Subgroups — Dic₃×C₁₉⋊(C₅²⋊C₃) #30685673

Order 17100.

80 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
2	C₅²×Dic₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉⋊(C₅²⋊C₃)	—	3	1	no	maximal
4	C₃×C₁₉⋊(C₅²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉⋊(C₅²⋊C₃)	—	2	1	no	—
6	C₂×C₁₉⋊(C₅²⋊C₃)	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₄×C₅²×C₁₉	—	3	1	no	Hall
9	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₉⋊(C₅²⋊C₃)	—	2	1	no	—
11	C₁₉⋊(C₅²⋊C₃)	Dic₃	1	1	yes	characteristic, direct product factor
12	C₅×Dic₃×C₁₉	—	3	2	no	—
13	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic
14	Dic₃×C₅²⋊C₃	—	19	1	no	maximal, Hall
15	Dic₃×C₁₉⋊C₃	—	25	1	no	maximal, Hall
16	C₂×C₃×C₅×C₁₉	—	3	2	no	—
17	C₅²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅²⋊C₃	—	19	1	no	—
19	C₄×C₅×C₁₉	—	9	2	no	—
20	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
21	C₅²×Dic₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
22	C₄×C₅²⋊C₃	—	57	1	no	—
23	C₃×C₅×C₁₉	—	3	2	no	—
24	Dic₃×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented
25	C₄×C₁₉⋊C₃	—	75	1	no	—
26	C₃×C₅²⋊C₃	—	19	1	no	Hall
27	C₂×C₅×C₁₉	—	3	2	no	—
28	C₃×C₁₉⋊C₃	—	25	1	no	Hall
29	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
30	C₂×C₅²⋊C₃	—	19	1	no	—
31	C₂×C₅²⋊C₃	—	38	1	no	—
32	C₂×C₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic
33	C₂×C₁₉⋊C₃	—	25	1	no	—
34	C₂×C₁₉⋊C₃	—	50	1	no	—
35	C₄×C₅²	—	3	1	no	Hall
36	C₅×C₁₉	—	3	2	no	—
37	C₄×C₁₉	—	3	1	no	Hall
38	C₃×C₅²	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
39	C₅²⋊C₃	—	19	1	no	—
40	C₅²⋊C₃	—	38	1	no	—
41	C₅×Dic₃	—	3	2	no	—
42	C₃×C₁₉	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	25	1	no	—
44	C₁₉⋊C₃	—	50	1	no	—
45	C₂×C₅²	D₃×C₁₉⋊C₃	1	1	yes	characteristic
46	C₂×C₁₉	D₃×C₅²⋊C₃	1	1	yes	characteristic
47	C₃×Dic₃	—	475	1	no	Hall
48	C₂×C₃×C₅	—	3	2	no	—
49	C₅²	Dic₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₄×C₅	—	9	2	no	—
51	C₁₉	Dic₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃²	—	475	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	1425	1	no	—
55	Dic₃	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
56	C₂×C₅	—	3	2	no	—
57	C₃²	—	475	1	no	Sylow
58	C₂×C₃	—	950	1	no	—
59	C₂×C₃	—	475	1	no	—
60	C₂×C₃	C₂×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic
61	C₅	—	3	2	no	—
62	C₄	—	3	1	no	Sylow
63	C₃	—	950	1	no	—
64	C₃	—	475	1	no	—
65	C₃	C₄×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, complemented
66	C₂	D₃×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₁₉⋊(C₅²⋊C₃)
commutator, hypocenter	C₃×C₅²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉⋊(C₅²⋊C₃)	C₂
LCS	G ▷ C₃×C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₅²×Dic₃×C₁₉	C₃	semidirect
4. C₃×C₁₉⋊(C₅²⋊C₃)	C₄	semidirect
9. C₃×C₅²×C₁₉	C₃×C₄	semidirect
11. C₁₉⋊(C₅²⋊C₃)	Dic₃	direct (N × H)
17. C₅²×C₁₉	C₃×Dic₃	semidirect
21. C₅²×Dic₃	C₁₉⋊C₃	semidirect
24. Dic₃×C₁₉	C₅²⋊C₃	semidirect
38. C₃×C₅²	C₄×C₁₉⋊C₃	semidirect
42. C₃×C₁₉	C₄×C₅²⋊C₃	semidirect
49. C₅²	Dic₃×C₁₉⋊C₃	semidirect
51. C₁₉	Dic₃×C₅²⋊C₃	semidirect
55. Dic₃	C₁₉⋊(C₅²⋊C₃)	direct (N × H)
65. C₃	C₄×C₁₉⋊(C₅²⋊C₃)	semidirect

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
C₅²×Dic₃×C₁₉	3
C₄×C₁₉⋊(C₅²⋊C₃)	3
Dic₃×C₅²⋊C₃	19
Dic₃×C₁₉⋊C₃	25

Subgroups — Dic3×C19⋊(C52⋊C3) #30685673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₁₉⋊(C₅²⋊C₃) #30685673