Subgroups — C₅×#689 #87796

Order 400.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₅×#168	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅²	—	2	1	no	—
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	—	2	1	no	—
7	C₅×Q₁₆	—	5	1	no	maximal
8	#689	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅×Q₈	—	2	2	no	—
11	C₅×Q₈	—	5	1	no	—
12	C₅×Q₈	D₅	1	1	yes	characteristic
13	C₅×Q₈	C₂×C₅	1	1	yes	characteristic
14	Dic₁₀	C₂×C₅	1	1	yes	characteristic
15	C₅×C₈	—	5	1	no	—
16	#168	C₂×C₅	1	1	yes	characteristic
17	C₅²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	2	4	no	—
19	C₄×C₅	—	2	1	no	—
20	C₄×C₅	—	2	1	no	—
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	—	10	1	no	—
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
25	Dic₅	—	2	1	no	—
26	Q₁₆	—	5	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
29	C₂×C₅	C₅×D₄	1	1	yes	characteristic
30	Q₈	—	5	1	no	—
31	Q₈	C₅×D₅	1	1	yes	characteristic
32	C₈	—	5	1	no	—
33	C₅	—	2	2	no	—
34	C₅	#689	1	1	yes	characteristic, direct product factor
35	C₅	C₅×Q₁₆	1	1	yes	characteristic, complemented
36	C₄	—	2	1	no	—
37	C₄	—	10	1	no	—
38	C₄	C₂×C₅×D₅	1	1	yes	characteristic
39	C₂	C₅×C₂²⋊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.