Subgroups — #87776

Order 400.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6045	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅²	C₂²	1	1	yes	characteristic
5	#1039	—	2	1	no	—
6	C₅×Dic₅	—	2	1	no	—
7	#689	—	5	1	no	maximal
8	Dic₂₀	—	5	1	no	maximal
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅×Q₈	—	5	1	no	—
11	Dic₁₀	—	5	1	no	—
12	Dic₁₀	—	5	1	no	—
13	Dic₁₀	—	10	2	no	—
14	Dic₁₀	D₅	1	1	yes	characteristic
15	C₅×C₈	—	5	1	no	—
16	#168	D₅	1	1	yes	characteristic
17	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	2	2	no	—
19	C₄×C₅	—	10	1	no	—
20	C₄×C₅	C₂×D₅	1	1	yes	characteristic
21	C₄×C₅	C₂×D₅	1	1	yes	characteristic
22	Dic₅	—	2	1	no	—
23	Dic₅	—	10	4	no	—
24	Dic₅	—	10	1	no	—
25	Dic₅	—	10	1	no	—
26	Q₁₆	—	25	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	D₂₀	1	1	yes	characteristic
29	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
30	Q₈	—	5	1	no	—
31	Q₈	—	25	1	no	—
32	C₈	—	5	1	no	—
33	C₅	—	2	2	no	—
34	C₅	Dic₂₀	1	1	yes	characteristic, complemented
35	C₅	#689	1	1	yes	characteristic, complemented
36	C₄	—	10	1	no	—
37	C₄	—	50	1	no	—
38	C₄	D₅²	1	1	yes	characteristic
39	C₂	#6038	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.