Subgroups — C₃²×D₁₃×D₁₉ #22580348

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₂₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₁₉	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₄₇	C₂×C₃	1	4	yes	complemented
7	C₃×C₁₉×D₁₃	C₂×C₃	1	4	yes	complemented
8	C₃×C₁₃×D₁₉	C₂×C₃	1	4	yes	complemented
9	D₁₃×D₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₁₃×C₁₉	C₂²×C₃	1	4	yes	complemented
11	C₂×C₃²×D₁₉	—	13	1	no	maximal, Hall
12	D₂₄₇	C₂×C₃²	1	1	yes	characteristic, complemented
13	C₁₃×D₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₁₉×D₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₂×C₃²×D₁₃	—	19	1	no	maximal, Hall
16	C₂×C₃²×C₁₉	—	13	1	no	—
17	C₃²×D₁₉	—	13	1	no	—
18	C₃²×D₁₉	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₁₃	—	19	1	no	—
21	C₃²×D₁₃	—	19	1	no	—
22	C₃²×D₁₃	D₁₉	1	1	yes	characteristic, direct product factor
23	C₂×C₃×D₁₉	—	13	4	no	—
24	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₃	—	19	4	no	—
26	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₉	—	13	4	no	—
28	C₃×D₁₉	—	13	4	no	—
29	C₃×D₁₉	C₃×D₁₃	1	4	yes	direct product factor
30	C₂×C₃×C₁₃	—	19	4	no	—
31	C₃×D₁₃	—	19	4	no	—
32	C₃×D₁₃	C₃×D₁₉	1	4	yes	direct product factor
33	C₂×D₁₉	—	13	1	no	Hall
34	C₃×C₁₉	C₂×C₃×D₁₃	1	4	yes	complemented
35	C₂×D₁₃	—	19	1	no	Hall
36	C₃×C₁₃	C₂×C₃×D₁₉	1	4	yes	complemented
37	C₂×C₁₉	—	13	1	no	—
38	D₁₉	—	13	1	no	—
39	D₁₉	C₃²×D₁₃	1	1	yes	characteristic, direct product factor
40	C₂²×C₃²	—	247	1	no	Hall
41	C₂×C₁₃	—	19	1	no	—
42	D₁₃	—	19	1	no	—
43	D₁₃	C₃²×D₁₉	1	1	yes	characteristic, direct product factor
44	C₁₉	C₂×C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²	—	13	1	no	—
46	C₂×C₃²	—	19	1	no	—
47	C₂×C₃²	—	247	1	no	—
48	C₁₃	C₂×C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	247	4	no	—
50	C₃²	D₁₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	13	4	no	—
52	C₂×C₃	—	19	4	no	—
53	C₂×C₃	—	247	4	no	—
54	C₂²	—	247	1	no	Sylow
55	C₃	C₃×D₁₃×D₁₉	1	4	yes	direct product factor
56	C₂	—	13	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	247	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₁₃×D₁₉
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₂₄₇	C₂	semidirect
2. C₃²×C₁₉×D₁₃	C₂	semidirect
3. C₃²×C₁₃×D₁₉	C₂	semidirect
4. C₃×D₁₃×D₁₉	C₃	direct (N × H)
5. C₃²×C₁₃×C₁₉	C₂²	semidirect
6. C₃×D₂₄₇	C₂×C₃	semidirect
7. C₃×C₁₉×D₁₃	C₂×C₃	semidirect
8. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
9. D₁₃×D₁₉	C₃²	direct (N × H)
10. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
12. D₂₄₇	C₂×C₃²	semidirect
13. C₁₃×D₁₉	C₂×C₃²	semidirect
14. C₁₉×D₁₃	C₂×C₃²	semidirect
18. C₃²×D₁₉	D₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂²×C₃²	semidirect
22. C₃²×D₁₃	D₁₉	direct (N × H)
24. C₃²×C₁₉	C₂×D₁₃	semidirect
26. C₃²×C₁₃	C₂×D₁₉	semidirect
29. C₃×D₁₉	C₃×D₁₃	direct (N × H)
32. C₃×D₁₃	C₃×D₁₉	direct (N × H)
34. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
36. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
39. D₁₉	C₃²×D₁₃	direct (N × H)
43. D₁₃	C₃²×D₁₉	direct (N × H)
44. C₁₉	C₂×C₃²×D₁₃	semidirect
48. C₁₃	C₂×C₃²×D₁₉	semidirect
50. C₃²	D₁₃×D₁₉	direct (N × H)
55. C₃	C₃×D₁₃×D₁₉	direct (N × H)

Subgroups — C32×D13×D19 #22580348

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×D₁₃×D₁₉ #22580348