Subgroups — C₁₃×C₂²⋊(C₅²⋊C₃) #16839196

Order 3900.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₅²×C₁₃	—	3	1	no	—
4	C₅²×C₁₃	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²⋊(C₅²⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₅×C₁₃	—	3	2	no	—
7	A₄×C₁₃	—	25	1	no	maximal, Hall
8	C₂×C₅×C₁₃	—	3	6	no	—
9	C₂²×C₅²	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₅²⋊C₃	—	4	1	no	Hall
11	C₅×C₁₃	—	3	2	no	—
12	C₂²×C₁₃	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅²	—	3	1	no	—
14	C₃×C₁₃	—	100	1	no	Hall
15	C₂×C₁₃	—	3	1	no	—
16	C₅²	A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₅	—	3	2	no	—
18	C₁₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
19	A₄	—	25	1	no	Hall
20	C₂×C₅	—	3	6	no	—
21	C₅	—	3	2	no	—
22	C₂²	C₁₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	100	1	no	Sylow
24	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₅²	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₃	C₃
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₁₃

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.