Supersolvable but not nilpotent groups

Groups with a normal series of cyclic factors but no central series. Each is shown with its largest nilpotent normal subgroup F(G), the part of it that is nilpotent, and the quotient over it.

order	group	F(G)	G/F(G)
56	C₄×D₇ #285	C₄×C₇	C₂
56	D₂₈ #286	C₄×C₇	C₂
56	C₂×Dic₇ #287	C₂²×C₇	C₂
56	C₂²⋊D₇ #288	C₂²×C₇	C₂
56	C₂²×D₇ #293	C₂²×C₇	C₂
57	C₁₉⋊C₃ #295	C₁₉	C₃
58	D₂₉ #297	C₂₉	C₂
60	C₅×Dic₃ #300	C₂×C₃×C₅	C₂
60	C₃×Dic₅ #301	C₂×C₃×C₅	C₂
60	Dic₁₅ #302	C₂×C₃×C₅	C₂
60	C₃×AGL(1,𝔽₅) #305	C₃×C₅	C₄
60	ΓL(1,𝔽₁₆) #306	C₃×C₅	C₄
60	D₃×D₅ #307	C₃×C₅	C₂²
60	C₂×C₃×D₅ #309	C₂×C₃×C₅	C₂
60	C₂×C₅×D₃ #310	C₂×C₃×C₅	C₂
60	C₂×D₁₅ #311	C₂×C₃×C₅	C₂
62	D₃₁ #314	C₃₁	C₂
63	C₇⋊C₉ #316	C₃×C₇	C₃
63	C₃×ΓL(1,𝔽₈) #318	C₃×C₇	C₃
66	D₃×C₁₁ #588	C₃×C₁₁	C₂
66	C₃×D₁₁ #589	C₃×C₁₁	C₂
66	D₃₃ #590	C₃×C₁₁	C₂
68	Dic₁₇ #593	C₂×C₁₇	C₂
68	#595	C₁₇	C₄
68	C₂×D₁₇ #596	C₂×C₁₇	C₂
70	C₇×D₅ #599	C₅×C₇	C₂
70	C₅×D₇ #600	C₅×C₇	C₂
70	D₃₅ #601	C₅×C₇	C₂
72	C₉⋊C₈ #604	C₄×C₉	C₂
72	Dic₁₈ #607	C₄×C₉	C₂
72	C₄×D₉ #608	C₄×C₉	C₂
72	D₃₆ #609	C₄×C₉	C₂
72	C₂×Dic₉ #610	C₂²×C₉	C₂
72	#611	C₂²×C₉	C₂
72	C₃×C₃⋊C₈ #615	C₃²×C₄	C₂
72	C₃⋊(C₃⋊C₈) #616	C₃²×C₄	C₂
72	C₂²×D₉ #620	C₂²×C₉	C₂
72	D₃×Dic₃ #623	C₂×C₃²	C₂²
72	#624	C₂×C₃²	C₂²
72	#625	C₂×C₃²	C₂²
72	#626	C₂×C₃²	C₂²
72	#627	C₂×C₃²	C₂²
72	C₃×Dic₆ #629	C₃²×C₄	C₂
72	C₃×C₄×D₃ #630	C₃²×C₄	C₂
72	C₃×D₁₂ #631	C₃²×C₄	C₂
72	C₂×C₃×Dic₃ #632	C₂²×C₃²	C₂
72	C₃×#67 #633	C₂²×C₃²	C₂
72	#634	C₃²×C₄	C₂
72	C₄×C₃⋊D₃ #635	C₃²×C₄	C₂
72	C₄⋊(C₃⋊D₃) #636	C₃²×C₄	C₂
72	C₂×C₃⋊Dic₃ #637	C₂²×C₃²	C₂
72	#638	C₂²×C₃²	C₂
72	C₂×D₃² #649	C₂×C₃²	C₂²
72	C₂²×C₃×D₃ #651	C₂²×C₃²	C₂
72	C₂²×C₃⋊D₃ #652	C₂²×C₃²	C₂
74	D₃₇ #655	C₃₇	C₂
76	Dic₁₉ #660	C₂×C₁₉	C₂
76	C₂×D₁₉ #662	C₂×C₁₉	C₂
78	D₁₃⋊C₃ #665	C₁₃	C₂×C₃
78	C₂×C₁₃⋊C₃ #666	C₂×C₁₃	C₃
78	D₃×C₁₃ #667	C₃×C₁₃	C₂
78	C₃×D₁₃ #668	C₃×C₁₃	C₂
78	D₃₉ #669	C₃×C₁₃	C₂
80	#672	C₅×C₈	C₂
80	#674	C₄×C₅	C₄
80	C₈×D₅ #675	C₅×C₈	C₂
80	#676	C₅×C₈	C₂
80	#677	C₅×C₈	C₂
80	D₄₀ #678	C₅×C₈	C₂
80	Dic₂₀ #679	C₅×C₈	C₂
80	C₂×#168 #680	C₂×C₄×C₅	C₂
80	#681	C₂×C₄×C₅	C₂
80	C₄×Dic₅ #682	C₂×C₄×C₅	C₂
80	#683	C₂×C₄×C₅	C₂
80	C₄⋊Dic₅ #684	C₂×C₄×C₅	C₂
80	#685	C₂×C₄×C₅	C₂
80	#686	C₅×D₄	C₂
80	#687	C₅×D₄	C₂
80	#688	C₅×Q₈	C₂
80	#689	C₅×Q₈	C₂
80	C₂²⋊Dic₅ #690	C₂³×C₅	C₂
80	D₅⋊C₈ #699	C₄×C₅	C₄
80	#700	C₄×C₅	C₄
80	C₄×AGL(1,𝔽₅) #701	C₄×C₅	C₄
80	C₄⋊AGL(1,𝔽₅) #702	C₄×C₅	C₄
80	C₂×#170 #703	C₂²×C₅	C₄
80	#704	C₂²×C₅	C₄
80	C₂²⋊AGL(1,𝔽₅) #705	C₂²×C₅	C₄
80	C₂×Dic₁₀ #706	C₂×C₄×C₅	C₂
80	C₂×C₄×D₅ #707	C₂×C₄×C₅	C₂
80	C₂×D₂₀ #708	C₂×C₄×C₅	C₂
80	#709	C₂×C₄×C₅	C₂
80	D₄×D₅ #710	C₅×D₄	C₂
80	#711	C₅×D₄	C₂
80	Q₈×D₅ #712	C₅×Q₈	C₂
80	#713	C₅×Q₈	C₂
80	C₂²×Dic₅ #714	C₂³×C₅	C₂
80	C₂×C₂²⋊D₅ #715	C₂³×C₅	C₂
80	C₂²×AGL(1,𝔽₅) #721	C₂²×C₅	C₄
80	C₂³×D₅ #722	C₂³×C₅	C₂

About supersolvable but not nilpotent groups →