Subgroups — D₅₇⋊D₆₉ #30628640

Order 15732.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₃₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₇⋊D₂₃	—	3	1	no	maximal
5	D₁₉×D₆₉	—	3	1	no	maximal
6	C₃²×C₁₉×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₃₁₁	D₃	1	1	yes	characteristic, complemented
8	C₂₃×D₅₇	D₃	1	1	yes	characteristic, complemented
9	C₁₉×D₆₉	—	3	1	no	—
10	C₁₉×D₆₉	—	3	1	no	—
11	C₁₉×D₆₉	—	6	1	no	—
12	C₃×D₄₃₇	—	3	1	no	—
13	C₃×C₂₃×D₁₉	—	3	1	no	—
14	D₁₉×D₂₃	—	9	1	no	Hall
15	C₃×C₁₉×C₂₃	—	2	1	no	—
16	C₃×C₁₉×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₄₃₇	—	3	1	no	—
19	C₁₉×D₂₃	—	9	1	no	—
20	C₂₃×D₁₉	—	3	1	no	—
21	D₃×D₆₉	—	19	1	no	maximal, Hall
22	(C₃⋊D₃)⋊D₁₉	—	23	1	no	maximal, Hall
23	C₁₉×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
24	C₃⋊D₆₉	D₁₉	1	1	yes	characteristic, complemented
25	C₃×D₆₉	—	19	1	no	—
26	C₃×D₃×C₂₃	—	19	1	no	—
27	C₃⋊D₃×C₁₉	—	23	1	no	—
28	C₃×D₅₇	—	23	1	no	—
29	C₃×D₅₇	D₂₃	1	1	yes	characteristic, complemented
30	C₂×D₆₉	—	57	1	no	—
31	D₃×D₂₃	—	57	1	no	—
32	D₃×D₁₉	—	69	1	no	—
33	D₃×D₁₉	—	69	1	no	—
34	C₃²×C₂₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
35	C₃²×C₁₉	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₂₃	—	57	1	no	—
37	D₆₉	—	3	1	no	—
38	D₆₉	—	3	1	no	—
39	D₆₉	—	6	1	no	—
40	D₆₉	—	19	1	no	—
41	C₃×D₂₃	—	57	1	no	—
42	D₃×C₂₃	—	19	1	no	—
43	D₅₇	—	23	1	no	—
44	D₅₇	D₆₉	1	1	yes	characteristic, complemented
45	C₃×D₁₉	—	3	1	no	—
46	C₃×D₁₉	—	69	1	no	—
47	D₃×C₁₉	—	69	1	no	—
48	D₃×C₁₉	—	69	1	no	—
49	D₃×C₁₉	—	138	1	no	—
50	C₂×D₂₃	—	171	1	no	Hall
51	C₂×D₁₉	—	207	1	no	Hall
52	C₃×C₂₃	—	2	1	no	—
53	C₃×C₂₃	D₃×D₁₉	1	1	yes	characteristic, complemented
54	C₃×C₂₃	D₃×D₁₉	1	1	yes	characteristic, complemented
55	C₃×C₁₉	—	2	1	no	—
56	C₃×C₁₉	D₃×D₂₃	1	1	yes	characteristic, complemented
57	C₃×C₁₉	C₂×D₆₉	1	1	yes	characteristic, complemented
58	C₂×C₂₃	—	57	1	no	—
59	D₂₃	—	9	1	no	—
60	D₂₃	—	57	1	no	—
61	C₂×C₁₉	—	207	1	no	—
62	D₁₉	—	3	1	no	—
63	D₁₉	—	69	1	no	—
64	D₃²	—	437	1	no	Hall
65	C₂₃	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
66	C₁₉	D₃×D₆₉	1	1	yes	characteristic, complemented, Sylow
67	C₃⋊D₃	—	23	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	437	1	no	—
70	C₂×D₃	—	1311	1	no	—
71	C₂×D₃	—	1311	1	no	—
72	C₃²	D₁₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	1311	1	no	—
74	C₂×C₃	—	57	1	no	—
75	D₃	—	19	1	no	—
76	D₃	—	69	1	no	—
77	D₃	—	69	1	no	—
78	D₃	—	138	1	no	—
79	D₃	—	437	1	no	—
80	C₂²	—	3933	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₉×D₆₉	1	1	yes	characteristic, complemented
83	C₃	D₅₇⋊D₂₃	1	1	yes	characteristic, complemented
84	C₂	—	1311	1	no	—
85	C₂	—	57	1	no	—
86	C₂	—	207	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₉×C₂₃	C₂²
LCS	G ▷ C₃²×C₁₉×C₂₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₃⋊D₆₉	C₂	semidirect
2. C₃×D₁₃₁₁	C₂	semidirect
3. C₃×C₂₃×D₅₇	C₂	semidirect
6. C₃²×C₁₉×C₂₃	C₂²	semidirect
7. D₁₃₁₁	D₃	semidirect
8. C₂₃×D₅₇	D₃	semidirect
16. C₃×C₁₉×C₂₃	C₂×D₃	semidirect
17. C₃×C₁₉×C₂₃	C₂×D₃	semidirect
23. C₁₉×C₂₃	D₃²	semidirect
24. C₃⋊D₆₉	D₁₉	semidirect
29. C₃×D₅₇	D₂₃	semidirect
34. C₃²×C₂₃	C₂×D₁₉	semidirect
35. C₃²×C₁₉	C₂×D₂₃	semidirect
44. D₅₇	D₆₉	semidirect
53. C₃×C₂₃	D₃×D₁₉	semidirect
54. C₃×C₂₃	D₃×D₁₉	semidirect
56. C₃×C₁₉	D₃×D₂₃	semidirect
57. C₃×C₁₉	C₂×D₆₉	semidirect
65. C₂₃	(C₃⋊D₃)⋊D₁₉	semidirect
66. C₁₉	D₃×D₆₉	semidirect
72. C₃²	D₁₉×D₂₃	semidirect
82. C₃	D₁₉×D₆₉	semidirect
83. C₃	D₅₇⋊D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₃⋊D₆₉	2
C₃×D₁₃₁₁	2
C₃×C₂₃×D₅₇	2
D₅₇⋊D₂₃	3
D₁₉×D₆₉	3
D₃×D₆₉	19
(C₃⋊D₃)⋊D₁₉	23

Subgroups — D57⋊D69 #30628640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇⋊D₆₉ #30628640