Subgroups — #10597117

Order 600.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊#1039	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×#1039	C₂	1	1	yes	maximal, characteristic
4	#6045	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
6	#1204	—	5	6	no	maximal
7	C₄×C₅²	—	3	1	no	—
8	#1039	—	3	1	no	—
9	#1039	D₃	1	1	yes	characteristic
10	C₃×C₅²	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₅	—	5	6	no	—
12	C₃×Dic₅	—	5	6	no	—
13	C₅×Dic₃	D₅	1	6	yes	—
14	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
15	Dic₁₀	—	15	6	no	—
16	C₂×C₃×C₅	C₂×D₅	1	6	yes	—
17	C₅²	Dic₆	1	1	yes	characteristic, complemented, Sylow
18	Dic₆	—	25	1	no	Hall
19	C₄×C₅	—	3	6	no	—
20	Dic₅	—	5	6	no	—
21	Dic₅	—	15	6	no	—
22	C₃×C₅	Dic₁₀	1	6	yes	complemented
23	C₃×C₄	—	25	1	no	—
24	Dic₃	—	25	1	no	—
25	Dic₃	C₅⋊D₅	1	1	yes	characteristic
26	C₂×C₅	D₃×D₅	1	6	yes	—
27	Q₈	—	75	1	no	Sylow
28	C₂×C₃	C₂×C₅⋊D₅	1	1	yes	characteristic
29	C₅	#1204	1	6	yes	complemented
30	C₄	—	3	1	no	—
31	C₄	—	25	1	no	—
32	C₄	—	75	1	no	—
33	C₃	#6045	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₅⋊D₅
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₅²	C₂²
hypocenter	C₃×C₅²	Q₈
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂

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.