Subgroups — #44440496

Order 29388.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20301165	C₂	1	1	yes	maximal, characteristic
2	Dic₂₄₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20301165	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×C₇₉	C₂×C₃	1	1	yes	characteristic
5	C₃₁×C₇₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₇₉⋊C₃)⋊C₄	—	31	1	no	maximal, Hall
7	C₂×C₇₉⋊C₃	—	62	1	no	—
8	(C₃₁⋊C₃)⋊C₄	—	79	1	no	maximal, Hall
9	Dic₇₉	—	31	1	no	Hall
10	C₇₉⋊C₃	—	62	1	no	Hall
11	C₂×C₃₁⋊C₃	—	158	1	no	—
12	C₂×C₇₉	D₃₁⋊C₃	1	1	yes	characteristic
13	Dic₃₁	—	79	1	no	Hall
14	C₃₁⋊C₃	—	158	1	no	Hall
15	C₇₉	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃₁	D₇₉⋊C₃	1	1	yes	characteristic
17	C₃₁	(C₇₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2449	1	no	Hall
19	C₂×C₃	—	4898	1	no	—
20	C₄	—	2449	1	no	Sylow
21	C₃	—	4898	1	no	Sylow
22	C₂	#28412815	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#28412815
commutator, hypocenter	C₃₁×C₇₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₁×C₇₉	C₂×C₃
prime radical	C₂×#20301165	C₂
LCS	G ▷ C₃₁×C₇₉
UCS	C₁ ◁ C₂

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

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