Subgroups — #87804

Order 400.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	#6029	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅²	C₄	1	1	yes	characteristic
4	C₄×C₅²	C₄	1	1	yes	characteristic
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	#681	—	5	6	no	maximal
7	C₂×C₅²	—	2	1	no	—
8	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅	D₅	1	6	yes	—
10	#168	—	5	12	no	—
11	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅	Dic₅	1	6	yes	—
13	C₄×C₅	Dic₅	1	6	yes	—
14	C₄×C₅	C₂×D₅	1	6	yes	—
15	M₁₆	—	25	1	no	Sylow
16	C₂×C₅	—	2	6	no	—
17	C₂×C₅	C₂×Dic₅	1	6	yes	—
18	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic
19	C₈	—	25	2	no	—
20	C₅	#681	1	6	yes	complemented
21	C₂²	#1039	1	1	yes	characteristic
22	C₄	#1039	1	1	yes	characteristic
23	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
24	C₂	—	2	1	no	—
25	C₂	C₂×#1039	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.