Subgroups — C₁₉×C₃⋊(#5997⋊C₃) #45692271

Order 33516.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#64424	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#5997	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#5997⋊C₃	—	3	1	no	maximal
4	C₃×C₁₉×#3861	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₁₉×#64424	—	2	1	no	—
7	C₁₉×#64424	D₃	1	1	yes	characteristic
8	C₁₉×#5997	—	3	1	no	Hall
9	C₁₉×#3861	—	2	1	no	—
10	C₁₉×#3861	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×C₁₉×AGL(1,𝔽₇)	—	14	4	no	—
13	C₁₉×C₇⋊D₇	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(#5997⋊C₃)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₁₉×ΓL(1,𝔽₈)	—	14	4	no	—
16	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃×#64424	C₂×C₁₉	1	1	yes	characteristic
18	C₃×D₇×C₁₉	—	14	4	no	—
19	C₁₉×AGL(1,𝔽₇)	—	14	4	no	—
20	C₁₉×AGL(1,𝔽₇)	—	14	8	no	—
21	C₃×Dic₃×C₁₉	—	49	1	no	maximal, Hall
22	C₃⋊#5997	C₃×C₁₉	1	1	yes	characteristic, complemented
23	#5997⋊C₃	—	3	1	no	—
24	C₃×#3861	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇×C₁₉	—	2	4	no	—
26	C₁₉×ΓL(1,𝔽₈)	—	14	4	no	—
27	C₁₉×ΓL(1,𝔽₈)	—	14	8	no	—
28	C₂×C₃²×C₁₉	—	49	1	no	—
29	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	1	yes	characteristic
30	#64424	—	2	1	no	—
31	#64424	D₃×C₁₉	1	1	yes	characteristic
32	D₇×C₁₉	—	14	4	no	—
33	C₃×C₄×C₁₉	—	147	1	no	—
34	Dic₃×C₁₉	—	49	1	no	—
35	#5997	—	3	1	no	Hall
36	C₃²×C₁₉	—	49	1	no	Hall
37	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
38	#3861	—	2	1	no	—
39	#3861	Dic₃×C₁₉	1	1	yes	characteristic, complemented
40	C₇×C₁₉	—	2	4	no	—
41	C₃×AGL(1,𝔽₇)	—	14	4	no	—
42	C₂×C₃×C₁₉	—	49	1	no	—
43	C₂×C₃×C₁₉	—	49	1	no	—
44	C₂×C₃×C₁₉	—	98	1	no	—
45	C₇⋊D₇	C₃×D₃×C₁₉	1	1	yes	characteristic
46	C₄×C₁₉	—	147	1	no	Hall
47	C₃×ΓL(1,𝔽₈)	—	14	4	no	—
48	C₃×C₁₉	—	49	1	no	—
49	C₃×C₁₉	—	98	1	no	—
50	C₃×C₁₉	#5997⋊C₃	1	1	yes	characteristic, complemented
51	C₇²	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
52	C₃×D₇	—	14	4	no	—
53	AGL(1,𝔽₇)	—	14	4	no	—
54	AGL(1,𝔽₇)	—	14	8	no	—
55	C₂×C₁₉	—	49	1	no	—
56	C₃×Dic₃	—	49	1	no	Hall
57	C₃×C₇	—	2	4	no	—
58	ΓL(1,𝔽₈)	—	14	4	no	—
59	ΓL(1,𝔽₈)	—	14	8	no	—
60	C₁₉	C₃⋊(#5997⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₃²	—	49	1	no	—
62	D₇	—	14	4	no	—
63	C₃×C₄	—	147	1	no	—
64	Dic₃	—	49	1	no	—
65	C₃²	—	49	1	no	Sylow
66	C₇	—	2	4	no	—
67	C₂×C₃	—	49	1	no	—
68	C₂×C₃	—	49	1	no	—
69	C₂×C₃	—	98	1	no	—
70	C₄	—	147	1	no	Sylow
71	C₃	—	49	1	no	—
72	C₃	—	98	1	no	—
73	C₃	C₁₉×#5997⋊C₃	1	1	yes	characteristic, complemented
74	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊(#5997⋊C₃)
commutator, hypocenter	C₃×C₇²	C₃×C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₃×C₄
prime radical	C₃×C₁₉×#64424	C₂
cosocle	C₃×C₇⋊D₇	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×C₃⋊#5997	C₃	semidirect
4. C₃×C₁₉×#3861	C₄	semidirect
10. C₁₉×#3861	Dic₃	semidirect
11. C₃×C₇²×C₁₉	C₃×C₄	semidirect
14. C₃⋊(#5997⋊C₃)	C₁₉	direct (N × H)
16. C₇²×C₁₉	C₃×Dic₃	semidirect
22. C₃⋊#5997	C₃×C₁₉	semidirect
24. C₃×#3861	C₄×C₁₉	semidirect
37. C₃×C₇²	C₃×C₄×C₁₉	semidirect
39. #3861	Dic₃×C₁₉	semidirect
50. C₃×C₁₉	#5997⋊C₃	semidirect
51. C₇²	C₃×Dic₃×C₁₉	semidirect
60. C₁₉	C₃⋊(#5997⋊C₃)	direct (N × H)
73. C₃	C₁₉×#5997⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#64424	2
C₁₉×C₃⋊#5997	3
C₁₉×#5997⋊C₃	3
C₃⋊(#5997⋊C₃)	19
C₃×Dic₃×C₁₉	49

Subgroups — C19×C3⋊(#5997⋊C3) #45692271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊(#5997⋊C₃) #45692271