Subgroups — D₁₃×D₆₁₁ #44540965

Order 31772.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃⋊D₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₆₁₁	—	13	1	no	maximal
6	D₁₃×D₄₇	—	13	1	no	maximal
7	C₂×C₁₃×C₄₇	—	13	1	no	—
8	D₆₁₁	—	13	1	no	—
9	D₆₁₁	—	13	1	no	—
10	D₆₁₁	—	26	6	no	—
11	D₆₁₁	D₁₃	1	1	yes	characteristic, direct product factor
12	C₁₃×D₄₇	—	13	1	no	—
13	D₁₃×C₄₇	D₁₃	1	1	yes	characteristic, complemented
14	D₁₃²	—	47	1	no	maximal, Hall
15	C₁₃×C₄₇	—	2	6	no	—
16	C₁₃×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented
17	C₁₃×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented
18	C₁₃⋊D₁₃	—	47	1	no	—
19	C₁₃×D₁₃	—	47	1	no	—
20	C₁₃×D₁₃	D₄₇	1	1	yes	characteristic, complemented
21	C₂×D₄₇	—	169	1	no	Hall
22	C₁₃²	C₂×D₄₇	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄₇	—	13	1	no	—
24	D₄₇	—	13	1	no	—
25	D₄₇	—	169	1	no	—
26	C₂×D₁₃	—	611	1	no	—
27	C₂×D₁₃	—	611	1	no	—
28	C₄₇	D₁₃²	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₃	—	13	1	no	—
30	C₂×C₁₃	—	611	1	no	—
31	D₁₃	—	47	1	no	—
32	D₁₃	—	611	1	no	—
33	D₁₃	—	611	1	no	—
34	D₁₃	—	1222	6	no	—
35	D₁₃	D₆₁₁	1	1	yes	characteristic, direct product factor
36	C₁₃	—	2	6	no	—
37	C₁₃	D₁₃×D₄₇	1	1	yes	characteristic, complemented
38	C₁₃	C₂×D₆₁₁	1	1	yes	characteristic, complemented
39	C₂²	—	7943	1	no	Sylow
40	C₂	—	7943	1	no	—
41	C₂	—	13	1	no	—
42	C₂	—	611	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₄₇	C₂²
LCS	G ▷ C₁₃²×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₃×C₄₇	C₂	semidirect
2. C₁₃×D₆₁₁	C₂	semidirect
3. C₁₃⋊D₆₁₁	C₂	semidirect
4. C₁₃²×C₄₇	C₂²	semidirect
11. D₆₁₁	D₁₃	direct (N × H)
13. D₁₃×C₄₇	D₁₃	semidirect
16. C₁₃×C₄₇	C₂×D₁₃	semidirect
17. C₁₃×C₄₇	C₂×D₁₃	semidirect
20. C₁₃×D₁₃	D₄₇	semidirect
22. C₁₃²	C₂×D₄₇	semidirect
28. C₄₇	D₁₃²	semidirect
35. D₁₃	D₆₁₁	direct (N × H)
37. C₁₃	D₁₃×D₄₇	semidirect
38. C₁₃	C₂×D₆₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₁₃×C₄₇	2
C₁₃×D₆₁₁	2
C₁₃⋊D₆₁₁	2
C₂×D₆₁₁	13
D₁₃×D₄₇	13
D₁₃²	47

Subgroups — D13×D611 #44540965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×D₆₁₁ #44540965