Subgroups — C₂²×C₁₃×D₃₂ #15720314

Order 3328.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×D₃₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×D₈	—	2	2	no	—
5	C₂×C₁₃×D₁₆	—	2	6	no	—
6	C₂×C₁₃×D₁₆	C₂²	1	12	yes	complemented
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₃×D₃₂	C₂²	1	16	yes	direct product factor
9	C₂×C₁₃×C₃₂	C₂²	1	6	yes	complemented
10	C₂²×D₄×C₁₃	—	4	2	no	—
11	C₂×C₁₃×D₈	—	2	12	no	—
12	C₂×C₁₃×D₈	—	4	6	no	—
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₁₃×D₁₆	—	2	12	no	—
15	C₁₃×D₁₆	C₂³	1	8	yes	complemented
16	C₂×C₁₃×C₁₆	D₄	1	3	yes	—
17	C₂×C₁₃×C₁₆	C₂³	1	3	yes	—
18	C₁₃×C₃₂	C₂³	1	4	yes	complemented
19	C₂²×D₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂⁴×C₁₃	—	8	2	no	—
21	C₂×D₄×C₁₃	—	4	12	no	—
22	C₂×D₄×C₁₃	—	8	6	no	—
23	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
24	C₁₃×D₈	—	2	8	no	—
25	C₁₃×D₈	—	4	12	no	—
26	C₂×C₈×C₁₃	D₈	1	3	yes	—
27	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
28	C₁₃×C₁₆	C₂×D₄	1	3	yes	—
29	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
30	C₂²×D₁₆	C₂×C₁₃	1	2	yes	complemented
31	C₂×D₃₂	C₂×C₁₃	1	12	yes	direct product factor
32	C₂²×C₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
33	C₂³×C₁₃	—	8	12	no	—
34	C₂³×C₁₃	—	16	8	no	—
35	C₂³×C₁₃	D₁₆	1	1	yes	characteristic
36	D₄×C₁₃	—	4	8	no	—
37	D₄×C₁₃	—	8	12	no	—
38	C₂×C₄×C₁₃	D₁₆	1	3	yes	—
39	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
40	C₈×C₁₃	C₂×D₈	1	3	yes	—
41	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
42	C₂²×D₈	—	2	2	no	—
43	C₂×D₁₆	—	2	6	no	—
44	C₂×D₁₆	C₂²×C₁₃	1	12	yes	complemented
45	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
46	D₃₂	C₂²×C₁₃	1	16	yes	direct product factor
47	C₂×C₃₂	C₂²×C₁₃	1	6	yes	complemented
48	C₂²×C₁₃	—	8	8	no	—
49	C₂²×C₁₃	—	16	24	no	—
50	C₂²×C₁₃	D₃₂	1	4	yes	direct product factor
51	C₂²×C₁₃	C₂×D₁₆	1	3	yes	—
52	C₄×C₁₃	C₂×D₁₆	1	3	yes	—
53	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
54	C₂²×D₄	—	4	2	no	—
55	C₂×D₈	—	2	12	no	—
56	C₂×D₈	—	4	6	no	—
57	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
58	D₁₆	—	2	12	no	—
59	D₁₆	C₂³×C₁₃	1	8	yes	complemented
60	C₂×C₁₆	D₄×C₁₃	1	3	yes	—
61	C₂×C₁₆	C₂³×C₁₃	1	3	yes	—
62	C₃₂	C₂³×C₁₃	1	4	yes	complemented
63	C₂×C₁₃	—	16	8	no	—
64	C₂×C₁₃	C₂×D₃₂	1	6	yes	direct product factor
65	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
66	C₂⁴	—	8	2	no	—
67	C₂×D₄	—	4	12	no	—
68	C₂×D₄	—	8	6	no	—
69	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
70	D₈	—	2	8	no	—
71	D₈	—	4	12	no	—
72	C₂×C₈	C₁₃×D₈	1	3	yes	—
73	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
74	C₁₆	C₂×D₄×C₁₃	1	3	yes	—
75	C₁₆	C₂⁴×C₁₃	1	1	yes	characteristic
76	C₁₃	C₂²×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³	—	8	12	no	—
78	C₂³	—	16	8	no	—
79	C₂³	C₁₃×D₁₆	1	1	yes	characteristic
80	D₄	—	4	8	no	—
81	D₄	—	8	12	no	—
82	C₂×C₄	C₁₃×D₁₆	1	3	yes	—
83	C₂×C₄	C₂×C₁₃×D₈	1	3	yes	—
84	C₈	C₂×C₁₃×D₈	1	3	yes	—
85	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
86	C₂²	—	8	8	no	—
87	C₂²	—	16	24	no	—
88	C₂²	C₁₃×D₃₂	1	4	yes	direct product factor
89	C₂²	C₂×C₁₃×D₁₆	1	3	yes	—
90	C₄	C₂×C₁₃×D₁₆	1	3	yes	—
91	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
92	C₂	—	16	8	no	—
93	C₂	C₂×C₁₃×D₃₂	1	6	yes	direct product factor
94	C₂	C₂²×C₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×D₁₆	C₂	semidirect
2. C₂×C₁₃×D₃₂	C₂	direct (N × H)
3. C₂²×C₁₃×C₃₂	C₂	semidirect
6. C₂×C₁₃×D₁₆	C₂²	semidirect
8. C₁₃×D₃₂	C₂²	direct (N × H)
9. C₂×C₁₃×C₃₂	C₂²	semidirect
15. C₁₃×D₁₆	C₂³	semidirect
18. C₁₃×C₃₂	C₂³	semidirect
19. C₂²×D₃₂	C₁₃	direct (N × H)
30. C₂²×D₁₆	C₂×C₁₃	semidirect
31. C₂×D₃₂	C₂×C₁₃	direct (N × H)
32. C₂²×C₃₂	C₂×C₁₃	semidirect
44. C₂×D₁₆	C₂²×C₁₃	semidirect
46. D₃₂	C₂²×C₁₃	direct (N × H)
47. C₂×C₃₂	C₂²×C₁₃	semidirect
50. C₂²×C₁₃	D₃₂	direct (N × H)
59. D₁₆	C₂³×C₁₃	semidirect
62. C₃₂	C₂³×C₁₃	semidirect
64. C₂×C₁₃	C₂×D₃₂	direct (N × H)
76. C₁₃	C₂²×D₃₂	direct (N × H)
88. C₂²	C₁₃×D₃₂	direct (N × H)
93. C₂	C₂×C₁₃×D₃₂	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×D₁₆	2
C₂×C₁₃×D₃₂	2
C₂²×C₁₃×C₃₂	2
C₂²×D₃₂	13

Subgroups — C22×C13×D32 #15720314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×D₃₂ #15720314