Subgroups — C₅²×C₁₃×D₂₉ #34038136

Order 18850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₃×D₂₉	C₅	1	6	yes	maximal, direct product factor
3	C₅×C₁₃×C₂₉	C₂×C₅	1	6	yes	complemented
4	C₅²×D₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃×D₂₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅²×C₂₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅²×C₁₃	—	29	1	no	maximal, Hall
8	C₁₃×C₂₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
9	C₅²×C₁₃	D₂₉	1	1	yes	characteristic, direct product factor, Hall
10	C₅×D₂₉	C₅×C₁₃	1	6	yes	direct product factor
11	C₅×C₂₉	C₂×C₅×C₁₃	1	6	yes	complemented
12	C₂×C₅×C₁₃	—	29	6	no	—
13	C₅×C₁₃	C₅×D₂₉	1	6	yes	direct product factor
14	D₂₉	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅²	—	29	1	no	Hall
16	C₂₉	C₂×C₅²×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₃	—	29	1	no	Hall
18	C₅²	C₁₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₅²×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₅	—	29	6	no	—
21	C₅	C₅×C₁₃×D₂₉	1	6	yes	direct product factor
22	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₃	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₂₉	C₂
LCS	G ▷ C₂₉
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.