Subgroups — C₁₉×#13183527 #45691516

Order 33516.

72 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	C₇×C₁₉×Dic₂₁	—	3	1	no	maximal
3	C₁₉×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
5	C₇×C₁₉×Dic₇	—	9	1	no	Hall
6	C₃×C₇²×C₁₉	Dic₃	1	1	yes	characteristic
7	C₂×C₁₉×C₇⋊C₉	—	14	1	no	—
8	C₂×C₇²×C₁₉	D₉	1	1	yes	characteristic
9	#13183527	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×Dic₂₁	—	3	1	no	—
11	C₇×Dic₃×C₁₉	—	21	1	no	—
12	C₁₉×C₇⋊C₉	—	14	1	no	—
13	C₇²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
14	C₂×#89205	C₂×C₁₉	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₉	—	2	1	no	—
16	C₂×C₃×C₇×C₁₉	—	3	1	no	—
17	C₂×C₃×C₇×C₁₉	—	3	1	no	—
18	C₁₉×Dic₉	—	49	1	no	maximal, Hall
19	C₇×Dic₂₁	—	3	1	no	—
20	C₄×C₇×C₁₉	—	63	1	no	—
21	C₁₉×Dic₇	—	9	1	no	—
22	#89205	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₇×C₁₉	—	2	1	no	—
24	C₃×C₇×C₁₉	—	3	1	no	—
25	C₃×C₇×C₁₉	—	3	1	no	—
26	C₂×C₉×C₁₉	—	49	1	no	—
27	C₂×C₃×C₇²	D₃×C₁₉	1	1	yes	characteristic
28	C₂×C₇×C₁₉	—	2	1	no	—
29	C₂×C₇×C₁₉	—	3	1	no	—
30	C₂×C₇×C₁₉	—	3	1	no	—
31	Dic₃×C₁₉	—	21	1	no	—
32	C₇×Dic₇	—	9	1	no	Hall
33	C₉×C₁₉	—	49	1	no	Hall
34	C₃×C₇²	Dic₃×C₁₉	1	1	yes	characteristic
35	C₇×C₁₉	—	2	1	no	—
36	C₇×C₁₉	—	3	1	no	—
37	C₇×C₁₉	—	3	1	no	—
38	C₂×C₇⋊C₉	—	14	1	no	—
39	C₂×C₃×C₁₉	#64418	1	1	yes	characteristic
40	C₂×C₇²	D₉×C₁₉	1	1	yes	characteristic
41	Dic₂₁	—	3	1	no	—
42	C₇×Dic₃	—	21	1	no	—
43	C₄×C₁₉	—	63	1	no	Hall
44	C₇⋊C₉	—	14	1	no	—
45	C₃×C₁₉	#10596868	1	1	yes	characteristic
46	C₇²	C₁₉×Dic₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃×C₇	—	2	1	no	—
48	C₂×C₃×C₇	—	3	1	no	—
49	C₂×C₃×C₇	—	3	1	no	—
50	C₂×C₁₉	#11725071	1	1	yes	characteristic
51	Dic₉	—	49	1	no	Hall
52	C₄×C₇	—	63	1	no	—
53	Dic₇	—	9	1	no	—
54	C₃×C₇	—	2	1	no	—
55	C₃×C₇	—	3	1	no	—
56	C₃×C₇	—	3	1	no	—
57	C₁₉	#13183527	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₉	—	49	1	no	—
59	C₂×C₇	—	2	1	no	—
60	C₂×C₇	—	3	1	no	—
61	C₂×C₇	—	3	1	no	—
62	Dic₃	—	21	1	no	—
63	C₉	—	49	1	no	Sylow
64	C₇	—	2	1	no	—
65	C₇	—	3	1	no	—
66	C₇	—	3	1	no	—
67	C₂×C₃	C₁₉×#64418	1	1	yes	characteristic
68	C₄	—	63	1	no	Sylow
69	C₃	C₁₉×#10596868	1	1	yes	characteristic
70	C₂	C₁₉×#11725071	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉	#11725071
commutator, hypocenter	#89205	C₄×C₁₉
Frattini	C₂×C₃	C₁₉×#64418
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	D₃
cosocle	C₂×#89205	C₂×C₁₉
LCS	G ▷ #89205
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₁₉×#89205	C₄	semidirect
9. #13183527	C₁₉	direct (N × H)
13. C₇²×C₁₉	Dic₉	semidirect
22. #89205	C₄×C₁₉	semidirect
46. C₇²	C₁₉×Dic₉	semidirect
57. C₁₉	#13183527	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×C₁₉×#89205	2
C₇×C₁₉×Dic₂₁	3
#13183527	19
C₁₉×Dic₉	49

Subgroups — C19×#13183527 #45691516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13183527 #45691516