Subgroups — Dic₁₉×#87704 #44476524

Order 30324.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#87704	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₉×Dic₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×#87704	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₁₉⋊C₃×Dic₁₉	—	7	1	no	maximal, Hall
6	C₇×C₁₉²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₉×C₁₉⋊C₃	—	7	1	no	—
8	C₄×#87704	—	19	1	no	maximal
9	ΓL(1,𝔽₈)×Dic₁₉	—	19	1	no	maximal
10	C₁₉×Dic₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₁₉×C₁₉⋊C₃	—	7	1	no	Hall
12	C₂×#87704	D₁₉	1	1	yes	characteristic
13	C₂×C₁₉×ΓL(1,𝔽₈)	—	19	1	no	—
14	C₂×C₁₉²	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₄×C₇×C₁₉	—	19	1	no	—
16	C₇×Dic₁₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
17	#87704	Dic₁₉	1	1	yes	characteristic, direct product factor
18	C₁₉×ΓL(1,𝔽₈)	—	19	1	no	—
19	C₁₉²	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₇×C₁₉	—	6	3	no	—
21	C₂×C₇×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic
22	C₂×C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic
23	C₃×Dic₁₉	—	133	1	no	—
24	C₄×C₁₉⋊C₃	—	133	1	no	—
25	C₇×C₁₉	—	6	3	no	—
26	C₇×C₁₉	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	C₇×C₁₉	C₃×Dic₁₉	1	1	yes	characteristic, complemented
28	C₂×C₃×C₁₉	—	133	1	no	—
29	C₂×C₁₉⋊C₃	—	7	1	no	—
30	C₄×ΓL(1,𝔽₈)	—	361	1	no	Hall
31	C₄×C₁₉	—	19	1	no	—
32	Dic₁₉	#87704	1	1	yes	characteristic, direct product factor
33	C₃×C₁₉	—	133	1	no	—
34	C₁₉⋊C₃	—	7	1	no	—
35	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
36	C₂×C₁₉	—	6	3	no	—
37	C₂×C₁₉	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic
38	C₂×C₁₉	C₂×#87704	1	1	yes	characteristic
39	C₄×C₇	—	19	1	no	Hall
40	ΓL(1,𝔽₈)	—	19	1	no	Hall
41	C₁₉	—	6	3	no	—
42	C₁₉	ΓL(1,𝔽₈)×Dic₁₉	1	1	yes	characteristic, complemented
43	C₁₉	C₄×#87704	1	1	yes	characteristic, complemented
44	C₂×C₇	D₁₉×C₁₉⋊C₃	1	1	yes	characteristic
45	C₃×C₄	—	2527	1	no	Hall
46	C₇	C₁₉⋊C₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	133	1	no	—
48	C₄	—	19	1	no	Sylow
49	C₃	—	133	1	no	Sylow
50	C₂	D₁₉×#87704	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₉×#87704
commutator, hypocenter	C₇×C₁₉²	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₉²	C₂×C₃
prime radical	C₂×C₁₉×#87704	C₂
LCS	G ▷ C₇×C₁₉²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₉×Dic₁₉	C₃	semidirect
3. C₁₉×#87704	C₄	semidirect
6. C₇×C₁₉²	C₃×C₄	semidirect
10. C₁₉×Dic₁₉	ΓL(1,𝔽₈)	semidirect
16. C₇×Dic₁₉	C₁₉⋊C₃	semidirect
17. #87704	Dic₁₉	direct (N × H)
19. C₁₉²	C₄×ΓL(1,𝔽₈)	semidirect
26. C₇×C₁₉	C₄×C₁₉⋊C₃	semidirect
27. C₇×C₁₉	C₃×Dic₁₉	semidirect
32. Dic₁₉	#87704	direct (N × H)
42. C₁₉	ΓL(1,𝔽₈)×Dic₁₉	semidirect
43. C₁₉	C₄×#87704	semidirect
46. C₇	C₁₉⋊C₃×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×#87704	2
C₇×C₁₉×Dic₁₉	3
C₁₉⋊C₃×Dic₁₉	7
C₄×#87704	19
ΓL(1,𝔽₈)×Dic₁₉	19

Subgroups — Dic19×#87704 #44476524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₉×#87704 #44476524