Subgroups — D₁₃×C₃⋊D₂₃₇ #49149643

Order 36972.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₃×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₂₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃₀₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₂₃₇	—	3	4	no	maximal
5	C₃²×C₁₃×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₀₈₁	—	3	4	no	—
7	C₁₃×D₂₃₇	—	3	4	no	—
8	C₃×D₁₃×C₇₉	D₃	1	4	yes	complemented
9	D₁₃×D₇₉	—	9	1	no	Hall
10	C₃×C₁₃×C₇₉	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₂₃₇	—	13	1	no	maximal, Hall
12	D₁₀₂₇	—	9	1	no	—
13	C₁₃×D₇₉	—	9	1	no	—
14	D₁₃×C₇₉	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₇₉	—	13	1	no	—
16	C₃⋊D₂₃₇	—	13	1	no	—
17	C₃⋊D₂₃₇	D₁₃	1	1	yes	characteristic, direct product factor
18	C₁₃×C₇₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₂₃₇	—	39	4	no	—
20	C₃²×C₇₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇₉	—	13	4	no	—
22	D₂₃₇	—	3	4	no	—
23	D₂₃₇	—	39	4	no	—
24	C₃⋊D₃×D₁₃	—	79	1	no	maximal, Hall
25	C₂×D₇₉	—	117	1	no	Hall
26	C₃×C₇₉	D₃×D₁₃	1	4	yes	complemented
27	C₃⋊D₃₉	—	79	1	no	—
28	C₁₃×C₃⋊D₃	—	79	1	no	—
29	C₃²×D₁₃	D₇₉	1	1	yes	characteristic, complemented
30	C₂×C₇₉	—	13	1	no	—
31	D₇₉	—	9	1	no	—
32	D₇₉	—	117	1	no	—
33	D₃×D₁₃	—	237	4	no	—
34	C₃²×C₁₃	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
35	C₇₉	C₃⋊D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
36	D₃₉	—	237	4	no	—
37	C₃×D₁₃	D₂₃₇	1	4	yes	complemented
38	D₃×C₁₃	—	237	4	no	—
39	C₂×D₁₃	—	711	1	no	Hall
40	C₃×C₁₃	C₂×D₂₃₇	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	1027	1	no	Hall
42	C₂×C₁₃	—	711	1	no	—
43	D₁₃	—	711	1	no	—
44	D₁₃	C₃⋊D₂₃₇	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	13	1	no	—
46	C₃⋊D₃	—	1027	1	no	—
47	C₃⋊D₃	—	79	1	no	—
48	C₁₃	C₂×C₃⋊D₂₃₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	3081	4	no	—
50	C₃²	D₁₃×D₇₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	13	4	no	—
52	D₃	—	3081	4	no	—
53	D₃	—	237	4	no	—
54	C₂²	—	9243	1	no	Sylow
55	C₃	D₁₃×D₂₃₇	1	4	yes	complemented
56	C₂	—	13	1	no	—
57	C₂	—	9243	1	no	—
58	C₂	—	711	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃×C₇₉	C₂²
LCS	G ▷ C₃²×C₁₃×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₃×C₇₉	C₂	semidirect
2. C₁₃×C₃⋊D₂₃₇	C₂	semidirect
3. C₃⋊D₃₀₈₁	C₂	semidirect
5. C₃²×C₁₃×C₇₉	C₂²	semidirect
8. C₃×D₁₃×C₇₉	D₃	semidirect
10. C₃×C₁₃×C₇₉	C₂×D₃	semidirect
14. D₁₃×C₇₉	C₃⋊D₃	semidirect
17. C₃⋊D₂₃₇	D₁₃	direct (N × H)
18. C₁₃×C₇₉	C₂×C₃⋊D₃	semidirect
20. C₃²×C₇₉	C₂×D₁₃	semidirect
26. C₃×C₇₉	D₃×D₁₃	semidirect
29. C₃²×D₁₃	D₇₉	semidirect
34. C₃²×C₁₃	C₂×D₇₉	semidirect
35. C₇₉	C₃⋊D₃×D₁₃	semidirect
37. C₃×D₁₃	D₂₃₇	semidirect
40. C₃×C₁₃	C₂×D₂₃₇	semidirect
44. D₁₃	C₃⋊D₂₃₇	direct (N × H)
48. C₁₃	C₂×C₃⋊D₂₃₇	semidirect
50. C₃²	D₁₃×D₇₉	semidirect
55. C₃	D₁₃×D₂₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₃×C₇₉	2
C₁₃×C₃⋊D₂₃₇	2
C₃⋊D₃₀₈₁	2
D₁₃×D₂₃₇	3
C₂×C₃⋊D₂₃₇	13
C₃⋊D₃×D₁₃	79

Subgroups — D13×C3⋊D237 #49149643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₃⋊D₂₃₇ #49149643