Subgroups — C₄×#14555735 #22580113

Order 8892.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555735	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic
3	#14555735	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₃×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic
7	C₄×#4294	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic
9	C₄×C₁₃⋊C₉	—	19	1	no	maximal, Hall
10	C₂×#4294	—	13	1	no	—
11	C₁₃×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₃⋊C₉	—	19	1	no	—
13	C₃×C₄×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic
14	#4294	—	13	1	no	Hall
15	C₃×C₄×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic
16	C₁₃⋊C₉	—	19	1	no	Hall
17	C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
19	C₄×C₁₉	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic
21	C₄×C₁₃	#4294	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic
23	C₂×C₁₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic
24	C₄×C₉	—	247	1	no	Hall
25	C₂×C₁₃	C₂×#4294	1	1	yes	characteristic
26	C₁₉	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	247	1	no	—
28	C₁₃	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	#10625202	1	1	yes	characteristic
30	C₉	—	247	1	no	Sylow
31	C₂×C₃	C₂×#10625202	1	1	yes	characteristic
32	C₄	#14555735	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×#10625202	1	1	yes	characteristic
34	C₂	C₂×#14555735	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#10625202
commutator, hypocenter	C₁₃×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₂×#10625202
Fitting	C₃×C₄×C₁₃×C₁₉	C₃
socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #14555735	C₄	direct (N × H)
5. C₄×C₁₃×C₁₉	C₉	semidirect
11. C₁₃×C₁₉	C₄×C₉	semidirect
19. C₄×C₁₉	C₁₃⋊C₉	semidirect
21. C₄×C₁₃	#4294	semidirect
26. C₁₉	C₄×C₁₃⋊C₉	semidirect
28. C₁₃	C₄×#4294	semidirect
32. C₄	#14555735	direct (N × H)

Subgroups — C4×#14555735 #22580113

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14555735 #22580113