Subgroups — C₂×C₃×D₁₉⋊(C₅²⋊C₃) #30685837

Order 17100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₉⋊(C₅²⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉⋊(C₅²⋊C₃)	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₁₉⋊(C₅²⋊C₃)	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×D₁₉	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₉⋊(C₅²⋊C₃)	C₂×C₃	1	3	yes	complemented
8	D₁₉⋊(C₅²⋊C₃)	C₂×C₃	1	6	yes	direct product factor
9	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₅²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₁₉⋊(C₅²⋊C₃)	C₂²×C₃	1	3	yes	complemented
13	C₂×C₃×C₅×D₁₉	—	3	2	no	—
14	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₅²×D₁₉	C₂×C₃²	1	2	yes	complemented
16	C₂²×C₃×C₅²⋊C₃	—	19	1	no	maximal, Hall
17	C₂×C₃×D₁₉⋊C₃	—	25	1	no	maximal, Hall
18	C₂×C₃×C₅×C₁₉	—	3	2	no	—
19	C₃×C₅×D₁₉	—	3	4	no	—
20	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅²⋊C₃	—	19	2	no	—
22	C₂×C₃×C₅²⋊C₃	—	19	1	no	—
23	C₂×C₅×D₁₉	—	3	2	no	—
24	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
25	C₃×D₁₉⋊C₃	—	25	2	no	—
26	C₂²×C₃×C₅²	—	57	1	no	—
27	C₂²×C₅²⋊C₃	—	19	3	no	—
28	C₃×C₅×C₁₉	—	3	2	no	—
29	C₂×C₃×D₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented
30	C₂×D₁₉⋊C₃	—	25	3	no	—
31	C₃×C₅²⋊C₃	—	19	1	no	Hall
32	C₂×C₅×C₁₉	—	3	2	no	—
33	C₅×D₁₉	—	3	4	no	—
34	C₃×C₁₉⋊C₃	—	25	1	no	Hall
35	C₂×C₃×C₅²	—	57	2	no	—
36	C₂×C₃×C₅²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
37	C₂×C₅²⋊C₃	—	19	6	no	—
38	C₂×C₅²⋊C₃	—	19	3	no	—
39	C₂×C₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
40	C₃×D₁₉	C₂×C₅²⋊C₃	1	2	yes	complemented
41	C₂×C₁₉⋊C₃	—	25	3	no	—
42	D₁₉⋊C₃	—	25	6	no	—
43	C₂²×C₅²	—	57	1	no	Hall
44	C₅×C₁₉	—	3	2	no	—
45	C₂×D₁₉	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₅²⋊C₃	—	19	3	no	—
48	C₂²×C₃×C₅	—	57	2	no	—
49	C₃×C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented
50	C₁₉⋊C₃	—	25	3	no	—
51	C₂×C₅²	—	57	2	no	—
52	C₂×C₅²	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
53	C₂×C₁₉	C₂×C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented
54	D₁₉	C₂×C₃×C₅²⋊C₃	1	2	yes	complemented
55	C₂²×C₃²	—	475	1	no	Hall
56	C₂×C₃×C₅	—	3	2	no	—
57	C₂×C₃×C₅	—	57	4	no	—
58	C₅²	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₅	—	57	2	no	—
60	C₁₉	C₂²×C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃²	—	475	2	no	—
62	C₂×C₃²	—	475	1	no	—
63	C₃×C₅	—	3	2	no	—
64	C₂²×C₃	—	57	1	no	—
65	C₂²×C₃	—	475	3	no	—
66	C₂×C₅	—	3	2	no	—
67	C₂×C₅	—	57	4	no	—
68	C₃²	—	475	1	no	Sylow
69	C₂×C₃	—	57	2	no	—
70	C₂×C₃	—	475	6	no	—
71	C₂×C₃	—	475	3	no	—
72	C₂×C₃	D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
73	C₅	—	3	2	no	—
74	C₂²	—	57	1	no	Sylow
75	C₃	—	475	3	no	—
76	C₃	C₂×D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
77	C₂	—	57	2	no	—
78	C₂	C₃×D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₉⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉⋊(C₅²⋊C₃)	C₂	semidirect
2. C₃×D₁₉⋊(C₅²⋊C₃)	C₂	direct (N × H)
3. C₂×C₃×C₅²×D₁₉	C₃	semidirect
4. C₂×D₁₉⋊(C₅²⋊C₃)	C₃	direct (N × H)
5. C₃×C₁₉⋊(C₅²⋊C₃)	C₂²	semidirect
6. C₃×C₅²×D₁₉	C₂×C₃	semidirect
7. C₂×C₁₉⋊(C₅²⋊C₃)	C₂×C₃	semidirect
8. D₁₉⋊(C₅²⋊C₃)	C₂×C₃	direct (N × H)
9. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
10. C₂×C₅²×D₁₉	C₃²	semidirect
11. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
12. C₁₉⋊(C₅²⋊C₃)	C₂²×C₃	semidirect
14. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
15. C₅²×D₁₉	C₂×C₃²	semidirect
20. C₅²×C₁₉	C₂²×C₃²	semidirect
29. C₂×C₃×D₁₉	C₅²⋊C₃	semidirect
36. C₂×C₃×C₅²	D₁₉⋊C₃	semidirect
39. C₂×C₃×C₁₉	C₂×C₅²⋊C₃	semidirect
40. C₃×D₁₉	C₂×C₅²⋊C₃	semidirect
45. C₂×D₁₉	C₃×C₅²⋊C₃	semidirect
46. C₃×C₅²	C₂×D₁₉⋊C₃	semidirect
49. C₃×C₁₉	C₂²×C₅²⋊C₃	semidirect
52. C₂×C₅²	C₃×D₁₉⋊C₃	semidirect
53. C₂×C₁₉	C₂×C₃×C₅²⋊C₃	semidirect
54. D₁₉	C₂×C₃×C₅²⋊C₃	semidirect
58. C₅²	C₂×C₃×D₁₉⋊C₃	semidirect
60. C₁₉	C₂²×C₃×C₅²⋊C₃	semidirect
72. C₂×C₃	D₁₉⋊(C₅²⋊C₃)	direct (N × H)
76. C₃	C₂×D₁₉⋊(C₅²⋊C₃)	direct (N × H)
78. C₂	C₃×D₁₉⋊(C₅²⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉⋊(C₅²⋊C₃)	2
C₃×D₁₉⋊(C₅²⋊C₃)	2
C₂×C₃×C₅²×D₁₉	3
C₂×D₁₉⋊(C₅²⋊C₃)	3
C₂²×C₃×C₅²⋊C₃	19
C₂×C₃×D₁₉⋊C₃	25

Subgroups — C2×C3×D19⋊(C52⋊C3) #30685837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₉⋊(C₅²⋊C₃) #30685837