Subgroups — C₂×Dic₅₂ #88159

Order 416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₆	C₂	1	2	yes	maximal
2	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	Dic₅₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₃	—	2	2	no	—
6	Dic₂₆	—	2	2	no	—
7	Dic₂₆	C₂²	1	4	yes	—
8	C₈×C₁₃	C₂²	1	2	yes	—
9	C₂²×C₁₃	D₄	1	1	yes	characteristic
10	C₄×C₁₃	D₄	1	1	yes	characteristic
11	C₄×C₁₃	C₂³	1	1	yes	characteristic
12	Dic₁₃	—	2	4	no	—
13	C₂×Q₁₆	—	13	1	no	maximal, Sylow
14	C₂×C₁₃	Q₁₆	1	2	yes	complemented
15	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
16	C₂×Q₈	—	13	2	no	—
17	Q₁₆	—	13	4	no	—
18	C₂×C₈	D₁₃	1	1	yes	characteristic
19	C₁₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
20	Q₈	—	13	4	no	—
21	Q₈	—	26	2	no	—
22	C₂×C₄	—	26	2	no	—
23	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
24	C₈	C₂×D₁₃	1	2	yes	—
25	C₂²	D₅₂	1	1	yes	characteristic
26	C₄	—	26	4	no	—
27	C₄	D₅₂	1	1	yes	characteristic
28	C₄	C₂²×D₁₃	1	1	yes	characteristic
29	C₂	Dic₅₂	1	2	yes	direct product factor
30	C₂	C₂×D₅₂	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.