Subgroups — #47977643

Order 35340.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#13183714	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₁₉⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#13183714	C₄	1	1	yes	characteristic, complemented, Hall
4	#20296616	—	5	1	no	maximal, Hall
5	D₅×C₁₉×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×#13183714	—	5	1	no	—
7	C₅×C₁₉×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃₁×Dic₁₉	—	5	1	no	Hall
9	AGL(1,𝔽₅)×C₃₁⋊C₃	—	19	1	no	maximal, Hall
10	#13183714	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₉×C₃₁	—	5	1	no	—
12	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	—	31	1	no	maximal, Hall
13	D₅×C₃₁⋊C₃	—	19	1	no	—
14	AGL(1,𝔽₅)×C₃₁	—	19	1	no	Hall
15	C₁₉×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
16	D₅×C₁₉⋊C₃	—	31	1	no	—
17	C₅×C₃₁⋊C₃	—	19	1	no	Hall
18	C₁₉⋊AGL(1,𝔽₅)	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₄×C₃₁⋊C₃	—	95	1	no	Hall
20	D₅×C₃₁	D₁₉⋊C₃	1	1	yes	characteristic
21	C₅×C₁₉⋊C₃	—	31	1	no	Hall
22	(C₁₉⋊C₃)⋊C₄	—	155	1	no	Hall
23	D₅×C₁₉	C₂×C₃₁⋊C₃	1	1	yes	characteristic
24	C₂×C₃₁⋊C₃	—	95	1	no	—
25	C₅×C₃₁	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
26	C₄×C₃₁	—	95	1	no	Hall
27	C₂×C₁₉⋊C₃	—	155	1	no	—
28	C₅×C₁₉	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃₁⋊C₃	—	19	1	no	Hall
30	Dic₁₉	—	5	1	no	Hall
31	C₂×C₃₁	—	5	1	no	—
32	C₃×AGL(1,𝔽₅)	—	589	1	no	Hall
33	C₁₉⋊C₃	—	31	1	no	Hall
34	C₂×C₁₉	—	5	1	no	—
35	C₃₁	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
36	C₃×D₅	—	589	1	no	—
37	AGL(1,𝔽₅)	—	19	1	no	Hall
38	C₁₉	AGL(1,𝔽₅)×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	589	1	no	Hall
40	C₃×C₄	—	2945	1	no	Hall
41	D₅	#16812972	1	1	yes	characteristic
42	C₂×C₃	—	2945	1	no	—
43	C₅	#20296616	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	95	1	no	Sylow
45	C₃	—	589	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉×C₃₁	C₃×C₄
prime radical	D₅×#13183714	C₂
cosocle	D₅×C₁₉×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₁₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃₁×C₁₉⋊AGL(1,𝔽₅)	C₃	semidirect
3. C₅×#13183714	C₄	semidirect
7. C₅×C₁₉×C₃₁	C₃×C₄	semidirect
10. #13183714	AGL(1,𝔽₅)	semidirect
15. C₁₉×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
18. C₁₉⋊AGL(1,𝔽₅)	C₃₁⋊C₃	semidirect
25. C₅×C₃₁	(C₁₉⋊C₃)⋊C₄	semidirect
28. C₅×C₁₉	C₄×C₃₁⋊C₃	semidirect
35. C₃₁	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	semidirect
38. C₁₉	AGL(1,𝔽₅)×C₃₁⋊C₃	semidirect
43. C₅	#20296616	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₅×#13183714	2
C₃₁×C₁₉⋊AGL(1,𝔽₅)	3
#20296616	5
AGL(1,𝔽₅)×C₃₁⋊C₃	19
(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	31