Subgroups — C₂²×C₁₉×#89205 #45691699

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	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#89205	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	3	yes	—
5	C₂²×C₁₉×C₇⋊C₉	—	7	2	no	maximal
6	C₂²×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₁₉×C₇⋊C₉	—	7	6	no	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	3	yes	complemented
10	C₂²×#89205	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₇×C₁₉	—	3	2	no	—
12	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	2	yes	—
13	C₁₉×C₇⋊C₉	—	7	2	no	—
14	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×#89205	C₂×C₁₉	1	3	yes	direct product factor
16	C₂×C₃×C₇×C₁₉	—	3	6	no	—
17	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	6	yes	—
18	C₂²×C₉×C₁₉	—	49	1	no	Hall
19	C₂²×C₃×C₇²	C₃×C₁₉	1	1	yes	characteristic
20	C₂²×C₇×C₁₉	—	3	2	no	—
21	C₂²×C₇×C₁₉	C₇⋊C₉	1	2	yes	complemented
22	#89205	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇×C₁₉	—	3	2	no	—
24	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	2	yes	—
25	C₂×C₉×C₁₉	—	49	3	no	—
26	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	3	yes	—
27	C₂×C₇×C₁₉	—	3	6	no	—
28	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	6	yes	complemented
29	C₂²×C₇⋊C₉	—	7	2	no	—
30	C₂²×C₃×C₁₉	#3862	1	1	yes	characteristic
31	C₂²×C₇²	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₉×C₁₉	—	49	1	no	Hall
33	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic
34	C₇×C₁₉	—	3	2	no	—
35	C₇×C₁₉	C₂²×C₇⋊C₉	1	2	yes	complemented
36	C₂×C₇⋊C₉	—	7	6	no	—
37	C₂×C₃×C₁₉	C₂×#3862	1	3	yes	—
38	C₂×C₇²	C₂×C₉×C₁₉	1	3	yes	complemented
39	C₂²×C₃×C₇	—	3	2	no	—
40	C₂²×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	2	yes	—
41	C₂²×C₁₉	#89205	1	1	yes	characteristic, direct product factor, Hall
42	C₇⋊C₉	—	7	2	no	—
43	C₃×C₁₉	C₂²×#3862	1	1	yes	characteristic
44	C₇²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₇	—	3	6	no	—
46	C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	6	yes	—
47	C₂×C₁₉	C₂×#89205	1	3	yes	direct product factor
48	C₂²×C₉	—	49	1	no	Hall
49	C₂²×C₇	—	3	2	no	—
50	C₂²×C₇	C₁₉×C₇⋊C₉	1	2	yes	complemented
51	C₃×C₇	—	3	2	no	—
52	C₃×C₇	C₂²×C₁₉×ΓL(1,𝔽₈)	1	2	yes	—
53	C₁₉	C₂²×#89205	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₉	—	49	3	no	—
55	C₂×C₇	—	3	6	no	—
56	C₂×C₇	C₂×C₁₉×C₇⋊C₉	1	6	yes	complemented
57	C₂²×C₃	C₁₉×#3862	1	1	yes	characteristic
58	C₉	—	49	1	no	Sylow
59	C₇	—	3	2	no	—
60	C₇	C₂²×C₁₉×C₇⋊C₉	1	2	yes	complemented
61	C₂×C₃	C₂×C₁₉×#3862	1	3	yes	—
62	C₂²	C₁₉×#89205	1	1	yes	characteristic, direct product factor, Sylow
63	C₃	C₂²×C₁₉×#3862	1	1	yes	characteristic
64	C₂	C₂×C₁₉×#89205	1	3	yes	direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#89205	C₂	direct (N × H)
3. C₁₉×#89205	C₂²	direct (N × H)
6. C₂²×C₇²×C₁₉	C₉	semidirect
9. C₂×C₇²×C₁₉	C₂×C₉	semidirect
10. C₂²×#89205	C₁₉	direct (N × H)
14. C₇²×C₁₉	C₂²×C₉	semidirect
15. C₂×#89205	C₂×C₁₉	direct (N × H)
21. C₂²×C₇×C₁₉	C₇⋊C₉	semidirect
22. #89205	C₂²×C₁₉	direct (N × H)
28. C₂×C₇×C₁₉	C₂×C₇⋊C₉	semidirect
31. C₂²×C₇²	C₉×C₁₉	semidirect
35. C₇×C₁₉	C₂²×C₇⋊C₉	semidirect
38. C₂×C₇²	C₂×C₉×C₁₉	semidirect
41. C₂²×C₁₉	#89205	direct (N × H)
44. C₇²	C₂²×C₉×C₁₉	semidirect
47. C₂×C₁₉	C₂×#89205	direct (N × H)
50. C₂²×C₇	C₁₉×C₇⋊C₉	semidirect
53. C₁₉	C₂²×#89205	direct (N × H)
56. C₂×C₇	C₂×C₁₉×C₇⋊C₉	semidirect
60. C₇	C₂²×C₁₉×C₇⋊C₉	semidirect
62. C₂²	C₁₉×#89205	direct (N × H)
64. C₂	C₂×C₁₉×#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
C₂²×C₃×C₇²×C₁₉	3
C₂²×C₁₉×C₇⋊C₉	7
C₂²×#89205	19

Subgroups — C22×C19×#89205 #45691699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#89205 #45691699