Subgroups — C₃×C₁₉×Dic₁₃₃ #44476554

Order 30324.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₉²	C₂	1	1	yes	maximal, characteristic
2	C₁₉×Dic₁₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₉²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₉×Dic₁₉	—	7	1	no	maximal, Hall
6	C₇×C₁₉²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₉²	D₇	1	1	yes	characteristic
8	C₃×Dic₁₃₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor
9	C₃×C₁₉×Dic₇	—	19	1	no	maximal
10	C₁₉×Dic₁₉	—	7	1	no	Hall
11	C₃×C₁₉²	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₉	—	2	9	no	—
13	C₂×C₃×C₇×C₁₉	D₁₉	1	1	yes	characteristic
14	C₂×C₃×C₇×C₁₉	C₂×C₁₉	1	1	yes	characteristic
15	C₂×C₁₉²	C₃×D₇	1	1	yes	characteristic
16	Dic₁₃₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor
17	C₁₉×Dic₇	—	19	1	no	—
18	C₃×C₇×C₁₉	—	2	9	no	—
19	C₃×C₇×C₁₉	Dic₁₉	1	1	yes	characteristic, complemented
20	C₃×C₇×C₁₉	C₄×C₁₉	1	1	yes	characteristic, complemented
21	C₁₉²	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₇×C₁₉	—	2	9	no	—
23	C₂×C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic
24	C₂×C₇×C₁₉	C₂×C₃×C₁₉	1	1	yes	characteristic
25	C₃×C₄×C₁₉	—	133	1	no	—
26	C₃×Dic₁₉	—	7	1	no	—
27	C₇×C₁₉	—	2	9	no	—
28	C₇×C₁₉	C₃×Dic₁₉	1	1	yes	characteristic, complemented
29	C₇×C₁₉	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
30	C₂×C₃×C₁₉	—	2	9	no	—
31	C₂×C₃×C₁₉	D₇×C₁₉	1	1	yes	characteristic
32	C₂×C₃×C₁₉	D₁₃₃	1	1	yes	characteristic
33	C₃×Dic₇	—	19	1	no	Hall
34	C₄×C₁₉	—	133	1	no	—
35	Dic₁₉	—	7	1	no	—
36	C₃×C₁₉	—	2	9	no	—
37	C₃×C₁₉	C₁₉×Dic₇	1	1	yes	characteristic, complemented
38	C₃×C₁₉	Dic₁₃₃	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₇	C₁₉×D₁₉	1	1	yes	characteristic
40	C₂×C₁₉	—	2	9	no	—
41	C₂×C₁₉	C₃×D₇×C₁₉	1	1	yes	characteristic
42	C₂×C₁₉	C₃×D₁₃₃	1	1	yes	characteristic
43	Dic₇	—	19	1	no	Hall
44	C₃×C₇	C₁₉×Dic₁₉	1	1	yes	characteristic, complemented, Hall
45	C₁₉	—	2	9	no	—
46	C₁₉	C₃×C₁₉×Dic₇	1	1	yes	characteristic, complemented
47	C₁₉	C₃×Dic₁₃₃	1	1	yes	characteristic, direct product factor
48	C₂×C₇	C₃×C₁₉×D₁₉	1	1	yes	characteristic
49	C₃×C₄	—	133	1	no	Hall
50	C₇	C₃×C₁₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	C₁₉×D₁₃₃	1	1	yes	characteristic
52	C₄	—	133	1	no	Sylow
53	C₃	C₁₉×Dic₁₃₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×C₁₉×D₁₃₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₃₃
commutator, hypocenter	C₇×C₁₉	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₁₃₃
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₉²	C₂
cosocle	C₂×C₇×C₁₉	C₂×C₃×C₁₉
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×Dic₁₃₃	C₃	direct (N × H)
3. C₃×C₇×C₁₉²	C₄	semidirect
6. C₇×C₁₉²	C₃×C₄	semidirect
8. C₃×Dic₁₃₃	C₁₉	direct (N × H)
11. C₃×C₁₉²	Dic₇	semidirect
16. Dic₁₃₃	C₃×C₁₉	direct (N × H)
19. C₃×C₇×C₁₉	Dic₁₉	semidirect
20. C₃×C₇×C₁₉	C₄×C₁₉	semidirect
21. C₁₉²	C₃×Dic₇	semidirect
28. C₇×C₁₉	C₃×Dic₁₉	semidirect
29. C₇×C₁₉	C₃×C₄×C₁₉	semidirect
37. C₃×C₁₉	C₁₉×Dic₇	semidirect
38. C₃×C₁₉	Dic₁₃₃	direct (N × H)
44. C₃×C₇	C₁₉×Dic₁₉	semidirect
46. C₁₉	C₃×C₁₉×Dic₇	semidirect
47. C₁₉	C₃×Dic₁₃₃	direct (N × H)
50. C₇	C₃×C₁₉×Dic₁₉	semidirect
53. C₃	C₁₉×Dic₁₃₃	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×C₇×C₁₉²	2
C₁₉×Dic₁₃₃	3
C₃×C₁₉×Dic₁₉	7
C₃×Dic₁₃₃	19
C₃×C₁₉×Dic₇	19

Subgroups — C3×C19×Dic133 #44476554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×Dic₁₃₃ #44476554