Subgroups — #88045

Order 416.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6127	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#6099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃	—	2	1	no	—
5	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²⋊D₁₃	—	2	1	no	—
7	D₅₂	C₄	1	1	yes	characteristic, complemented
8	C₄×D₁₃	—	2	1	no	—
9	Dic₂₆	C₄	1	1	yes	characteristic, complemented
10	#1055	—	2	1	no	—
11	C₂²×C₁₃	D₄	1	1	yes	characteristic
12	C₂×D₁₃	—	2	1	no	—
13	C₄×C₁₃	—	2	2	no	—
14	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₁₃	D₄	1	1	yes	characteristic
16	Dic₁₃	—	2	1	no	—
17	#104	—	13	1	no	maximal, Sylow
18	C₂×C₁₃	—	2	1	no	—
19	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	D₁₃	—	4	1	no	—
21	#41	—	13	1	no	—
22	M₁₆	—	13	1	no	—
23	C₄²	D₁₃	1	1	yes	characteristic, complemented
24	C₁₃	#104	1	1	yes	characteristic, complemented, Sylow
25	Q₈	—	13	1	no	—
26	D₄	—	13	1	no	—
27	D₄	—	26	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	26	1	no	—
30	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
31	C₈	—	26	1	no	—
32	C₂²	—	26	1	no	—
33	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	26	1	no	—
36	C₄	C₄×D₁₃	1	1	yes	characteristic
37	C₄	D₅₂	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	52	1	no	—
40	C₂	#6103	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.