Subgroups — C₂×C₁₉×#11725078 #45691624

Order 33516.

160 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, complemented
2	C₁₉×#11725078	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
4	C₁₉×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₁₉×D₇⋊C₉	—	7	2	no	maximal
8	C₂×C₁₉×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₁₉×C₇⋊C₉	—	7	2	no	—
11	C₁₉×D₇⋊C₉	—	7	4	no	—
12	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₉×C₇⋊D₇	C₂×C₉	1	2	yes	complemented
14	C₂×#11725078	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×D₇×C₁₉	—	7	2	no	—
16	C₂×C₃×D₇×C₁₉	—	21	2	no	—
17	C₁₉×C₇⋊C₉	—	7	2	no	—
18	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×#89205	C₂×C₁₉	1	1	yes	characteristic, complemented
20	#11725078	C₂×C₁₉	1	2	yes	direct product factor
21	C₂×C₃×C₇×C₁₉	—	3	2	no	—
22	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	—
23	C₃×D₇×C₁₉	—	7	4	no	—
24	C₃×D₇×C₁₉	—	21	4	no	—
25	C₂²×C₉×C₁₉	—	49	1	no	Hall
26	C₂×C₃×C₇⋊D₇	C₃×C₁₉	1	1	yes	characteristic
27	C₂×D₇×C₁₉	—	7	2	no	—
28	C₂×D₇×C₁₉	—	21	2	no	—
29	#89205	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×C₇×C₁₉	—	3	2	no	—
31	C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	2	yes	—
32	C₂×C₉×C₁₉	—	49	2	no	—
33	C₂×C₉×C₁₉	—	49	1	no	—
34	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
35	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	2	yes	—
36	C₂×C₇×C₁₉	—	3	2	no	—
37	C₂×C₇×C₁₉	D₇⋊C₉	1	2	yes	complemented
38	D₇×C₁₉	—	7	4	no	—
39	D₇×C₁₉	—	21	4	no	—
40	C₂×D₇⋊C₉	—	7	2	no	—
41	C₂²×C₃×C₁₉	—	49	1	no	—
42	C₂×C₇⋊D₇	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₉×C₁₉	—	49	1	no	Hall
44	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic
45	C₇×C₁₉	—	3	2	no	—
46	C₇×C₁₉	C₂×D₇⋊C₉	1	2	yes	complemented
47	C₂×C₇⋊C₉	—	7	2	no	—
48	D₇⋊C₉	—	7	4	no	—
49	C₂×C₃×C₁₉	—	49	2	no	—
50	C₂×C₃×C₁₉	#64425	1	1	yes	characteristic
51	C₂×C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
52	C₇⋊D₇	C₂×C₉×C₁₉	1	2	yes	complemented
53	C₂×C₃×D₇	—	7	2	no	—
54	C₂×C₃×D₇	—	21	2	no	—
55	C₂²×C₁₉	—	49	1	no	Hall
56	C₇⋊C₉	—	7	2	no	—
57	C₃×C₁₉	C₂×#64425	1	1	yes	characteristic
58	C₇²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	3	2	no	—
60	C₂×C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	2	yes	—
61	C₃×D₇	—	7	4	no	—
62	C₃×D₇	—	21	4	no	—
63	C₂×C₁₉	—	49	2	no	—
64	C₂×C₁₉	#11725078	1	1	yes	characteristic, direct product factor
65	C₂²×C₉	—	49	1	no	Hall
66	C₂×D₇	—	7	2	no	—
67	C₂×D₇	—	21	2	no	—
68	C₃×C₇	—	3	2	no	—
69	C₃×C₇	C₂×C₁₉×AGL(1,𝔽₇)	1	2	yes	—
70	C₁₉	C₂×#11725078	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₉	—	49	2	no	—
72	C₂×C₉	—	49	1	no	—
73	C₂×C₇	—	3	2	no	—
74	C₂×C₇	C₁₉×D₇⋊C₉	1	2	yes	complemented
75	D₇	—	7	4	no	—
76	D₇	—	21	4	no	—
77	C₂²×C₃	—	49	1	no	—
78	C₉	—	49	1	no	Sylow
79	C₇	—	3	2	no	—
80	C₇	C₂×C₁₉×D₇⋊C₉	1	2	yes	complemented
81	C₂×C₃	—	49	2	no	—
82	C₂×C₃	C₁₉×#64425	1	1	yes	characteristic
83	C₂²	—	49	1	no	Sylow
84	C₃	C₂×C₁₉×#64425	1	1	yes	characteristic
85	C₂	—	49	2	no	—
86	C₂	C₁₉×#11725078	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	#64425
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×#64425
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂²×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
1. C₂×C₁₉×#89205	C₂	semidirect
2. C₁₉×#11725078	C₂	direct (N × H)
4. C₁₉×#89205	C₂²	semidirect
8. C₂×C₁₉×C₇⋊D₇	C₉	semidirect
12. C₂×C₇²×C₁₉	C₂×C₉	semidirect
13. C₁₉×C₇⋊D₇	C₂×C₉	semidirect
14. C₂×#11725078	C₁₉	direct (N × H)
18. C₇²×C₁₉	C₂²×C₉	semidirect
19. C₂×#89205	C₂×C₁₉	semidirect
20. #11725078	C₂×C₁₉	direct (N × H)
29. #89205	C₂²×C₁₉	semidirect
37. C₂×C₇×C₁₉	D₇⋊C₉	semidirect
42. C₂×C₇⋊D₇	C₉×C₁₉	semidirect
46. C₇×C₁₉	C₂×D₇⋊C₉	semidirect
51. C₂×C₇²	C₂×C₉×C₁₉	semidirect
52. C₇⋊D₇	C₂×C₉×C₁₉	semidirect
58. C₇²	C₂²×C₉×C₁₉	semidirect
64. C₂×C₁₉	#11725078	direct (N × H)
70. C₁₉	C₂×#11725078	direct (N × H)
74. C₂×C₇	C₁₉×D₇⋊C₉	semidirect
80. C₇	C₂×C₁₉×D₇⋊C₉	semidirect
86. C₂	C₁₉×#11725078	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
C₁₉×#11725078	2
C₂×C₃×C₁₉×C₇⋊D₇	3
C₂×C₁₉×D₇⋊C₉	7
C₂×#11725078	19

Subgroups — C2×C19×#11725078 #45691624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#11725078 #45691624