Subgroups — #88254

Order 416.

146 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	#6131	C₂	1	4	yes	maximal, complemented
3	Q₈×D₁₃	C₂	1	4	yes	maximal, complemented
4	#6127	C₂	1	6	yes	maximal, complemented
5	Q₈×C₁₃	C₂²	1	4	yes	—
6	C₂×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂²⋊D₁₃	C₂²	1	4	yes	—
8	D₅₂	C₂²	1	6	yes	—
9	C₄×D₁₃	C₂²	1	12	yes	—
10	Dic₂₆	C₂²	1	6	yes	—
11	C₂²×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×D₁₃	C₂³	1	4	yes	—
13	C₄×C₁₃	C₂³	1	6	yes	—
14	Dic₁₃	C₂³	1	4	yes	—
15	2₋¹⁺⁴	—	13	1	no	maximal, Sylow
16	C₂×C₁₃	—	2	1	no	—
17	C₂×C₁₃	C₂⁴	1	1	yes	characteristic
18	D₁₃	—	2	4	no	—
19	#41	—	13	4	no	—
20	#41	—	13	6	no	—
21	C₂×Q₈	—	13	4	no	—
22	C₂×Q₈	D₁₃	1	1	yes	characteristic, complemented
23	C₁₃	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
24	Q₈	—	13	6	no	—
25	Q₈	C₂×D₁₃	1	4	yes	—
26	D₄	—	13	4	no	—
27	D₄	—	13	6	no	—
28	C₂×C₄	—	13	12	no	—
29	C₂×C₄	C₂×D₁₃	1	3	yes	—
30	C₂²	—	13	4	no	—
31	C₂²	C₂²×D₁₃	1	1	yes	characteristic
32	C₄	—	13	4	no	—
33	C₄	C₂²×D₁₃	1	6	yes	—
34	C₂	—	2	1	no	—
35	C₂	—	26	4	no	—
36	C₂	C₂³×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.