Subgroups — C₁₉×#13183534 #45691481

Order 33516.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#89205	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×Dic₇⋊C₉	—	7	2	no	maximal
6	C₁₉×C₇⋊Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₁₉×C₇⋊C₉	—	7	2	no	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
10	#13183534	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₉×Dic₇	—	7	2	no	—
12	C₃×C₁₉×Dic₇	—	21	2	no	—
13	C₁₉×C₇⋊C₉	—	7	2	no	—
14	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×#89205	C₂×C₁₉	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₉	—	3	2	no	—
17	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	—
18	C₄×C₉×C₁₉	—	49	1	no	Hall
19	C₃×C₇⋊Dic₇	C₃×C₁₉	1	1	yes	characteristic
20	C₁₉×Dic₇	—	7	2	no	—
21	C₁₉×Dic₇	—	21	2	no	—
22	#89205	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	—	3	2	no	—
24	C₃×C₇×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
25	C₂×C₉×C₁₉	—	49	1	no	—
26	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
27	C₂×C₇×C₁₉	—	3	2	no	—
28	C₂×C₇×C₁₉	D₇⋊C₉	1	2	yes	—
29	Dic₇⋊C₉	—	7	2	no	—
30	C₃×C₄×C₁₉	—	49	1	no	—
31	C₇⋊Dic₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₉×C₁₉	—	49	1	no	Hall
33	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic
34	C₇×C₁₉	—	3	2	no	—
35	C₇×C₁₉	Dic₇⋊C₉	1	2	yes	complemented
36	C₂×C₇⋊C₉	—	7	2	no	—
37	C₂×C₃×C₁₉	#64425	1	1	yes	characteristic
38	C₂×C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic
39	C₃×Dic₇	—	7	2	no	—
40	C₃×Dic₇	—	21	2	no	—
41	C₄×C₁₉	—	49	1	no	Hall
42	C₇⋊C₉	—	7	2	no	—
43	C₃×C₁₉	#10596875	1	1	yes	characteristic
44	C₇²	C₄×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₇	—	3	2	no	—
46	C₂×C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	2	yes	—
47	C₂×C₁₉	#11725078	1	1	yes	characteristic
48	C₄×C₉	—	49	1	no	Hall
49	Dic₇	—	7	2	no	—
50	Dic₇	—	21	2	no	—
51	C₃×C₇	—	3	2	no	—
52	C₃×C₇	C₁₉×ΓL(1,𝔽₈)⋊C₄	1	2	yes	—
53	C₁₉	#13183534	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₉	—	49	1	no	—
55	C₂×C₇	—	3	2	no	—
56	C₂×C₇	C₁₉×D₇⋊C₉	1	2	yes	—
57	C₃×C₄	—	49	1	no	—
58	C₉	—	49	1	no	Sylow
59	C₇	—	3	2	no	—
60	C₇	C₁₉×Dic₇⋊C₉	1	2	yes	complemented
61	C₂×C₃	C₁₉×#64425	1	1	yes	characteristic
62	C₄	—	49	1	no	Sylow
63	C₃	C₁₉×#10596875	1	1	yes	characteristic
64	C₂	C₁₉×#11725078	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	#64425
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₂×C₃	C₁₉×#64425
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₁₉×#89205	C₄	semidirect
6. C₁₉×C₇⋊Dic₇	C₉	semidirect
10. #13183534	C₁₉	direct (N × H)
14. C₇²×C₁₉	C₄×C₉	semidirect
22. #89205	C₄×C₁₉	semidirect
31. C₇⋊Dic₇	C₉×C₁₉	semidirect
35. C₇×C₁₉	Dic₇⋊C₉	semidirect
44. C₇²	C₄×C₉×C₁₉	semidirect
53. C₁₉	#13183534	direct (N × H)
60. C₇	C₁₉×Dic₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#89205	2
C₃×C₁₉×C₇⋊Dic₇	3
C₁₉×Dic₇⋊C₉	7
#13183534	19

Subgroups — C19×#13183534 #45691481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13183534 #45691481