Subgroups — C₅×S₅ #10597163

Order 600.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×S₄	—	5	1	no	maximal
3	S₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×AGL(1,𝔽₅)	—	6	1	no	maximal
5	C₂×C₅×D₃	—	10	1	no	maximal
6	C₅×A₄	—	5	1	no	—
7	A₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅×D₅	—	6	1	no	—
9	C₅×D₄	—	15	1	no	—
10	C₂×C₃×C₅	—	10	1	no	—
11	C₅×D₃	—	10	1	no	—
12	C₅×D₃	—	10	1	no	—
13	C₅²	—	6	1	no	Sylow
14	S₄	—	5	1	no	Hall
15	C₂²×C₅	—	5	1	no	—
16	C₂²×C₅	—	15	1	no	—
17	AGL(1,𝔽₅)	—	6	1	no	—
18	C₄×C₅	—	15	1	no	—
19	C₃×C₅	—	10	1	no	—
20	C₂×D₃	—	10	1	no	—
21	A₄	—	5	1	no	—
22	C₂×C₅	—	10	1	no	—
23	C₂×C₅	—	15	1	no	—
24	D₅	—	6	1	no	—
25	D₄	—	15	1	no	Sylow
26	C₂×C₃	—	10	1	no	—
27	D₃	—	10	1	no	—
28	D₃	—	10	1	no	—
29	C₅	—	6	1	no	—
30	C₅	—	24	1	no	—
31	C₅	S₅	1	1	yes	characteristic, direct product factor
32	C₂²	—	5	1	no	—
33	C₂²	—	15	1	no	—
34	C₄	—	15	1	no	—
35	C₃	—	10	1	no	Sylow
36	C₂	—	10	1	no	—
37	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₅	S₅
commutator, cosocle, hypocenter	A₅	C₂×C₅
Frattini	C₁	G
socle	C₅×A₅	C₂
LCS	G ▷ A₅
UCS	C₁ ◁ C₅

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.