Subgroups — C₁₁²×#63122 #44538245

Order 31460.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁²×#261	—	5	1	no	maximal, Hall
4	C₁₁²×D₁₃	—	5	1	no	—
5	C₁₁×#63122	C₁₁	1	12	yes	maximal, direct product factor
6	C₁₁²×AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
7	C₁₁²×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₁₁×D₆₅	C₂×C₁₁	1	12	yes	—
9	D₅×C₁₁²	—	13	1	no	—
10	C₅×C₁₁×C₁₃	C₄×C₁₁	1	12	yes	complemented
11	C₅×C₁₁²	#261	1	1	yes	characteristic, complemented, Hall
12	C₁₁×#261	—	5	12	no	—
13	C₄×C₁₁²	—	65	1	no	Hall
14	C₁₁×D₁₃	—	5	12	no	—
15	#63122	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₁²	—	65	1	no	—
17	C₁₁×AGL(1,𝔽₅)	—	13	12	no	—
18	C₁₁×C₁₃	C₁₁×AGL(1,𝔽₅)	1	12	yes	complemented
19	D₆₅	C₂×C₁₁²	1	1	yes	characteristic
20	C₁₁²	#63122	1	1	yes	characteristic, direct product factor, Sylow
21	D₅×C₁₁	—	13	12	no	—
22	C₅×C₁₃	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₁	C₁₁×#261	1	12	yes	complemented
24	#261	—	5	1	no	Hall
25	C₄×C₁₁	—	65	12	no	—
26	D₁₃	—	5	1	no	—
27	C₂×C₁₁	—	65	12	no	—
28	AGL(1,𝔽₅)	—	13	1	no	Hall
29	C₁₃	C₁₁²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₁₁×#63122	1	12	yes	direct product factor
31	D₅	—	13	1	no	—
32	C₅	C₁₁²×#261	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	65	1	no	Sylow
34	C₂	—	65	1	no	—

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.