Subgroups — #88063

Order 416.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₃	C₄	1	2	yes	—
5	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	D₅₂	—	2	1	no	—
7	D₅₂	—	2	1	no	—
8	C₈×C₁₃	—	2	1	no	—
9	#1055	—	2	1	no	—
10	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₃	—	2	2	no	—
12	C₂×D₁₃	—	4	2	no	—
13	C₄×C₁₃	D₄	1	1	yes	characteristic
14	C₄×C₁₃	D₄	1	1	yes	characteristic
15	#100	—	13	1	no	maximal, Sylow
16	C₂×C₁₃	—	2	1	no	—
17	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₃	—	4	2	no	—
19	C₂×D₄	—	13	1	no	—
20	M₁₆	—	13	1	no	—
21	M₁₆	D₁₃	1	1	yes	characteristic, complemented
22	C₁₃	#100	1	1	yes	characteristic, complemented, Sylow
23	C₂³	—	13	2	no	—
24	D₄	—	26	1	no	—
25	D₄	—	26	1	no	—
26	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	26	1	no	—
29	C₂²	—	26	2	no	—
30	C₂²	—	52	2	no	—
31	C₂²	C₄×D₁₃	1	1	yes	characteristic
32	C₄	D₅₂	1	1	yes	characteristic
33	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	—	52	2	no	—
36	C₂	#6103	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.