Subgroups — #88111

Order 416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#1057	C₂	1	2	yes	maximal, complemented
3	C₂²×D₁₃	C₄	1	1	yes	characteristic
4	C₂×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₄×D₁₃	—	2	2	no	—
7	#1057	—	2	2	no	—
8	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×D₁₃	—	2	1	no	—
10	C₂×D₁₃	—	2	1	no	—
11	C₂×D₁₃	C₈	1	2	yes	complemented
12	C₄×C₁₃	—	2	1	no	—
13	Dic₁₃	D₄	1	2	yes	—
14	C₂²⋊C₈	—	13	1	no	maximal, Sylow
15	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₃	M₁₆	1	1	yes	characteristic
18	D₁₃	—	2	2	no	—
19	C₂²×C₄	—	13	1	no	—
20	C₂×C₈	—	13	2	no	—
21	C₁₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂³	—	13	1	no	—
23	C₂×C₄	—	13	1	no	—
24	C₂×C₄	—	26	2	no	—
25	C₂×C₄	#261	1	1	yes	characteristic
26	C₈	—	26	2	no	—
27	C₂²	—	13	2	no	—
28	C₂²	—	26	1	no	—
29	C₂²	—	26	1	no	—
30	C₂²	C₂×#261	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	13	2	no	—
33	C₂	—	26	2	no	—
34	C₂	D₁₃⋊C₈	1	1	yes	characteristic
35	C₂	#6118	1	1	yes	characteristic
36	C₂	C₂²⋊#261	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.