Subgroups — #14522751

Order 2000.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758758	C₂	1	2	yes	maximal
2	C₅×#6034	C₂	1	1	yes	maximal, characteristic
3	C₅×#1039	—	2	2	no	—
4	C₅×#1039	C₂²	1	1	yes	characteristic
5	#87839	—	5	1	no	maximal
6	C₂×C₅³	D₄	1	1	yes	characteristic
7	#6039	—	5	2	no	—
8	#6039	—	10	2	no	—
9	#6034	D₅	1	1	yes	characteristic
10	C₅×#170	—	10	1	no	—
11	C₅³	Q₁₆	1	1	yes	characteristic, complemented, Sylow
12	#1039	—	2	2	no	—
13	#1039	C₂×D₅	1	1	yes	characteristic
14	C₅×Dic₅	—	10	1	no	—
15	C₅×Dic₅	—	10	2	no	—
16	C₅×Dic₅	—	10	2	no	—
17	C₅×Dic₅	—	10	2	no	—
18	C₅×Dic₅	—	20	4	no	—
19	Dic₂₀	—	25	1	no	maximal
20	C₂×C₅²	—	2	2	no	—
21	C₂×C₅²	—	2	1	no	—
22	C₂×C₅²	—	4	4	no	—
23	C₂×C₅²	—	8	1	no	—
24	C₂×C₅²	D₂₀	1	1	yes	characteristic
25	Dic₁₀	—	25	2	no	—
26	Dic₁₀	—	50	2	no	—
27	#170	—	10	1	no	—
28	C₅×C₈	—	25	1	no	—
29	C₅²	—	2	2	no	—
30	C₅²	—	2	1	no	—
31	C₅²	—	4	4	no	—
32	C₅²	—	8	1	no	—
33	C₅²	Dic₂₀	1	1	yes	characteristic, complemented
34	C₄×C₅	—	25	1	no	—
35	C₄×C₅	—	50	2	no	—
36	Dic₅	—	10	1	no	—
37	Dic₅	—	10	2	no	—
38	Dic₅	—	10	2	no	—
39	Dic₅	—	10	2	no	—
40	Dic₅	—	20	4	no	—
41	Q₁₆	—	125	1	no	Sylow
42	C₂×C₅	—	2	2	no	—
43	C₂×C₅	—	2	1	no	—
44	C₂×C₅	—	4	4	no	—
45	C₂×C₅	—	8	1	no	—
46	C₂×C₅	D₅²⋊C₂	1	1	yes	characteristic
47	Q₈	—	125	2	no	—
48	C₈	—	25	1	no	—
49	C₅	—	2	2	no	—
50	C₅	—	2	1	no	—
51	C₅	—	4	4	no	—
52	C₅	—	8	1	no	—
53	C₅	#87839	1	1	yes	characteristic, complemented
54	C₄	—	25	1	no	—
55	C₄	—	50	2	no	—
56	C₂	#11758794	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#11758794
commutator, cosocle	C₅×#1039	C₂²
Fitting, socle, prime radical	C₂×C₅³	D₄
hypocenter	C₅³	Q₁₆
LCS	G ▷ C₅×#1039 ▷ 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.