Subgroups — #88071

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	C₂³×C₁₃	C₂²	1	1	yes	characteristic
4	C₂×C₄×C₁₃	—	2	2	no	—
5	C₂×C₄×C₁₃	C₄	1	2	yes	complemented
6	C₂×Dic₁₃	—	2	2	no	—
7	C₂×Dic₁₃	—	2	2	no	—
8	C₂×Dic₁₃	C₄	1	4	yes	complemented
9	C₂²×C₁₃	C₂×C₄	1	2	yes	—
10	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₃	D₄	1	1	yes	characteristic
12	C₂²×C₁₃	D₄	1	2	yes	—
13	C₂²×C₁₃	Q₈	1	1	yes	characteristic
14	C₄×C₁₃	—	2	2	no	—
15	Dic₁₃	—	2	4	no	—
16	#95	—	13	1	no	maximal, Sylow
17	C₂×C₁₃	C₄²	1	1	yes	characteristic
18	C₂×C₁₃	C₂²⋊C₄	1	2	yes	—
19	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₁₃	C₄⋊C₄	1	2	yes	—
21	C₂×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄	—	13	2	no	—
23	C₂²×C₄	D₁₃	1	1	yes	characteristic
24	C₁₃	#95	1	1	yes	characteristic, complemented, Sylow
25	C₂³	C₂×D₁₃	1	1	yes	characteristic
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	13	4	no	—
28	C₂×C₄	—	26	2	no	—
29	C₂×C₄	—	26	2	no	—
30	C₂×C₄	Dic₁₃	1	2	yes	complemented
31	C₂²	Dic₂₆	1	1	yes	characteristic
32	C₂²	C₄×D₁₃	1	2	yes	—
33	C₂²	D₅₂	1	1	yes	characteristic
34	C₂²	C₂×Dic₁₃	1	1	yes	characteristic
35	C₂²	C₂²⋊D₁₃	1	2	yes	—
36	C₄	—	2	2	no	—
37	C₄	—	26	4	no	—
38	C₂	C₄×Dic₁₃	1	1	yes	characteristic
39	C₂	#6101	1	2	yes	—
40	C₂	C₄⋊Dic₁₃	1	1	yes	characteristic
41	C₂	#6103	1	2	yes	—
42	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.