Subgroups — C₂₉⋊#11716322 #37529032

Order 23142.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₉×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉⋊(D₁₉⋊C₃)	—	7	1	no	maximal, Hall
5	C₂₉×C₁₉⋊C₃	—	7	1	no	Hall
6	ΓL(1,𝔽₈)×D₂₉	—	19	1	no	maximal, Hall
7	D₅₅₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	#11716322	—	29	1	no	maximal, Hall
9	ΓL(1,𝔽₈)×C₂₉	—	19	1	no	Hall
10	C₁₉×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₇×D₂₉	—	57	1	no	Hall
12	#87705	D₂₉	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₉	—	29	1	no	Hall
14	C₇×C₂₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₂₉	—	133	1	no	Hall
16	C₇×C₁₉	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
17	D₁₉⋊C₃	—	203	1	no	Hall
18	C₃×C₂₉	—	133	1	no	Hall
19	D₂₉	—	57	1	no	Hall
20	C₁₉⋊C₃	—	7	1	no	Hall
21	C₂×ΓL(1,𝔽₈)	—	551	1	no	Hall
22	D₁₉	—	29	1	no	Hall
23	C₂₉	#11716322	1	1	yes	characteristic, complemented, Sylow
24	ΓL(1,𝔽₈)	—	19	1	no	Hall
25	C₁₉	ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	1653	1	no	Hall
27	C₇	C₂₉⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3857	1	no	Hall
29	C₃	—	133	1	no	Sylow
30	C₂	—	1653	1	no	Sylow

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

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.