Subgroups — C₂×D₁₉×#89205 #45691650

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	D₁₉×#89205	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic
4	C₁₉×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×D₁₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₉×C₇⋊C₉	—	7	2	no	maximal
8	C₂×C₇²×D₁₉	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	D₁₉×C₇⋊C₉	—	7	4	no	—
12	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇²×D₁₉	C₂×C₉	1	2	yes	complemented
14	C₂²×#89205	—	19	1	no	maximal, Hall
15	C₂×C₃×C₇×D₁₉	—	3	2	no	—
16	C₂×C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	2	yes	—
17	C₁₉×C₇⋊C₉	—	7	2	no	—
18	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×#89205	—	19	2	no	—
20	C₂×#89205	D₁₉	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₇×C₁₉	—	3	2	no	—
22	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
23	C₃×C₇×D₁₉	—	3	4	no	—
24	C₃×C₇×D₁₉	C₂×ΓL(1,𝔽₈)	1	4	yes	—
25	C₂×C₉×D₁₉	—	49	1	no	Hall
26	C₂²×C₃×C₇²	—	19	1	no	—
27	C₂×C₇×D₁₉	—	3	2	no	—
28	C₂×C₇×D₁₉	C₇⋊C₉	1	2	yes	complemented
29	#89205	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₇×C₁₉	—	3	2	no	—
31	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	2	yes	—
32	C₂×C₉×C₁₉	—	49	1	no	—
33	C₉×D₁₉	—	49	2	no	—
34	C₂×C₃×C₇²	—	19	2	no	—
35	C₂×C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic
36	C₂×C₇×C₁₉	—	3	2	no	—
37	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	2	yes	complemented
38	C₇×D₁₉	—	3	4	no	—
39	C₇×D₁₉	C₂×C₇⋊C₉	1	4	yes	complemented
40	C₂²×C₇⋊C₉	—	133	2	no	—
41	C₂×C₃×D₁₉	#3862	1	1	yes	characteristic
42	C₂²×C₇²	—	19	1	no	Hall
43	C₉×C₁₉	—	49	1	no	Hall
44	C₃×C₇²	C₂×C₃×D₁₉	1	1	yes	characteristic
45	C₇×C₁₉	—	3	2	no	—
46	C₇×C₁₉	C₂²×C₇⋊C₉	1	2	yes	complemented
47	C₂×C₇⋊C₉	—	7	2	no	—
48	C₂×C₇⋊C₉	—	133	4	no	—
49	C₂×C₃×C₁₉	C₂×#3862	1	1	yes	characteristic
50	C₃×D₁₉	C₂×#3862	1	2	yes	—
51	C₂×C₇²	—	19	2	no	—
52	C₂×C₇²	C₉×D₁₉	1	1	yes	characteristic, complemented
53	C₂²×C₃×C₇	—	19	2	no	—
54	C₂²×C₃×C₇	—	57	2	no	—
55	C₂×D₁₉	#89205	1	1	yes	characteristic, direct product factor, Hall
56	C₇⋊C₉	—	7	2	no	—
57	C₃×C₁₉	C₂²×#3862	1	1	yes	characteristic
58	C₇²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	—	3	2	no	—
60	C₂×C₃×C₇	—	19	4	no	—
61	C₂×C₃×C₇	—	57	4	no	—
62	C₂×C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	2	yes	—
63	C₂×C₁₉	C₂×#89205	1	1	yes	characteristic, complemented
64	D₁₉	C₂×#89205	1	2	yes	direct product factor
65	C₂²×C₉	—	931	1	no	Hall
66	C₂²×C₇	—	19	2	no	—
67	C₂²×C₇	—	57	2	no	—
68	C₃×C₇	—	3	2	no	—
69	C₃×C₇	C₂×ΓL(1,𝔽₈)×D₁₉	1	2	yes	—
70	C₁₉	C₂²×#89205	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₉	—	49	1	no	—
72	C₂×C₉	—	931	2	no	—
73	C₂×C₇	—	3	2	no	—
74	C₂×C₇	—	19	4	no	—
75	C₂×C₇	—	57	4	no	—
76	C₂×C₇	D₁₉×C₇⋊C₉	1	2	yes	complemented
77	C₂²×C₃	—	19	1	no	—
78	C₉	—	49	1	no	Sylow
79	C₇	—	3	2	no	—
80	C₇	C₂×D₁₉×C₇⋊C₉	1	2	yes	complemented
81	C₂×C₃	—	19	2	no	—
82	C₂×C₃	D₁₉×#3862	1	1	yes	characteristic
83	C₂²	—	19	1	no	Sylow
84	C₃	C₂×D₁₉×#3862	1	1	yes	characteristic
85	C₂	—	19	2	no	—
86	C₂	D₁₉×#89205	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₉×#3862
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×D₁₉×#3862
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇²×D₁₉	C₃
cosocle	C₃×C₇²×C₁₉	C₂²×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#89205	C₂	semidirect
2. D₁₉×#89205	C₂	direct (N × H)
4. C₁₉×#89205	C₂²	semidirect
8. C₂×C₇²×D₁₉	C₉	semidirect
12. C₂×C₇²×C₁₉	C₂×C₉	semidirect
13. C₇²×D₁₉	C₂×C₉	semidirect
18. C₇²×C₁₉	C₂²×C₉	semidirect
20. C₂×#89205	D₁₉	direct (N × H)
28. C₂×C₇×D₁₉	C₇⋊C₉	semidirect
29. #89205	C₂×D₁₉	direct (N × H)
37. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
39. C₇×D₁₉	C₂×C₇⋊C₉	semidirect
46. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
52. C₂×C₇²	C₉×D₁₉	semidirect
55. C₂×D₁₉	#89205	direct (N × H)
58. C₇²	C₂×C₉×D₁₉	semidirect
63. C₂×C₁₉	C₂×#89205	semidirect
64. D₁₉	C₂×#89205	direct (N × H)
70. C₁₉	C₂²×#89205	semidirect
76. C₂×C₇	D₁₉×C₇⋊C₉	semidirect
80. C₇	C₂×D₁₉×C₇⋊C₉	semidirect
86. C₂	D₁₉×#89205	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
D₁₉×#89205	2
C₂×C₃×C₇²×D₁₉	3
C₂×D₁₉×C₇⋊C₉	7
C₂²×#89205	19

Subgroups — C2×D19×#89205 #45691650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₉×#89205 #45691650