Subgroups — C₂×D₇×C₁₉⋊C₃ #13097607

Order 1596.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₇×C₁₉	C₂×C₃	1	2	yes	complemented
7	C₂²×C₁₉⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₉⋊C₃	—	7	2	no	—
10	C₂×C₁₉⋊C₃	D₇	1	1	yes	characteristic, direct product factor
11	C₂×C₃×D₇	—	19	1	no	maximal, Hall
12	C₂²×C₁₉	—	7	1	no	Hall
13	C₁₉⋊C₃	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	—	19	1	no	—
15	C₃×D₇	—	19	2	no	—
16	C₂×C₁₉	—	7	2	no	—
17	C₂×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
18	C₂×D₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₇	—	19	1	no	Hall
20	C₁₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
22	D₇	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
23	C₂²×C₃	—	133	1	no	Hall
24	C₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	19	1	no	—
26	C₂×C₃	—	133	2	no	—
27	C₂²	—	7	1	no	Sylow
28	C₃	—	19	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	D₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₇×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂

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.