Subgroups — #44476522

Order 30324.

84 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	#13097582	—	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)	—	38	1	no	—
14	C₂×C₁₉²	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₇×Dic₁₉	—	19	1	no	—
16	C₇×Dic₁₉	—	19	1	no	—
17	C₇×Dic₁₉	—	57	6	no	—
18	#87704	Dic₁₉	1	1	yes	characteristic, complemented
19	C₁₉×ΓL(1,𝔽₈)	—	38	1	no	—
20	C₁₉²	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₇×C₁₉	—	3	6	no	—
22	C₂×C₇×C₁₉	D₁₉⋊C₃	1	1	yes	characteristic
23	C₂×C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic
24	C₃×Dic₁₉	—	133	1	no	—
25	(C₁₉⋊C₃)⋊C₄	—	133	1	no	—
26	C₇×C₁₉	—	3	6	no	—
27	C₇×C₁₉	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
28	C₇×C₁₉	C₃×Dic₁₉	1	1	yes	characteristic, complemented
29	C₂×C₃×C₁₉	—	133	1	no	—
30	C₂×C₁₉⋊C₃	—	7	1	no	—
31	C₄×ΓL(1,𝔽₈)	—	361	1	no	Hall
32	Dic₁₉	—	19	1	no	—
33	Dic₁₉	—	19	1	no	—
34	Dic₁₉	—	57	6	no	—
35	C₃×C₁₉	—	133	1	no	—
36	C₁₉⋊C₃	—	7	1	no	—
37	C₂×ΓL(1,𝔽₈)	—	38	1	no	—
38	C₂×C₁₉	—	3	6	no	—
39	C₂×C₁₉	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic
40	C₂×C₁₉	#11716321	1	1	yes	characteristic
41	C₄×C₇	—	361	1	no	Hall
42	ΓL(1,𝔽₈)	—	38	1	no	Hall
43	C₁₉	—	3	6	no	—
44	C₁₉	ΓL(1,𝔽₈)×Dic₁₉	1	1	yes	characteristic, complemented
45	C₁₉	#13097582	1	1	yes	characteristic, complemented
46	C₂×C₇	(C₁₉⋊C₃)⋊D₁₉	1	1	yes	characteristic
47	C₃×C₄	—	2527	1	no	Hall
48	C₇	(C₁₉⋊C₃)⋊Dic₁₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	133	1	no	—
50	C₄	—	361	1	no	Sylow
51	C₃	—	133	1	no	Sylow
52	C₂	#29503130	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#29503130
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
18. #87704	Dic₁₉	semidirect
20. C₁₉²	C₄×ΓL(1,𝔽₈)	semidirect
27. C₇×C₁₉	(C₁₉⋊C₃)⋊C₄	semidirect
28. C₇×C₁₉	C₃×Dic₁₉	semidirect
44. C₁₉	ΓL(1,𝔽₈)×Dic₁₉	semidirect
45. C₁₉	#13097582	semidirect
48. 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
#13097582	19
ΓL(1,𝔽₈)×Dic₁₉	19