Subgroups — C₁₃×C₂²⋊#89205 #37524595

Order 22932.

104 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×#89205	—	4	1	no	maximal, Hall
3	C₂×C₃×C₇²×C₁₃	—	3	1	no	—
4	C₁₃×C₂²⋊(C₇⋊C₉)	—	7	2	no	maximal
5	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇²×C₁₃	A₄	1	1	yes	characteristic
7	C₂²⋊#89205	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇²×C₁₃	—	3	1	no	—
9	C₂²×C₃×C₇×C₁₃	—	3	2	no	—
10	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	1	2	yes	—
11	C₁₃×C₇⋊C₉	—	28	2	no	—
12	C₇²×C₁₃	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₃×C₇²	C₃×C₁₃	1	1	yes	characteristic
14	C₂×C₃×C₇×C₁₃	—	3	6	no	—
15	C₂×C₃×C₇×C₁₃	—	3	2	no	—
16	C₁₃×C₂²⋊C₉	—	49	1	no	Hall
17	#89205	—	4	1	no	Hall
18	C₂²×C₇×C₁₃	—	3	2	no	—
19	C₂²×C₇×C₁₃	C₇⋊C₉	1	2	yes	complemented
20	C₂×C₃×C₇²	—	3	1	no	—
21	C₃×C₇×C₁₃	—	3	2	no	—
22	C₃×C₇×C₁₃	C₂²⋊ΓL(1,𝔽₈)	1	2	yes	—
23	C₂²⋊(C₇⋊C₉)	—	7	2	no	—
24	C₂²×C₇²	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₃	—	3	6	no	—
26	C₂×C₇×C₁₃	—	3	2	no	—
27	C₂²×C₃×C₁₃	#3862	1	1	yes	characteristic
28	C₃×C₇²	A₄×C₁₃	1	1	yes	characteristic
29	C₉×C₁₃	—	196	1	no	Hall
30	C₂×C₇²	—	3	1	no	—
31	C₇×C₁₃	—	3	2	no	—
32	C₇×C₁₃	C₂²⋊(C₇⋊C₉)	1	2	yes	complemented
33	C₂²×C₃×C₇	—	3	2	no	—
34	C₂²×C₃×C₇	C₁₃×ΓL(1,𝔽₈)	1	2	yes	—
35	C₂×C₃×C₁₃	—	3	1	no	—
36	C₇⋊C₉	—	28	2	no	—
37	C₂²×C₁₃	#89205	1	1	yes	characteristic, complemented, Hall
38	C₇²	C₁₃×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃×C₇	—	3	6	no	—
40	C₂×C₃×C₇	—	3	2	no	—
41	C₃×C₁₃	C₂²⋊#3862	1	1	yes	characteristic
42	C₂²⋊C₉	—	49	1	no	Hall
43	C₂²×C₇	—	3	2	no	—
44	C₂²×C₇	C₁₃×C₇⋊C₉	1	2	yes	complemented
45	C₂×C₁₃	—	3	1	no	—
46	C₃×C₇	—	3	2	no	—
47	C₃×C₇	C₁₃×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	—
48	C₂×C₇	—	3	6	no	—
49	C₂×C₇	—	3	2	no	—
50	C₁₃	C₂²⋊#89205	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₃	C₁₃×#3862	1	1	yes	characteristic
52	C₉	—	196	1	no	Sylow
53	C₇	—	3	2	no	—
54	C₇	C₁₃×C₂²⋊(C₇⋊C₉)	1	2	yes	complemented
55	C₂×C₃	—	3	1	no	—
56	C₂²	C₁₃×#89205	1	1	yes	characteristic, complemented, Sylow
57	C₃	C₁₃×C₂²⋊#3862	1	1	yes	characteristic
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₂²⋊#3862
commutator, hypocenter	C₂²×C₇²	C₉×C₁₃
Frattini	C₃	C₁₃×C₂²⋊#3862
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⋊#89205	C₁₃	direct (N × H)
12. C₇²×C₁₃	C₂²⋊C₉	semidirect
19. C₂²×C₇×C₁₃	C₇⋊C₉	semidirect
24. C₂²×C₇²	C₉×C₁₃	semidirect
32. C₇×C₁₃	C₂²⋊(C₇⋊C₉)	semidirect
37. C₂²×C₁₃	#89205	semidirect
38. C₇²	C₁₃×C₂²⋊C₉	semidirect
44. C₂²×C₇	C₁₃×C₇⋊C₉	semidirect
50. C₁₃	C₂²⋊#89205	direct (N × H)
54. C₇	C₁₃×C₂²⋊(C₇⋊C₉)	semidirect
56. C₂²	C₁₃×#89205	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×#89205	4
C₁₃×C₂²⋊(C₇⋊C₉)	7
C₂²⋊#89205	13

Subgroups — C13×C22⋊#89205 #37524595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂²⋊#89205 #37524595