Subgroups — C₅²×C₁₃×C₃₁⋊C₃ #44475239

Order 30225.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×C₃₁⋊C₃	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₃₁⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₃₁	C₃×C₅	1	6	yes	complemented
5	C₁₃×C₃₁⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅²×C₁₃	—	31	1	no	maximal, Hall
7	C₅²×C₃₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₅×C₃₁⋊C₃	C₅×C₁₃	1	6	yes	direct product factor
9	C₁₃×C₃₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
10	C₅²×C₁₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₁₃	—	31	6	no	—
12	C₅×C₃₁	C₃×C₅×C₁₃	1	6	yes	complemented
13	C₃₁⋊C₃	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅²	—	31	1	no	Hall
15	C₅×C₁₃	C₅×C₃₁⋊C₃	1	6	yes	direct product factor
16	C₃×C₁₃	—	31	1	no	Hall
17	C₃₁	C₃×C₅²×C₁₃	1	1	yes	characteristic, complemented, Sylow
18	C₅²	C₁₃×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	—	31	6	no	—
20	C₁₃	C₅²×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₅×C₁₃×C₃₁⋊C₃	1	6	yes	direct product factor
22	C₃	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₃	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₃₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅²×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.