Subgroups — C₂×(C₁₃₉⋊C₃)⋊D₁₉ #44540102

Order 31692.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃₉⋊C₃)⋊D₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₉×C₁₃₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₆₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₁₃₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₆₄₁	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₁₃₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₃₉⋊C₃	—	19	1	no	maximal, Hall
9	C₂×C₁₃₉⋊C₃	D₁₉	1	1	yes	characteristic, complemented
10	D₁₃₉⋊C₃	—	19	2	no	—
11	C₂×D₁₃₉	—	19	1	no	Hall
12	C₁₃₉⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₃₉	C₃×D₁₉	1	1	yes	characteristic, complemented
14	D₁₃₉	—	19	2	no	—
15	C₂×C₃×D₁₉	—	139	1	no	maximal, Hall
16	C₁₃₉	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₉	—	139	1	no	—
18	C₃×D₁₉	—	139	2	no	—
19	C₂×D₁₉	—	139	1	no	Hall
20	C₃×C₁₉	—	139	1	no	Hall
21	C₂×C₁₉	D₁₃₉⋊C₃	1	1	yes	characteristic, complemented
22	D₁₉	—	139	2	no	—
23	C₁₉	C₂×D₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2641	1	no	Hall
25	C₂×C₃	—	2641	2	no	—
26	C₂×C₃	—	139	1	no	—
27	C₂²	—	2641	1	no	Sylow
28	C₃	—	139	1	no	Sylow
29	C₂	—	2641	2	no	—
30	C₂	(C₁₃₉⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₃₉⋊C₃)⋊D₁₉
commutator, cosocle, hypocenter	C₁₉×C₁₃₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₃₉	C₂×C₃
LCS	G ▷ C₁₉×C₁₃₉
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.