Subgroups — D₂₃×#10597244 #42123722

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, complemented, Hall
2	C₁₁²×D₂₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₂₃×C₁₁⋊C₅	—	11	2	no	maximal
5	C₂₃×C₁₁⋊C₅	—	11	2	no	—
6	C₂×#10597244	—	23	1	no	maximal, Hall
7	#10597244	D₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×D₂₃	—	5	2	no	—
9	C₁₁×D₂₃	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	—	23	1	no	Hall
13	C₅×D₂₃	—	121	1	no	Hall
14	C₁₁²	C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₂₃	—	121	1	no	Hall
16	C₂×C₁₁⋊C₅	—	253	2	no	—
17	C₁₁⋊C₅	—	11	2	no	—
18	D₂₃	#10597244	1	1	yes	characteristic, direct product factor, Hall
19	C₂₃	C₂×#10597244	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₁₁	—	23	2	no	—
21	C₂×C₁₁	—	115	2	no	—
22	C₁₁	—	5	2	no	—
23	C₁₁	D₂₃×C₁₁⋊C₅	1	2	yes	complemented
24	C₂×C₅	—	2783	1	no	Hall
25	C₅	—	121	1	no	Sylow
26	C₂	—	23	1	no	Sylow

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

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.