Subgroups — #11758755

Order 1000.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#92553	C₂	1	1	yes	maximal, characteristic
2	C₅×#1039	C₂	1	1	yes	maximal, characteristic
3	C₅²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅³	C₂²	1	1	yes	characteristic
5	#6045	—	5	1	no	maximal
6	#6039	—	5	6	no	maximal
7	C₅³	Q₈	1	1	yes	characteristic, complemented, Sylow
8	C₄×C₅²	—	5	1	no	—
9	#1039	—	5	1	no	—
10	#1039	—	5	6	no	—
11	#1039	—	10	12	no	—
12	#1039	D₅	1	1	yes	characteristic
13	C₅×Dic₅	—	5	6	no	—
14	C₅×Dic₅	D₅	1	6	yes	—
15	C₂×C₅²	—	2	12	no	—
16	C₂×C₅²	C₂×D₅	1	6	yes	—
17	C₂×C₅²	C₂×D₅	1	1	yes	characteristic
18	Dic₁₀	—	25	6	no	—
19	Dic₁₀	—	25	1	no	—
20	C₅²	—	2	12	no	—
21	C₅²	Dic₁₀	1	6	yes	complemented
22	C₅²	Dic₁₀	1	1	yes	characteristic, complemented
23	C₄×C₅	—	5	6	no	—
24	C₄×C₅	—	25	1	no	—
25	Dic₅	—	5	6	no	—
26	Dic₅	—	25	6	no	—
27	Dic₅	—	25	1	no	—
28	Dic₅	—	50	12	no	—
29	Dic₅	C₅⋊D₅	1	1	yes	characteristic
30	C₂×C₅	—	2	12	no	—
31	C₂×C₅	D₅²	1	6	yes	—
32	C₂×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
33	Q₈	—	125	1	no	Sylow
34	C₅	—	2	12	no	—
35	C₅	#6039	1	6	yes	complemented
36	C₅	#6045	1	1	yes	characteristic, complemented
37	C₄	—	5	1	no	—
38	C₄	—	25	1	no	—
39	C₄	—	125	1	no	—
40	C₂	D₅×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×C₅⋊D₅
commutator, Fitting, socle, prime radical, cosocle	C₂×C₅³	C₂²
hypocenter	C₅³	Q₈
LCS	G ▷ C₂×C₅³ ▷ 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.