Subgroups — D₁₃×C₃⋊D₅₇ #22580362

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₅₇	—	3	4	no	maximal
5	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₇₄₁	—	3	4	no	—
7	C₁₃×D₅₇	—	3	4	no	—
8	C₃×C₁₉×D₁₃	D₃	1	4	yes	complemented
9	D₁₃×D₁₉	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₅₇	—	13	1	no	maximal, Hall
12	D₂₄₇	—	9	1	no	—
13	C₁₃×D₁₉	—	9	1	no	—
14	C₁₉×D₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₃⋊D₃×D₁₃	—	19	1	no	maximal, Hall
16	C₂×C₃²×C₁₉	—	13	1	no	—
17	C₃⋊D₅₇	—	13	1	no	—
18	C₃⋊D₅₇	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃⋊D₃₉	—	19	1	no	—
21	C₁₃×C₃⋊D₃	—	19	1	no	—
22	C₃²×D₁₃	D₁₉	1	1	yes	characteristic, complemented
23	C₂×D₅₇	—	39	4	no	—
24	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	D₃×D₁₃	—	57	4	no	—
26	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₉	—	13	4	no	—
28	D₅₇	—	3	4	no	—
29	D₅₇	—	39	4	no	—
30	D₃₉	—	57	4	no	—
31	C₃×D₁₃	D₅₇	1	4	yes	complemented
32	D₃×C₁₃	—	57	4	no	—
33	C₂×D₁₉	—	117	1	no	Hall
34	C₃×C₁₉	D₃×D₁₃	1	4	yes	complemented
35	C₂×D₁₃	—	171	1	no	Hall
36	C₃×C₁₃	C₂×D₅₇	1	4	yes	complemented
37	C₂×C₁₉	—	13	1	no	—
38	D₁₉	—	9	1	no	—
39	D₁₉	—	117	1	no	—
40	C₂×C₃⋊D₃	—	247	1	no	Hall
41	C₂×C₁₃	—	171	1	no	—
42	D₁₃	—	171	1	no	—
43	D₁₃	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
44	C₁₉	C₃⋊D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²	—	13	1	no	—
46	C₃⋊D₃	—	19	1	no	—
47	C₃⋊D₃	—	247	1	no	—
48	C₁₃	C₂×C₃⋊D₅₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	741	4	no	—
50	C₃²	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	13	4	no	—
52	D₃	—	57	4	no	—
53	D₃	—	741	4	no	—
54	C₂²	—	2223	1	no	Sylow
55	C₃	D₁₃×D₅₇	1	4	yes	complemented
56	C₂	—	13	1	no	—
57	C₂	—	171	1	no	—
58	C₂	—	2223	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₇₄₁	C₂	semidirect
2. C₁₃×C₃⋊D₅₇	C₂	semidirect
3. C₃²×C₁₉×D₁₃	C₂	semidirect
5. C₃²×C₁₃×C₁₉	C₂²	semidirect
8. C₃×C₁₉×D₁₃	D₃	semidirect
10. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
14. C₁₉×D₁₃	C₃⋊D₃	semidirect
18. C₃⋊D₅₇	D₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂×C₃⋊D₃	semidirect
22. C₃²×D₁₃	D₁₉	semidirect
24. C₃²×C₁₉	C₂×D₁₃	semidirect
26. C₃²×C₁₃	C₂×D₁₉	semidirect
31. C₃×D₁₃	D₅₇	semidirect
34. C₃×C₁₉	D₃×D₁₃	semidirect
36. C₃×C₁₃	C₂×D₅₇	semidirect
43. D₁₃	C₃⋊D₅₇	direct (N × H)
44. C₁₉	C₃⋊D₃×D₁₃	semidirect
48. C₁₃	C₂×C₃⋊D₅₇	semidirect
50. C₃²	D₁₃×D₁₉	semidirect
55. C₃	D₁₃×D₅₇	semidirect

Subgroups — D13×C3⋊D57 #22580362

Conjugacy classes of subgroups

Complements

Subgroups — D₁₃×C₃⋊D₅₇ #22580362