Subgroups — #11923913

Order 1160.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₂₉	C₂²	1	1	yes	characteristic
5	D₁₄₅	—	2	1	no	—
6	D₅×C₂₉	—	2	1	no	—
7	C₂²⋊D₂₉	—	5	1	no	maximal, Hall
8	C₅×C₂₉	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₂₉	—	5	1	no	—
10	C₂×D₂₉	—	5	1	no	—
11	Dic₂₉	D₅	1	1	yes	characteristic, complemented
12	C₂×C₂₉	—	10	1	no	—
13	C₂×C₂₉	C₂×D₅	1	1	yes	characteristic
14	D₂₉	—	10	1	no	—
15	D₂₀	—	29	1	no	maximal, Hall
16	C₂₉	D₂₀	1	1	yes	characteristic, complemented, Sylow
17	C₂×D₅	—	29	1	no	—
18	C₂×D₅	D₂₉	1	1	yes	characteristic, complemented
19	C₄×C₅	—	29	1	no	—
20	C₂×C₅	C₂×D₂₉	1	1	yes	characteristic
21	D₅	—	2	1	no	—
22	D₅	—	58	1	no	—
23	D₄	—	145	1	no	Sylow
24	C₅	C₂²⋊D₂₉	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	5	1	no	—
26	C₂²	—	145	1	no	—
27	C₄	—	29	1	no	—
28	C₂	—	10	1	no	—
29	C₂	—	290	1	no	—
30	C₂	D₅×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₂₉
commutator, Fitting, socle, cosocle	C₂×C₅×C₂₉	C₂²
hypocenter	C₅×C₂₉	D₄
LCS	G ▷ C₂×C₅×C₂₉ ▷ C₅×C₂₉
UCS	C₁ ◁ C₂

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.