Subgroups — C₄₉×C₁₉⋊D₁₉ #47978024

Order 35378.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉²×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₉⋊D₁₉	C₇	1	1	yes	maximal, characteristic
3	C₇×C₁₉²	C₂×C₇	1	1	yes	characteristic
4	D₁₉×C₄₉	—	19	20	no	maximal
5	C₁₉×C₄₉	D₁₉	1	20	yes	complemented
6	C₁₉⋊D₁₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₉²	C₂×C₄₉	1	1	yes	characteristic, complemented, Sylow
8	C₇×D₁₉	—	19	20	no	—
9	C₇×C₁₉	C₇×D₁₉	1	20	yes	—
10	C₂×C₄₉	—	361	1	no	Hall
11	C₄₉	C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₁₉	—	19	20	no	—
13	C₁₉	D₁₉×C₄₉	1	20	yes	complemented
14	C₂×C₇	—	361	1	no	—
15	C₇	C₇×C₁₉⋊D₁₉	1	1	yes	characteristic
16	C₂	—	361	1	no	Sylow

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.