Subgroups — C₃×D₁₃×D₁₂₁ #34038342

Order 18876.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₅₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₃×C₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₁₂₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₁₁×D₁₃	—	11	1	no	maximal
10	C₁₃×C₁₂₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₁₂₁	—	13	1	no	maximal, Hall
12	C₃×D₁₄₃	—	11	1	no	—
13	C₃×C₁₃×D₁₁	—	11	1	no	—
14	C₃×C₁₁×D₁₃	D₁₁	1	1	yes	characteristic
15	C₂×C₃×C₁₂₁	—	13	1	no	—
16	C₃×D₁₂₁	—	13	1	no	—
17	C₃×D₁₂₁	D₁₃	1	1	yes	characteristic, direct product factor
18	D₁₁×D₁₃	—	11	1	no	—
19	C₂×D₁₂₁	—	13	1	no	Hall
20	C₃×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic
21	C₃×C₁₂₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
22	D₁₄₃	—	11	1	no	—
23	C₁₁×D₁₃	C₃×D₁₁	1	1	yes	characteristic
24	C₁₃×D₁₁	—	11	1	no	—
25	C₂×C₁₂₁	—	13	1	no	—
26	D₁₂₁	—	13	1	no	—
27	D₁₂₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
28	C₂×C₃×D₁₃	—	121	1	no	Hall
29	C₁₁×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic
30	C₂×C₃×D₁₁	—	143	1	no	—
31	C₁₂₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₁₃	—	121	1	no	—
33	C₃×D₁₃	—	121	1	no	—
34	C₃×D₁₃	D₁₂₁	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₁₁	—	13	1	no	—
36	C₃×D₁₁	—	11	1	no	—
37	C₃×D₁₁	—	143	1	no	—
38	C₂×D₁₃	—	121	1	no	Hall
39	C₂×D₁₁	—	143	1	no	—
40	C₃×C₁₃	C₂×D₁₂₁	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₁	D₁₁×D₁₃	1	1	yes	characteristic
42	C₂×C₁₃	—	121	1	no	—
43	D₁₃	—	121	1	no	—
44	D₁₃	C₃×D₁₂₁	1	1	yes	characteristic, direct product factor
45	C₂×C₁₁	—	13	1	no	—
46	D₁₁	—	11	1	no	—
47	D₁₁	—	143	1	no	—
48	C₁₃	C₂×C₃×D₁₂₁	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	1573	1	no	Hall
50	C₁₁	C₃×D₁₁×D₁₃	1	1	yes	characteristic
51	C₂×C₃	—	13	1	no	—
52	C₂×C₃	—	1573	1	no	—
53	C₂×C₃	—	121	1	no	—
54	C₂²	—	1573	1	no	Sylow
55	C₃	D₁₃×D₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	13	1	no	—
57	C₂	—	1573	1	no	—
58	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₁₂₁
commutator, cosocle, hypocenter	C₁₃×C₁₂₁	C₂²×C₃
Frattini	C₁₁	C₃×D₁₁×D₁₃
Fitting	C₃×C₁₃×C₁₂₁	C₂²
socle	C₃×C₁₁×C₁₃	C₂×D₁₁
LCS	G ▷ C₁₃×C₁₂₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₅₇₃	C₂	semidirect
2. C₃×C₁₃×D₁₂₁	C₂	semidirect
3. C₃×D₁₃×C₁₂₁	C₂	semidirect
4. D₁₃×D₁₂₁	C₃	direct (N × H)
5. C₃×C₁₃×C₁₂₁	C₂²	semidirect
6. D₁₅₇₃	C₂×C₃	semidirect
7. D₁₃×C₁₂₁	C₂×C₃	semidirect
8. C₁₃×D₁₂₁	C₂×C₃	semidirect
10. C₁₃×C₁₂₁	C₂²×C₃	semidirect
17. C₃×D₁₂₁	D₁₃	direct (N × H)
21. C₃×C₁₂₁	C₂×D₁₃	semidirect
27. D₁₂₁	C₃×D₁₃	direct (N × H)
31. C₁₂₁	C₂×C₃×D₁₃	semidirect
34. C₃×D₁₃	D₁₂₁	direct (N × H)
40. C₃×C₁₃	C₂×D₁₂₁	semidirect
44. D₁₃	C₃×D₁₂₁	direct (N × H)
48. C₁₃	C₂×C₃×D₁₂₁	semidirect
55. C₃	D₁₃×D₁₂₁	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×D₁₅₇₃	2
C₃×C₁₃×D₁₂₁	2
C₃×D₁₃×C₁₂₁	2
D₁₃×D₁₂₁	3
C₃×D₁₁×D₁₃	11
C₂×C₃×D₁₂₁	13

Subgroups — C3×D13×D121 #34038342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₁₂₁ #34038342