Subgroups — C₂×#23751217 #34063597

Order 19220.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18012458	C₂	1	1	yes	maximal, characteristic, complemented
2	#23751217	C₂	1	2	yes	maximal, direct product factor
3	#18012458	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃₁²	C₂×C₅	1	1	yes	characteristic, complemented
6	C₃₁×D₃₁	C₂×C₅	1	2	yes	complemented
7	C₃₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂²×ΓL(1,𝔽₃₂)	—	31	1	no	maximal
9	C₂×D₃₁⋊C₅	—	31	1	no	maximal
10	C₂×ΓL(1,𝔽₃₂)	—	31	2	no	—
11	C₂×ΓL(1,𝔽₃₂)	—	31	1	no	—
12	C₂×ΓL(1,𝔽₃₂)	—	31	1	no	—
13	D₃₁⋊C₅	—	31	2	no	—
14	ΓL(1,𝔽₃₂)	—	31	1	no	—
15	ΓL(1,𝔽₃₂)	—	31	1	no	—
16	C₂²×C₃₁	—	155	1	no	—
17	C₂×D₃₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
18	C₂×C₃₁	—	10	3	no	—
19	C₂×C₃₁	—	155	2	no	—
20	C₂×C₃₁	D₃₁⋊C₅	1	1	yes	characteristic, complemented
21	C₂×C₃₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
22	D₃₁	C₂×ΓL(1,𝔽₃₂)	1	2	yes	complemented
23	C₃₁	—	10	3	no	—
24	C₃₁	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented
25	C₃₁	C₂²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
26	C₂²×C₅	—	961	1	no	Hall
27	C₂×C₅	—	961	2	no	—
28	C₂×C₅	—	961	1	no	—
29	C₅	—	961	1	no	Sylow
30	C₂²	—	155	1	no	Sylow
31	C₂	—	155	2	no	—
32	C₂	#23751217	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#23751217
commutator, cosocle, hypocenter	C₃₁²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃₁²	C₂×C₅
LCS	G ▷ C₃₁²
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.