Subgroups — #88180

Order 416.

76 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	C₄⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	C₂³×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₃	C₄	1	4	yes	complemented
7	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₃	C₂²	1	4	yes	—
10	C₂²×C₁₃	—	2	2	no	—
11	C₂²×C₁₃	C₂×C₄	1	2	yes	—
12	C₂²×C₁₃	C₂³	1	1	yes	characteristic
13	C₄×C₁₃	C₂×C₄	1	2	yes	—
14	C₄×C₁₃	C₂×C₄	1	2	yes	—
15	Dic₁₃	—	2	4	no	—
16	#117	—	13	1	no	maximal, Sylow
17	C₂×C₁₃	—	2	2	no	—
18	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₁₃	#41	1	2	yes	—
20	C₂²×C₄	D₁₃	1	1	yes	characteristic
21	C₄⋊C₄	—	13	2	no	—
22	C₂²⋊C₄	—	13	2	no	—
23	C₄²	—	13	2	no	—
24	C₁₃	#117	1	1	yes	characteristic, complemented, Sylow
25	C₂³	C₂×D₁₃	1	1	yes	characteristic
26	C₂×C₄	—	13	4	no	—
27	C₂×C₄	Dic₁₃	1	4	yes	complemented
28	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
29	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₁₃	1	2	yes	—
32	C₂²	C₂²×D₁₃	1	1	yes	characteristic
33	C₄	—	26	4	no	—
34	C₄	C₂×Dic₁₃	1	2	yes	—
35	C₄	C₂×Dic₁₃	1	2	yes	—
36	C₂	—	2	2	no	—
37	C₂	#6127	1	2	yes	—
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.