Subgroups — #87806

Order 400.

104 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	C₂×#1039	C₂	1	1	yes	maximal, characteristic
3	C₂×#1039	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₄×C₅²	—	2	1	no	—
6	#1039	—	2	1	no	—
7	#1039	C₄	1	2	yes	complemented
8	#683	—	5	6	no	maximal
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₅²	D₄	1	1	yes	characteristic
11	C₂×C₅²	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₅	D₅	1	6	yes	—
13	C₂×Dic₅	—	5	6	no	—
14	C₂×Dic₅	—	5	6	no	—
15	C₅²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	C₂×D₅	1	6	yes	—
17	C₄×C₅	—	2	6	no	—
18	Dic₅	—	5	12	no	—
19	Dic₅	—	10	6	no	—
20	C₄⋊C₄	—	25	1	no	Sylow
21	C₂×C₅	Dic₁₀	1	6	yes	—
22	C₂×C₅	C₄×D₅	1	6	yes	—
23	C₂×C₅	C₂²⋊D₅	1	6	yes	—
24	C₂×C₄	—	25	1	no	—
25	C₂×C₄	—	25	1	no	—
26	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic
27	C₅	#683	1	6	yes	complemented
28	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
29	C₄	—	2	1	no	—
30	C₄	—	25	2	no	—
31	C₄	—	50	1	no	—
32	C₂	#6045	1	1	yes	characteristic
33	C₂	C₄×C₅⋊D₅	1	1	yes	characteristic
34	C₂	C₂²⋊(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.