Subgroups — #87849

Order 400.

43 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	#6032	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₅	C₄	1	1	yes	characteristic
4	C₄×C₅²	C₄	1	1	yes	characteristic
5	C₅×Dic₅	C₂²	1	1	yes	characteristic
6	#700	—	5	1	no	maximal
7	#681	—	5	1	no	maximal
8	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₅×D₅	—	2	1	no	—
10	C₂×C₄×C₅	—	5	1	no	—
11	C₄×D₅	D₅	1	1	yes	characteristic
12	#170	—	5	2	no	—
13	#168	—	5	2	no	—
14	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	5	1	no	—
16	C₂×D₅	Dic₅	1	1	yes	characteristic
17	C₄×C₅	—	4	1	no	—
18	C₄×C₅	—	5	1	no	—
19	C₄×C₅	Dic₅	1	1	yes	characteristic
20	C₄×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
21	Dic₅	C₂×D₅	1	1	yes	characteristic
22	M₁₆	—	25	1	no	Sylow
23	C₂×C₅	—	4	1	no	—
24	C₂×C₅	—	10	1	no	—
25	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
26	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
27	D₅	—	2	1	no	—
28	C₂×C₄	—	5	1	no	—
29	C₈	—	25	2	no	—
30	C₅	—	4	1	no	—
31	C₅	#681	1	1	yes	characteristic, complemented
32	C₅	#700	1	1	yes	characteristic, complemented
33	C₂²	—	5	1	no	—
34	C₄	—	5	1	no	—
35	C₄	#1042	1	1	yes	characteristic
36	C₂	—	10	1	no	—
37	C₂	C₂×#1042	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.