Subgroups — Dic₁₉×#89205 #45691507

Order 33516.

96 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	C₃×C₇²×Dic₁₉	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₇⋊C₉×Dic₁₉	—	7	2	no	maximal
6	C₇²×Dic₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₁₉×C₇⋊C₉	—	7	2	no	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
10	C₄×#89205	—	19	1	no	maximal, Hall
11	C₃×C₇×Dic₁₉	—	3	2	no	—
12	C₃×C₇×Dic₁₉	ΓL(1,𝔽₈)	1	2	yes	—
13	C₁₉×C₇⋊C₉	—	7	2	no	—
14	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×#89205	D₁₉	1	1	yes	characteristic
16	C₂×C₃×C₇×C₁₉	—	3	2	no	—
17	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
18	C₉×Dic₁₉	—	49	1	no	Hall
19	C₃×C₄×C₇²	—	19	1	no	—
20	C₇×Dic₁₉	—	3	2	no	—
21	C₇×Dic₁₉	C₇⋊C₉	1	2	yes	complemented
22	#89205	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₇×C₁₉	—	3	2	no	—
24	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	2	yes	—
25	C₂×C₉×C₁₉	—	49	1	no	—
26	C₂×C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic
27	C₂×C₇×C₁₉	—	3	2	no	—
28	C₂×C₇×C₁₉	C₂×C₇⋊C₉	1	2	yes	—
29	C₄×C₇⋊C₉	—	133	2	no	—
30	C₃×Dic₁₉	#3862	1	1	yes	characteristic
31	C₄×C₇²	—	19	1	no	Hall
32	C₉×C₁₉	—	49	1	no	Hall
33	C₃×C₇²	C₃×Dic₁₉	1	1	yes	characteristic
34	C₇×C₁₉	—	3	2	no	—
35	C₇×C₁₉	C₄×C₇⋊C₉	1	2	yes	complemented
36	C₂×C₇⋊C₉	—	7	2	no	—
37	C₂×C₃×C₁₉	C₂×#3862	1	1	yes	characteristic
38	C₂×C₇²	C₉×D₁₉	1	1	yes	characteristic
39	C₃×C₄×C₇	—	19	2	no	—
40	C₃×C₄×C₇	—	57	2	no	—
41	Dic₁₉	#89205	1	1	yes	characteristic, direct product factor, Hall
42	C₇⋊C₉	—	7	2	no	—
43	C₃×C₁₉	C₄×#3862	1	1	yes	characteristic
44	C₇²	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₇	—	3	2	no	—
46	C₂×C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	2	yes	—
47	C₂×C₁₉	C₂×#89205	1	1	yes	characteristic
48	C₄×C₉	—	931	1	no	Hall
49	C₄×C₇	—	19	2	no	—
50	C₄×C₇	—	57	2	no	—
51	C₃×C₇	—	3	2	no	—
52	C₃×C₇	ΓL(1,𝔽₈)×Dic₁₉	1	2	yes	—
53	C₁₉	C₄×#89205	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₉	—	49	1	no	—
55	C₂×C₇	—	3	2	no	—
56	C₂×C₇	D₁₉×C₇⋊C₉	1	2	yes	—
57	C₃×C₄	—	19	1	no	—
58	C₉	—	49	1	no	Sylow
59	C₇	—	3	2	no	—
60	C₇	C₇⋊C₉×Dic₁₉	1	2	yes	complemented
61	C₂×C₃	D₁₉×#3862	1	1	yes	characteristic
62	C₄	—	19	1	no	Sylow
63	C₃	Dic₁₉×#3862	1	1	yes	characteristic
64	C₂	D₁₉×#89205	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₁₉×#3862
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×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
3. C₁₉×#89205	C₄	semidirect
6. C₇²×Dic₁₉	C₉	semidirect
14. C₇²×C₁₉	C₄×C₉	semidirect
21. C₇×Dic₁₉	C₇⋊C₉	semidirect
22. #89205	Dic₁₉	direct (N × H)
35. C₇×C₁₉	C₄×C₇⋊C₉	semidirect
41. Dic₁₉	#89205	direct (N × H)
44. C₇²	C₉×Dic₁₉	semidirect
53. C₁₉	C₄×#89205	semidirect
60. C₇	C₇⋊C₉×Dic₁₉	semidirect

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
C₃×C₇²×Dic₁₉	3
C₇⋊C₉×Dic₁₉	7
C₄×#89205	19

Subgroups — Dic19×#89205 #45691507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₉×#89205 #45691507