Subgroups — C₁₃×#15668502 #49179366

Order 37700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₇₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₂₅×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×#10596814	—	5	1	no	maximal
4	C₁₃×D₁₄₅	—	5	1	no	—
5	#15668502	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic
7	C₁₃×#1181	—	25	1	no	Hall
8	D₇₂₅	C₂×C₁₃	1	1	yes	characteristic
9	C₁₃×#1035	—	29	1	no	maximal, Hall
10	C₁₃×D₂₉	—	25	1	no	—
11	C₂₅×C₂₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×D₂₅	—	29	1	no	—
13	#10596814	—	5	1	no	—
14	C₁₃×C₂₉	#1035	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₂₅	#1181	1	1	yes	characteristic, complemented, Hall
16	D₁₄₅	—	5	1	no	—
17	C₁₃×AGL(1,𝔽₅)	—	145	1	no	—
18	C₅×C₂₉	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic
19	D₅×C₁₃	—	145	1	no	—
20	#1181	—	25	1	no	Hall
21	#1035	—	29	1	no	Hall
22	C₅×C₁₃	#10596814	1	1	yes	characteristic
23	D₂₉	—	25	1	no	—
24	C₄×C₁₃	—	725	1	no	Hall
25	D₂₅	—	29	1	no	—
26	C₂₉	C₁₃×#1035	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₃	—	725	1	no	—
28	C₂₅	C₁₃×#1181	1	1	yes	characteristic, complemented, Sylow
29	AGL(1,𝔽₅)	—	145	1	no	—
30	C₁₃	#15668502	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	145	1	no	—
32	C₅	C₁₃×#10596814	1	1	yes	characteristic
33	C₄	—	725	1	no	Sylow
34	C₂	—	725	1	no	—

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.