Subgroups — C₅²×C₂²⋊(C₁₃⋊C₃) #16839195

Order 3900.

80 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	C₅²×C₁₃⋊C₃	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₁₃⋊C₃)	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₃	—	3	1	no	—
5	C₅²×C₁₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₅²×A₄	—	13	1	no	maximal, Hall
7	C₂²×C₅×C₁₃	C₃×C₅	1	6	yes	complemented
8	C₅×C₁₃⋊C₃	—	4	6	no	—
9	C₂²⋊(C₁₃⋊C₃)	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₃	—	3	6	no	—
11	C₂²×C₅²	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅²	—	52	1	no	Hall
13	C₅×C₁₃	C₅×A₄	1	6	yes	complemented
14	C₅×A₄	—	13	6	no	—
15	C₂²×C₁₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅²	—	3	1	no	—
17	C₁₃⋊C₃	—	4	1	no	Hall
18	C₂×C₁₃	—	3	1	no	—
19	C₅²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²×C₅	C₅×C₁₃⋊C₃	1	6	yes	complemented
21	C₃×C₅	—	52	6	no	—
22	C₁₃	C₅²×A₄	1	1	yes	characteristic, complemented, Sylow
23	A₄	—	13	1	no	Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×C₂²⋊(C₁₃⋊C₃)	1	6	yes	direct product factor
26	C₂²	C₅²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	52	1	no	Sylow
28	C₂	—	3	1	no	—

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

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.