Subgroups — C₂³×C₁₃×2₋¹⁺⁴ #15749438

Order 3328.

59806 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×2₋¹⁺⁴	C₂	1	112	yes	maximal, direct product factor
2	C₂³×C₁₃×#41	C₂	1	10	yes	maximal, complemented
3	C₂⁴×Q₈×C₁₃	C₂	1	5	yes	maximal, complemented
4	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1792	yes	direct product factor
5	C₂²×C₁₃×#41	C₂²	1	560	yes	complemented
6	C₂³×Q₈×C₁₃	C₂²	1	10	yes	—
7	C₂³×Q₈×C₁₃	C₂²	1	280	yes	complemented
8	C₂³×D₄×C₁₃	C₂²	1	10	yes	—
9	C₂⁴×C₄×C₁₃	C₂²	1	15	yes	—
10	C₂⁵×C₁₃	C₂³	1	5	yes	—
11	C₁₃×2₋¹⁺⁴	C₂³	1	4096	yes	direct product factor
12	C₂×C₁₃×#41	C₂³	1	4480	yes	complemented
13	C₂²×Q₈×C₁₃	C₂³	1	280	yes	—
14	C₂²×Q₈×C₁₃	C₂³	1	2240	yes	complemented
15	C₂²×D₄×C₁₃	C₂³	1	280	yes	—
16	C₂³×C₄×C₁₃	C₂³	1	420	yes	—
17	C₂³×C₄×C₁₃	C₂³	1	10	yes	—
18	C₂³×2₋¹⁺⁴	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂⁴×C₁₃	—	2	40	no	—
20	C₂⁴×C₁₃	C₂⁴	1	70	yes	—
21	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
22	C₁₃×#41	C₂⁴	1	5120	yes	complemented
23	C₂×Q₈×C₁₃	C₂⁴	1	1120	yes	—
24	C₂×Q₈×C₁₃	C₂⁴	1	2560	yes	complemented
25	C₂×D₄×C₁₃	C₂⁴	1	1120	yes	—
26	C₂²×C₄×C₁₃	C₂⁴	1	140	yes	—
27	C₂²×C₄×C₁₃	C₂⁴	1	1680	yes	—
28	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	112	yes	direct product factor
29	C₂³×#41	C₂×C₁₃	1	10	yes	complemented
30	C₂⁴×Q₈	C₂×C₁₃	1	5	yes	complemented
31	C₂³×C₁₃	—	2	280	no	—
32	C₂³×C₁₃	2₋¹⁺⁴	1	8	yes	direct product factor
33	C₂³×C₁₃	C₂⁵	1	140	yes	—
34	C₂³×C₁₃	C₂⁵	1	7	yes	—
35	Q₈×C₁₃	C₂⁵	1	640	yes	—
36	D₄×C₁₃	C₂⁵	1	640	yes	—
37	C₂×C₄×C₁₃	C₂⁵	1	280	yes	—
38	C₂×C₄×C₁₃	C₂⁵	1	960	yes	—
39	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1792	yes	direct product factor
40	C₂²×#41	C₂²×C₁₃	1	560	yes	complemented
41	C₂³×Q₈	C₂²×C₁₃	1	10	yes	—
42	C₂³×Q₈	C₂²×C₁₃	1	280	yes	complemented
43	C₂³×D₄	C₂²×C₁₃	1	10	yes	—
44	C₂⁴×C₄	C₂²×C₁₃	1	15	yes	—
45	C₂²×C₁₃	—	2	280	no	—
46	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	28	yes	direct product factor
47	C₂²×C₁₃	C₂⁶	1	40	yes	—
48	C₂²×C₁₃	C₂⁶	1	7	yes	—
49	C₄×C₁₃	C₂⁶	1	80	yes	—
50	C₂⁵	C₂³×C₁₃	1	5	yes	—
51	2₋¹⁺⁴	C₂³×C₁₃	1	4096	yes	direct product factor
52	C₂×#41	C₂³×C₁₃	1	4480	yes	complemented
53	C₂²×Q₈	C₂³×C₁₃	1	280	yes	—
54	C₂²×Q₈	C₂³×C₁₃	1	2240	yes	complemented
55	C₂²×D₄	C₂³×C₁₃	1	280	yes	—
56	C₂³×C₄	C₂³×C₁₃	1	10	yes	—
57	C₂³×C₄	C₂³×C₁₃	1	420	yes	—
58	C₂×C₁₃	—	2	40	no	—
59	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	14	yes	direct product factor
60	C₂×C₁₃	C₂⁷	1	1	yes	characteristic
61	C₂⁴	—	2	40	no	—
62	C₂⁴	C₂⁴×C₁₃	1	70	yes	—
63	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
64	#41	C₂⁴×C₁₃	1	5120	yes	complemented
65	C₂×Q₈	C₂⁴×C₁₃	1	1120	yes	—
66	C₂×Q₈	C₂⁴×C₁₃	1	2560	yes	complemented
67	C₂×D₄	C₂⁴×C₁₃	1	1120	yes	—
68	C₂²×C₄	C₂⁴×C₁₃	1	140	yes	—
69	C₂²×C₄	C₂⁴×C₁₃	1	1680	yes	—
70	C₁₃	C₂³×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³	—	2	280	no	—
72	C₂³	C₁₃×2₋¹⁺⁴	1	8	yes	direct product factor
73	C₂³	C₂⁵×C₁₃	1	140	yes	—
74	C₂³	C₂⁵×C₁₃	1	7	yes	—
75	Q₈	C₂⁵×C₁₃	1	640	yes	—
76	D₄	C₂⁵×C₁₃	1	640	yes	—
77	C₂×C₄	C₂⁵×C₁₃	1	280	yes	—
78	C₂×C₄	C₂⁵×C₁₃	1	960	yes	—
79	C₂²	—	2	280	no	—
80	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	28	yes	direct product factor
81	C₂²	C₂⁶×C₁₃	1	40	yes	—
82	C₂²	C₂⁶×C₁₃	1	7	yes	—
83	C₄	C₂⁶×C₁₃	1	80	yes	—
84	C₂	—	2	40	no	—
85	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	14	yes	direct product factor
86	C₂	C₂⁷×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁷×C₁₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×2₋¹⁺⁴	C₂	direct (N × H)
2. C₂³×C₁₃×#41	C₂	semidirect
3. C₂⁴×Q₈×C₁₃	C₂	semidirect
4. C₂×C₁₃×2₋¹⁺⁴	C₂²	direct (N × H)
5. C₂²×C₁₃×#41	C₂²	semidirect
7. C₂³×Q₈×C₁₃	C₂²	semidirect
11. C₁₃×2₋¹⁺⁴	C₂³	direct (N × H)
12. C₂×C₁₃×#41	C₂³	semidirect
14. C₂²×Q₈×C₁₃	C₂³	semidirect
18. C₂³×2₋¹⁺⁴	C₁₃	direct (N × H)
22. C₁₃×#41	C₂⁴	semidirect
24. C₂×Q₈×C₁₃	C₂⁴	semidirect
28. C₂²×2₋¹⁺⁴	C₂×C₁₃	direct (N × H)
29. C₂³×#41	C₂×C₁₃	semidirect
30. C₂⁴×Q₈	C₂×C₁₃	semidirect
32. C₂³×C₁₃	2₋¹⁺⁴	direct (N × H)
39. C₂×2₋¹⁺⁴	C₂²×C₁₃	direct (N × H)
40. C₂²×#41	C₂²×C₁₃	semidirect
42. C₂³×Q₈	C₂²×C₁₃	semidirect
46. C₂²×C₁₃	C₂×2₋¹⁺⁴	direct (N × H)
51. 2₋¹⁺⁴	C₂³×C₁₃	direct (N × H)
52. C₂×#41	C₂³×C₁₃	semidirect
54. C₂²×Q₈	C₂³×C₁₃	semidirect
59. C₂×C₁₃	C₂²×2₋¹⁺⁴	direct (N × H)
64. #41	C₂⁴×C₁₃	semidirect
66. C₂×Q₈	C₂⁴×C₁₃	semidirect
70. C₁₃	C₂³×2₋¹⁺⁴	direct (N × H)
72. C₂³	C₁₃×2₋¹⁺⁴	direct (N × H)
80. C₂²	C₂×C₁₃×2₋¹⁺⁴	direct (N × H)
85. C₂	C₂²×C₁₃×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×2₋¹⁺⁴	2
C₂³×C₁₃×#41	2
C₂⁴×Q₈×C₁₃	2
C₂³×2₋¹⁺⁴	13

Subgroups — C23×C13×2−1+4 #15749438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₃×2₋¹⁺⁴ #15749438