Subgroups — C₄×C₅₃×#4296 #49136246

Order 36252.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#4296	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₅₃×#4296	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₉×C₅₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅₃×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
7	C₂×C₁₉×C₅₃	C₂×C₉	1	1	yes	characteristic
8	C₄×C₉×C₅₃	—	19	1	no	maximal, Hall
9	C₁₉×C₅₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₉×C₅₃	—	19	1	no	—
11	C₄×#4296	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₄×C₅₃	—	19	1	no	—
13	C₉×C₅₃	—	19	1	no	Hall
14	C₂×#4296	C₂×C₅₃	1	1	yes	characteristic
15	C₂×C₃×C₅₃	—	19	1	no	—
16	C₄×C₁₉⋊C₃	C₃×C₅₃	1	1	yes	characteristic
17	C₄×C₅₃	#4296	1	1	yes	characteristic, direct product factor, Hall
18	#4296	C₄×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅₃	—	19	1	no	—
20	C₂×C₁₉⋊C₃	C₂×C₃×C₅₃	1	1	yes	characteristic
21	C₂×C₅₃	C₂×#4296	1	1	yes	characteristic
22	C₄×C₁₉	C₉×C₅₃	1	1	yes	characteristic, complemented, Hall
23	C₁₉⋊C₃	C₃×C₄×C₅₃	1	1	yes	characteristic
24	C₅₃	C₄×#4296	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	C₂×C₉×C₅₃	1	1	yes	characteristic
26	C₄×C₉	—	19	1	no	Hall
27	C₁₉	C₄×C₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	19	1	no	—
29	C₃×C₄	—	19	1	no	—
30	C₉	—	19	1	no	Sylow
31	C₂×C₃	—	19	1	no	—
32	C₄	C₅₃×#4296	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	19	1	no	—
34	C₂	C₂×C₅₃×#4296	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅₃	#4296
commutator, hypocenter	C₁₉	C₄×C₉×C₅₃
Frattini	C₂	C₂×C₅₃×#4296
Fitting	C₄×C₁₉×C₅₃	C₉
socle	C₂×C₁₉×C₅₃	C₂×C₉
prime radical	C₂×C₅₃×C₁₉⋊C₃	C₂×C₃
cosocle	C₂×C₁₉⋊C₃	C₂×C₃×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₅₃

Complements

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

N	H ≅ G/N	type
3. C₅₃×#4296	C₄	direct (N × H)
5. C₄×C₁₉×C₅₃	C₉	semidirect
9. C₁₉×C₅₃	C₄×C₉	semidirect
11. C₄×#4296	C₅₃	direct (N × H)
17. C₄×C₅₃	#4296	direct (N × H)
18. #4296	C₄×C₅₃	direct (N × H)
22. C₄×C₁₉	C₉×C₅₃	semidirect
24. C₅₃	C₄×#4296	direct (N × H)
27. C₁₉	C₄×C₉×C₅₃	semidirect
32. C₄	C₅₃×#4296	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×C₅₃×#4296	2
C₄×C₅₃×C₁₉⋊C₃	3
C₄×C₉×C₅₃	19
C₄×#4296	53

Subgroups — C4×C53×#4296 #49136246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅₃×#4296 #49136246