Subgroups — C₃×Q₈⋊(C₅²⋊C₃) #14268317

Order 1800.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×Q₈	C₃	1	1	yes	maximal, characteristic, complemented
2	Q₈⋊(C₅²⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₅²⋊C₃	—	4	1	no	maximal
4	C₃×C₄×C₅²	—	3	1	no	—
5	C₃×C₅²⋊C₃	—	4	1	no	Hall
6	C₅²×Q₈	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₅²	A₄	1	1	yes	characteristic
8	C₂×C₅²⋊C₃	—	4	3	no	—
9	C₃×C₅×Q₈	—	3	2	no	—
10	C₄×C₅²	—	3	1	no	—
11	C₃×C₅²	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
12	C₅²⋊C₃	—	4	3	no	—
13	C₃×SL(2,𝔽₃)	—	25	1	no	maximal, Hall
14	C₃×C₄×C₅	—	3	6	no	—
15	C₂×C₅²	C₃×A₄	1	1	yes	characteristic
16	C₅×Q₈	—	3	2	no	—
17	C₂×C₃×C₅	—	3	2	no	—
18	C₅²	C₃×SL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
19	C₃×Q₈	C₅²⋊C₃	1	1	yes	characteristic, complemented
20	SL(2,𝔽₃)	—	25	3	no	—
21	C₄×C₅	—	3	6	no	—
22	C₂×C₃²	—	100	1	no	—
23	C₃×C₅	—	3	2	no	—
24	C₃×C₄	—	3	1	no	—
25	C₂×C₅	—	3	2	no	—
26	C₃²	—	100	1	no	Sylow
27	Q₈	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	100	3	no	—
29	C₂×C₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
30	C₅	—	3	2	no	—
31	C₄	—	3	1	no	—
32	C₃	—	100	3	no	—
33	C₃	Q₈⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
34	C₂	C₃×C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×Q₈	C₃²
Frattini	C₂	C₃×C₂²⋊(C₅²⋊C₃)
Fitting	C₃×C₅²×Q₈	C₃
socle	C₂×C₃×C₅²	A₄
LCS	G ▷ C₅²×Q₈
UCS	C₁ ◁ C₂×C₃

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.