Subgroups — #14522603

Order 2000.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1039	C₂	1	3	yes	maximal
2	C₂²×C₅³	C₂²	1	1	yes	characteristic
3	C₅×#1039	C₄	1	6	yes	complemented
4	Dic₅²	—	5	3	no	maximal
5	C₂×C₅³	C₂×C₄	1	3	yes	—
6	C₂×#1039	D₅	1	3	yes	—
7	C₂×C₅×Dic₅	—	5	6	no	—
8	C₂×C₅×Dic₅	—	10	6	no	—
9	C₅³	C₄²	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₅²	—	2	6	no	—
11	C₂²×C₅²	—	4	4	no	—
12	C₂²×C₅²	C₂×D₅	1	3	yes	—
13	#1039	Dic₅	1	6	yes	complemented
14	C₅×Dic₅	—	5	12	no	—
15	C₅×Dic₅	—	10	12	no	—
16	C₄×Dic₅	—	25	3	no	—
17	C₂×C₅²	—	2	12	no	—
18	C₂×C₅²	—	2	6	no	—
19	C₂×C₅²	—	4	12	no	—
20	C₂×C₅²	C₄×D₅	1	6	yes	—
21	C₂×C₅²	C₂×Dic₅	1	3	yes	—
22	C₂×C₄×C₅	—	25	3	no	—
23	C₂×Dic₅	—	5	6	no	—
24	C₂×Dic₅	—	10	6	no	—
25	C₅²	—	2	6	no	—
26	C₅²	—	4	4	no	—
27	C₅²	C₄×Dic₅	1	3	yes	complemented
28	C₂²×C₅	—	2	6	no	—
29	C₂²×C₅	—	4	4	no	—
30	C₂²×C₅	D₅²	1	3	yes	—
31	C₄×C₅	—	25	6	no	—
32	Dic₅	—	5	12	no	—
33	Dic₅	—	10	12	no	—
34	C₄²	—	125	1	no	Sylow
35	C₂×C₅	—	2	12	no	—
36	C₂×C₅	—	2	6	no	—
37	C₂×C₅	—	4	12	no	—
38	C₂×C₅	D₅×Dic₅	1	6	yes	—
39	C₂×C₅	#6036	1	3	yes	—
40	C₂×C₄	—	25	3	no	—
41	C₅	—	2	6	no	—
42	C₅	—	4	4	no	—
43	C₅	Dic₅²	1	3	yes	complemented
44	C₂²	#92566	1	1	yes	characteristic
45	C₄	—	25	6	no	—
46	C₂	#11758756	1	3	yes	—

	subgroup	G/H
center, Frattini, hypercenter	C₂²	#92566
commutator, hypocenter	C₅³	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₅³	C₂²
LCS	G ▷ C₅³
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.

subgroup	index
C₂×C₅×#1039	2
Dic₅²	5