Subgroups — #10620301

Order 656.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₁	C₂	1	1	yes	maximal, characteristic
2	#66493	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄₁	C₄	1	1	yes	characteristic
4	Dic₄₁	C₄	1	1	yes	characteristic
5	Dic₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₄₁	—	2	1	no	—
7	C₂×C₄₁	C₂×C₄	1	1	yes	characteristic
8	C₄₁	M₁₆	1	1	yes	characteristic, complemented, Sylow
9	M₁₆	—	41	1	no	maximal, Sylow
10	C₂×C₄	—	41	1	no	—
11	C₈	—	41	2	no	—
12	C₂²	#4223	1	1	yes	characteristic
13	C₄	—	41	1	no	—
14	C₄	—	41	1	no	—
15	C₂	—	2	1	no	—
16	C₂	C₂×#4223	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #66493	C₂	semidirect
8. C₄₁	M₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.