Subgroups — #10597728

Order 624.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#1057	C₂	1	2	yes	maximal, complemented
3	#6122	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₃×Dic₁₃	C₄	1	1	yes	characteristic
6	C₃×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₃	D₃	1	1	yes	characteristic
8	#1057	—	3	2	no	—
9	C₂×C₃×C₁₃	—	2	1	no	—
10	C₂×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₃	Dic₃	1	1	yes	characteristic
12	Dic₁₃	Dic₃	1	1	yes	characteristic
13	Dic₁₃	C₂×D₃	1	1	yes	characteristic
14	#208	—	13	1	no	maximal, Hall
15	C₃×C₁₃	M₁₆	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	2	1	no	—
17	C₂×C₁₃	C₂×Dic₃	1	1	yes	characteristic
18	C₂×C₃×C₄	—	13	1	no	—
19	C₃⋊C₈	—	13	2	no	—
20	M₁₆	—	39	1	no	Sylow
21	C₁₃	#208	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₃	#261	1	1	yes	characteristic
23	C₃×C₄	—	13	1	no	—
24	C₃×C₄	—	13	1	no	—
25	C₂×C₄	—	13	1	no	—
26	C₈	—	39	2	no	—
27	C₂×C₃	—	2	1	no	—
28	C₂×C₃	C₂×#261	1	1	yes	characteristic
29	C₂²	C₃⋊#261	1	1	yes	characteristic
30	C₄	—	13	1	no	—
31	C₄	—	13	1	no	—
32	C₃	#6122	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	2	1	no	—
34	C₂	C₂×C₃⋊#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.