Subgroups — C₂³×C₁₃×Q₃₂ #15748966

Order 3328.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×Q₁₆	C₂	1	2	yes	maximal
2	C₂²×C₁₃×Q₃₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×Q₈×C₁₃	—	2	2	no	—
5	C₂²×C₁₃×Q₁₆	—	2	14	no	—
6	C₂²×C₁₃×Q₁₆	C₂²	1	28	yes	—
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×Q₃₂	C₂²	1	112	yes	direct product factor
9	C₂²×C₁₃×C₁₆	C₂²	1	14	yes	—
10	C₂²×Q₈×C₁₃	—	2	28	no	—
11	C₂²×Q₈×C₁₃	—	4	14	no	—
12	C₂³×C₄×C₁₃	—	4	2	no	—
13	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₁₃×Q₁₆	—	2	84	no	—
15	C₂×C₁₃×Q₁₆	C₂³	1	56	yes	—
16	C₂²×C₈×C₁₃	D₄	1	7	yes	—
17	C₂²×C₈×C₁₃	C₂³	1	7	yes	—
18	C₁₃×Q₃₂	C₂³	1	64	yes	direct product factor
19	C₂×C₁₃×C₁₆	C₂³	1	28	yes	—
20	C₂³×Q₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
22	C₂×Q₈×C₁₃	—	2	56	no	—
23	C₂×Q₈×C₁₃	—	4	84	no	—
24	C₂²×C₄×C₁₃	—	4	28	no	—
25	C₂²×C₄×C₁₃	D₈	1	7	yes	—
26	C₂²×C₄×C₁₃	C₂×D₄	1	7	yes	—
27	C₁₃×Q₁₆	—	2	56	no	—
28	C₁₃×Q₁₆	C₂⁴	1	16	yes	—
29	C₂×C₈×C₁₃	C₂×D₄	1	21	yes	—
30	C₂×C₈×C₁₃	C₂⁴	1	7	yes	—
31	C₁₃×C₁₆	C₂⁴	1	8	yes	—
32	C₂³×Q₁₆	C₂×C₁₃	1	2	yes	—
33	C₂²×Q₃₂	C₂×C₁₃	1	28	yes	direct product factor
34	C₂³×C₁₆	C₂×C₁₃	1	1	yes	characteristic
35	C₂³×C₁₃	Q₃₂	1	8	yes	direct product factor
36	C₂³×C₁₃	C₂×D₈	1	7	yes	—
37	Q₈×C₁₃	—	2	16	no	—
38	Q₈×C₁₃	—	4	56	no	—
39	C₂×C₄×C₁₃	—	4	56	no	—
40	C₂×C₄×C₁₃	C₂×D₈	1	21	yes	—
41	C₂×C₄×C₁₃	C₂²×D₄	1	7	yes	—
42	C₈×C₁₃	C₂²×D₄	1	7	yes	—
43	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
44	C₂³×Q₈	—	2	2	no	—
45	C₂²×Q₁₆	—	2	14	no	—
46	C₂²×Q₁₆	C₂²×C₁₃	1	28	yes	—
47	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
48	C₂×Q₃₂	C₂²×C₁₃	1	112	yes	direct product factor
49	C₂²×C₁₆	C₂²×C₁₃	1	14	yes	—
50	C₂²×C₁₃	C₂×Q₃₂	1	28	yes	direct product factor
51	C₂²×C₁₃	C₂²×D₈	1	7	yes	—
52	C₄×C₁₃	—	4	16	no	—
53	C₄×C₁₃	C₂²×D₈	1	7	yes	—
54	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
55	C₂²×Q₈	—	2	28	no	—
56	C₂²×Q₈	—	4	14	no	—
57	C₂³×C₄	—	4	2	no	—
58	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
59	C₂×Q₁₆	—	2	84	no	—
60	C₂×Q₁₆	C₂³×C₁₃	1	56	yes	—
61	C₂²×C₈	D₄×C₁₃	1	7	yes	—
62	C₂²×C₈	C₂³×C₁₃	1	7	yes	—
63	Q₃₂	C₂³×C₁₃	1	64	yes	direct product factor
64	C₂×C₁₆	C₂³×C₁₃	1	28	yes	—
65	C₂×C₁₃	C₂²×Q₃₂	1	14	yes	direct product factor
66	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
67	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
68	C₂×Q₈	—	2	56	no	—
69	C₂×Q₈	—	4	84	no	—
70	C₂²×C₄	—	4	28	no	—
71	C₂²×C₄	C₁₃×D₈	1	7	yes	—
72	C₂²×C₄	C₂×D₄×C₁₃	1	7	yes	—
73	Q₁₆	—	2	56	no	—
74	Q₁₆	C₂⁴×C₁₃	1	16	yes	—
75	C₂×C₈	C₂×D₄×C₁₃	1	21	yes	—
76	C₂×C₈	C₂⁴×C₁₃	1	7	yes	—
77	C₁₆	C₂⁴×C₁₃	1	8	yes	—
78	C₁₃	C₂³×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³	C₁₃×Q₃₂	1	8	yes	direct product factor
80	C₂³	C₂×C₁₃×D₈	1	7	yes	—
81	Q₈	—	2	16	no	—
82	Q₈	—	4	56	no	—
83	C₂×C₄	—	4	56	no	—
84	C₂×C₄	C₂×C₁₃×D₈	1	21	yes	—
85	C₂×C₄	C₂²×D₄×C₁₃	1	7	yes	—
86	C₈	C₂²×D₄×C₁₃	1	7	yes	—
87	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
88	C₂²	C₂×C₁₃×Q₃₂	1	28	yes	direct product factor
89	C₂²	C₂²×C₁₃×D₈	1	7	yes	—
90	C₄	—	4	16	no	—
91	C₄	C₂²×C₁₃×D₈	1	7	yes	—
92	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
93	C₂	C₂²×C₁₃×Q₃₂	1	14	yes	direct product factor
94	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×Q₃₂	C₂	direct (N × H)
8. C₂×C₁₃×Q₃₂	C₂²	direct (N × H)
18. C₁₃×Q₃₂	C₂³	direct (N × H)
20. C₂³×Q₃₂	C₁₃	direct (N × H)
33. C₂²×Q₃₂	C₂×C₁₃	direct (N × H)
35. C₂³×C₁₃	Q₃₂	direct (N × H)
48. C₂×Q₃₂	C₂²×C₁₃	direct (N × H)
50. C₂²×C₁₃	C₂×Q₃₂	direct (N × H)
63. Q₃₂	C₂³×C₁₃	direct (N × H)
65. C₂×C₁₃	C₂²×Q₃₂	direct (N × H)
78. C₁₃	C₂³×Q₃₂	direct (N × H)
79. C₂³	C₁₃×Q₃₂	direct (N × H)
88. C₂²	C₂×C₁₃×Q₃₂	direct (N × H)
93. C₂	C₂²×C₁₃×Q₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×Q₁₆	2
C₂²×C₁₃×Q₃₂	2
C₂³×C₁₃×C₁₆	2
C₂³×Q₃₂	13

Subgroups — C23×C13×Q32 #15748966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₃×Q₃₂ #15748966