Subgroups — C₁₆×D₅₂₃ #30660310

Order 16736.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₅₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₅₂₃	C₄	1	1	yes	characteristic
5	C₅₂₃⋊C₈	C₄	1	1	yes	characteristic
6	C₈×C₅₂₃	C₂²	1	1	yes	characteristic
7	C₂×D₅₂₃	C₈	1	1	yes	characteristic
8	C₄×C₅₂₃	C₂×C₄	1	1	yes	characteristic
9	Dic₅₂₃	C₈	1	1	yes	characteristic
10	C₂×C₅₂₃	C₂×C₈	1	1	yes	characteristic
11	D₅₂₃	C₁₆	1	2	yes	direct product factor
12	C₅₂₃	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₆	—	523	1	no	maximal, Sylow
14	C₂×C₈	—	523	1	no	—
15	C₁₆	—	523	1	no	—
16	C₁₆	D₅₂₃	1	1	yes	characteristic, direct product factor
17	C₂×C₄	—	523	1	no	—
18	C₈	—	523	1	no	—
19	C₈	C₂×D₅₂₃	1	1	yes	characteristic
20	C₂²	—	523	1	no	—
21	C₄	—	523	1	no	—
22	C₄	C₄×D₅₂₃	1	1	yes	characteristic
23	C₂	—	523	2	no	—
24	C₂	C₈×D₅₂₃	1	1	yes	characteristic

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.