Subgroups — #88158

Order 416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6127	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#6095	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²⋊D₁₃	—	2	2	no	—
8	D₅₂	C₂²	1	2	yes	—
9	C₄×D₁₃	—	2	2	no	—
10	Dic₂₆	C₂²	1	2	yes	—
11	C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃	D₄	1	1	yes	characteristic
14	C₂×D₁₃	—	2	2	no	—
15	C₄×C₁₃	D₄	1	1	yes	characteristic
16	C₄×C₁₃	C₂³	1	1	yes	characteristic
17	Dic₁₃	—	2	2	no	—
18	#135	—	13	1	no	maximal, Sylow
19	C₂×C₁₃	—	2	1	no	—
20	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
21	D₁₃	—	4	2	no	—
22	#41	—	13	2	no	—
23	Q₁₆	—	13	1	no	—
24	SD₁₆	—	13	2	no	—
25	D₈	—	13	1	no	—
26	C₂×C₈	D₁₃	1	1	yes	characteristic, complemented
27	C₁₃	#135	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	13	2	no	—
29	D₄	—	13	2	no	—
30	D₄	—	26	2	no	—
31	C₂×C₄	—	26	2	no	—
32	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
33	C₈	C₂×D₁₃	1	1	yes	characteristic
34	C₈	C₂×D₁₃	1	1	yes	characteristic
35	C₂²	—	26	2	no	—
36	C₂²	D₅₂	1	1	yes	characteristic
37	C₄	—	26	2	no	—
38	C₄	D₅₂	1	1	yes	characteristic
39	C₄	C₂²×D₁₃	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	52	2	no	—
42	C₂	C₂×D₅₂	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.