Subgroups — C₁₉×C₂²⋊C₉×C₃₇ #38760921

Order 25308.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₉×C₃₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₉×C₃₇	—	4	1	no	maximal, Hall
3	C₂×C₃×C₁₉×C₃₇	—	3	1	no	—
4	C₂²×C₁₉×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₃₇	A₄	1	1	yes	characteristic
6	C₂×C₁₉×C₃₇	—	3	1	no	—
7	C₂²⋊C₉×C₃₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₉×C₃₇	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₁₉×C₂²⋊C₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₃₇	C₃×C₁₉	1	1	yes	characteristic
11	C₉×C₃₇	—	4	1	no	Hall
12	C₂²×C₃×C₁₉	C₃×C₃₇	1	1	yes	characteristic
13	C₂×C₃×C₃₇	—	3	1	no	—
14	C₉×C₁₉	—	4	1	no	Hall
15	C₂²×C₃₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₉	—	3	1	no	—
17	C₃×C₃₇	A₄×C₁₉	1	1	yes	characteristic
18	C₂²×C₁₉	C₉×C₃₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₇	—	3	1	no	—
20	C₃×C₁₉	A₄×C₃₇	1	1	yes	characteristic
21	C₂×C₁₉	—	3	1	no	—
22	C₃₇	C₁₉×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²⋊C₉	C₁₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
24	C₁₉	C₂²⋊C₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₃×C₁₉×C₃₇	1	1	yes	characteristic
26	C₉	—	4	1	no	Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₉×C₁₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	A₄×C₁₉×C₃₇	1	1	yes	characteristic
30	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₉×C₃₇	A₄
commutator, hypocenter	C₂²	C₉×C₁₉×C₃₇
Frattini	C₃	A₄×C₁₉×C₃₇
Fitting, socle	C₂²×C₃×C₁₉×C₃₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₉×C₃₇

Complements

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

N	H ≅ G/N	type
4. C₂²×C₁₉×C₃₇	C₉	semidirect
7. C₂²⋊C₉×C₃₇	C₁₉	direct (N × H)
8. C₁₉×C₃₇	C₂²⋊C₉	direct (N × H)
9. C₁₉×C₂²⋊C₉	C₃₇	direct (N × H)
15. C₂²×C₃₇	C₉×C₁₉	semidirect
18. C₂²×C₁₉	C₉×C₃₇	semidirect
22. C₃₇	C₁₉×C₂²⋊C₉	direct (N × H)
23. C₂²⋊C₉	C₁₉×C₃₇	direct (N × H)
24. C₁₉	C₂²⋊C₉×C₃₇	direct (N × H)
28. C₂²	C₉×C₁₉×C₃₇	semidirect

Subgroups — C19×C22⋊C9×C37 #38760921

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉×C₂²⋊C₉×C₃₇ #38760921