Subgroups — C₂×C₂₅×C₃⋊D₅₇ #30685524

Order 17100.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₃⋊D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₅×D₅₇	—	3	4	no	maximal
4	C₃²×C₁₉×C₂₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₃⋊D₅₇	C₅	1	1	yes	maximal, characteristic
6	C₂₅×D₅₇	—	3	8	no	—
7	C₂×C₃×C₁₉×C₂₅	D₃	1	4	yes	complemented
8	C₂×C₂₅×D₁₉	—	9	1	no	Hall
9	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	1	yes	characteristic
10	C₅×C₃⋊D₅₇	C₂×C₅	1	2	yes	—
11	C₃×C₁₉×C₂₅	C₂×D₃	1	4	yes	complemented
12	C₂×C₅×D₅₇	—	3	4	no	—
13	C₂×C₁₉×C₂₅	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₂₅×D₁₉	—	9	2	no	—
15	C₂×C₃⋊D₃×C₂₅	—	19	1	no	maximal, Hall
16	C₃²×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic
17	C₂×C₃⋊D₅₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₁₉	C₅×D₃	1	4	yes	—
19	C₅×D₅₇	—	3	8	no	—
20	C₁₉×C₂₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₂₅	D₁₉	1	1	yes	characteristic, complemented
22	C₃⋊D₃×C₂₅	—	19	2	no	—
23	C₂×C₅×D₁₉	—	9	1	no	—
24	C₂×C₃²×C₁₉	C₂×C₂₅	1	1	yes	characteristic, complemented
25	C₃⋊D₅₇	C₂×C₂₅	1	2	yes	direct product factor
26	C₂×D₃×C₂₅	—	57	4	no	—
27	C₃×C₅×C₁₉	C₂×C₅×D₃	1	4	yes	—
28	C₂×D₅₇	—	3	4	no	—
29	C₃²×C₂₅	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	C₅×C₃⋊D₃	1	1	yes	characteristic
31	C₅×D₁₉	—	9	2	no	—
32	C₂×C₅×C₃⋊D₃	—	19	1	no	—
33	C₃²×C₁₉	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₅	D₅₇	1	4	yes	complemented
35	D₃×C₂₅	—	57	8	no	—
36	C₂×C₃×C₁₉	D₃×C₂₅	1	4	yes	complemented
37	D₅₇	—	3	8	no	—
38	C₂²×C₂₅	—	171	1	no	Hall
39	C₅×C₁₉	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic
40	C₂×C₃²×C₅	C₅×D₁₉	1	1	yes	characteristic
41	C₅×C₃⋊D₃	—	19	2	no	—
42	C₂×D₁₉	—	9	1	no	Hall
43	C₃×C₂₅	C₂×D₅₇	1	4	yes	complemented
44	C₂×C₅×D₃	—	57	4	no	—
45	C₃×C₁₉	C₂×D₃×C₂₅	1	4	yes	complemented
46	C₂×C₂₅	—	171	2	no	—
47	C₂×C₂₅	C₃⋊D₅₇	1	1	yes	characteristic, direct product factor
48	C₃²×C₅	C₂×C₅×D₁₉	1	1	yes	characteristic
49	C₂×C₁₉	C₃⋊D₃×C₂₅	1	1	yes	characteristic, complemented
50	D₁₉	—	9	2	no	—
51	C₂×C₃⋊D₃	—	19	1	no	Hall
52	C₂×C₃×C₅	C₅×D₅₇	1	4	yes	—
53	C₅×D₃	—	57	8	no	—
54	C₂₅	C₂×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	—	171	1	no	—
56	C₁₉	C₂×C₃⋊D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃²	C₂₅×D₁₉	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	19	2	no	—
59	C₃×C₅	C₂×C₅×D₅₇	1	4	yes	—
60	C₂×D₃	—	57	4	no	—
61	C₂×C₅	—	171	2	no	—
62	C₂×C₅	C₅×C₃⋊D₅₇	1	1	yes	characteristic
63	C₃²	C₂×C₂₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₂₅×D₅₇	1	4	yes	complemented
65	D₃	—	57	8	no	—
66	C₅	C₂×C₅×C₃⋊D₅₇	1	1	yes	characteristic
67	C₂²	—	171	1	no	Sylow
68	C₃	C₂×C₂₅×D₅₇	1	4	yes	complemented
69	C₂	—	171	2	no	—
70	C₂	C₂₅×C₃⋊D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅	C₃⋊D₅₇
commutator, hypocenter	C₃²×C₁₉	C₂²×C₂₅
Frattini	C₅	C₂×C₅×C₃⋊D₅₇
Fitting	C₂×C₃²×C₁₉×C₂₅	C₂
socle	C₂×C₃²×C₅×C₁₉	C₂×C₅
prime radical	C₂×C₅×C₃⋊D₅₇	C₅
cosocle	C₃²×C₅×C₁₉	C₂²×C₅
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×C₃⋊D₅₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₂₅	C₂	semidirect
4. C₃²×C₁₉×C₂₅	C₂²	semidirect
7. C₂×C₃×C₁₉×C₂₅	D₃	semidirect
11. C₃×C₁₉×C₂₅	C₂×D₃	semidirect
13. C₂×C₁₉×C₂₅	C₃⋊D₃	semidirect
17. C₂×C₃⋊D₅₇	C₂₅	direct (N × H)
20. C₁₉×C₂₅	C₂×C₃⋊D₃	semidirect
21. C₂×C₃²×C₂₅	D₁₉	semidirect
24. C₂×C₃²×C₁₉	C₂×C₂₅	semidirect
25. C₃⋊D₅₇	C₂×C₂₅	direct (N × H)
29. C₃²×C₂₅	C₂×D₁₉	semidirect
33. C₃²×C₁₉	C₂²×C₂₅	semidirect
34. C₂×C₃×C₂₅	D₅₇	semidirect
36. C₂×C₃×C₁₉	D₃×C₂₅	semidirect
43. C₃×C₂₅	C₂×D₅₇	semidirect
45. C₃×C₁₉	C₂×D₃×C₂₅	semidirect
47. C₂×C₂₅	C₃⋊D₅₇	direct (N × H)
49. C₂×C₁₉	C₃⋊D₃×C₂₅	semidirect
54. C₂₅	C₂×C₃⋊D₅₇	direct (N × H)
56. C₁₉	C₂×C₃⋊D₃×C₂₅	semidirect
57. C₂×C₃²	C₂₅×D₁₉	semidirect
63. C₃²	C₂×C₂₅×D₁₉	semidirect
64. C₂×C₃	C₂₅×D₅₇	semidirect
68. C₃	C₂×C₂₅×D₅₇	semidirect
70. C₂	C₂₅×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
C₂₅×C₃⋊D₅₇	2
C₂×C₃²×C₁₉×C₂₅	2
C₂×C₂₅×D₅₇	3
C₂×C₅×C₃⋊D₅₇	5
C₂×C₃⋊D₃×C₂₅	19

Subgroups — C2×C25×C3⋊D57 #30685524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×C₃⋊D₅₇ #30685524