Subgroups — #330

Order 64.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#125	C₂	1	1	yes	maximal, characteristic
2	#97	C₂	1	2	yes	maximal
3	C₂×C₈	—	2	2	no	—
4	C₄⋊C₄	—	2	2	no	—
5	C₄⋊C₄	C₄	1	2	yes	—
6	C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₄	—	2	2	no	—
8	C₂×C₄	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄	D₄	1	2	yes	—
10	C₈	—	2	4	no	—
11	C₂²	C₂²⋊C₄	1	1	yes	characteristic
12	C₄	—	2	1	no	—
13	C₄	—	2	2	no	—
14	C₄	—	4	2	no	—
15	C₂	#101	1	1	yes	characteristic
16	C₂	#104	1	2	yes	—

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

subgroup	index
#125	2
#97	2