Subgroups — #30681145⋊C₂ #46777430

Order 33620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681146	C₂	1	1	yes	maximal, characteristic, complemented
2	#30681145	C₂	1	2	yes	maximal, complemented
3	#22554263	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₄₁²	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄₁⋊D₄₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₁×D₄₁	C₂×C₅	1	2	yes	complemented
7	C₄₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₄₁⋊C₅	—	41	2	no	maximal
9	C₂×C₄₁⋊C₅	—	41	2	no	—
10	D₄₁⋊C₅	—	41	2	no	—
11	D₄₁⋊C₅	—	41	2	no	—
12	C₄₁⋊C₅	—	41	2	no	—
13	C₂×D₄₁	—	41	2	no	—
14	C₂×C₄₁	—	41	2	no	—
15	D₄₁	—	41	2	no	—
16	D₄₁	—	410	4	no	—
17	D₄₁	D₄₁⋊C₅	1	2	yes	complemented
18	C₄₁	—	10	4	no	—
19	C₄₁	C₂×D₄₁⋊C₅	1	2	yes	complemented
20	C₂²×C₅	—	1681	1	no	Hall
21	C₂×C₅	—	1681	2	no	—
22	C₂×C₅	—	1681	1	no	—
23	C₅	—	1681	1	no	Sylow
24	C₂²	—	1681	1	no	Sylow
25	C₂	—	41	2	no	—
26	C₂	—	1681	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₁²	C₂²×C₅
LCS	G ▷ C₄₁²
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.