Subgroups — C₇²×C₁₇×D₁₉ #44539608

Order 31654.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₁₉	C₇	1	8	yes	maximal, direct product factor
3	C₇×C₁₇×C₁₉	C₂×C₇	1	8	yes	complemented
4	C₇²×D₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇²×C₁₇	—	19	1	no	maximal, Hall
6	C₇²×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₇²×C₁₇	D₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₁₇×D₁₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₁₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
10	C₇×D₁₉	C₇×C₁₇	1	8	yes	direct product factor
11	C₂×C₇×C₁₇	—	19	8	no	—
12	C₇×C₁₉	C₂×C₇×C₁₇	1	8	yes	complemented
13	C₇×C₁₇	C₇×D₁₉	1	8	yes	direct product factor
14	C₂×C₇²	—	19	1	no	Hall
15	C₇²	C₁₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	D₁₉	C₇²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₇	—	19	1	no	Hall
18	C₁₉	C₂×C₇²×C₁₇	1	1	yes	characteristic, complemented, Sylow
19	C₁₇	C₇²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₇	—	19	8	no	—
21	C₇	C₇×C₁₇×D₁₉	1	8	yes	direct product factor
22	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₁₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₇²×C₁₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇²×C₁₇

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.