Subgroups — C₁₃×C₂²⋊(C₆₇⋊C₉) #44535628

Order 31356.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₆₇⋊C₉	—	4	1	no	maximal, Hall
3	C₂×C₃×C₁₃×C₆₇	—	3	1	no	—
4	C₂²×C₁₃×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₆₇	A₄	1	1	yes	characteristic
6	C₂²⋊(C₆₇⋊C₉)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₆₇	—	3	1	no	—
8	C₁₃×C₆₇	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₃×C₆₇	C₃×C₁₃	1	1	yes	characteristic
10	C₆₇⋊C₉	—	4	1	no	Hall
11	C₁₃×C₂²⋊C₉	—	67	1	no	maximal, Hall
12	C₂×C₃×C₆₇	—	3	1	no	—
13	C₂²×C₆₇	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₆₇	A₄×C₁₃	1	1	yes	characteristic
15	C₂²×C₃×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic
16	C₂×C₆₇	—	3	1	no	—
17	C₉×C₁₃	—	268	1	no	Hall
18	C₂×C₃×C₁₃	—	3	1	no	—
19	C₆₇	C₁₃×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₃	C₆₇⋊C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₃	C₂²⋊(C₆₇⋊C₃)	1	1	yes	characteristic
22	C₂²⋊C₉	—	67	1	no	Hall
23	C₂×C₁₃	—	3	1	no	—
24	C₁₃	C₂²⋊(C₆₇⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₁₃×C₆₇⋊C₃	1	1	yes	characteristic
26	C₉	—	268	1	no	Sylow
27	C₂×C₃	—	3	1	no	—
28	C₂²	C₁₃×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₃×C₂²⋊(C₆₇⋊C₃)	1	1	yes	characteristic
30	C₂	—	3	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.