Subgroups — C₂×D₁₀₄ #88157

Order 416.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₄	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₁₃	—	2	2	no	—
5	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	D₅₂	—	2	2	no	—
7	D₅₂	C₂²	1	4	yes	complemented
8	C₈×C₁₃	C₂²	1	2	yes	complemented
9	C₂²×C₁₃	D₄	1	1	yes	characteristic
10	C₂×D₁₃	—	2	4	no	—
11	C₂×D₁₃	—	4	4	no	—
12	C₄×C₁₃	D₄	1	1	yes	characteristic
13	C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×D₈	—	13	1	no	maximal, Sylow
15	C₂×C₁₃	D₈	1	2	yes	complemented
16	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
17	D₁₃	—	4	4	no	—
18	C₂×D₄	—	13	2	no	—
19	D₈	—	13	4	no	—
20	C₂×C₈	D₁₃	1	1	yes	characteristic, complemented
21	C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
22	C₂³	—	26	2	no	—
23	D₄	—	13	4	no	—
24	D₄	—	26	2	no	—
25	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
26	C₈	C₂×D₁₃	1	2	yes	complemented
27	C₂²	—	26	4	no	—
28	C₂²	—	52	4	no	—
29	C₂²	D₅₂	1	1	yes	characteristic
30	C₄	D₅₂	1	1	yes	characteristic
31	C₄	C₂²×D₁₃	1	1	yes	characteristic
32	C₂	—	52	4	no	—
33	C₂	D₁₀₄	1	2	yes	direct product factor
34	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.