Subgroups — #1042×#4294 #30685542

Order 17100.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#1042	C₃	1	1	yes	maximal, characteristic
3	C₅²×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×#4294	—	5	1	no	maximal
5	Dic₅×#4294	—	5	1	no	maximal
6	C₃×C₅×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₁₉×#1042	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×#4294	—	5	1	no	—
9	D₅×#4294	D₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic
11	C₃×C₁₉×AGL(1,𝔽₅)	—	5	1	no	—
12	C₃×C₁₉×Dic₅	—	5	1	no	—
13	C₅×D₅×C₁₉	C₂×C₉	1	1	yes	characteristic
14	C₉×#1042	—	19	1	no	maximal, Hall
15	C₅×#4294	—	4	1	no	—
16	C₅×#4294	Dic₅	1	1	yes	characteristic, complemented
17	C₅×#4294	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₄×#4294	—	25	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	5	1	no	—
20	C₃×D₅×C₁₉	C₃×D₅	1	1	yes	characteristic
21	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
22	C₅×C₉×D₅	—	19	1	no	—
23	C₁₉×AGL(1,𝔽₅)	—	5	1	no	—
24	C₁₉×Dic₅	—	5	1	no	—
25	C₂×#4294	—	5	1	no	—
26	C₃×#1042	C₁₉⋊C₃	1	1	yes	characteristic
27	C₃×C₅×C₁₉	—	4	1	no	—
28	C₃×C₅×C₁₉	C₃×Dic₅	1	1	yes	characteristic
29	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₃×C₄×C₁₉	—	25	1	no	—
31	C₅²×C₉	—	19	1	no	Hall
32	C₂×C₅×C₁₉	—	5	1	no	—
33	D₅×C₁₉	C₉×D₅	1	1	yes	characteristic
34	C₉×AGL(1,𝔽₅)	—	95	1	no	—
35	C₉×Dic₅	—	95	1	no	—
36	#4294	#1042	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅×D₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
38	C₂×C₃×C₁₉	—	5	1	no	—
39	#1042	#4294	1	1	yes	characteristic, direct product factor, Hall
40	C₅×C₁₉	—	4	1	no	—
41	C₅×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
43	C₂×C₅×C₉	—	95	1	no	—
44	C₉×D₅	—	19	1	no	—
45	C₄×C₁₉	—	25	1	no	Hall
46	C₃×C₅²	C₄×C₁₉⋊C₃	1	1	yes	characteristic
47	C₃×AGL(1,𝔽₅)	—	5	1	no	—
48	C₃×Dic₅	—	5	1	no	—
49	C₃×C₁₉	C₃×#1042	1	1	yes	characteristic
50	C₅×D₅	C₂×#4294	1	1	yes	characteristic
51	C₅×C₉	—	19	1	no	—
52	C₅×C₉	—	19	1	no	—
53	C₅×C₉	—	76	1	no	—
54	C₂×C₁₉	—	5	1	no	—
55	C₄×C₉	—	475	1	no	Hall
56	C₂×C₃×C₅	—	5	1	no	—
57	C₃×D₅	D₅×C₁₉⋊C₃	1	1	yes	characteristic
58	C₅²	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
59	AGL(1,𝔽₅)	—	5	1	no	—
60	Dic₅	—	5	1	no	—
61	C₁₉	C₉×#1042	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₉	—	95	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	Dic₅×C₁₉⋊C₃	1	1	yes	characteristic
65	C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	1	1	yes	characteristic
66	C₃×C₄	—	25	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	D₅×#4294	1	1	yes	characteristic
69	C₉	—	19	1	no	Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	Dic₅×#4294	1	1	yes	characteristic, complemented
73	C₅	AGL(1,𝔽₅)×#4294	1	1	yes	characteristic, complemented
74	C₄	—	25	1	no	Sylow
75	C₃	C₁₉⋊C₃×#1042	1	1	yes	characteristic
76	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₉⋊C₃×#1042
commutator, hypocenter	C₅²×C₁₉	C₄×C₉
Fitting, socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical, cosocle	C₃×C₅×D₅×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅²×#4294	C₄	semidirect
7. C₁₉×#1042	C₉	semidirect
16. C₅×#4294	Dic₅	semidirect
17. C₅×#4294	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	C₄×C₉	semidirect
36. #4294	#1042	direct (N × H)
39. #1042	#4294	direct (N × H)
41. C₅×C₁₉	C₉×Dic₅	semidirect
42. C₅×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
58. C₅²	C₄×#4294	semidirect
61. C₁₉	C₉×#1042	semidirect
72. C₅	Dic₅×#4294	semidirect
73. C₅	AGL(1,𝔽₅)×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×#4294	2
C₃×C₁₉×#1042	3
AGL(1,𝔽₅)×#4294	5
Dic₅×#4294	5
C₉×#1042	19