Subgroups — C₂²×Dic₂₆ #88245

Order 416.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₃	C₂	1	2	yes	maximal
3	C₂×Dic₂₆	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₃	C₂²	1	6	yes	—
6	C₂×Dic₁₃	C₂²	1	12	yes	—
7	Dic₂₆	C₂²	1	16	yes	direct product factor
8	C₂²×C₁₃	Q₈	1	4	yes	complemented
9	C₂²×C₁₃	C₂³	1	3	yes	—
10	C₄×C₁₃	C₂³	1	4	yes	—
11	Dic₁₃	C₂³	1	8	yes	—
12	C₂²×Q₈	—	13	1	no	maximal, Sylow
13	C₂×C₁₃	C₂×Q₈	1	6	yes	complemented
14	C₂×C₁₃	C₂⁴	1	1	yes	characteristic
15	C₂×Q₈	—	13	12	no	—
16	C₂²×C₄	—	13	2	no	—
17	C₂²×C₄	D₁₃	1	1	yes	characteristic
18	C₁₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³	C₂×D₁₃	1	1	yes	characteristic
20	Q₈	—	13	16	no	—
21	C₂×C₄	—	13	12	no	—
22	C₂×C₄	C₂×D₁₃	1	6	yes	—
23	C₂²	Dic₂₆	1	4	yes	direct product factor
24	C₂²	C₂²×D₁₃	1	3	yes	—
25	C₄	—	13	8	no	—
26	C₄	C₂²×D₁₃	1	4	yes	—
27	C₂	C₂×Dic₂₆	1	6	yes	direct product factor
28	C₂	C₂³×D₁₃	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.