Subgroups — C₁₁²×D₁₅₅ #49176018

Order 37510.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁²×D₃₁	—	5	1	no	maximal, Hall
3	C₁₁²×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₁₅₅	C₁₁	1	12	yes	maximal, direct product factor
5	C₅×C₁₁×C₃₁	C₂×C₁₁	1	12	yes	complemented
6	D₅×C₁₁²	—	31	1	no	maximal, Hall
7	C₁₁×D₃₁	—	5	12	no	—
8	C₅×C₁₁²	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₃₁	D₅×C₁₁	1	12	yes	complemented
10	D₁₅₅	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁²	—	155	1	no	Hall
12	C₅×C₃₁	C₂×C₁₁²	1	1	yes	characteristic, complemented, Hall
13	C₁₁²	D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
14	D₅×C₁₁	—	31	12	no	—
15	D₃₁	—	5	1	no	Hall
16	C₅×C₁₁	C₁₁×D₃₁	1	12	yes	complemented
17	C₃₁	D₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁	—	155	12	no	—
19	C₁₁	C₁₁×D₁₅₅	1	12	yes	direct product factor
20	D₅	—	31	1	no	Hall
21	C₅	C₁₁²×D₃₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	155	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁²	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂×C₁₁²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₁₁²

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.