Subgroups — #46777396

Order 33620.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22554263	C₂	1	1	yes	maximal, characteristic
2	#22554263	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄₁×Dic₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₄₁²	C₂×C₅	1	1	yes	characteristic
5	C₄₁²	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
6	C₄×C₄₁⋊C₅	—	41	1	no	maximal
7	Dic₄₁⋊C₅	—	41	1	no	maximal
8	C₂×C₄₁⋊C₅	—	41	1	no	—
9	C₂×C₄₁⋊C₅	—	41	1	no	—
10	C₄₁⋊C₅	—	41	1	no	—
11	C₄₁⋊C₅	—	41	1	no	—
12	C₄×C₄₁	—	41	1	no	—
13	Dic₄₁	C₄₁⋊C₅	1	1	yes	characteristic, complemented
14	C₂×C₄₁	—	10	4	no	—
15	C₂×C₄₁	D₄₁⋊C₅	1	1	yes	characteristic
16	C₂×C₄₁	C₂×C₄₁⋊C₅	1	1	yes	characteristic
17	C₄₁	—	10	4	no	—
18	C₄₁	Dic₄₁⋊C₅	1	1	yes	characteristic, complemented
19	C₄₁	C₄×C₄₁⋊C₅	1	1	yes	characteristic, complemented
20	C₄×C₅	—	1681	1	no	Hall
21	C₂×C₅	—	1681	1	no	—
22	C₅	—	1681	1	no	Sylow
23	C₄	—	41	1	no	Sylow
24	C₂	#30681145	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#30681145
commutator, hypocenter	C₄₁²	C₄×C₅
Fitting, socle, cosocle	C₂×C₄₁²	C₂×C₅
prime radical	C₂×#22554263	C₂
LCS	G ▷ C₄₁²
UCS	C₁ ◁ C₂

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.