Subgroups — C₃×C₅²×Q₈ #10597162

Order 600.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅²	C₂	1	3	yes	maximal
2	C₅²×Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
4	C₃×C₅×Q₈	C₅	1	6	yes	maximal, direct product factor
5	C₄×C₅²	C₂×C₃	1	3	yes	—
6	C₃×C₅²	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₄×C₅	C₂×C₅	1	18	yes	—
8	C₂×C₅²	C₂²×C₃	1	1	yes	characteristic
9	C₅×Q₈	C₃×C₅	1	6	yes	direct product factor
10	C₂×C₃×C₅	C₂²×C₅	1	6	yes	—
11	C₅²	C₃×Q₈	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×Q₈	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅	C₂×C₃×C₅	1	18	yes	—
14	C₃×C₅	C₅×Q₈	1	6	yes	direct product factor
15	C₃×C₄	C₂×C₅²	1	3	yes	—
16	C₂×C₅	C₂²×C₃×C₅	1	6	yes	—
17	Q₈	C₃×C₅²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	C₂²×C₅²	1	1	yes	characteristic
19	C₅	C₃×C₅×Q₈	1	6	yes	direct product factor
20	C₄	C₂×C₃×C₅²	1	3	yes	—
21	C₃	C₅²×Q₈	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂²×C₃×C₅²	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃×C₅²	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃×C₅²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅² ◁ G

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.