Subgroups — #88126

Order 416.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#6103	C₂	1	2	yes	maximal
4	#6101	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₃	C₂²	1	2	yes	—
10	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₄×D₁₃	C₄	1	4	yes	complemented
12	C₂²×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×D₁₃	—	2	2	no	—
14	C₂×D₁₃	C₂×C₄	1	2	yes	—
15	C₄×C₁₃	—	2	2	no	—
16	C₄×C₁₃	C₂×C₄	1	2	yes	—
17	Dic₁₃	—	2	2	no	—
18	Dic₁₃	C₂×C₄	1	2	yes	—
19	#117	—	13	1	no	maximal, Sylow
20	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₁₃	#41	1	2	yes	—
22	D₁₃	—	2	2	no	—
23	C₂²×C₄	—	13	1	no	—
24	C₄⋊C₄	—	13	2	no	—
25	C₂²⋊C₄	—	13	2	no	—
26	C₄²	—	13	1	no	—
27	C₄²	D₁₃	1	1	yes	characteristic, complemented
28	C₁₃	#117	1	1	yes	characteristic, complemented, Sylow
29	C₂³	—	13	1	no	—
30	C₂×C₄	—	13	1	no	—
31	C₂×C₄	—	13	4	no	—
32	C₂×C₄	—	13	2	no	—
33	C₂×C₄	C₂×D₁₃	1	2	yes	—
34	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
35	C₂²	—	13	2	no	—
36	C₂²	—	26	2	no	—
37	C₂²	C₂²×D₁₃	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	13	2	no	—
40	C₄	—	26	2	no	—
41	C₄	C₄×D₁₃	1	2	yes	—
42	C₂	—	26	2	no	—
43	C₂	C₂×C₄×D₁₃	1	1	yes	characteristic
44	C₂	#6127	1	2	yes	—

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.