Subgroups — C₃×D₅×D₅₇ #16811908

Order 3420.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₁₉	—	3	1	no	maximal
6	C₃²×C₅×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×D₅₇	—	5	1	no	maximal, Hall
8	D₂₈₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₉₅	—	3	1	no	—
11	C₃×D₅×C₁₉	—	2	1	no	—
12	C₃×D₅×C₁₉	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₁₉	—	3	1	no	—
15	D₅×D₁₉	—	3	1	no	Hall
16	C₂×C₃²×C₁₉	—	5	1	no	—
17	C₃×D₅₇	—	5	1	no	—
18	C₃×D₅₇	D₅	1	1	yes	characteristic, direct product factor
19	C₃×C₅×C₁₉	—	2	1	no	—
20	C₃×C₅×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×D₅₇	—	5	1	no	—
23	C₂×C₃×D₁₉	—	15	1	no	—
24	D₉₅	—	3	1	no	—
25	C₅×D₁₉	—	3	1	no	—
26	D₅×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
27	C₃×D₃×D₅	—	19	1	no	maximal, Hall
28	C₃²×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₁₉	—	5	1	no	—
30	C₂×C₃×C₁₉	—	5	1	no	—
31	C₂×C₃×C₁₉	—	10	1	no	—
32	D₅₇	—	5	1	no	—
33	D₅₇	C₃×D₅	1	1	yes	characteristic, direct product factor
34	C₃×D₁₉	—	3	1	no	—
35	C₃×D₁₉	—	15	1	no	—
36	C₅×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
37	C₃×D₁₅	—	19	1	no	—
38	C₃×C₅×D₃	—	19	1	no	—
39	C₃²×D₅	D₁₉	1	1	yes	characteristic, complemented
40	C₂×D₁₉	—	15	1	no	Hall
41	C₂×C₃×D₅	—	57	1	no	—
42	D₃×D₅	—	19	1	no	—
43	C₃×C₁₉	—	2	1	no	—
44	C₃×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented
45	C₃×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
46	C₃²×C₅	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₁₉	—	5	1	no	—
48	D₁₉	—	3	1	no	—
49	D₁₉	—	15	1	no	—
50	C₂×C₃×D₃	—	95	1	no	Hall
51	C₂×C₃×C₅	—	57	1	no	—
52	D₁₅	—	19	1	no	—
53	C₃×D₅	—	2	1	no	—
54	C₃×D₅	—	57	1	no	—
55	C₃×D₅	C₃×D₁₉	1	1	yes	characteristic, complemented
56	C₃×D₅	D₅₇	1	1	yes	characteristic, direct product factor
57	C₅×D₃	—	19	1	no	—
58	C₂×D₅	—	57	1	no	Hall
59	C₁₉	C₃×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃²	—	5	1	no	—
61	C₃×D₃	—	19	1	no	—
62	C₃×D₃	—	95	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₅₇	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	285	1	no	—
67	C₂×D₃	—	95	1	no	—
68	C₂×C₅	—	57	1	no	—
69	D₅	—	57	1	no	—
70	D₅	C₃×D₅₇	1	1	yes	characteristic, direct product factor
71	C₃²	D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	5	1	no	—
73	C₂×C₃	—	5	1	no	—
74	C₂×C₃	—	10	1	no	—
75	C₂×C₃	—	285	1	no	—
76	C₂×C₃	—	57	1	no	—
77	D₃	—	19	1	no	—
78	D₃	—	95	1	no	—
79	C₅	C₂×C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	285	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₅×D₁₉	1	1	yes	characteristic, complemented
83	C₃	D₅×D₅₇	1	1	yes	characteristic, direct product factor
84	C₂	—	5	1	no	—
85	C₂	—	285	1	no	—
86	C₂	—	57	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₅₇
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₈₅	C₂	semidirect
2. C₃×C₅×D₅₇	C₂	semidirect
3. C₃²×D₅×C₁₉	C₂	semidirect
4. D₅×D₅₇	C₃	direct (N × H)
6. C₃²×C₅×C₁₉	C₂²	semidirect
8. D₂₈₅	C₂×C₃	semidirect
9. C₅×D₅₇	C₂×C₃	semidirect
12. C₃×D₅×C₁₉	D₃	semidirect
13. C₃×D₅×C₁₉	C₂×C₃	semidirect
18. C₃×D₅₇	D₅	direct (N × H)
20. C₃×C₅×C₁₉	C₂×D₃	semidirect
21. C₃×C₅×C₁₉	C₂²×C₃	semidirect
26. D₅×C₁₉	C₃×D₃	semidirect
28. C₃²×C₁₉	C₂×D₅	semidirect
33. D₅₇	C₃×D₅	direct (N × H)
36. C₅×C₁₉	C₂×C₃×D₃	semidirect
39. C₃²×D₅	D₁₉	semidirect
44. C₃×C₁₉	D₃×D₅	semidirect
45. C₃×C₁₉	C₂×C₃×D₅	semidirect
46. C₃²×C₅	C₂×D₁₉	semidirect
55. C₃×D₅	C₃×D₁₉	semidirect
56. C₃×D₅	D₅₇	direct (N × H)
59. C₁₉	C₃×D₃×D₅	semidirect
64. C₃×C₅	C₂×C₃×D₁₉	semidirect
65. C₃×C₅	C₂×D₅₇	semidirect
70. D₅	C₃×D₅₇	direct (N × H)
71. C₃²	D₅×D₁₉	semidirect
79. C₅	C₂×C₃×D₅₇	semidirect
82. C₃	C₃×D₅×D₁₉	semidirect
83. C₃	D₅×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
C₃×D₂₈₅	2
C₃×C₅×D₅₇	2
C₃²×D₅×C₁₉	2
D₅×D₅₇	3
C₃×D₅×D₁₉	3
C₂×C₃×D₅₇	5
C₃×D₃×D₅	19

Subgroups — C3×D5×D57 #16811908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₅₇ #16811908