2	yes	complemented
11	C₂×Dic₅	—	5	1	no	—
12	C₄×D₅	—	5	1	no	—
13	#170	—	5	1	no	—
14	#170	—	5	1	no	—
15	#170	—	5	1	no	—
16	#170	—	5	1	no	—
17	#170	—	10	2	no	—
18	C₅²	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	5	1	no	—
20	C₂×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₄×C₅	—	5	1	no	—
22	Dic₅	—	5	1	no	—
23	Dic₅	—	5	1	no	—
24	Dic₅	—	10	2	no	—
25	Dic₅	AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₂×C₈	—	25	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	—	5	2	no	—
29	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
31	D₅	#170	1	2	yes	complemented
32	C₂×C₄	—	25	1	no	—
33	C₈	—	25	1	no	—
34	C₈	—	25	1	no	—
35	C₅	—	2	2	no	—
36	C₅	D₅⋊C₈	1	1	yes	characteristic, complemented
37	C₅	C₂×#170	1	1	yes	characteristic, complemented
38	C₂²	—	5	1	no	—
39	C₄	—	5	1	no	—
40	C₄	—	25	1	no	—
41	C₂	—	5	2	no	—
42	C₂	D₅⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²	C₂×C₈
Fitting, socle	C₂×C₅²	C₂×C₄
prime radical	C₂×C₅×D₅	C₄
cosocle	#1039	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂

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.