Subgroups — C₂×#22547865 #30630607

Order 15996.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22547865	C₂	1	2	yes	maximal, direct product factor
2	C₂×#16860687	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#16860687	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄₃×D₃₁	C₂×C₃	1	2	yes	complemented
7	C₃₁×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₄₃⋊C₃	—	31	1	no	maximal, Hall
9	C₂×D₃₁⋊C₃	—	43	1	no	maximal, Hall
10	C₂×C₄₃⋊C₃	—	31	2	no	—
11	C₂×C₄₃⋊C₃	—	62	1	no	—
12	C₂×C₃₁⋊C₃	—	43	1	no	—
13	D₃₁⋊C₃	—	43	2	no	—
14	C₂²×C₄₃	—	31	1	no	Hall
15	C₄₃⋊C₃	—	62	1	no	Hall
16	C₂×D₃₁	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃₁⋊C₃	—	43	1	no	Hall
18	C₂×C₄₃	—	31	2	no	—
19	C₂×C₄₃	D₃₁⋊C₃	1	1	yes	characteristic, complemented
20	C₂×C₃₁	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
21	D₃₁	C₂×C₄₃⋊C₃	1	2	yes	complemented
22	C₄₃	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃₁	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1333	1	no	Hall
25	C₂×C₃	—	1333	2	no	—
26	C₂×C₃	—	2666	1	no	—
27	C₂²	—	31	1	no	Sylow
28	C₃	—	2666	1	no	Sylow
29	C₂	—	31	2	no	—
30	C₂	#22547865	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#22547865
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃₁×C₄₃
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.