Subgroups — #88196

Order 416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#6127	C₂	1	1	yes	maximal, characteristic
3	#6107	C₂	1	2	yes	maximal, complemented
4	#6106	C₂	1	2	yes	maximal, complemented
5	#6099	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₃	—	2	1	no	—
7	Q₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₁₃	—	2	1	no	—
9	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₃	—	2	1	no	—
11	D₅₂	C₂²	1	1	yes	characteristic
12	C₄×D₁₃	—	2	1	no	—
13	Dic₂₆	C₂²	1	1	yes	characteristic
14	#1055	C₂²	1	2	yes	—
15	C₂²×C₁₃	D₄	1	1	yes	characteristic
16	C₂×D₁₃	—	2	1	no	—
17	C₄×C₁₃	—	2	2	no	—
18	C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₄×C₁₃	C₂³	1	1	yes	characteristic
20	Dic₁₃	—	2	1	no	—
21	#137	—	13	1	no	maximal, Sylow
22	C₂×C₁₃	—	2	1	no	—
23	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
24	D₁₃	—	4	1	no	—
25	#41	—	13	1	no	—
26	C₂×Q₈	D₁₃	1	1	yes	characteristic, complemented
27	Q₁₆	—	13	2	no	—
28	SD₁₆	—	13	2	no	—
29	M₁₆	—	13	1	no	—
30	C₁₃	#137	1	1	yes	characteristic, complemented, Sylow
31	Q₈	—	2	1	no	—
32	Q₈	—	13	1	no	—
33	Q₈	C₂×D₁₃	1	2	yes	—
34	D₄	—	13	1	no	—
35	D₄	—	26	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	26	1	no	—
38	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
39	C₈	—	13	2	no	—
40	C₂²	—	26	1	no	—
41	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	26	1	no	—
44	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
45	C₄	C₂²×D₁₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	52	1	no	—
48	C₂	C₂×C₂²⋊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.