Subgroups — C₂×C₅²⋊C₃×D₅₇ #30685854

Order 17100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²⋊C₃×D₅₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉×C₅²⋊C₃	—	3	1	no	maximal
5	C₃×C₁₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅²×D₅₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₉×C₅²⋊C₃	—	2	1	no	—
8	C₂×C₁₉×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
9	D₁₉×C₅²⋊C₃	—	3	2	no	—
10	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅²×D₁₉	—	3	1	no	Hall
12	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₉×C₅²⋊C₃	—	2	1	no	—
14	C₁₉×C₅²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₅×D₅₇	—	3	2	no	—
16	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
17	C₅²×D₁₉	—	3	2	no	—
18	C₂×D₃×C₅²⋊C₃	—	19	1	no	maximal, Hall
19	C₂×C₃×D₅₇	—	25	1	no	maximal, Hall
20	C₂×C₃×C₅×C₁₉	—	3	2	no	—
21	C₅×D₅₇	—	3	4	no	—
22	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅²⋊C₃	D₁₉	1	1	yes	characteristic, complemented
24	D₃×C₅²⋊C₃	—	19	2	no	—
25	C₂×C₅×D₁₉	—	9	2	no	—
26	C₂×C₃²×C₁₉	—	25	1	no	—
27	C₃×D₅₇	—	25	2	no	—
28	C₂×C₅²×D₃	—	19	1	no	—
29	C₂²×C₅²⋊C₃	—	57	1	no	—
30	C₃×C₅×C₁₉	—	3	2	no	—
31	C₂×D₅₇	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃×D₁₉	—	75	1	no	—
33	C₃×C₅²⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₅×C₁₉	—	3	2	no	—
35	C₅×D₁₉	—	9	4	no	—
36	C₃²×C₁₉	—	25	1	no	Hall
37	C₂×C₃×C₅²	C₃×D₁₉	1	1	yes	characteristic, complemented
38	C₅²×D₃	—	19	2	no	—
39	C₂×C₅²⋊C₃	—	2	1	no	—
40	C₂×C₅²⋊C₃	—	57	2	no	—
41	C₂×C₅²⋊C₃	D₅₇	1	1	yes	characteristic, direct product factor
42	C₂×C₃×C₁₉	—	25	1	no	—
43	C₂×C₃×C₁₉	—	50	1	no	—
44	C₂×C₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
45	D₅₇	C₂×C₅²⋊C₃	1	2	yes	direct product factor
46	C₃×D₁₉	—	75	2	no	—
47	C₂²×C₅²	—	57	1	no	Hall
48	C₅×C₁₉	—	3	2	no	—
49	C₂×D₁₉	—	3	1	no	Hall
50	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
51	C₅²⋊C₃	—	2	1	no	—
52	C₅²⋊C₃	C₂×D₅₇	1	1	yes	characteristic, direct product factor
53	C₂×C₅×D₃	—	57	2	no	—
54	C₃×C₁₉	—	25	1	no	—
55	C₃×C₁₉	—	50	1	no	—
56	C₃×C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented
57	C₂×C₅²	—	57	2	no	—
58	C₂×C₅²	C₃×D₅₇	1	1	yes	characteristic, complemented
59	C₂×C₁₉	D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented
60	D₁₉	—	3	2	no	—
61	C₂×C₃×D₃	—	475	1	no	Hall
62	C₂×C₃×C₅	—	3	2	no	—
63	C₅×D₃	—	57	4	no	—
64	C₅²	C₂×C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₅	—	171	2	no	—
66	C₁₉	C₂×D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	25	1	no	—
68	C₃×D₃	—	475	2	no	—
69	C₃×C₅	—	3	2	no	—
70	C₂²×C₃	—	1425	1	no	—
71	C₂×D₃	—	19	1	no	—
72	C₂×C₅	—	3	2	no	—
73	C₂×C₅	—	171	4	no	—
74	C₃²	—	25	1	no	Sylow
75	C₂×C₃	—	25	1	no	—
76	C₂×C₃	—	50	1	no	—
77	C₂×C₃	—	1425	2	no	—
78	C₂×C₃	D₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
79	D₃	—	19	2	no	—
80	C₅	—	3	2	no	—
81	C₂²	—	57	1	no	Sylow
82	C₃	—	25	1	no	—
83	C₃	—	50	1	no	—
84	C₃	C₂×D₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
85	C₂	—	57	2	no	—
86	C₂	C₅²⋊C₃×D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅²⋊C₃×D₅₇
commutator, cosocle, hypocenter	C₃×C₅²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×C₅²⋊C₃	C₂	semidirect
2. C₅²⋊C₃×D₅₇	C₂	direct (N × H)
3. C₂×C₅²×D₅₇	C₃	semidirect
5. C₃×C₁₉×C₅²⋊C₃	C₂²	semidirect
6. C₅²×D₅₇	C₂×C₃	semidirect
8. C₂×C₁₉×C₅²⋊C₃	D₃	semidirect
10. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
12. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
14. C₁₉×C₅²⋊C₃	C₂×D₃	semidirect
16. C₂×C₅²×C₁₉	C₃×D₃	semidirect
22. C₅²×C₁₉	C₂×C₃×D₃	semidirect
23. C₂×C₃×C₅²⋊C₃	D₁₉	semidirect
31. C₂×D₅₇	C₅²⋊C₃	direct (N × H)
33. C₃×C₅²⋊C₃	C₂×D₁₉	semidirect
37. C₂×C₃×C₅²	C₃×D₁₉	semidirect
41. C₂×C₅²⋊C₃	D₅₇	direct (N × H)
44. C₂×C₃×C₁₉	C₂×C₅²⋊C₃	semidirect
45. D₅₇	C₂×C₅²⋊C₃	direct (N × H)
50. C₃×C₅²	C₂×C₃×D₁₉	semidirect
52. C₅²⋊C₃	C₂×D₅₇	direct (N × H)
56. C₃×C₁₉	C₂²×C₅²⋊C₃	semidirect
58. C₂×C₅²	C₃×D₅₇	semidirect
59. C₂×C₁₉	D₃×C₅²⋊C₃	semidirect
64. C₅²	C₂×C₃×D₅₇	semidirect
66. C₁₉	C₂×D₃×C₅²⋊C₃	semidirect
78. C₂×C₃	D₁₉×C₅²⋊C₃	semidirect
84. C₃	C₂×D₁₉×C₅²⋊C₃	semidirect
86. C₂	C₅²⋊C₃×D₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×C₅²⋊C₃	2
C₅²⋊C₃×D₅₇	2
C₂×C₅²×D₅₇	3
C₂×D₁₉×C₅²⋊C₃	3
C₂×D₃×C₅²⋊C₃	19
C₂×C₃×D₅₇	25

Subgroups — C2×C52⋊C3×D57 #30685854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²⋊C₃×D₅₇ #30685854