Subgroups — C₂×C₃×D₁₃×C₁₂₁ #34038352

Order 18876.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×C₁₂₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₃×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₁×D₁₃	C₁₁	1	1	yes	maximal, characteristic
8	C₁₃×C₁₂₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₃×C₁₂₁	—	13	1	no	maximal, Hall
10	C₂×C₃×C₁₁×C₁₃	C₂×C₁₁	1	1	yes	characteristic
11	C₃×C₁₁×D₁₃	C₂×C₁₁	1	2	yes	—
12	C₂×C₃×C₁₂₁	—	13	2	no	—
13	C₂×C₃×C₁₂₁	D₁₃	1	1	yes	characteristic, direct product factor
14	C₂×C₁₁×D₁₃	C₃×C₁₁	1	1	yes	characteristic
15	C₂²×C₁₂₁	—	13	1	no	Hall
16	C₃×C₁₁×C₁₃	C₂²×C₁₁	1	1	yes	characteristic
17	C₃×C₁₂₁	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₁₁×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
19	C₁₁×D₁₃	C₂×C₃×C₁₁	1	2	yes	—
20	C₂×C₁₂₁	—	13	2	no	—
21	C₂×C₁₂₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃×D₁₃	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
23	C₁₁×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic
24	C₂²×C₃×C₁₁	—	13	1	no	—
25	C₁₂₁	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃×C₁₃	C₂×C₁₂₁	1	1	yes	characteristic, complemented
27	C₃×D₁₃	C₂×C₁₂₁	1	2	yes	direct product factor
28	C₂×C₃×C₁₁	—	13	2	no	—
29	C₂×C₃×C₁₁	C₁₁×D₁₃	1	1	yes	characteristic
30	C₂×D₁₃	C₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₁₁	—	13	1	no	—
32	C₃×C₁₃	C₂²×C₁₂₁	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₁	C₂×C₁₁×D₁₃	1	1	yes	characteristic
34	C₂×C₁₃	C₂×C₃×C₁₂₁	1	1	yes	characteristic, complemented
35	D₁₃	C₂×C₃×C₁₂₁	1	2	yes	direct product factor
36	C₂×C₁₁	—	13	2	no	—
37	C₂×C₁₁	C₃×C₁₁×D₁₃	1	1	yes	characteristic
38	C₁₃	C₂²×C₃×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	1	no	Hall
40	C₁₁	C₂×C₃×C₁₁×D₁₃	1	1	yes	characteristic
41	C₂×C₃	—	13	2	no	—
42	C₂×C₃	D₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×D₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	13	2	no	—
46	C₂	C₃×D₁₃×C₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₂₁	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₁₂₁
Frattini	C₁₁	C₂×C₃×C₁₁×D₁₃
Fitting	C₂×C₃×C₁₃×C₁₂₁	C₂
socle	C₂×C₃×C₁₁×C₁₃	C₂×C₁₁
prime radical	C₂×C₃×C₁₁×D₁₃	C₁₁
cosocle	C₁₁×C₁₃	C₂²×C₃×C₁₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₂₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃×C₁₂₁	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₂₁	C₂	semidirect
3. C₂×D₁₃×C₁₂₁	C₃	direct (N × H)
4. C₃×C₁₃×C₁₂₁	C₂²	semidirect
5. D₁₃×C₁₂₁	C₂×C₃	direct (N × H)
6. C₂×C₁₃×C₁₂₁	C₂×C₃	semidirect
8. C₁₃×C₁₂₁	C₂²×C₃	semidirect
13. C₂×C₃×C₁₂₁	D₁₃	direct (N × H)
17. C₃×C₁₂₁	C₂×D₁₃	direct (N × H)
21. C₂×C₁₂₁	C₃×D₁₃	direct (N × H)
22. C₂×C₃×D₁₃	C₁₂₁	direct (N × H)
25. C₁₂₁	C₂×C₃×D₁₃	direct (N × H)
26. C₂×C₃×C₁₃	C₂×C₁₂₁	semidirect
27. C₃×D₁₃	C₂×C₁₂₁	direct (N × H)
30. C₂×D₁₃	C₃×C₁₂₁	direct (N × H)
32. C₃×C₁₃	C₂²×C₁₂₁	semidirect
34. C₂×C₁₃	C₂×C₃×C₁₂₁	semidirect
35. D₁₃	C₂×C₃×C₁₂₁	direct (N × H)
38. C₁₃	C₂²×C₃×C₁₂₁	semidirect
42. C₂×C₃	D₁₃×C₁₂₁	direct (N × H)
44. C₃	C₂×D₁₃×C₁₂₁	direct (N × H)
46. C₂	C₃×D₁₃×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
C₃×D₁₃×C₁₂₁	2
C₂×C₃×C₁₃×C₁₂₁	2
C₂×D₁₃×C₁₂₁	3
C₂×C₃×C₁₁×D₁₃	11
C₂²×C₃×C₁₂₁	13

Subgroups — C2×C3×D13×C121 #34038352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₃×C₁₂₁ #34038352