Subgroups — C₁₃×D₃₃⋊D₁₉ #45656802

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₁₁×D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₂₀₉	D₃	1	1	yes	characteristic, complemented
7	C₁₃×C₁₉×D₁₁	—	3	1	no	—
8	C₁₁×C₁₃×D₁₉	—	3	1	no	—
9	D₃×C₁₃×D₁₉	—	11	1	no	maximal, Hall
10	C₁₁×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃₃⋊D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₁₃×D₁₁	—	19	1	no	maximal, Hall
13	C₁₃×D₅₇	D₁₁	1	1	yes	characteristic, complemented
14	D₃×C₁₃×C₁₉	—	11	1	no	—
15	C₃×C₁₃×D₁₉	—	11	1	no	—
16	C₁₉×D₃₃	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₁₁×D₅₇	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃×D₂₀₉	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₂×C₁₃×D₁₉	—	33	1	no	Hall
20	C₁₃×D₃₃	D₁₉	1	1	yes	characteristic, complemented
21	D₃×C₁₁×C₁₃	—	19	1	no	—
22	C₃×C₁₃×D₁₁	—	19	1	no	—
23	D₁₁×D₁₉	—	3	1	no	Hall
24	C₃×C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃×D₁₁	—	57	1	no	Hall
27	C₂×C₁₃×C₁₉	—	33	1	no	—
28	C₁₃×D₁₉	—	3	1	no	—
29	C₁₃×D₁₉	—	11	1	no	—
30	C₃×C₁₁×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	D₂₀₉	D₃×C₁₃	1	1	yes	characteristic, complemented
32	C₁₁×D₁₉	—	3	1	no	—
33	C₁₉×D₁₁	—	3	1	no	—
34	C₂×C₁₁×C₁₃	—	57	1	no	—
35	C₁₃×D₁₁	—	3	1	no	—
36	C₁₃×D₁₁	—	19	1	no	—
37	C₁₃×C₁₉	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
38	D₃×D₁₉	—	11	1	no	Hall
39	C₁₁×C₁₉	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₁₃	—	209	1	no	Hall
41	C₁₁×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
42	D₃×D₁₁	—	19	1	no	Hall
43	D₅₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented
44	C₃×D₁₉	—	11	1	no	—
45	D₃×C₁₉	—	11	1	no	—
46	C₂×C₃×C₁₃	—	209	1	no	—
47	D₃×C₁₃	—	11	1	no	—
48	D₃×C₁₃	—	19	1	no	—
49	C₂×D₁₉	—	33	1	no	Hall
50	D₃₃	C₁₃×D₁₉	1	1	yes	characteristic, complemented
51	C₃×D₁₁	—	19	1	no	—
52	D₃×C₁₁	—	19	1	no	—
53	C₃×C₁₉	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₁₃	—	627	1	no	Hall
55	C₂×D₁₁	—	57	1	no	Hall
56	C₃×C₁₃	D₁₁×D₁₉	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₉	—	33	1	no	—
58	D₁₉	—	3	1	no	—
59	D₁₉	—	11	1	no	—
60	C₃×C₁₁	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
61	C₂×C₁₃	—	33	1	no	—
62	C₂×C₁₃	—	57	1	no	—
63	C₂×C₁₃	—	209	1	no	—
64	C₂×C₁₁	—	57	1	no	—
65	D₁₁	—	3	1	no	—
66	D₁₁	—	19	1	no	—
67	C₁₉	D₃×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
68	C₁₃	D₃₃⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×D₃	—	209	1	no	Hall
70	C₁₁	D₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	209	1	no	—
72	D₃	—	11	1	no	—
73	D₃	—	19	1	no	—
74	C₂²	—	627	1	no	Sylow
75	C₃	C₁₃×D₁₁×D₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	33	1	no	—
77	C₂	—	57	1	no	—
78	C₂	—	209	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃₃⋊D₁₉
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₁×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×D₃₃	C₂	semidirect
2. C₁₁×C₁₃×D₅₇	C₂	semidirect
3. C₃×C₁₃×D₂₀₉	C₂	semidirect
5. C₃×C₁₁×C₁₃×C₁₉	C₂²	semidirect
6. C₁₃×D₂₀₉	D₃	semidirect
10. C₁₁×C₁₃×C₁₉	C₂×D₃	semidirect
11. D₃₃⋊D₁₉	C₁₃	direct (N × H)
13. C₁₃×D₅₇	D₁₁	semidirect
16. C₁₉×D₃₃	C₂×C₁₃	semidirect
17. C₁₁×D₅₇	C₂×C₁₃	semidirect
18. C₃×D₂₀₉	C₂×C₁₃	semidirect
20. C₁₃×D₃₃	D₁₉	semidirect
24. C₃×C₁₃×C₁₉	C₂×D₁₁	semidirect
25. C₃×C₁₁×C₁₉	C₂²×C₁₃	semidirect
30. C₃×C₁₁×C₁₃	C₂×D₁₉	semidirect
31. D₂₀₉	D₃×C₁₃	semidirect
37. C₁₃×C₁₉	D₃×D₁₁	semidirect
39. C₁₁×C₁₉	C₂×D₃×C₁₃	semidirect
41. C₁₁×C₁₃	D₃×D₁₉	semidirect
43. D₅₇	C₁₃×D₁₁	semidirect
50. D₃₃	C₁₃×D₁₉	semidirect
53. C₃×C₁₉	C₂×C₁₃×D₁₁	semidirect
56. C₃×C₁₃	D₁₁×D₁₉	semidirect
60. C₃×C₁₁	C₂×C₁₃×D₁₉	semidirect
67. C₁₉	D₃×C₁₃×D₁₁	semidirect
68. C₁₃	D₃₃⋊D₁₉	direct (N × H)
70. C₁₁	D₃×C₁₃×D₁₉	semidirect
75. C₃	C₁₃×D₁₁×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×D₃₃	2
C₁₁×C₁₃×D₅₇	2
C₃×C₁₃×D₂₀₉	2
C₁₃×D₁₁×D₁₉	3
D₃×C₁₃×D₁₉	11
D₃₃⋊D₁₉	13
D₃×C₁₃×D₁₁	19

Subgroups — C13×D33⋊D19 #45656802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₃₃⋊D₁₉ #45656802