Subgroups — #88074

Order 416.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃	C₄	1	1	yes	characteristic, complemented
4	C₂³×C₁₃	C₂²	1	1	yes	characteristic
5	D₄×C₁₃	—	2	2	no	—
6	C₂×C₄×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂×Dic₁₃	—	2	2	no	—
8	C₂²×C₁₃	—	2	1	no	—
9	C₂²×C₁₃	—	4	1	no	—
10	C₂²×C₁₃	—	4	1	no	—
11	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₁₃	D₄	1	2	yes	—
13	C₄×C₁₃	—	2	1	no	—
14	Dic₁₃	—	4	2	no	—
15	#99	—	13	1	no	maximal, Sylow
16	C₂×C₁₃	—	2	2	no	—
17	C₂×C₁₃	—	2	1	no	—
18	C₂×C₁₃	—	4	1	no	—
19	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×D₄	D₁₃	1	1	yes	characteristic
21	C₂²⋊C₄	—	13	2	no	—
22	C₁₃	#99	1	1	yes	characteristic, complemented, Sylow
23	C₂³	Dic₁₃	1	1	yes	characteristic, complemented
24	C₂³	C₂×D₁₃	1	1	yes	characteristic
25	D₄	—	2	2	no	—
26	C₂×C₄	—	26	2	no	—
27	C₂×C₄	Dic₁₃	1	1	yes	characteristic, complemented
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×Dic₁₃	1	1	yes	characteristic
32	C₂²	C₂²⋊D₁₃	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	52	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	C₂²⋊Dic₁₃	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.