Subgroups — C₄×C₁₉⋊C₃×C₁₂₁ #42119913

Order 27588.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₁₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊C₃×C₁₂₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₉×C₁₂₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₁×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic
6	C₁₉×C₁₂₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₂₁	—	19	1	no	maximal, Hall
8	C₂×C₁₁×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic
9	C₄×C₁₁×C₁₉	C₃×C₁₁	1	1	yes	characteristic
10	C₂×C₃×C₁₂₁	—	19	1	no	—
11	C₁₁×C₁₉⋊C₃	C₄×C₁₁	1	1	yes	characteristic
12	C₄×C₁₂₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₁×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic
14	C₃×C₁₂₁	—	19	1	no	Hall
15	C₂×C₁₂₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic
16	C₄×C₁₉⋊C₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₉	C₃×C₄×C₁₁	1	1	yes	characteristic
18	C₃×C₄×C₁₁	—	19	1	no	—
19	C₁₂₁	C₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₁₉⋊C₃	C₂×C₁₂₁	1	1	yes	characteristic
21	C₄×C₁₉	C₃×C₁₂₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₁	—	19	1	no	—
23	C₁₉⋊C₃	C₄×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₁₁	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
25	C₂×C₁₉	C₂×C₃×C₁₂₁	1	1	yes	characteristic
26	C₃×C₁₁	—	19	1	no	—
27	C₂×C₁₁	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
28	C₁₉	C₃×C₄×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	19	1	no	Hall
30	C₁₁	C₄×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
31	C₂×C₃	—	19	1	no	—
32	C₄	C₁₉⋊C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	19	1	no	Sylow
34	C₂	C₂×C₁₉⋊C₃×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₂₁	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃×C₄×C₁₂₁
Frattini	C₂×C₁₁	C₂×C₁₁×C₁₉⋊C₃
Fitting	C₄×C₁₉×C₁₂₁	C₃
socle, cosocle	C₂×C₁₁×C₁₉	C₂×C₃×C₁₁
prime radical	C₂×C₁₁×C₁₉⋊C₃	C₂×C₁₁
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₂₁

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×C₁₂₁	C₃	semidirect
3. C₁₉⋊C₃×C₁₂₁	C₄	direct (N × H)
6. C₁₉×C₁₂₁	C₃×C₄	semidirect
12. C₄×C₁₂₁	C₁₉⋊C₃	direct (N × H)
16. C₄×C₁₉⋊C₃	C₁₂₁	direct (N × H)
19. C₁₂₁	C₄×C₁₉⋊C₃	direct (N × H)
21. C₄×C₁₉	C₃×C₁₂₁	semidirect
23. C₁₉⋊C₃	C₄×C₁₂₁	direct (N × H)
28. C₁₉	C₃×C₄×C₁₂₁	semidirect
32. C₄	C₁₉⋊C₃×C₁₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉⋊C₃×C₁₂₁	2
C₄×C₁₉×C₁₂₁	3
C₄×C₁₁×C₁₉⋊C₃	11
C₃×C₄×C₁₂₁	19

Subgroups — C4×C19⋊C3×C121 #42119913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉⋊C₃×C₁₂₁ #42119913