Subgroups — #87828

Order 400.

43 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	#6032	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	C₄	1	1	yes	characteristic
5	#1039	C₄	1	1	yes	characteristic
6	C₅×Dic₅	C₂²	1	1	yes	characteristic
7	#704	—	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×Dic₅	—	5	1	no	—
12	C₄×D₅	—	5	1	no	—
13	#170	—	5	1	no	—
14	#170	D₅	1	1	yes	characteristic, complemented
15	C₅×C₈	—	5	1	no	—
16	#168	—	5	1	no	—
17	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅	—	5	1	no	—
19	C₂×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₄×C₅	—	5	1	no	—
21	Dic₅	—	5	1	no	—
22	Dic₅	—	5	1	no	—
23	Dic₅	—	20	1	no	—
24	Dic₅	C₂×D₅	1	1	yes	characteristic
25	M₁₆	—	25	1	no	Sylow
26	C₂×C₅	—	4	1	no	—
27	C₂×C₅	—	10	1	no	—
28	C₂×C₅	C₄×D₅	1	1	yes	characteristic
29	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
30	D₅	—	2	1	no	—
31	C₂×C₄	—	25	1	no	—
32	C₈	—	5	1	no	—
33	C₈	—	25	1	no	—
34	C₅	—	4	1	no	—
35	C₅	#676	1	1	yes	characteristic, complemented
36	C₅	#704	1	1	yes	characteristic, complemented
37	C₂²	—	5	1	no	—
38	C₄	—	5	1	no	—
39	C₄	—	25	1	no	—
40	C₂	—	10	1	no	—
41	C₂	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×AGL(1,𝔽₅)
commutator, Fitting, socle	C₂×C₅²	C₂×C₄
prime radical	C₂×C₅×D₅	C₄
cosocle	C₅×Dic₅	C₂²
hypocenter	C₅²	M₁₆
LCS	G ▷ C₂×C₅² ▷ 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.