Subgroups — C₂₉×C₅⋊(D₁₉⋊C₃) #30658362

Order 16530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×D₁₉⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂₉×C₁₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₁₉	—	5	1	no	Hall
7	C₃×D₅×C₂₉	—	19	1	no	maximal, Hall
8	C₅⋊(D₁₉⋊C₃)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₉×C₂₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₂₉	—	19	1	no	Hall
11	D₅×C₂₉	—	19	1	no	Hall
12	C₅×C₁₉⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
13	D₉₅	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₂₉	—	95	1	no	Hall
15	C₅×C₂₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
16	D₁₉⋊C₃	—	5	1	no	Hall
17	C₅×C₁₉	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
18	C₃×C₂₉	—	19	1	no	Hall
19	C₂×C₂₉	—	95	1	no	Hall
20	C₁₉⋊C₃	D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
21	D₁₉	—	5	1	no	Hall
22	C₃×D₅	—	19	1	no	Hall
23	C₂₉	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
24	C₁₉	C₃×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	19	1	no	Hall
26	D₅	—	19	1	no	Hall
27	C₂×C₃	—	95	1	no	Hall
28	C₅	C₂₉×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	19	1	no	Sylow
30	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₅⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₂₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂₉

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.