Subgroups — C₂×C₁₃⋊C₃×D₂₃₇ #49149608

Order 36972.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊C₃×D₂₃₇
commutator, cosocle, hypocenter	C₃×C₁₃×C₇₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃⋊C₃×C₇₉	C₂	semidirect
2. C₁₃⋊C₃×D₂₃₇	C₂	direct (N × H)
3. C₂×C₁₃×D₂₃₇	C₃	semidirect
5. C₃×C₁₃⋊C₃×C₇₉	C₂²	semidirect
7. C₁₃×D₂₃₇	C₂×C₃	semidirect
9. C₂×C₁₃⋊C₃×C₇₉	D₃	semidirect
10. C₂×C₃×C₁₃×C₇₉	C₂×C₃	semidirect
12. C₃×C₁₃×C₇₉	C₂²×C₃	semidirect
14. C₁₃⋊C₃×C₇₉	C₂×D₃	semidirect
16. C₂×C₁₃×C₇₉	C₃×D₃	semidirect
20. C₁₃×C₇₉	C₂×C₃×D₃	semidirect
21. C₂×D₂₃₇	C₁₃⋊C₃	direct (N × H)
26. C₂×C₃×C₇₉	C₂×C₁₃⋊C₃	semidirect
27. D₂₃₇	C₂×C₁₃⋊C₃	direct (N × H)
33. C₃×C₇₉	C₂²×C₁₃⋊C₃	semidirect
34. C₂×C₃×C₁₃⋊C₃	D₇₉	semidirect
36. C₂×C₇₉	D₃×C₁₃⋊C₃	semidirect
40. C₃×C₁₃⋊C₃	C₂×D₇₉	semidirect
41. C₇₉	C₂×D₃×C₁₃⋊C₃	semidirect
42. C₂×C₃×C₁₃	C₃×D₇₉	semidirect
46. C₂×C₁₃⋊C₃	D₂₃₇	direct (N × H)
48. C₃×C₁₃	C₂×C₃×D₇₉	semidirect
50. C₁₃⋊C₃	C₂×D₂₃₇	direct (N × H)
53. C₂×C₁₃	C₃×D₂₃₇	semidirect
56. C₁₃	C₂×C₃×D₂₃₇	semidirect
63. C₂×C₃	C₁₃⋊C₃×D₇₉	semidirect
68. C₃	C₂×C₁₃⋊C₃×D₇₉	semidirect
70. C₂	C₁₃⋊C₃×D₂₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃⋊C₃×C₇₉	2
C₁₃⋊C₃×D₂₃₇	2
C₂×C₁₃×D₂₃₇	3
C₂×C₁₃⋊C₃×D₇₉	3
C₂×C₃×D₂₃₇	13
C₂×D₃×C₁₃⋊C₃	79

Subgroups — C2×C13⋊C3×D237 #49149608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃⋊C₃×D₂₃₇ #49149608