Subgroups — C₂₅⋊(#10620321⋊C₂) #45659409

Order 32850.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#10620321	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₈₂₅	C₃	1	1	yes	maximal, characteristic
3	C₅⋊(#10620321⋊C₂)	—	5	1	no	maximal
4	C₃×C₂₅×C₇₃	C₂×C₃	1	1	yes	characteristic
5	D₁₈₂₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₅×#10620321	D₅	1	1	yes	characteristic
7	C₃×D₃₆₅	—	5	1	no	—
8	C₂₅×C₇₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	#10620321⋊C₂	—	25	1	no	Hall
10	C₃×C₅×C₇₃	C₃×D₅	1	1	yes	characteristic
11	D₃₆₅	—	5	1	no	—
12	#10620321	D₂₅	1	1	yes	characteristic, complemented, Hall
13	C₉×D₂₅	—	73	1	no	maximal, Hall
14	C₃×D₇₃	—	25	1	no	—
15	C₅×C₇₃	C₉×D₅	1	1	yes	characteristic
16	C₉×C₂₅	—	73	1	no	Hall
17	C₃×C₇₃	C₃×D₂₅	1	1	yes	characteristic
18	C₃×D₂₅	—	73	1	no	—
19	D₇₃	—	25	1	no	Hall
20	C₉×D₅	—	365	1	no	—
21	C₃×C₂₅	D₇₃⋊C₃	1	1	yes	characteristic
22	C₇₃	C₉×D₂₅	1	1	yes	characteristic, complemented, Sylow
23	D₂₅	—	73	1	no	Hall
24	C₅×C₉	—	73	1	no	—
25	C₃×D₅	—	365	1	no	—
26	C₂₅	#10620321⋊C₂	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	1825	1	no	Hall
28	C₃×C₅	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic
29	D₅	—	365	1	no	—
30	C₉	—	73	1	no	Sylow
31	C₂×C₃	—	1825	1	no	—
32	C₅	C₅⋊(#10620321⋊C₂)	1	1	yes	characteristic
33	C₃	C₂₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic
34	C₂	—	1825	1	no	Sylow

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.