Subgroups — C₅×#681 #87788

Order 400.

56 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	C₅×#168	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	C₅×M₁₆	—	5	1	no	maximal
7	#681	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₅²	—	2	1	no	—
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅	—	2	2	no	—
11	C₂×C₄×C₅	D₅	1	1	yes	characteristic
12	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
13	C₅×C₈	—	5	2	no	—
14	#168	C₂×C₅	1	2	yes	complemented
15	C₅²	M₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	—	2	2	no	—
17	C₂²×C₅	Dic₅	1	1	yes	characteristic
18	C₂²×C₅	C₄×C₅	1	1	yes	characteristic
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	—	2	2	no	—
21	C₄×C₅	Dic₅	1	1	yes	characteristic
22	C₄×C₅	C₄×C₅	1	1	yes	characteristic
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
25	M₁₆	—	5	1	no	Sylow
26	C₂×C₅	—	2	4	no	—
27	C₂×C₅	—	2	1	no	—
28	C₂×C₅	—	2	1	no	—
29	C₂×C₅	—	2	2	no	—
30	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
31	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
32	C₂×C₄	C₅×D₅	1	1	yes	characteristic
33	C₈	—	5	2	no	—
34	C₅	—	2	2	no	—
35	C₅	#681	1	1	yes	characteristic, direct product factor
36	C₅	C₅×M₁₆	1	1	yes	characteristic, complemented
37	C₂²	C₅×Dic₅	1	1	yes	characteristic
38	C₄	C₅×Dic₅	1	1	yes	characteristic
39	C₄	C₂×C₅×D₅	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	C₂×C₅×Dic₅	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.