Subgroups — C₁₃×C₁₉×C₇⋊D₇ #37564150

Order 24206.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₁₉	—	7	8	no	maximal
3	C₁₉×C₇⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₃×C₁₉	D₇	1	8	yes	complemented
5	C₁₃×C₇⋊D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₇²×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×C₁₉	—	49	1	no	Hall
9	D₇×C₁₉	—	7	8	no	—
10	C₁₃×C₁₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃×D₇	—	7	8	no	—
12	C₇×C₁₉	C₁₃×D₇	1	8	yes	complemented
13	C₇⋊D₇	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₃	D₇×C₁₉	1	8	yes	complemented
15	C₇²	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	49	1	no	Hall
17	C₂×C₁₃	—	49	1	no	Hall
18	C₁₉	C₁₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
19	D₇	—	7	8	no	—
20	C₁₃	C₁₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₁₃×D₇×C₁₉	1	8	yes	complemented
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃×C₁₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₃×C₁₉

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.