Subgroups — C₁₂₁×Dic₁₃⋊C₃ #34038320

Order 18876.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₁₂₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₂₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₂₁	C₂×C₃	1	1	yes	characteristic
5	C₁₁×Dic₁₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic
6	C₁₃×C₁₂₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₁₂₁	—	13	1	no	maximal, Hall
8	C₂×C₁₁×C₁₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic
9	C₂×C₃×C₁₂₁	—	13	1	no	—
10	C₁₁×Dic₁₃	C₃×C₁₁	1	1	yes	characteristic
11	C₄×C₁₂₁	—	13	1	no	Hall
12	C₁₁×C₁₃⋊C₃	C₄×C₁₁	1	1	yes	characteristic
13	C₃×C₁₂₁	—	13	1	no	Hall
14	C₂×C₁₁×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
15	C₂×C₁₂₁	D₁₃⋊C₃	1	1	yes	characteristic
16	Dic₁₃⋊C₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₃	C₃×C₄×C₁₁	1	1	yes	characteristic
18	C₃×C₄×C₁₁	—	13	1	no	—
19	C₁₂₁	Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₁₃⋊C₃	C₂×C₁₂₁	1	1	yes	characteristic
21	C₂×C₃×C₁₁	—	13	1	no	—
22	Dic₁₃	C₃×C₁₂₁	1	1	yes	characteristic, complemented, Hall
23	C₄×C₁₁	—	13	1	no	—
24	C₁₃⋊C₃	C₄×C₁₂₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁	—	13	1	no	—
26	C₂×C₁₃	C₂×C₃×C₁₂₁	1	1	yes	characteristic
27	C₂×C₁₁	C₁₁×D₁₃⋊C₃	1	1	yes	characteristic
28	C₁₃	C₃×C₄×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	Hall
30	C₁₁	C₁₁×Dic₁₃⋊C₃	1	1	yes	characteristic
31	C₂×C₃	—	13	1	no	—
32	C₄	—	13	1	no	Sylow
33	C₃	—	13	1	no	Sylow
34	C₂	D₁₃⋊C₃×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₂₁	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄×C₁₂₁
Frattini	C₂×C₁₁	C₁₁×D₁₃⋊C₃
Fitting	C₂×C₁₃×C₁₂₁	C₂×C₃
socle, cosocle	C₂×C₁₁×C₁₃	C₂×C₃×C₁₁
prime radical	C₂×C₁₁×C₁₃⋊C₃	C₂×C₁₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₂₁

Complements

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

N	H ≅ G/N	type
2. Dic₁₃×C₁₂₁	C₃	semidirect
3. C₁₃⋊C₃×C₁₂₁	C₄	semidirect
6. C₁₃×C₁₂₁	C₃×C₄	semidirect
16. Dic₁₃⋊C₃	C₁₂₁	direct (N × H)
19. C₁₂₁	Dic₁₃⋊C₃	direct (N × H)
22. Dic₁₃	C₃×C₁₂₁	semidirect
24. C₁₃⋊C₃	C₄×C₁₂₁	semidirect
28. C₁₃	C₃×C₄×C₁₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃⋊C₃×C₁₂₁	2
Dic₁₃×C₁₂₁	3
C₁₁×Dic₁₃⋊C₃	11
C₃×C₄×C₁₂₁	13

Subgroups — C121×Dic13⋊C3 #34038320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₂₁×Dic₁₃⋊C₃ #34038320