Subgroups — C₂×C₁₉×#89205 #30660621

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#89205	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₉×C₇⋊C₉	—	7	2	no	maximal
5	C₂×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₇⋊C₉	—	7	2	no	—
7	C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×#89205	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₁₉	—	3	2	no	—
10	C₂×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	2	yes	—
11	#89205	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇×C₁₉	—	3	2	no	—
13	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
14	C₂×C₉×C₁₉	—	49	1	no	Hall
15	C₂×C₃×C₇²	C₃×C₁₉	1	1	yes	characteristic
16	C₂×C₇×C₁₉	—	3	2	no	—
17	C₂×C₇×C₁₉	C₇⋊C₉	1	2	yes	complemented
18	C₉×C₁₉	—	49	1	no	Hall
19	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
20	C₇×C₁₉	—	3	2	no	—
21	C₇×C₁₉	C₂×C₇⋊C₉	1	2	yes	complemented
22	C₂×C₇⋊C₉	—	7	2	no	—
23	C₂×C₃×C₁₉	#3862	1	1	yes	characteristic
24	C₂×C₇²	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₇⋊C₉	—	7	2	no	—
26	C₃×C₁₉	C₂×#3862	1	1	yes	characteristic
27	C₇²	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃×C₇	—	3	2	no	—
29	C₂×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	2	yes	—
30	C₂×C₁₉	#89205	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₇	—	3	2	no	—
32	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	2	yes	—
33	C₁₉	C₂×#89205	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₉	—	49	1	no	Hall
35	C₂×C₇	—	3	2	no	—
36	C₂×C₇	C₁₉×C₇⋊C₉	1	2	yes	complemented
37	C₉	—	49	1	no	Sylow
38	C₇	—	3	2	no	—
39	C₇	C₂×C₁₉×C₇⋊C₉	1	2	yes	complemented
40	C₂×C₃	C₁₉×#3862	1	1	yes	characteristic
41	C₃	C₂×C₁₉×#3862	1	1	yes	characteristic
42	C₂	C₁₉×#89205	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	#3862
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×#3862
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	C₃
cosocle	C₃×C₇²	C₂×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. C₁₉×#89205	C₂	direct (N × H)
5. C₂×C₇²×C₁₉	C₉	semidirect
7. C₇²×C₁₉	C₂×C₉	semidirect
8. C₂×#89205	C₁₉	direct (N × H)
11. #89205	C₂×C₁₉	direct (N × H)
17. C₂×C₇×C₁₉	C₇⋊C₉	semidirect
21. C₇×C₁₉	C₂×C₇⋊C₉	semidirect
24. C₂×C₇²	C₉×C₁₉	semidirect
27. C₇²	C₂×C₉×C₁₉	semidirect
30. C₂×C₁₉	#89205	direct (N × H)
33. C₁₉	C₂×#89205	direct (N × H)
36. C₂×C₇	C₁₉×C₇⋊C₉	semidirect
39. C₇	C₂×C₁₉×C₇⋊C₉	semidirect
42. 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
C₁₉×#89205	2
C₂×C₃×C₇²×C₁₉	3
C₂×C₁₉×C₇⋊C₉	7
C₂×#89205	19

Subgroups — C2×C19×#89205 #30660621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#89205 #30660621