Subgroups — C₅²×C₃⋊Dic₅₇ #30685690

Order 17100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×Dic₅₇	—	3	4	no	maximal
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊Dic₅₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₃×C₅²×C₁₉	D₃	1	4	yes	—
6	C₅²×Dic₁₉	—	9	1	no	Hall
7	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	6	yes	—
8	C₃×C₅²×C₁₉	Dic₃	1	4	yes	complemented
9	C₅×Dic₅₇	—	3	24	no	—
10	C₂×C₅²×C₁₉	C₃⋊D₃	1	1	yes	characteristic
11	C₅²×C₃⋊Dic₃	—	19	1	no	maximal, Hall
12	C₃²×C₅×C₁₉	C₄×C₅	1	6	yes	complemented
13	C₃⋊Dic₅₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₁₉	C₅×D₃	1	24	yes	—
15	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃²×C₅²	D₁₉	1	1	yes	characteristic
17	C₅×Dic₁₉	—	9	6	no	—
18	C₂×C₃²×C₁₉	C₂×C₅²	1	1	yes	characteristic
19	C₅²×Dic₃	—	57	4	no	—
20	C₃×C₅×C₁₉	C₅×Dic₃	1	24	yes	complemented
21	Dic₅₇	—	3	4	no	—
22	C₃²×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₉	C₅×C₃⋊D₃	1	6	yes	—
24	C₅×C₃⋊Dic₃	—	19	6	no	—
25	C₃²×C₁₉	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅²	D₅₇	1	4	yes	—
27	C₂×C₃×C₁₉	C₅²×D₃	1	4	yes	—
28	C₄×C₅²	—	171	1	no	Hall
29	C₅×C₁₉	C₅×C₃⋊Dic₃	1	6	yes	complemented
30	C₂×C₃²×C₅	C₅×D₁₉	1	6	yes	—
31	Dic₁₉	—	9	1	no	Hall
32	C₃×C₅²	Dic₅₇	1	4	yes	complemented
33	C₅×Dic₃	—	57	24	no	—
34	C₃×C₁₉	C₅²×Dic₃	1	4	yes	complemented
35	C₂×C₅²	C₃⋊D₅₇	1	1	yes	characteristic
36	C₃²×C₅	C₅×Dic₁₉	1	6	yes	complemented
37	C₂×C₁₉	C₅²×C₃⋊D₃	1	1	yes	characteristic
38	C₃⋊Dic₃	—	19	1	no	Hall
39	C₂×C₃×C₅	C₅×D₅₇	1	24	yes	—
40	C₅²	C₃⋊Dic₅₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₄×C₅	—	171	6	no	—
42	C₁₉	C₅²×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃²	C₅²×D₁₉	1	1	yes	characteristic
44	C₃×C₅	C₅×Dic₅₇	1	24	yes	complemented
45	Dic₃	—	57	4	no	—
46	C₂×C₅	C₅×C₃⋊D₅₇	1	6	yes	—
47	C₃²	C₅²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₅²×D₅₇	1	4	yes	—
49	C₅	C₅×C₃⋊Dic₅₇	1	6	yes	direct product factor
50	C₄	—	171	1	no	Sylow
51	C₃	C₅²×Dic₅₇	1	4	yes	complemented
52	C₂	C₅²×C₃⋊D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅²	C₃⋊D₅₇
commutator, hypocenter	C₃²×C₁₉	C₄×C₅²
Frattini	C₂	C₅²×C₃⋊D₅₇
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₁₉	C₂
cosocle	C₂×C₃²×C₁₉	C₂×C₅²
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₉	C₄	semidirect
4. C₅×C₃⋊Dic₅₇	C₅	direct (N × H)
8. C₃×C₅²×C₁₉	Dic₃	semidirect
12. C₃²×C₅×C₁₉	C₄×C₅	semidirect
13. C₃⋊Dic₅₇	C₅²	direct (N × H)
15. C₅²×C₁₉	C₃⋊Dic₃	semidirect
20. C₃×C₅×C₁₉	C₅×Dic₃	semidirect
22. C₃²×C₅²	Dic₁₉	semidirect
25. C₃²×C₁₉	C₄×C₅²	semidirect
29. C₅×C₁₉	C₅×C₃⋊Dic₃	semidirect
32. C₃×C₅²	Dic₅₇	semidirect
34. C₃×C₁₉	C₅²×Dic₃	semidirect
36. C₃²×C₅	C₅×Dic₁₉	semidirect
40. C₅²	C₃⋊Dic₅₇	direct (N × H)
42. C₁₉	C₅²×C₃⋊Dic₃	semidirect
44. C₃×C₅	C₅×Dic₅₇	semidirect
47. C₃²	C₅²×Dic₁₉	semidirect
49. C₅	C₅×C₃⋊Dic₅₇	direct (N × H)
51. C₃	C₅²×Dic₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅²×C₁₉	2
C₅²×Dic₅₇	3
C₅×C₃⋊Dic₅₇	5
C₅²×C₃⋊Dic₃	19

Subgroups — C52×C3⋊Dic57 #30685690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₃⋊Dic₅₇ #30685690