Subgroups — #88173

Order 416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6131	C₂	1	2	yes	maximal, complemented
2	C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6106	C₂	1	2	yes	maximal, complemented
4	D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₃	C₂²	1	2	yes	—
7	D₅₂	—	2	2	no	—
8	D₅₂	C₂²	1	2	yes	—
9	C₄×D₁₃	—	2	2	no	—
10	C₄×D₁₃	C₂²	1	1	yes	characteristic
11	C₈×C₁₃	C₂²	1	1	yes	characteristic
12	#1055	C₂²	1	1	yes	characteristic
13	C₂×D₁₃	—	2	2	no	—
14	C₂×D₁₃	D₄	1	1	yes	characteristic
15	C₄×C₁₃	—	2	2	no	—
16	C₄×C₁₃	C₂³	1	1	yes	characteristic
17	Dic₁₃	D₄	1	1	yes	characteristic
18	#135	—	13	1	no	maximal, Sylow
19	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
20	D₁₃	—	2	1	no	—
21	D₁₃	—	4	2	no	—
22	#41	—	13	2	no	—
23	Q₁₆	D₁₃	1	1	yes	characteristic, complemented
24	SD₁₆	—	13	2	no	—
25	D₈	—	13	1	no	—
26	C₂×C₈	—	13	1	no	—
27	C₁₃	#135	1	1	yes	characteristic, complemented, Sylow
28	Q₈	C₂×D₁₃	1	2	yes	—
29	D₄	—	13	2	no	—
30	D₄	—	26	2	no	—
31	C₂×C₄	—	13	1	no	—
32	C₂×C₄	—	26	2	no	—
33	C₈	—	13	1	no	—
34	C₈	C₂×D₁₃	1	1	yes	characteristic
35	C₂²	—	13	1	no	—
36	C₂²	—	26	2	no	—
37	C₄	—	2	2	no	—
38	C₄	—	13	1	no	—
39	C₄	C₂²×D₁₃	1	1	yes	characteristic
40	C₂	—	26	1	no	—
41	C₂	—	52	2	no	—
42	C₂	D₄×D₁₃	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.