Subgroups — C₂×C₁₉⋊C₃×D₁₃₇ #44530331

Order 31236.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₁₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₉⋊C₃×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₁₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉⋊C₃×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₃₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₉×D₁₃₇	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₁₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₃₇	—	19	1	no	maximal, Hall
9	C₂×C₃×C₁₃₇	—	19	1	no	—
10	C₃×D₁₃₇	—	19	2	no	—
11	C₂×D₁₃₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₃₇	—	19	1	no	Hall
13	C₂×C₁₃₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
14	D₁₃₇	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
15	C₂²×C₁₉⋊C₃	—	137	1	no	maximal, Hall
16	C₁₃₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₉⋊C₃	—	137	2	no	—
18	C₂×C₁₉⋊C₃	D₁₃₇	1	1	yes	characteristic, direct product factor
19	C₂²×C₁₉	—	137	1	no	Hall
20	C₁₉⋊C₃	C₂×D₁₃₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₉	—	137	2	no	—
22	C₂×C₁₉	C₃×D₁₃₇	1	1	yes	characteristic, complemented
23	C₁₉	C₂×C₃×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2603	1	no	Hall
25	C₂×C₃	—	19	1	no	—
26	C₂×C₃	—	2603	2	no	—
27	C₂²	—	137	1	no	Sylow
28	C₃	—	19	1	no	Sylow
29	C₂	—	137	2	no	—
30	C₂	C₁₉⋊C₃×D₁₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊C₃×D₁₃₇
commutator, cosocle, hypocenter	C₁₉×C₁₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₃₇	C₂×C₃
LCS	G ▷ C₁₉×C₁₃₇
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉⋊C₃×D₁₃₇	C₂	direct (N × H)
2. C₂×C₁₉⋊C₃×C₁₃₇	C₂	semidirect
3. C₂×C₁₉×D₁₃₇	C₃	semidirect
4. C₁₉⋊C₃×C₁₃₇	C₂²	semidirect
5. C₂×C₁₉×C₁₃₇	C₂×C₃	semidirect
6. C₁₉×D₁₃₇	C₂×C₃	semidirect
7. C₁₉×C₁₃₇	C₂²×C₃	semidirect
11. C₂×D₁₃₇	C₁₉⋊C₃	direct (N × H)
13. C₂×C₁₃₇	C₂×C₁₉⋊C₃	semidirect
14. D₁₃₇	C₂×C₁₉⋊C₃	direct (N × H)
16. C₁₃₇	C₂²×C₁₉⋊C₃	semidirect
18. C₂×C₁₉⋊C₃	D₁₃₇	direct (N × H)
20. C₁₉⋊C₃	C₂×D₁₃₇	direct (N × H)
22. C₂×C₁₉	C₃×D₁₃₇	semidirect
23. C₁₉	C₂×C₃×D₁₃₇	semidirect
30. C₂	C₁₉⋊C₃×D₁₃₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉⋊C₃×D₁₃₇	2
C₂×C₁₉⋊C₃×C₁₃₇	2
C₂×C₁₉×D₁₃₇	3
C₂×C₃×D₁₃₇	19
C₂²×C₁₉⋊C₃	137

Subgroups — C2×C19⋊C3×D137 #44530331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉⋊C₃×D₁₃₇ #44530331