Subgroups — D₅₇⋊D₃₉ #22580370

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₁₉	—	3	1	no	maximal
5	D₁₉×D₃₉	—	3	1	no	maximal
6	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₇₄₁	D₃	1	1	yes	characteristic, complemented
8	C₁₉×D₃₉	—	3	1	no	—
9	C₁₉×D₃₉	—	3	1	no	—
10	C₁₉×D₃₉	—	6	1	no	—
11	C₁₃×D₅₇	D₃	1	1	yes	characteristic, complemented
12	C₃×D₂₄₇	—	3	1	no	—
13	C₃×C₁₃×D₁₉	—	3	1	no	—
14	D₁₃×D₁₉	—	9	1	no	Hall
15	C₃×C₁₃×C₁₉	—	2	1	no	—
16	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
18	(C₃⋊D₃)⋊D₁₉	—	13	1	no	maximal, Hall
19	D₂₄₇	—	3	1	no	—
20	C₁₃×D₁₉	—	3	1	no	—
21	C₁₉×D₁₃	—	9	1	no	—
22	D₃×D₃₉	—	19	1	no	maximal, Hall
23	C₃⋊D₃×C₁₉	—	13	1	no	—
24	C₃×D₅₇	—	13	1	no	—
25	C₃×D₅₇	D₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
27	C₃⋊D₃₉	D₁₉	1	1	yes	characteristic, complemented
28	C₃×D₃₉	—	19	1	no	—
29	C₃×D₃×C₁₃	—	19	1	no	—
30	D₃×D₁₉	—	39	1	no	—
31	D₃×D₁₉	—	39	1	no	—
32	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃₉	—	57	1	no	—
34	D₃×D₁₃	—	57	1	no	—
35	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	D₅₇	—	13	1	no	—
37	D₅₇	D₃₉	1	1	yes	characteristic, complemented
38	C₃×D₁₉	—	3	1	no	—
39	C₃×D₁₉	—	39	1	no	—
40	D₃×C₁₉	—	39	1	no	—
41	D₃×C₁₉	—	39	1	no	—
42	D₃×C₁₉	—	78	1	no	—
43	C₂×C₃×C₁₃	—	57	1	no	—
44	D₃₉	—	3	1	no	—
45	D₃₉	—	3	1	no	—
46	D₃₉	—	6	1	no	—
47	D₃₉	—	19	1	no	—
48	C₃×D₁₃	—	57	1	no	—
49	D₃×C₁₃	—	19	1	no	—
50	C₂×D₁₉	—	117	1	no	Hall
51	C₃×C₁₉	—	2	1	no	—
52	C₃×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	171	1	no	Hall
55	C₃×C₁₃	—	2	1	no	—
56	C₃×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	117	1	no	—
59	D₁₉	—	3	1	no	—
60	D₁₉	—	39	1	no	—
61	D₃²	—	247	1	no	Hall
62	C₂×C₁₃	—	57	1	no	—
63	D₁₃	—	9	1	no	—
64	D₁₃	—	57	1	no	—
65	C₁₉	D₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
66	C₃⋊D₃	—	13	1	no	—
67	C₃×D₃	—	19	1	no	—
68	C₃×D₃	—	247	1	no	—
69	C₁₃	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	741	1	no	—
71	C₂×D₃	—	741	1	no	—
72	C₃²	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	57	1	no	—
74	C₂×C₃	—	741	1	no	—
75	D₃	—	19	1	no	—
76	D₃	—	39	1	no	—
77	D₃	—	39	1	no	—
78	D₃	—	78	1	no	—
79	D₃	—	247	1	no	—
80	C₂²	—	2223	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₉×D₃₉	1	1	yes	characteristic, complemented
83	C₃	D₃₉⋊D₁₉	1	1	yes	characteristic, complemented
84	C₂	—	57	1	no	—
85	C₂	—	117	1	no	—
86	C₂	—	741	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. C₁₉×C₃⋊D₃₉	C₂	semidirect
2. C₃×D₇₄₁	C₂	semidirect
3. C₃×C₁₃×D₅₇	C₂	semidirect
6. C₃²×C₁₃×C₁₉	C₂²	semidirect
7. D₇₄₁	D₃	semidirect
11. C₁₃×D₅₇	D₃	semidirect
16. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
25. C₃×D₅₇	D₁₃	semidirect
26. C₁₃×C₁₉	D₃²	semidirect
27. C₃⋊D₃₉	D₁₉	semidirect
32. C₃²×C₁₉	C₂×D₁₃	semidirect
35. C₃²×C₁₃	C₂×D₁₉	semidirect
37. D₅₇	D₃₉	semidirect
52. C₃×C₁₉	D₃×D₁₃	semidirect
53. C₃×C₁₉	C₂×D₃₉	semidirect
56. C₃×C₁₃	D₃×D₁₉	semidirect
57. C₃×C₁₃	D₃×D₁₉	semidirect
65. C₁₉	D₃×D₃₉	semidirect
69. C₁₃	(C₃⋊D₃)⋊D₁₉	semidirect
72. C₃²	D₁₃×D₁₉	semidirect
82. C₃	D₁₉×D₃₉	semidirect
83. C₃	D₃₉⋊D₁₉	semidirect

Subgroups — D57⋊D39 #22580370

Conjugacy classes of subgroups

Complements

Subgroups — D₅₇⋊D₃₉ #22580370