Subgroups — C₁₃×#239 #10597784

Order 624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₁₂	C₂	1	3	yes	maximal, complemented
3	C₄×D₃×C₁₃	C₂	1	3	yes	maximal, complemented
4	C₁₃×#41	—	3	1	no	maximal, Hall
5	C₂×D₃×C₁₃	C₂²	1	3	yes	—
6	C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	Dic₃×C₁₃	C₂²	1	1	yes	characteristic
8	Q₈×C₁₃	D₃	1	1	yes	characteristic, complemented
9	D₄×C₁₃	—	3	3	no	—
10	C₂×C₄×C₁₃	—	3	3	no	—
11	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	D₃×C₁₃	—	2	3	no	—
13	C₂²×C₁₃	—	3	3	no	—
14	C₄×C₁₃	—	3	1	no	—
15	C₄×C₁₃	C₂×D₃	1	3	yes	—
16	#239	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₁₃	#41	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃	—	6	3	no	—
19	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
20	C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
21	D₁₂	C₂×C₁₃	1	3	yes	complemented
22	C₄×D₃	C₂×C₁₃	1	3	yes	complemented
23	#41	—	3	1	no	Sylow
24	C₁₃	#239	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×D₃	C₂²×C₁₃	1	3	yes	—
26	C₃×C₄	C₂²×C₁₃	1	3	yes	—
27	Dic₃	C₂²×C₁₃	1	1	yes	characteristic
28	Q₈	D₃×C₁₃	1	1	yes	characteristic, complemented
29	D₄	—	3	3	no	—
30	C₂×C₄	—	3	3	no	—
31	C₂×C₃	C₂³×C₁₃	1	1	yes	characteristic
32	D₃	—	2	3	no	—
33	C₂²	—	3	3	no	—
34	C₄	—	3	1	no	—
35	C₄	C₂×D₃×C₁₃	1	3	yes	—
36	C₃	C₁₃×#41	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	6	3	no	—
38	C₂	C₂²×D₃×C₁₃	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.