Subgroups — #88117

Order 416.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#261	—	2	1	no	—
5	Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
6	C₄×D₁₃	—	2	1	no	—
7	C₄×D₁₃	C₂²	1	1	yes	characteristic
8	Dic₂₆	—	2	1	no	—
9	Dic₂₆	C₄	1	1	yes	characteristic, complemented
10	#1057	—	2	1	no	—
11	C₂×D₁₃	D₄	1	1	yes	characteristic
12	#261	—	4	1	no	—
13	C₄×C₁₃	—	2	1	no	—
14	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	Dic₁₃	—	2	1	no	—
16	Dic₁₃	D₄	1	1	yes	characteristic
17	#103	—	13	1	no	maximal, Sylow
18	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
19	D₁₃	SD₁₆	1	1	yes	characteristic
20	D₁₃	Q₁₆	1	1	yes	characteristic
21	C₂×Q₈	—	13	1	no	—
22	C₂×C₈	—	13	1	no	—
23	C₄⋊C₄	—	13	1	no	—
24	C₁₃	#103	1	1	yes	characteristic, complemented, Sylow
25	Q₈	—	13	1	no	—
26	Q₈	—	26	1	no	—
27	Q₈	#261	1	1	yes	characteristic, complemented
28	C₂×C₄	—	13	1	no	—
29	C₂×C₄	—	26	1	no	—
30	C₂×C₄	—	26	1	no	—
31	C₈	—	26	1	no	—
32	C₂²	—	13	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	13	1	no	—
35	C₄	—	26	1	no	—
36	C₄	—	52	1	no	—
37	C₄	C₂×#261	1	1	yes	characteristic
38	C₂	—	13	1	no	—
39	C₂	—	13	1	no	—
40	C₂	C₂²⋊#261	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.