Subgroups — C₁₁×D₁₉×D₁₃⋊C₃ #45656708

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×(C₁₃⋊C₃)⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₁₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₁×C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₁×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₉×D₁₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₁×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₁×D₁₉	—	13	1	no	maximal, Hall
12	C₂×C₁₁×D₁₃⋊C₃	—	19	1	no	maximal, Hall
13	(C₁₃⋊C₃)⋊D₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₁₉×D₁₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₁₉×C₁₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₁×C₁₉	—	13	1	no	—
17	C₃×C₁₁×D₁₉	—	13	1	no	—
18	C₃×C₁₁×D₁₉	—	13	1	no	—
19	D₁₃×D₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁×C₁₃⋊C₃	—	19	1	no	—
21	C₁₁×D₁₃⋊C₃	—	19	1	no	—
22	C₁₁×D₁₃⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
23	C₂×C₁₁×D₁₉	—	13	1	no	Hall
24	C₁₉×C₁₃⋊C₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×C₁₉	—	13	1	no	Hall
26	C₂×C₁₁×D₁₃	—	19	1	no	Hall
27	D₂₄₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
28	C₁₃×D₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
29	C₁₉×D₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
30	C₁₁×C₁₃⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₁₁×C₁₉	—	13	1	no	—
32	C₁₁×D₁₉	—	13	1	no	—
33	C₁₁×D₁₉	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
34	C₂×C₁₁×C₁₃	—	19	1	no	—
35	C₁₁×D₁₃	—	19	1	no	—
36	C₁₁×D₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
37	C₁₃×C₁₉	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃×D₁₉	—	13	1	no	Hall
39	C₁₁×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₁₃⋊C₃	—	19	1	no	Hall
41	C₁₁×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃×C₁₁	—	247	1	no	Hall
43	C₂×C₃×C₁₉	—	13	1	no	—
44	C₃×D₁₉	—	13	1	no	—
45	C₃×D₁₉	—	13	1	no	—
46	C₂×C₁₃⋊C₃	—	19	1	no	—
47	D₁₃⋊C₃	—	19	1	no	—
48	D₁₃⋊C₃	C₁₁×D₁₉	1	1	yes	characteristic, direct product factor
49	C₂×D₁₉	—	13	1	no	Hall
50	C₂×C₃×C₁₁	—	13	1	no	—
51	C₂×C₃×C₁₁	—	247	1	no	—
52	C₂×C₃×C₁₁	—	247	1	no	—
53	C₃×C₁₉	—	13	1	no	Hall
54	C₂×D₁₃	—	19	1	no	Hall
55	C₂²×C₁₁	—	247	1	no	Hall
56	C₁₃⋊C₃	C₂×C₁₁×D₁₉	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₉	—	13	1	no	—
58	D₁₉	—	13	1	no	—
59	D₁₉	C₁₁×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
60	C₃×C₁₁	—	13	1	no	Hall
61	C₂×C₁₃	—	19	1	no	—
62	D₁₃	—	19	1	no	—
63	D₁₃	C₃×C₁₁×D₁₉	1	1	yes	characteristic, complemented
64	C₂×C₁₁	—	13	1	no	—
65	C₂×C₁₁	—	19	1	no	—
66	C₂×C₁₁	—	247	1	no	—
67	C₁₉	C₂×C₁₁×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
68	C₁₃	C₂×C₃×C₁₁×D₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	247	1	no	Hall
70	C₁₁	D₁₉×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	247	1	no	—
73	C₂×C₃	—	247	1	no	—
74	C₂²	—	247	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	13	1	no	—
77	C₂	—	19	1	no	—
78	C₂	—	247	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₁₉×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×(C₁₃⋊C₃)⋊D₁₉	C₂	semidirect
2. C₁₁×C₁₉×D₁₃⋊C₃	C₂	semidirect
3. C₁₁×D₁₉×C₁₃⋊C₃	C₂	semidirect
4. C₁₁×D₁₃×D₁₉	C₃	semidirect
5. C₁₁×C₁₉×C₁₃⋊C₃	C₂²	semidirect
6. C₁₁×D₂₄₇	C₂×C₃	semidirect
7. C₁₁×C₁₉×D₁₃	C₂×C₃	semidirect
8. C₁₁×C₁₃×D₁₉	C₂×C₃	semidirect
9. D₁₉×D₁₃⋊C₃	C₁₁	direct (N × H)
10. C₁₁×C₁₃×C₁₉	C₂²×C₃	semidirect
13. (C₁₃⋊C₃)⋊D₁₉	C₂×C₁₁	semidirect
14. C₁₉×D₁₃⋊C₃	C₂×C₁₁	semidirect
15. D₁₉×C₁₃⋊C₃	C₂×C₁₁	semidirect
19. D₁₃×D₁₉	C₃×C₁₁	semidirect
22. C₁₁×D₁₃⋊C₃	D₁₉	direct (N × H)
24. C₁₉×C₁₃⋊C₃	C₂²×C₁₁	semidirect
27. D₂₄₇	C₂×C₃×C₁₁	semidirect
28. C₁₃×D₁₉	C₂×C₃×C₁₁	semidirect
29. C₁₉×D₁₃	C₂×C₃×C₁₁	semidirect
30. C₁₁×C₁₃⋊C₃	C₂×D₁₉	semidirect
33. C₁₁×D₁₉	D₁₃⋊C₃	direct (N × H)
36. C₁₁×D₁₃	C₃×D₁₉	semidirect
37. C₁₃×C₁₉	C₂²×C₃×C₁₁	semidirect
39. C₁₁×C₁₉	C₂×D₁₃⋊C₃	semidirect
41. C₁₁×C₁₃	C₂×C₃×D₁₉	semidirect
48. D₁₃⋊C₃	C₁₁×D₁₉	direct (N × H)
56. C₁₃⋊C₃	C₂×C₁₁×D₁₉	semidirect
59. D₁₉	C₁₁×D₁₃⋊C₃	direct (N × H)
63. D₁₃	C₃×C₁₁×D₁₉	semidirect
67. C₁₉	C₂×C₁₁×D₁₃⋊C₃	semidirect
68. C₁₃	C₂×C₃×C₁₁×D₁₉	semidirect
70. C₁₁	D₁₉×D₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×(C₁₃⋊C₃)⋊D₁₉	2
C₁₁×C₁₉×D₁₃⋊C₃	2
C₁₁×D₁₉×C₁₃⋊C₃	2
C₁₁×D₁₃×D₁₉	3
D₁₉×D₁₃⋊C₃	11
C₂×C₃×C₁₁×D₁₉	13
C₂×C₁₁×D₁₃⋊C₃	19

Subgroups — C11×D19×D13⋊C3 #45656708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₉×D₁₃⋊C₃ #45656708