Subgroups — C₂₉×#11716328 #37529044

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	C₂₉×D₁₃₃	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	C₂₉×AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
7	C₂₉×D₁₉	—	7	1	no	Hall
8	#11716328	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	ΓL(1,𝔽₈)×C₂₉	—	19	1	no	Hall
10	C₁₉×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
11	D₇×C₂₉	—	19	1	no	Hall
12	#87705	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
13	D₁₃₃	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
14	C₇×C₂₉	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₂₉	—	133	1	no	Hall
16	C₇×C₁₉	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
17	D₁₉⋊C₃	—	7	1	no	Hall
18	C₃×C₂₉	—	133	1	no	Hall
19	C₂×C₂₉	—	133	1	no	Hall
20	C₁₉⋊C₃	—	7	1	no	Hall
21	AGL(1,𝔽₇)	—	19	1	no	Hall
22	D₁₉	—	7	1	no	Hall
23	C₂₉	#11716328	1	1	yes	characteristic, direct product factor, Sylow
24	ΓL(1,𝔽₈)	—	19	1	no	Hall
25	C₁₉	C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	19	1	no	Hall
27	C₇	C₂₉×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	133	1	no	Hall
29	C₃	—	133	1	no	Sylow
30	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	#11716328
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₂₉	C₂×C₃
LCS	G ▷ 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.