Subgroups — C₁₃×C₂²⋊#89204 #37524601

Order 22932.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#89204	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇²×C₁₃	—	3	1	no	—
4	C₁₃×C₂²⋊(C₇⋊C₉)	—	7	8	no	maximal
5	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇²×C₁₃	A₄	1	1	yes	characteristic
7	C₂²⋊#89204	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇²×C₁₃	—	3	1	no	—
9	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	1	8	yes	—
10	C₁₃×C₇⋊C₉	—	28	8	no	—
11	C₇²×C₁₃	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₇²	C₃×C₁₃	1	1	yes	characteristic
13	C₂×C₃×C₇×C₁₃	—	3	8	no	—
14	C₁₃×C₂²⋊C₉	—	49	1	no	Hall
15	#89204	—	4	1	no	Hall
16	C₂²×C₇×C₁₃	C₇⋊C₉	1	8	yes	complemented
17	C₂×C₃×C₇²	—	3	1	no	—
18	C₃×C₇×C₁₃	C₂²⋊ΓL(1,𝔽₈)	1	8	yes	—
19	C₂²⋊(C₇⋊C₉)	—	7	8	no	—
20	C₂²×C₇²	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₁₃	—	3	8	no	—
22	C₂²×C₃×C₁₃	#3861	1	1	yes	characteristic
23	C₃×C₇²	A₄×C₁₃	1	1	yes	characteristic
24	C₉×C₁₃	—	196	1	no	Hall
25	C₂×C₇²	—	3	1	no	—
26	C₇×C₁₃	C₂²⋊(C₇⋊C₉)	1	8	yes	complemented
27	C₂²×C₃×C₇	C₁₃×ΓL(1,𝔽₈)	1	8	yes	—
28	C₂×C₃×C₁₃	—	3	1	no	—
29	C₇⋊C₉	—	28	8	no	—
30	C₂²×C₁₃	#89204	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₁₃×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	3	8	no	—
33	C₃×C₁₃	C₂²⋊#3861	1	1	yes	characteristic
34	C₂²⋊C₉	—	49	1	no	Hall
35	C₂²×C₇	C₁₃×C₇⋊C₉	1	8	yes	complemented
36	C₂×C₁₃	—	3	1	no	—
37	C₃×C₇	C₁₃×C₂²⋊ΓL(1,𝔽₈)	1	8	yes	—
38	C₂×C₇	—	3	8	no	—
39	C₁₃	C₂²⋊#89204	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²×C₃	C₁₃×#3861	1	1	yes	characteristic
41	C₉	—	196	1	no	Sylow
42	C₇	C₁₃×C₂²⋊(C₇⋊C₉)	1	8	yes	complemented
43	C₂×C₃	—	3	1	no	—
44	C₂²	C₁₃×#89204	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₃×C₂²⋊#3861	1	1	yes	characteristic
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₂²⋊#3861
commutator, hypocenter	C₂²×C₇²	C₉×C₁₃
Frattini	C₃	C₁₃×C₂²⋊#3861
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₃	C₃
cosocle	C₂²×C₃×C₇²	C₃×C₁₃
LCS	G ▷ C₂²×C₇²
UCS	C₁ ◁ C₃×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₂²×C₇²×C₁₃	C₉	semidirect
7. C₂²⋊#89204	C₁₃	direct (N × H)
11. C₇²×C₁₃	C₂²⋊C₉	semidirect
16. C₂²×C₇×C₁₃	C₇⋊C₉	semidirect
20. C₂²×C₇²	C₉×C₁₃	semidirect
26. C₇×C₁₃	C₂²⋊(C₇⋊C₉)	semidirect
30. C₂²×C₁₃	#89204	semidirect
31. C₇²	C₁₃×C₂²⋊C₉	semidirect
35. C₂²×C₇	C₁₃×C₇⋊C₉	semidirect
39. C₁₃	C₂²⋊#89204	direct (N × H)
42. C₇	C₁₃×C₂²⋊(C₇⋊C₉)	semidirect
44. C₂²	C₁₃×#89204	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₇²×C₁₃	3
C₁₃×#89204	4
C₁₃×C₂²⋊(C₇⋊C₉)	7
C₂²⋊#89204	13

Subgroups — C13×C22⋊#89204 #37524601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂²⋊#89204 #37524601