Subgroups — C₃×C₁₃×Dic₅₇ #22580227

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₃×Dic₁₉	—	3	1	no	maximal
4	C₃²×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	—	2	1	no	—
6	C₂×C₃×C₁₃×C₁₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₁₃×Dic₁₉	—	3	1	no	Hall
9	C₃×C₁₃×C₁₉	—	2	1	no	—
10	C₃×C₁₃×C₁₉	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₅₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic
14	C₃×Dic₃×C₁₃	—	19	1	no	maximal, Hall
15	C₂×C₃²×C₁₉	C₂×C₁₃	1	1	yes	characteristic
16	C₁₃×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₁₃	D₁₉	1	1	yes	characteristic
18	Dic₅₇	C₃×C₁₃	1	1	yes	characteristic, direct product factor
19	C₃×Dic₁₉	—	3	1	no	—
20	C₃²×C₁₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₄×C₁₃	—	57	1	no	—
22	Dic₃×C₁₃	—	19	1	no	—
23	C₃²×C₁₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₉	—	2	1	no	—
25	C₂×C₃×C₁₉	D₃×C₁₃	1	1	yes	characteristic
26	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
27	C₂×C₃×C₁₃	—	2	1	no	—
28	C₂×C₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic
29	C₂×C₃×C₁₃	D₅₇	1	1	yes	characteristic
30	Dic₁₉	—	3	1	no	Hall
31	C₃×C₁₉	—	2	1	no	—
32	C₃×C₁₉	Dic₃×C₁₃	1	1	yes	characteristic, complemented
33	C₃×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
34	C₄×C₁₃	—	57	1	no	Hall
35	C₃×C₁₃	—	2	1	no	—
36	C₃×C₁₃	C₃×Dic₁₉	1	1	yes	characteristic, complemented
37	C₃×C₁₃	Dic₅₇	1	1	yes	characteristic, direct product factor
38	C₂×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic
39	C₃×Dic₃	—	19	1	no	Hall
40	C₂×C₁₃	C₃×D₅₇	1	1	yes	characteristic
41	C₁₉	C₃×Dic₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃²	C₁₃×D₁₉	1	1	yes	characteristic
43	C₁₃	C₃×Dic₅₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₃×C₄	—	57	1	no	—
45	Dic₃	—	19	1	no	—
46	C₃²	C₁₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×C₁₃×D₁₉	1	1	yes	characteristic
49	C₂×C₃	C₁₃×D₅₇	1	1	yes	characteristic
50	C₄	—	57	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₁₃×Dic₁₉	1	1	yes	characteristic, complemented
53	C₃	C₁₃×Dic₅₇	1	1	yes	characteristic, direct product factor
54	C₂	C₃×C₁₃×D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₅₇
commutator, hypocenter	C₃×C₁₉	C₃×C₄×C₁₃
Frattini	C₂	C₃×C₁₃×D₅₇
Fitting, socle	C₂×C₃²×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×Dic₅₇	C₃	direct (N × H)
4. C₃²×C₁₃×C₁₉	C₄	semidirect
10. C₃×C₁₃×C₁₉	Dic₃	semidirect
11. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
12. C₃×Dic₅₇	C₁₃	direct (N × H)
16. C₁₃×C₁₉	C₃×Dic₃	semidirect
18. Dic₅₇	C₃×C₁₃	direct (N × H)
20. C₃²×C₁₉	C₄×C₁₃	semidirect
23. C₃²×C₁₃	Dic₁₉	semidirect
32. C₃×C₁₉	Dic₃×C₁₃	semidirect
33. C₃×C₁₉	C₃×C₄×C₁₃	semidirect
36. C₃×C₁₃	C₃×Dic₁₉	semidirect
37. C₃×C₁₃	Dic₅₇	direct (N × H)
41. C₁₉	C₃×Dic₃×C₁₃	semidirect
43. C₁₃	C₃×Dic₅₇	direct (N × H)
46. C₃²	C₁₃×Dic₁₉	semidirect
52. C₃	C₃×C₁₃×Dic₁₉	semidirect
53. C₃	C₁₃×Dic₅₇	direct (N × H)

Subgroups — C3×C13×Dic57 #22580227

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×Dic₅₇ #22580227