Subgroups — C₂²⋊(C₁₉⋊#92789) #50310522

Order 38532.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊#92789	—	4	1	no	maximal, Hall
3	C₂×C₁₃²×C₁₉	—	3	1	no	—
4	C₁₃²×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²⋊#10625203	—	13	1	no	maximal
6	C₂²⋊#10625202	—	13	1	no	maximal
7	C₂²⋊#92789	—	19	1	no	maximal, Hall
8	C₂²×C₁₃×C₁₉	—	3	4	no	—
9	C₂²×C₁₃×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
10	C₂²×C₁₃×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	#10625203	—	52	1	no	—
12	#10625202	—	52	1	no	—
13	C₂²×C₁₃²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	#92789	—	76	1	no	Hall
15	C₂×C₁₃×C₁₉	—	3	12	no	—
16	C₂×C₁₃×C₁₉	—	3	1	no	—
17	C₂×C₁₃×C₁₉	—	3	1	no	—
18	C₂×C₁₃²	—	3	1	no	—
19	C₁₃×C₁₉	—	3	4	no	—
20	C₁₃×C₁₉	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
21	C₁₃×C₁₉	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
22	C₂²⋊(C₁₉⋊C₃)	—	169	1	no	Hall
23	C₁₃²	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
24	C₂²⋊(C₁₃⋊C₃)	—	247	1	no	—
25	C₂²⋊(C₁₃⋊C₃)	—	247	1	no	—
26	C₂²×C₁₉	#92789	1	1	yes	characteristic, complemented, Hall
27	C₁₉⋊C₃	—	676	1	no	Hall
28	C₂²×C₁₃	—	3	4	no	—
29	C₂²×C₁₃	#10625202	1	1	yes	characteristic, complemented
30	C₂²×C₁₃	#10625203	1	1	yes	characteristic, complemented
31	C₁₃⋊C₃	—	988	1	no	—
32	C₁₃⋊C₃	—	988	1	no	—
33	C₂×C₁₉	—	3	1	no	—
34	C₂×C₁₃	—	3	12	no	—
35	C₂×C₁₃	—	3	1	no	—
36	C₂×C₁₃	—	3	1	no	—
37	C₁₉	C₂²⋊#92789	1	1	yes	characteristic, complemented, Sylow
38	C₁₃	—	3	4	no	—
39	C₁₃	C₂²⋊#10625202	1	1	yes	characteristic, complemented
40	C₁₃	C₂²⋊#10625203	1	1	yes	characteristic, complemented
41	A₄	—	3211	1	no	Hall
42	C₂²	C₁₉⋊#92789	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	12844	1	no	Sylow
44	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₃²×C₁₉	C₃
LCS	G ▷ C₂²×C₁₃²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃²×C₁₉	C₃	semidirect
4. C₁₃²×C₁₉	A₄	semidirect
9. C₂²×C₁₃×C₁₉	C₁₃⋊C₃	semidirect
10. C₂²×C₁₃×C₁₉	C₁₃⋊C₃	semidirect
13. C₂²×C₁₃²	C₁₉⋊C₃	semidirect
20. C₁₃×C₁₉	C₂²⋊(C₁₃⋊C₃)	semidirect
21. C₁₃×C₁₉	C₂²⋊(C₁₃⋊C₃)	semidirect
23. C₁₃²	C₂²⋊(C₁₉⋊C₃)	semidirect
26. C₂²×C₁₉	#92789	semidirect
29. C₂²×C₁₃	#10625202	semidirect
30. C₂²×C₁₃	#10625203	semidirect
37. C₁₉	C₂²⋊#92789	semidirect
39. C₁₃	C₂²⋊#10625202	semidirect
40. C₁₃	C₂²⋊#10625203	semidirect
42. C₂²	C₁₉⋊#92789	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃²×C₁₉	3
C₁₉⋊#92789	4
C₂²⋊#10625203	13
C₂²⋊#10625202	13
C₂²⋊#92789	19

Subgroups — C22⋊(C19⋊#92789) #50310522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₁₉⋊#92789) #50310522