Subgroups — C₂₉×D₂₅₅ #28414413

Order 14790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₈₅	—	3	1	no	maximal, Hall
3	C₂₉×D₅₁	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₂₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₂₉	D₅	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₁₇	—	15	1	no	Hall
7	C₂₉×D₁₅	—	17	1	no	maximal, Hall
8	D₂₅₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₇×C₂₉	D₁₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₂₉	D₁₇	1	1	yes	characteristic, complemented, Hall
11	D₅×C₂₉	—	51	1	no	Hall
12	C₃×C₅×C₁₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
13	D₃×C₂₉	—	85	1	no	Hall
14	D₈₅	—	3	1	no	Hall
15	C₅×C₂₉	D₅₁	1	1	yes	characteristic, complemented, Hall
16	D₅₁	—	5	1	no	Hall
17	C₃×C₂₉	D₈₅	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₇	D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₂₉	—	255	1	no	Hall
20	C₃×C₁₇	D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
21	D₁₇	—	15	1	no	Hall
22	D₁₅	—	17	1	no	Hall
23	C₂₉	D₂₅₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₁₇	C₂₉×D₁₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	C₂₉×D₁₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	51	1	no	Hall
27	D₃	—	85	1	no	Hall
28	C₅	C₂₉×D₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₂₉×D₈₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	255	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	D₂₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₉	C₂
LCS	G ▷ C₃×C₅×C₁₇
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.