Subgroups — #14522665

Order 2000.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#6033	C₂	1	1	yes	maximal, characteristic
2	C₅×#1039	C₄	1	1	yes	characteristic
3	#87822	—	5	1	no	maximal
4	C₂×C₅³	C₈	1	1	yes	characteristic
5	#6033	D₅	1	1	yes	characteristic
6	C₅×#170	—	10	3	no	—
7	C₅³	C₁₆	1	1	yes	characteristic, complemented, Sylow
8	#1039	Dic₅	1	1	yes	characteristic
9	C₅×Dic₅	—	10	3	no	—
10	#672	—	25	1	no	maximal
11	C₂×C₅²	—	2	3	no	—
12	C₂×C₅²	—	8	3	no	—
13	C₂×C₅²	#168	1	1	yes	characteristic
14	#170	—	10	3	no	—
15	C₅×C₈	—	25	1	no	—
16	C₅²	—	2	3	no	—
17	C₅²	—	8	3	no	—
18	C₅²	#672	1	1	yes	characteristic, complemented
19	C₄×C₅	—	25	1	no	—
20	Dic₅	—	10	3	no	—
21	C₁₆	—	125	1	no	Sylow
22	C₂×C₅	—	2	3	no	—
23	C₂×C₅	—	8	3	no	—
24	C₂×C₅	#6053	1	1	yes	characteristic
25	C₈	—	25	1	no	—
26	C₅	—	2	3	no	—
27	C₅	—	8	3	no	—
28	C₅	#87822	1	1	yes	characteristic, complemented
29	C₄	—	25	1	no	—
30	C₂	#11758780	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#11758780
commutator, hypocenter	C₅³	C₁₆
Fitting, socle, prime radical	C₂×C₅³	C₈
cosocle	C₅×#6033	C₂
LCS	G ▷ C₅³
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.