Subgroups — #44538258

Order 31460.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	#20262574	—	5	1	no	maximal, Hall
4	C₁₃×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic
5	#14559102	—	13	1	no	maximal, Hall
6	C₁₁²×C₁₃	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₃×D₁₁	—	22	6	no	—
8	C₅×C₁₁⋊D₁₁	D₁₃	1	1	yes	characteristic
9	C₅×C₁₁×C₁₃	—	2	6	no	—
10	C₅×C₁₁²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
11	#92150	—	65	1	no	Hall
12	C₁₃×D₁₁	—	22	6	no	—
13	Dic₆₅	—	121	1	no	maximal, Hall
14	C₁₁⋊D₁₁	D₆₅	1	1	yes	characteristic
15	C₁₁×C₁₃	—	2	6	no	—
16	C₂×C₅×C₁₃	—	121	1	no	—
17	C₁₁²	Dic₆₅	1	1	yes	characteristic, complemented, Sylow
18	C₅×D₁₁	—	22	6	no	—
19	C₅×C₁₃	#92150	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₁	—	2	6	no	—
21	Dic₁₃	—	605	1	no	Hall
22	C₂×C₁₃	—	121	1	no	—
23	D₁₁	—	22	6	no	—
24	Dic₅	—	1573	1	no	Hall
25	C₁₃	#14559102	1	1	yes	characteristic, complemented, Sylow
26	C₁₁	—	2	6	no	—
27	C₂×C₅	—	121	1	no	—
28	C₅	#20262574	1	1	yes	characteristic, complemented, Sylow
29	C₄	—	7865	1	no	Sylow
30	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁²×C₁₃	C₄
prime radical, cosocle	C₅×C₁₃×C₁₁⋊D₁₁	C₂
LCS	G ▷ C₅×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.