Subgroups — D₅₃×C₃⋊(D₁₉⋊C₃) #49136277

Order 36252.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅₃⋊(D₁₉⋊C₃))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×C₃⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉⋊C₃×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₃×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
5	D₅₃×D₁₉⋊C₃	—	3	1	no	maximal
6	C₃×C₅₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₅₃⋊(D₁₉⋊C₃)	—	3	1	no	—
8	C₅₃×D₁₉⋊C₃	—	3	1	no	—
9	C₁₉⋊C₃×D₅₃	—	2	1	no	—
10	C₁₉⋊C₃×D₅₃	D₃	1	1	yes	characteristic, complemented
11	D₃₀₂₁	C₂×C₃	1	1	yes	characteristic, complemented
12	C₅₃×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₁₉×D₅₃	C₂×C₃	1	1	yes	characteristic, complemented
14	D₁₉×D₅₃	—	3	1	no	Hall
15	C₃×C₁₉×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₅₃×C₁₉⋊C₃	—	2	1	no	—
17	C₅₃×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₁₀₀₇	—	3	1	no	—
19	C₁₉×D₅₃	C₃×D₃	1	1	yes	characteristic, complemented
20	D₁₉×C₅₃	—	3	1	no	—
21	C₃×D₃×D₅₃	—	19	1	no	maximal, Hall
22	C₁₉×C₅₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₃×D₁₅₉	—	19	1	no	—
24	C₃×D₃×C₅₃	—	19	1	no	—
25	C₃²×D₅₃	—	19	1	no	—
26	C₂×C₃⋊(D₁₉⋊C₃)	—	53	1	no	maximal, Hall
27	C₂×C₃×D₅₃	—	57	1	no	—
28	D₃×D₅₃	—	19	1	no	—
29	C₃²×C₅₃	—	19	1	no	Hall
30	C₂×C₃×C₁₉⋊C₃	—	53	1	no	—
31	C₃⋊(D₁₉⋊C₃)	—	53	1	no	—
32	C₃⋊(D₁₉⋊C₃)	D₅₃	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₅₃	—	57	1	no	—
34	D₁₅₉	—	19	1	no	—
35	C₃×D₅₃	—	19	1	no	—
36	C₃×D₅₃	—	38	1	no	—
37	C₃×D₅₃	—	57	1	no	—
38	C₃×D₅₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
39	D₃×C₅₃	—	19	1	no	—
40	C₂×D₅₇	—	53	1	no	—
41	C₂×D₁₉⋊C₃	—	159	1	no	—
42	C₂×D₅₃	—	57	1	no	Hall
43	C₃×C₁₉⋊C₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
44	C₃×C₅₃	—	19	1	no	—
45	C₃×C₅₃	—	38	1	no	—
46	C₃×C₅₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₂×C₃×C₁₉	—	53	1	no	—
48	D₅₇	—	53	1	no	—
49	D₅₇	C₃×D₅₃	1	1	yes	characteristic, complemented
50	C₂×C₁₉⋊C₃	—	53	1	no	—
51	C₂×C₁₉⋊C₃	—	106	1	no	—
52	D₁₉⋊C₃	—	3	1	no	—
53	D₁₉⋊C₃	—	159	1	no	—
54	C₂×C₅₃	—	57	1	no	—
55	D₅₃	—	57	1	no	—
56	D₅₃	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
57	C₂×D₁₉	—	159	1	no	Hall
58	C₃×C₁₉	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented
59	C₁₉⋊C₃	—	2	1	no	—
60	C₁₉⋊C₃	D₃×D₅₃	1	1	yes	characteristic, complemented
61	C₅₃	C₂×C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	53	1	no	—
63	D₁₉	—	3	1	no	—
64	D₁₉	—	159	1	no	—
65	C₂×C₃×D₃	—	1007	1	no	Hall
66	C₁₉	C₃×D₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	1007	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	1007	1	no	—
70	C₂²×C₃	—	3021	1	no	—
71	C₂×D₃	—	1007	1	no	—
72	C₃²	—	19	1	no	Sylow
73	C₂×C₃	—	53	1	no	—
74	C₂×C₃	—	57	1	no	—
75	C₂×C₃	—	3021	1	no	—
76	C₂×C₃	—	2014	1	no	—
77	C₂×C₃	—	1007	1	no	—
78	D₃	—	19	1	no	—
79	D₃	—	1007	1	no	—
80	C₂²	—	3021	1	no	Sylow
81	C₃	—	19	1	no	—
82	C₃	—	38	1	no	—
83	C₃	D₅₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	53	1	no	—
85	C₂	—	57	1	no	—
86	C₂	—	3021	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₅₃	C₂²×C₃
LCS	G ▷ C₃×C₁₉×C₅₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅₃⋊(D₁₉⋊C₃))	C₂	semidirect
2. C₅₃×C₃⋊(D₁₉⋊C₃)	C₂	semidirect
3. C₃×C₁₉⋊C₃×D₅₃	C₂	semidirect
4. D₅₃×D₅₇	C₃	semidirect
6. C₃×C₅₃×C₁₉⋊C₃	C₂²	semidirect
10. C₁₉⋊C₃×D₅₃	D₃	semidirect
11. D₃₀₂₁	C₂×C₃	semidirect
12. C₅₃×D₅₇	C₂×C₃	semidirect
13. C₃×C₁₉×D₅₃	C₂×C₃	semidirect
15. C₃×C₁₉×C₅₃	C₂²×C₃	semidirect
17. C₅₃×C₁₉⋊C₃	C₂×D₃	semidirect
19. C₁₉×D₅₃	C₃×D₃	semidirect
22. C₁₉×C₅₃	C₂×C₃×D₃	semidirect
32. C₃⋊(D₁₉⋊C₃)	D₅₃	direct (N × H)
38. C₃×D₅₃	D₁₉⋊C₃	semidirect
43. C₃×C₁₉⋊C₃	C₂×D₅₃	semidirect
46. C₃×C₅₃	C₂×D₁₉⋊C₃	semidirect
49. D₅₇	C₃×D₅₃	semidirect
56. D₅₃	C₃⋊(D₁₉⋊C₃)	direct (N × H)
58. C₃×C₁₉	C₂×C₃×D₅₃	semidirect
60. C₁₉⋊C₃	D₃×D₅₃	semidirect
61. C₅₃	C₂×C₃⋊(D₁₉⋊C₃)	semidirect
66. C₁₉	C₃×D₃×D₅₃	semidirect
83. C₃	D₅₃×D₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅₃⋊(D₁₉⋊C₃))	2
C₅₃×C₃⋊(D₁₉⋊C₃)	2
C₃×C₁₉⋊C₃×D₅₃	2
D₅₃×D₅₇	3
D₅₃×D₁₉⋊C₃	3
C₃×D₃×D₅₃	19
C₂×C₃⋊(D₁₉⋊C₃)	53

Subgroups — D53×C3⋊(D19⋊C3) #49136277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×C₃⋊(D₁₉⋊C₃) #49136277