Subgroups — #87799

Order 400.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#6029	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₅	C₄	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	#1039	C₄	1	1	yes	characteristic
7	#676	—	5	6	no	maximal
8	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₅⋊D₅	—	2	1	no	—
10	C₄×D₅	—	5	6	no	—
11	C₅×C₈	D₅	1	6	yes	complemented
12	#168	—	5	6	no	—
13	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	5	6	no	—
15	C₄×C₅	C₂×D₅	1	6	yes	—
16	Dic₅	—	5	6	no	—
17	M₁₆	—	25	1	no	Sylow
18	C₂×C₅	C₄×D₅	1	6	yes	—
19	D₅	—	10	6	no	—
20	C₂×C₄	—	25	1	no	—
21	C₈	—	25	1	no	—
22	C₈	C₅⋊D₅	1	1	yes	characteristic, complemented
23	C₅	#676	1	6	yes	complemented
24	C₂²	—	25	1	no	—
25	C₄	—	25	1	no	—
26	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
27	C₂	—	50	1	no	—
28	C₂	C₄×C₅⋊D₅	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.