Subgroups — D₁₃×#10597243 #30628516

Order 15730.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×D₁₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₁⋊C₅	—	11	12	no	maximal
5	C₂×#10597243	—	13	1	no	maximal, Hall
6	C₁₃×C₁₁⋊C₅	—	11	12	no	—
7	#10597243	D₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×D₁₃	C₁₁⋊C₅	1	12	yes	complemented
9	C₂×C₁₁²	—	13	1	no	Hall
10	C₁₁×C₁₃	C₂×C₁₁⋊C₅	1	12	yes	complemented
11	C₅×D₁₃	—	121	1	no	Hall
12	C₁₁²	C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₁⋊C₅	—	143	12	no	—
14	C₅×C₁₃	—	121	1	no	Hall
15	C₁₁⋊C₅	—	11	12	no	—
16	D₁₃	#10597243	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	—	13	12	no	—
18	C₁₃	C₂×#10597243	1	1	yes	characteristic, complemented, Sylow
19	C₁₁	D₁₃×C₁₁⋊C₅	1	12	yes	complemented
20	C₂×C₅	—	1573	1	no	Hall
21	C₅	—	121	1	no	Sylow
22	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₁₃	C₂×C₅
LCS	G ▷ C₁₁²×C₁₃
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.