Subgroups — C₁₃⋊C₃×D₄₂₉ #45689602

Order 33462.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₂₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃⋊C₃×D₁₄₃	—	3	1	no	maximal
4	C₁₁×C₁₃×C₁₃⋊C₃	—	2	1	no	—
5	C₁₁×C₁₃×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₁×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₄₃	—	3	1	no	Hall
8	C₁₃⋊C₃×D₃₉	—	11	1	no	maximal, Hall
9	C₃×D₄₂₉	—	13	1	no	maximal
10	C₁₃⋊C₃×D₃₃	—	13	1	no	maximal
11	C₁₁×C₁₃²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₁₁×C₁₃	—	13	1	no	—
14	C₃×C₁₁×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
15	C₁₃×D₃₉	—	11	1	no	—
16	D₁₃×C₁₃⋊C₃	—	33	1	no	—
17	D₄₂₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
18	C₁₃×D₃₃	—	13	1	no	—
19	C₃×D₁₄₃	—	39	1	no	—
20	D₁₁×C₁₃⋊C₃	—	39	1	no	—
21	C₃×C₁₃²	C₃×D₁₁	1	1	yes	characteristic, complemented
22	C₁₃×C₁₃⋊C₃	—	2	1	no	—
23	C₁₃×C₁₃⋊C₃	D₃₃	1	1	yes	characteristic, complemented
24	C₃×C₁₁×C₁₃	—	6	2	no	—
25	C₃×C₁₁×C₁₃	—	13	1	no	—
26	C₃×C₁₁×C₁₃	—	26	1	no	—
27	C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₃×C₁₁×C₁₃	C₃×D₁₃	1	1	yes	characteristic, complemented
29	C₁₁×C₁₃⋊C₃	—	2	1	no	—
30	C₁₁×C₁₃⋊C₃	D₃₉	1	1	yes	characteristic, complemented
31	C₁₃×D₁₃	—	33	1	no	Hall
32	D₁₄₃	—	3	1	no	—
33	C₁₃×D₁₁	—	39	1	no	—
34	C₃×D₃₉	—	143	1	no	—
35	D₃×C₁₃⋊C₃	—	143	1	no	—
36	C₃×D₃₃	—	169	1	no	Hall
37	C₁₃²	C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
38	C₁₁×C₁₃	—	6	2	no	—
39	C₁₁×C₁₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
40	C₁₁×C₁₃	C₃×D₃₉	1	1	yes	characteristic, complemented
41	C₃²×C₁₃	—	13	1	no	—
42	C₃×C₁₃⋊C₃	D₁₄₃	1	1	yes	characteristic, complemented
43	C₃²×C₁₁	—	13	1	no	Hall
44	D₃₉	—	11	1	no	—
45	C₃×D₁₃	—	429	1	no	—
46	D₃×C₁₃	—	143	1	no	—
47	C₂×C₁₃⋊C₃	—	429	1	no	—
48	D₃₃	—	13	1	no	—
49	C₃×D₁₁	—	507	1	no	—
50	C₃×C₁₃	—	6	2	no	—
51	C₃×C₁₃	—	13	1	no	—
52	C₃×C₁₃	—	26	1	no	—
53	C₃×C₁₃	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₃×C₁₃	C₃×D₁₄₃	1	1	yes	characteristic, complemented
55	C₁₃⋊C₃	—	2	1	no	—
56	C₁₃⋊C₃	D₄₂₉	1	1	yes	characteristic, direct product factor
57	C₃×C₁₁	—	13	1	no	—
58	C₃×C₁₁	—	26	1	no	—
59	C₃×C₁₁	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
60	C₂×C₁₃	—	429	1	no	—
61	D₁₃	—	33	1	no	—
62	D₁₁	—	39	1	no	Hall
63	C₃×D₃	—	1859	1	no	Hall
64	C₁₃	—	6	2	no	—
65	C₁₃	C₁₃⋊C₃×D₃₃	1	1	yes	characteristic, complemented
66	C₁₃	C₃×D₄₂₉	1	1	yes	characteristic, complemented
67	C₁₁	C₁₃⋊C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
68	C₃²	—	13	1	no	Sylow
69	C₂×C₃	—	5577	1	no	—
70	D₃	—	143	1	no	—
71	C₃	—	13	1	no	—
72	C₃	—	26	1	no	—
73	C₃	C₁₃⋊C₃×D₁₄₃	1	1	yes	characteristic, complemented
74	C₂	—	429	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₃²	C₂×C₃
LCS	G ▷ C₃×C₁₁×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×D₄₂₉	C₃	semidirect
5. C₁₁×C₁₃×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₁₁×C₁₃²	C₂×C₃	semidirect
11. C₁₁×C₁₃²	C₃×D₃	semidirect
12. C₃×C₁₃×C₁₃⋊C₃	D₁₁	semidirect
14. C₃×C₁₁×C₁₃⋊C₃	D₁₃	semidirect
17. D₄₂₉	C₁₃⋊C₃	direct (N × H)
21. C₃×C₁₃²	C₃×D₁₁	semidirect
23. C₁₃×C₁₃⋊C₃	D₃₃	semidirect
27. C₃×C₁₁×C₁₃	C₂×C₁₃⋊C₃	semidirect
28. C₃×C₁₁×C₁₃	C₃×D₁₃	semidirect
30. C₁₁×C₁₃⋊C₃	D₃₉	semidirect
37. C₁₃²	C₃×D₃₃	semidirect
39. C₁₁×C₁₃	D₃×C₁₃⋊C₃	semidirect
40. C₁₁×C₁₃	C₃×D₃₉	semidirect
42. C₃×C₁₃⋊C₃	D₁₄₃	semidirect
53. C₃×C₁₃	D₁₁×C₁₃⋊C₃	semidirect
54. C₃×C₁₃	C₃×D₁₄₃	semidirect
56. C₁₃⋊C₃	D₄₂₉	direct (N × H)
59. C₃×C₁₁	D₁₃×C₁₃⋊C₃	semidirect
65. C₁₃	C₁₃⋊C₃×D₃₃	semidirect
66. C₁₃	C₃×D₄₂₉	semidirect
67. C₁₁	C₁₃⋊C₃×D₃₉	semidirect
73. C₃	C₁₃⋊C₃×D₁₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₁₃×C₁₃⋊C₃	2
C₁₃×D₄₂₉	3
C₁₃⋊C₃×D₁₄₃	3
C₁₃⋊C₃×D₃₉	11
C₃×D₄₂₉	13
C₁₃⋊C₃×D₃₃	13

Subgroups — C13⋊C3×D429 #45689602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×D₄₂₉ #45689602