Subgroups — C₁₉×#11725071⋊C₂ #45691592

Order 33516.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#11725071	C₂	1	2	yes	maximal, complemented
2	C₁₉×#11725078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×D₂₁⋊D₇	—	3	1	no	maximal
4	C₁₉×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₉×D₂₁	—	3	2	no	—
6	C₃×C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic
7	D₇²×C₁₉	—	9	1	no	Hall
8	C₃×C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic
9	C₁₉×D₇⋊C₉	—	14	1	no	—
10	C₁₉×C₇⋊D₇	D₉	1	1	yes	characteristic, complemented
11	C₇×D₇×C₁₉	—	9	2	no	—
12	#11725071⋊C₂	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	D₃×D₇×C₁₉	—	21	2	no	—
14	C₁₉×C₇⋊C₉	—	14	1	no	—
15	C₇²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	#11725078	C₂×C₁₉	1	1	yes	characteristic, complemented
17	#11725071	C₂×C₁₉	1	2	yes	complemented
18	C₁₉×D₂₁	—	3	2	no	—
19	D₃×C₇×C₁₉	—	21	2	no	—
20	C₃×D₇×C₁₉	—	14	1	no	—
21	C₃×D₇×C₁₉	—	21	2	no	—
22	C₂×D₉×C₁₉	—	49	1	no	maximal, Hall
23	D₂₁⋊D₇	—	3	1	no	—
24	C₂×D₇×C₁₉	—	63	2	no	—
25	#89205	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₃×C₇×C₁₉	—	2	1	no	—
27	C₃×C₇×C₁₉	—	3	2	no	—
28	C₂×C₉×C₁₉	—	49	1	no	—
29	D₉×C₁₉	—	49	2	no	—
30	C₇×D₂₁	—	3	2	no	—
31	C₃×C₇⋊D₇	D₃×C₁₉	1	1	yes	characteristic
32	C₂×C₇×C₁₉	—	63	2	no	—
33	D₇×C₁₉	—	9	2	no	—
34	D₇×C₁₉	—	14	1	no	—
35	D₇×C₁₉	—	21	2	no	—
36	C₂×D₃×C₁₉	—	147	1	no	—
37	D₇²	—	9	1	no	Hall
38	C₉×C₁₉	—	49	1	no	Hall
39	C₃×C₇²	C₂×D₃×C₁₉	1	1	yes	characteristic
40	C₇×C₁₉	—	2	1	no	—
41	C₇×C₁₉	—	3	2	no	—
42	D₇⋊C₉	—	14	1	no	—
43	C₂×C₃×C₁₉	—	49	1	no	—
44	D₃×C₁₉	—	21	2	no	—
45	C₇⋊D₇	D₉×C₁₉	1	1	yes	characteristic, complemented
46	C₇×D₇	—	9	2	no	—
47	D₃×D₇	—	21	2	no	—
48	C₂²×C₁₉	—	441	1	no	Hall
49	C₇⋊C₉	—	14	1	no	—
50	C₃×C₁₉	#64418⋊C₂	1	1	yes	characteristic
51	C₇²	C₂×D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
52	D₂₁	—	3	2	no	—
53	C₃×D₇	—	14	1	no	—
54	C₃×D₇	—	21	2	no	—
55	D₃×C₇	—	21	2	no	—
56	C₂×C₁₉	—	49	1	no	—
57	C₂×C₁₉	—	63	2	no	—
58	C₂×D₉	—	49	1	no	Hall
59	C₂×D₇	—	63	2	no	—
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	—	3	2	no	—
62	C₁₉	#11725071⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₉	—	49	1	no	—
64	D₉	—	49	2	no	—
65	C₂×C₇	—	63	2	no	—
66	D₇	—	9	2	no	—
67	D₇	—	14	1	no	—
68	D₇	—	21	2	no	—
69	C₂×D₃	—	147	1	no	—
70	C₉	—	49	1	no	Sylow
71	C₇	—	2	1	no	—
72	C₇	—	3	2	no	—
73	C₂×C₃	—	49	1	no	—
74	D₃	—	21	2	no	—
75	C₂²	—	441	1	no	Sylow
76	C₃	C₁₉×#64418⋊C₂	1	1	yes	characteristic
77	C₂	—	49	1	no	—
78	C₂	—	63	2	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11725071⋊C₂
commutator, cosocle, hypocenter	#89205	C₂²×C₁₉
Frattini	C₃	C₁₉×#64418⋊C₂
Fitting, socle	C₃×C₇²×C₁₉	C₂×D₃
LCS	G ▷ #89205
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×#11725071	C₂	semidirect
2. C₁₉×#11725078	C₂	semidirect
4. C₁₉×#89205	C₂²	semidirect
10. C₁₉×C₇⋊D₇	D₉	semidirect
12. #11725071⋊C₂	C₁₉	direct (N × H)
15. C₇²×C₁₉	C₂×D₉	semidirect
16. #11725078	C₂×C₁₉	semidirect
17. #11725071	C₂×C₁₉	semidirect
25. #89205	C₂²×C₁₉	semidirect
45. C₇⋊D₇	D₉×C₁₉	semidirect
51. C₇²	C₂×D₉×C₁₉	semidirect
62. C₁₉	#11725071⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#11725071	2
C₁₉×#11725078	2
C₁₉×D₂₁⋊D₇	3
#11725071⋊C₂	19
C₂×D₉×C₁₉	49

Subgroups — C19×#11725071⋊C2 #45691592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11725071⋊C₂ #45691592