Subgroups — C₂₉×D₃₉₉ #37529012

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₁₃₃	—	3	1	no	maximal, Hall
3	C₇×C₁₉×C₂₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉×D₅₇	—	7	1	no	maximal, Hall
5	C₃×C₁₉×C₂₉	D₇	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₂₁	—	19	1	no	maximal, Hall
7	C₂₉×D₁₉	—	21	1	no	Hall
8	D₃₉₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇×C₂₉	D₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×C₂₉	D₂₁	1	1	yes	characteristic, complemented, Hall
11	D₇×C₂₉	—	57	1	no	Hall
12	C₃×C₇×C₁₉	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
13	D₁₃₃	—	3	1	no	Hall
14	C₇×C₂₉	D₅₇	1	1	yes	characteristic, complemented, Hall
15	D₃×C₂₉	—	133	1	no	Hall
16	C₇×C₁₉	D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
17	D₅₇	—	7	1	no	Hall
18	C₃×C₂₉	D₁₃₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₂₉	—	399	1	no	Hall
20	C₃×C₁₉	D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
21	D₂₁	—	19	1	no	Hall
22	D₁₉	—	21	1	no	Hall
23	C₂₉	D₃₉₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₇	C₂₉×D₁₉	1	1	yes	characteristic, complemented, Hall
25	C₁₉	C₂₉×D₂₁	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	57	1	no	Hall
27	C₇	C₂₉×D₅₇	1	1	yes	characteristic, complemented, Sylow
28	D₃	—	133	1	no	Hall
29	C₃	C₂₉×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	399	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	D₃₉₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₃×C₇×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.