Subgroups — C₅×D₅×D₅₇ #19152869

Order 5700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×D₅₇	—	5	1	no	maximal
7	D₅×D₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×D₉₅	—	3	1	no	—
9	C₅×D₅×C₁₉	D₃	1	1	yes	characteristic, complemented
10	C₅²×D₁₉	—	3	1	no	—
11	C₂×C₃×C₅×C₁₉	—	5	1	no	—
12	D₂₈₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₅₇	—	2	2	no	—
14	C₅×D₅₇	—	5	1	no	—
15	C₅×D₅₇	D₅	1	1	yes	characteristic, direct product factor
16	C₅×D₅₇	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×D₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₁₉	—	15	1	no	—
20	D₅×D₁₉	—	3	1	no	—
21	C₅×D₃×D₅	—	19	1	no	maximal, Hall
22	C₃×C₅×C₁₉	—	2	2	no	—
23	C₃×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
25	C₂×D₅₇	—	5	1	no	Hall
26	C₂×C₅×C₁₉	—	5	1	no	—
27	D₉₅	—	3	1	no	—
28	C₅×D₁₉	—	3	1	no	—
29	C₅×D₁₉	—	3	1	no	—
30	C₅×D₁₉	—	6	2	no	—
31	C₅×D₁₉	—	15	1	no	—
32	D₅×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
33	C₅×D₁₅	—	19	1	no	—
34	C₅²×D₃	—	19	1	no	—
35	C₃×C₅×D₅	D₁₉	1	1	yes	characteristic, complemented
36	C₂×C₃×C₁₉	—	5	1	no	—
37	D₅₇	—	5	1	no	—
38	D₅₇	C₅×D₅	1	1	yes	characteristic, direct product factor
39	C₂×C₅×D₅	—	57	1	no	Hall
40	C₅×C₁₉	—	2	2	no	—
41	C₅×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented
43	C₂×D₁₉	—	15	1	no	Hall
44	C₃×C₅²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×D₃	—	95	1	no	—
46	D₃×D₅	—	19	1	no	—
47	C₃×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅²	—	57	1	no	—
49	C₅×D₅	—	57	1	no	—
50	C₅×D₅	D₅₇	1	1	yes	characteristic, direct product factor
51	C₂×C₁₉	—	5	1	no	—
52	D₁₉	—	3	1	no	—
53	D₁₉	—	15	1	no	—
54	C₂×C₃×C₅	—	5	1	no	—
55	D₁₅	—	19	1	no	—
56	C₃×D₅	C₅×D₁₉	1	1	yes	characteristic, complemented
57	C₅×D₃	—	19	1	no	—
58	C₅×D₃	—	19	1	no	—
59	C₅×D₃	—	38	2	no	—
60	C₅×D₃	—	95	1	no	—
61	C₅²	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₅	—	285	1	no	—
63	C₂×D₅	—	57	1	no	—
64	C₁₉	C₅×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₉	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
68	C₂×D₃	—	95	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	285	1	no	—
71	C₂×C₅	—	57	1	no	—
72	C₂×C₅	—	57	1	no	—
73	C₂×C₅	—	114	2	no	—
74	D₅	—	57	1	no	—
75	D₅	C₅×D₅₇	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	D₃	—	19	1	no	—
78	D₃	—	95	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₅×D₅₇	1	1	yes	characteristic, direct product factor
81	C₅	C₂×C₅×D₅₇	1	1	yes	characteristic, complemented
82	C₂²	—	285	1	no	Sylow
83	C₃	C₅×D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	285	1	no	—
86	C₂	—	57	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅×D₅₇
commutator, hypocenter	C₃×C₅×C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₂₈₅	C₂	semidirect
2. C₅²×D₅₇	C₂	semidirect
3. C₃×C₅×D₅×C₁₉	C₂	semidirect
5. C₃×C₅²×C₁₉	C₂²	semidirect
7. D₅×D₅₇	C₅	direct (N × H)
9. C₅×D₅×C₁₉	D₃	semidirect
12. D₂₈₅	C₂×C₅	semidirect
15. C₅×D₅₇	D₅	direct (N × H)
16. C₅×D₅₇	C₂×C₅	semidirect
17. C₃×D₅×C₁₉	C₂×C₅	semidirect
18. C₅²×C₁₉	C₂×D₃	semidirect
23. C₃×C₅×C₁₉	C₂×D₅	semidirect
24. C₃×C₅×C₁₉	C₂²×C₅	semidirect
32. D₅×C₁₉	C₅×D₃	semidirect
35. C₃×C₅×D₅	D₁₉	semidirect
38. D₅₇	C₅×D₅	direct (N × H)
41. C₅×C₁₉	D₃×D₅	semidirect
42. C₅×C₁₉	C₂×C₅×D₃	semidirect
44. C₃×C₅²	C₂×D₁₉	semidirect
47. C₃×C₁₉	C₂×C₅×D₅	semidirect
50. C₅×D₅	D₅₇	direct (N × H)
56. C₃×D₅	C₅×D₁₉	semidirect
61. C₅²	C₂×D₅₇	semidirect
64. C₁₉	C₅×D₃×D₅	semidirect
66. C₃×C₅	D₅×D₁₉	semidirect
67. C₃×C₅	C₂×C₅×D₁₉	semidirect
75. D₅	C₅×D₅₇	direct (N × H)
80. C₅	D₅×D₅₇	direct (N × H)
81. C₅	C₂×C₅×D₅₇	semidirect
83. C₃	C₅×D₅×D₁₉	semidirect

Subgroups — C5×D5×D57 #19152869

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₅×D₅₇ #19152869