Subgroups — C₂×C₂₃×#10597244 #42123736

Order 27830.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#10597244	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁²×C₂₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×C₁₁⋊C₅	—	11	2	no	maximal
5	C₂₃×C₁₁⋊C₅	—	11	2	no	—
6	C₂×#10597244	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	#10597244	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₁×C₂₃	—	5	2	no	—
9	C₂×C₁₁×C₂₃	C₁₁⋊C₅	1	2	yes	complemented
10	C₁₁×C₂₃	—	5	2	no	—
11	C₁₁×C₂₃	C₂×C₁₁⋊C₅	1	2	yes	complemented
12	C₂×C₁₁²	C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₂₃	—	121	1	no	Hall
14	C₁₁²	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₂₃	—	121	1	no	Hall
16	C₂×C₁₁⋊C₅	—	11	2	no	—
17	C₁₁⋊C₅	—	11	2	no	—
18	C₂×C₂₃	#10597244	1	1	yes	characteristic, direct product factor, Hall
19	C₂₃	C₂×#10597244	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₁₁	—	5	2	no	—
21	C₂×C₁₁	C₂₃×C₁₁⋊C₅	1	2	yes	complemented
22	C₁₁	—	5	2	no	—
23	C₁₁	C₂×C₂₃×C₁₁⋊C₅	1	2	yes	complemented
24	C₂×C₅	—	121	1	no	Hall
25	C₅	—	121	1	no	Sylow
26	C₂	C₂₃×#10597244	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₂₃	#10597244
commutator, cosocle, hypocenter	C₁₁²	C₂×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₂₃	C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₂₃

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.