Subgroups — #87713

Order 400.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₀	C₂	1	1	yes	maximal, characteristic
2	Dic₅₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₅	—	2	1	no	—
5	C₄×C₂₅	C₂²	1	1	yes	characteristic
6	Dic₂₅	—	2	1	no	—
7	#677	—	5	1	no	maximal
8	C₂×C₂₅	D₄	1	1	yes	characteristic
9	D₂₅	—	4	1	no	—
10	D₂₀	—	5	1	no	—
11	Dic₁₀	—	5	1	no	—
12	C₅×C₈	D₅	1	1	yes	characteristic
13	C₂₅	SD₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	10	1	no	—
15	C₄×C₅	C₂×D₅	1	1	yes	characteristic
16	Dic₅	—	10	1	no	—
17	SD₁₆	—	25	1	no	Sylow
18	C₂×C₅	D₂₀	1	1	yes	characteristic
19	D₅	—	20	1	no	—
20	Q₈	—	25	1	no	—
21	D₄	—	25	1	no	—
22	C₈	D₂₅	1	1	yes	characteristic, complemented
23	C₅	#677	1	1	yes	characteristic
24	C₂²	—	50	1	no	—
25	C₄	—	50	1	no	—
26	C₄	C₂×D₂₅	1	1	yes	characteristic
27	C₂	—	100	1	no	—
28	C₂	D₁₀₀	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.