Subgroups — C₂×C₃₂×C₂₅₇ #30656238

Order 16448.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₃₂×C₂₅₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₂₅₇	C₄	1	1	yes	characteristic
4	C₁₆×C₂₅₇	C₄	1	1	yes	characteristic
5	C₁₆×C₂₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₂₅₇	C₈	1	1	yes	characteristic
7	C₈×C₂₅₇	C₈	1	1	yes	characteristic
8	C₈×C₂₅₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₂₅₇	C₁₆	1	1	yes	characteristic
10	C₄×C₂₅₇	C₁₆	1	1	yes	characteristic
11	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₂₅₇	C₃₂	1	2	yes	direct product factor
13	C₂×C₂₅₇	C₂×C₁₆	1	1	yes	characteristic
14	C₂₅₇	C₂×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃₂	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₁₆	C₂×C₂₅₇	1	1	yes	characteristic
17	C₃₂	C₂×C₂₅₇	1	2	yes	direct product factor
18	C₂×C₈	C₄×C₂₅₇	1	1	yes	characteristic
19	C₁₆	C₄×C₂₅₇	1	1	yes	characteristic
20	C₁₆	C₂²×C₂₅₇	1	1	yes	characteristic
21	C₂×C₄	C₈×C₂₅₇	1	1	yes	characteristic
22	C₈	C₈×C₂₅₇	1	1	yes	characteristic
23	C₈	C₂×C₄×C₂₅₇	1	1	yes	characteristic
24	C₂²	C₁₆×C₂₅₇	1	1	yes	characteristic
25	C₄	C₁₆×C₂₅₇	1	1	yes	characteristic
26	C₄	C₂×C₈×C₂₅₇	1	1	yes	characteristic
27	C₂	C₃₂×C₂₅₇	1	2	yes	direct product factor
28	C₂	C₂×C₁₆×C₂₅₇	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.