Subgroups — C₇²×D₁₃×C₂₉ #49149237

Order 36946.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₃×C₂₉	C₇	1	8	yes	maximal, direct product factor
3	C₂×C₇²×C₂₉	—	13	1	no	maximal, Hall
4	C₇×C₁₃×C₂₉	C₂×C₇	1	8	yes	complemented
5	C₇²×C₂₉	D₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₇²×D₁₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₁₃×C₂₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇²×C₁₃	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₂₉	—	13	8	no	—
10	C₁₃×C₂₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
11	C₇×C₂₉	C₇×D₁₃	1	8	yes	direct product factor
12	C₇×D₁₃	C₇×C₂₉	1	8	yes	direct product factor
13	C₂×C₇²	—	13	1	no	Hall
14	C₇×C₁₃	C₂×C₇×C₂₉	1	8	yes	complemented
15	C₂×C₂₉	—	13	1	no	Hall
16	C₇²	D₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₉	C₇²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₃	C₇²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇	—	13	8	no	—
20	C₁₃	C₂×C₇²×C₂₉	1	1	yes	characteristic, complemented, Sylow
21	C₇	C₇×D₁₃×C₂₉	1	8	yes	direct product factor
22	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₂₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₇²×C₂₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃×C₂₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₇²×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.