Subgroups — #14522215

Order 2000.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758682	C₂	1	2	yes	maximal
2	C₅×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₂₅	C₂²	1	1	yes	characteristic
4	#92524	—	2	2	no	—
5	#87802	—	5	1	no	maximal
6	Dic₁₀₀	—	5	5	no	maximal
7	C₂×C₅×C₂₅	D₄	1	1	yes	characteristic
8	#6045	—	5	2	no	—
9	C₅²×C₈	D₅	1	1	yes	characteristic
10	Dic₅₀	—	5	10	no	—
11	C₈×C₂₅	D₅	1	5	yes	—
12	C₅×C₂₅	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₄×C₅²	C₂×D₅	1	1	yes	characteristic
14	#1039	—	10	2	no	—
15	C₄×C₂₅	C₂×D₅	1	5	yes	—
16	Dic₂₅	—	10	10	no	—
17	Dic₂₀	—	25	1	no	—
18	Dic₂₀	—	25	5	no	—
19	C₂×C₅²	D₂₀	1	1	yes	characteristic
20	C₂×C₂₅	D₂₀	1	5	yes	—
21	Dic₁₀	—	25	10	no	—
22	Dic₁₀	—	25	2	no	—
23	C₅×C₈	D₂₅	1	5	yes	—
24	C₅×C₈	C₅⋊D₅	1	1	yes	characteristic
25	C₅²	Dic₂₀	1	1	yes	characteristic
26	C₂₅	Dic₂₀	1	5	yes	complemented
27	C₄×C₅	C₂×D₂₅	1	5	yes	—
28	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
29	Dic₅	—	50	10	no	—
30	Dic₅	—	50	2	no	—
31	Q₁₆	—	125	1	no	Sylow
32	C₂×C₅	D₁₀₀	1	5	yes	—
33	C₂×C₅	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
34	Q₈	—	125	2	no	—
35	C₈	C₅⋊D₂₅	1	1	yes	characteristic
36	C₅	Dic₁₀₀	1	5	yes	complemented
37	C₅	#87802	1	1	yes	characteristic
38	C₄	—	250	2	no	—
39	C₄	C₂×C₅⋊D₂₅	1	1	yes	characteristic
40	C₂	C₄⋊(C₅⋊D₂₅)	1	1	yes	characteristic

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.