Subgroups — D₁₃×#11925890 #44538151

Order 31460.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊#11925890	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#11925890	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×#10597245	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#10597245	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₁₁×D₁₃	—	5	1	no	maximal, Hall
6	C₁₁×D₁₄₃	—	5	1	no	—
7	C₁₁×C₁₃×D₁₁	—	5	1	no	—
8	C₁₁²×D₁₃	D₅	1	1	yes	characteristic, complemented
9	C₂×#11925890	—	13	1	no	maximal, Hall
10	C₁₁²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₁₃×C₁₁⋊C₅	—	22	1	no	—
12	C₂×#10597245	—	13	1	no	—
13	#11925890	—	13	1	no	—
14	#11925890	D₁₃	1	1	yes	characteristic, direct product factor
15	C₁₃×C₁₁⋊C₅	—	22	1	no	—
16	#10597245	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×D₁₃	—	55	1	no	—
18	D₁₁×D₁₃	—	5	1	no	—
19	C₂×C₁₁×D₁₁	—	65	1	no	Hall
20	C₂×C₁₁×C₁₃	—	55	1	no	—
21	D₁₄₃	—	5	1	no	—
22	C₁₁×D₁₃	—	2	1	no	—
23	C₁₁×D₁₃	—	5	1	no	—
24	C₁₁×D₁₃	—	5	1	no	—
25	C₁₁×D₁₃	—	55	1	no	—
26	C₁₃×D₁₁	—	5	1	no	—
27	D₅×D₁₃	—	121	1	no	maximal, Hall
28	C₂×C₁₁²	—	13	1	no	—
29	C₁₁×D₁₁	—	5	1	no	—
30	C₁₁×D₁₁	—	65	1	no	—
31	C₁₁×C₁₃	—	2	1	no	—
32	C₁₁×C₁₃	—	5	1	no	—
33	C₁₁×C₁₃	—	5	1	no	—
34	D₆₅	—	121	1	no	—
35	C₅×D₁₃	—	121	1	no	—
36	D₅×C₁₃	—	121	1	no	—
37	C₁₁²	D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁⋊C₅	—	286	1	no	—
39	C₅×C₁₃	—	121	1	no	Hall
40	C₁₁⋊C₅	—	22	1	no	—
41	C₂×D₁₃	—	55	1	no	Hall
42	C₂²×C₁₁	—	715	1	no	—
43	C₂×D₁₁	—	65	1	no	—
44	C₂×C₁₃	—	55	1	no	—
45	D₁₃	—	55	1	no	—
46	D₁₃	#11925890	1	1	yes	characteristic, direct product factor
47	C₂×C₁₁	—	26	1	no	—
48	C₂×C₁₁	—	55	1	no	—
49	C₂×C₁₁	—	65	1	no	—
50	C₂×C₁₁	—	65	1	no	—
51	C₂×C₁₁	—	715	1	no	—
52	D₁₁	—	5	1	no	—
53	D₁₁	—	65	1	no	—
54	C₂×D₅	—	1573	1	no	Hall
55	C₁₃	C₂×#11925890	1	1	yes	characteristic, complemented, Sylow
56	C₁₁	—	2	1	no	—
57	C₁₁	—	5	1	no	—
58	C₁₁	—	5	1	no	—
59	C₂×C₅	—	1573	1	no	—
60	D₅	—	1573	1	no	—
61	D₅	—	121	1	no	—
62	C₅	—	121	1	no	Sylow
63	C₂²	—	715	1	no	Sylow
64	C₂	—	13	1	no	—
65	C₂	—	55	1	no	—
66	C₂	—	715	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₃×#10597245	C₂²
Fitting, socle	C₁₁²×C₁₃	C₂×D₅
LCS	G ▷ C₁₃×#10597245
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊#11925890	C₂	semidirect
2. C₁₃×#11925890	C₂	semidirect
3. D₁₃×#10597245	C₂	semidirect
4. C₁₃×#10597245	C₂²	semidirect
8. C₁₁²×D₁₃	D₅	semidirect
10. C₁₁²×C₁₃	C₂×D₅	semidirect
14. #11925890	D₁₃	direct (N × H)
16. #10597245	C₂×D₁₃	semidirect
37. C₁₁²	D₅×D₁₃	semidirect
46. D₁₃	#11925890	direct (N × H)
55. C₁₃	C₂×#11925890	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊#11925890	2
C₁₃×#11925890	2
D₁₃×#10597245	2
C₁₁×D₁₁×D₁₃	5
C₂×#11925890	13
D₅×D₁₃	121

Subgroups — D13×#11925890 #44538151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#11925890 #44538151