Subgroups — #72259197

Order 2704.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic
2	#13062574	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃⋊D₁₃	C₄	1	1	yes	characteristic
4	C₄×C₁₃²	C₄	1	1	yes	characteristic
5	#10621725	C₂²	1	1	yes	characteristic
6	C₂×C₁₃²	C₂×C₄	1	1	yes	characteristic
7	C₁₃⋊D₁₃	—	2	1	no	—
8	#6118	—	13	2	no	maximal
9	C₁₃²	M₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄×D₁₃	—	13	2	no	—
11	C₄×D₁₃	—	26	6	no	—
12	#1057	—	13	4	no	—
13	C₂×D₁₃	—	13	2	no	—
14	C₂×D₁₃	—	26	6	no	—
15	C₄×C₁₃	—	2	6	no	—
16	C₄×C₁₃	#261	1	2	yes	—
17	Dic₁₃	—	13	2	no	—
18	Dic₁₃	—	26	6	no	—
19	C₂×C₁₃	—	2	6	no	—
20	C₂×C₁₃	C₂×#261	1	2	yes	—
21	D₁₃	—	26	12	no	—
22	D₁₃	—	26	2	no	—
23	M₁₆	—	169	1	no	Sylow
24	C₁₃	—	2	6	no	—
25	C₁₃	#6118	1	2	yes	complemented
26	C₂×C₄	—	169	1	no	—
27	C₈	—	169	2	no	—
28	C₂²	—	169	1	no	—
29	C₄	—	169	1	no	—
30	C₄	#10621729	1	1	yes	characteristic
31	C₂	—	338	1	no	—
32	C₂	C₂×#10621729	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.