Subgroups — C₅²×#4296⋊C₄ #30685630

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#4296	C₂	1	1	yes	maximal, characteristic
2	C₅²×(C₁₉⋊C₃)⋊C₄	C₃	1	1	yes	maximal, characteristic
3	C₅²×#4296	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×#4296⋊C₄	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₅²×Dic₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×#4296	C₂×C₅	1	6	yes	—
8	C₅²×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
9	C₅×(C₁₉⋊C₃)⋊C₄	C₃×C₅	1	6	yes	—
10	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic
11	C₄×C₅²×C₉	—	19	1	no	maximal, Hall
12	C₅×#4296	C₄×C₅	1	6	yes	complemented
13	#4296⋊C₄	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₉⋊C₃	C₂×C₃×C₅	1	6	yes	—
15	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅²×C₉	—	19	1	no	—
17	C₅×Dic₁₉	C₅×C₉	1	6	yes	complemented
18	C₂×#4296	C₂×C₅²	1	1	yes	characteristic
19	C₃×C₄×C₅²	—	19	1	no	—
20	C₅×C₁₉⋊C₃	C₃×C₄×C₅	1	6	yes	—
21	(C₁₉⋊C₃)⋊C₄	C₃×C₅²	1	1	yes	characteristic
22	C₅²×C₉	—	19	1	no	Hall
23	C₂×C₅×C₁₉	C₂×C₅×C₉	1	6	yes	—
24	C₄×C₅×C₉	—	19	6	no	—
25	#4296	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅²	—	19	1	no	—
27	C₂×C₁₉⋊C₃	C₂×C₃×C₅²	1	1	yes	characteristic
28	C₄×C₅²	—	19	1	no	Hall
29	C₅×C₁₉	C₄×C₅×C₉	1	6	yes	complemented
30	C₂×C₅×C₉	—	19	6	no	—
31	Dic₁₉	C₅²×C₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₅²	—	19	1	no	—
33	C₃×C₄×C₅	—	19	6	no	—
34	C₁₉⋊C₃	C₃×C₄×C₅²	1	1	yes	characteristic
35	C₂×C₅²	AGL(1,𝔽₁₉)	1	1	yes	characteristic
36	C₅×C₉	—	19	6	no	—
37	C₂×C₁₉	C₂×C₅²×C₉	1	1	yes	characteristic
38	C₄×C₉	—	19	1	no	Hall
39	C₂×C₃×C₅	—	19	6	no	—
40	C₅²	#4296⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
41	C₄×C₅	—	19	6	no	—
42	C₁₉	C₄×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₉	—	19	1	no	—
44	C₃×C₅	—	19	6	no	—
45	C₃×C₄	—	19	1	no	—
46	C₂×C₅	C₅×AGL(1,𝔽₁₉)	1	6	yes	—
47	C₉	—	19	1	no	Sylow
48	C₂×C₃	—	19	1	no	—
49	C₅	C₅×#4296⋊C₄	1	6	yes	direct product factor
50	C₄	—	19	1	no	Sylow
51	C₃	—	19	1	no	—
52	C₂	C₅²×AGL(1,𝔽₁₉)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅²	AGL(1,𝔽₁₉)
commutator, hypocenter	C₁₉	C₄×C₅²×C₉
Frattini	C₂	C₅²×AGL(1,𝔽₁₉)
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical	C₂×C₅²×C₁₉⋊C₃	C₂×C₃
cosocle	C₂×C₁₉⋊C₃	C₂×C₃×C₅²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
3. C₅²×#4296	C₄	semidirect
4. C₅×#4296⋊C₄	C₅	direct (N × H)
6. C₅²×Dic₁₉	C₉	semidirect
12. C₅×#4296	C₄×C₅	semidirect
13. #4296⋊C₄	C₅²	direct (N × H)
15. C₅²×C₁₉	C₄×C₉	semidirect
17. C₅×Dic₁₉	C₅×C₉	semidirect
25. #4296	C₄×C₅²	semidirect
29. C₅×C₁₉	C₄×C₅×C₉	semidirect
31. Dic₁₉	C₅²×C₉	semidirect
40. C₅²	#4296⋊C₄	direct (N × H)
42. C₁₉	C₄×C₅²×C₉	semidirect
49. C₅	C₅×#4296⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×#4296	2
C₅²×(C₁₉⋊C₃)⋊C₄	3
C₅×#4296⋊C₄	5
C₄×C₅²×C₉	19

Subgroups — C52×#4296⋊C4 #30685630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×#4296⋊C₄ #30685630