Subgroups — C₂³×C₅×Q₃₂ #11985347

Order 1280.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₂²×C₅×Q₃₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₅×Q₈	—	2	2	no	—
5	C₂²×C₅×Q₁₆	—	2	14	no	—
6	C₂²×C₅×Q₁₆	C₂²	1	28	yes	—
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₅×Q₃₂	C₂²	1	112	yes	direct product factor
9	C₂²×C₅×C₁₆	C₂²	1	14	yes	—
10	C₂³×Q₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₅×Q₈	—	2	28	no	—
12	C₂²×C₅×Q₈	—	4	14	no	—
13	C₂³×C₄×C₅	—	4	2	no	—
14	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
15	C₂×C₅×Q₁₆	—	2	84	no	—
16	C₂×C₅×Q₁₆	C₂³	1	56	yes	—
17	C₂²×C₅×C₈	D₄	1	7	yes	—
18	C₂²×C₅×C₈	C₂³	1	7	yes	—
19	C₅×Q₃₂	C₂³	1	64	yes	direct product factor
20	C₂×C₅×C₁₆	C₂³	1	28	yes	—
21	C₂³×Q₁₆	C₂×C₅	1	2	yes	—
22	C₂²×Q₃₂	C₂×C₅	1	28	yes	direct product factor
23	C₂³×C₁₆	C₂×C₅	1	1	yes	characteristic
24	C₂⁴×C₅	D₈	1	1	yes	characteristic
25	C₂×C₅×Q₈	—	2	56	no	—
26	C₂×C₅×Q₈	—	4	84	no	—
27	C₂²×C₄×C₅	—	4	28	no	—
28	C₂²×C₄×C₅	D₈	1	7	yes	—
29	C₂²×C₄×C₅	C₂×D₄	1	7	yes	—
30	C₅×Q₁₆	—	2	56	no	—
31	C₅×Q₁₆	C₂⁴	1	16	yes	—
32	C₂×C₅×C₈	C₂×D₄	1	21	yes	—
33	C₂×C₅×C₈	C₂⁴	1	7	yes	—
34	C₅×C₁₆	C₂⁴	1	8	yes	—
35	C₂³×Q₈	—	2	2	no	—
36	C₂²×Q₁₆	—	2	14	no	—
37	C₂²×Q₁₆	C₂²×C₅	1	28	yes	—
38	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
39	C₂×Q₃₂	C₂²×C₅	1	112	yes	direct product factor
40	C₂²×C₁₆	C₂²×C₅	1	14	yes	—
41	C₂³×C₅	Q₃₂	1	8	yes	direct product factor
42	C₂³×C₅	C₂×D₈	1	7	yes	—
43	C₅×Q₈	—	2	16	no	—
44	C₅×Q₈	—	4	56	no	—
45	C₂×C₄×C₅	—	4	56	no	—
46	C₂×C₄×C₅	C₂×D₈	1	21	yes	—
47	C₂×C₄×C₅	C₂²×D₄	1	7	yes	—
48	C₅×C₈	C₂²×D₄	1	7	yes	—
49	C₅×C₈	C₂⁵	1	1	yes	characteristic
50	C₂²×Q₈	—	2	28	no	—
51	C₂²×Q₈	—	4	14	no	—
52	C₂³×C₄	—	4	2	no	—
53	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
54	C₂×Q₁₆	—	2	84	no	—
55	C₂×Q₁₆	C₂³×C₅	1	56	yes	—
56	C₂²×C₈	C₅×D₄	1	7	yes	—
57	C₂²×C₈	C₂³×C₅	1	7	yes	—
58	Q₃₂	C₂³×C₅	1	64	yes	direct product factor
59	C₂×C₁₆	C₂³×C₅	1	28	yes	—
60	C₂²×C₅	C₂×Q₃₂	1	28	yes	direct product factor
61	C₂²×C₅	C₂²×D₈	1	7	yes	—
62	C₄×C₅	—	4	16	no	—
63	C₄×C₅	C₂²×D₈	1	7	yes	—
64	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
65	C₂⁴	C₅×D₈	1	1	yes	characteristic
66	C₂×Q₈	—	2	56	no	—
67	C₂×Q₈	—	4	84	no	—
68	C₂²×C₄	—	4	28	no	—
69	C₂²×C₄	C₅×D₈	1	7	yes	—
70	C₂²×C₄	C₂×C₅×D₄	1	7	yes	—
71	Q₁₆	—	2	56	no	—
72	Q₁₆	C₂⁴×C₅	1	16	yes	—
73	C₂×C₈	C₂×C₅×D₄	1	21	yes	—
74	C₂×C₈	C₂⁴×C₅	1	7	yes	—
75	C₁₆	C₂⁴×C₅	1	8	yes	—
76	C₂×C₅	C₂²×Q₃₂	1	14	yes	direct product factor
77	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
78	C₂³	C₅×Q₃₂	1	8	yes	direct product factor
79	C₂³	C₂×C₅×D₈	1	7	yes	—
80	Q₈	—	2	16	no	—
81	Q₈	—	4	56	no	—
82	C₂×C₄	—	4	56	no	—
83	C₂×C₄	C₂×C₅×D₈	1	21	yes	—
84	C₂×C₄	C₂²×C₅×D₄	1	7	yes	—
85	C₈	C₂²×C₅×D₄	1	7	yes	—
86	C₈	C₂⁵×C₅	1	1	yes	characteristic
87	C₅	C₂³×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
88	C₂²	C₂×C₅×Q₃₂	1	28	yes	direct product factor
89	C₂²	C₂²×C₅×D₈	1	7	yes	—
90	C₄	—	4	16	no	—
91	C₄	C₂²×C₅×D₈	1	7	yes	—
92	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
93	C₂	C₂²×C₅×Q₃₂	1	14	yes	direct product factor
94	C₂	C₂³×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×Q₃₂	C₂	direct (N × H)
8. C₂×C₅×Q₃₂	C₂²	direct (N × H)
10. C₂³×Q₃₂	C₅	direct (N × H)
19. C₅×Q₃₂	C₂³	direct (N × H)
22. C₂²×Q₃₂	C₂×C₅	direct (N × H)
39. C₂×Q₃₂	C₂²×C₅	direct (N × H)
41. C₂³×C₅	Q₃₂	direct (N × H)
58. Q₃₂	C₂³×C₅	direct (N × H)
60. C₂²×C₅	C₂×Q₃₂	direct (N × H)
76. C₂×C₅	C₂²×Q₃₂	direct (N × H)
78. C₂³	C₅×Q₃₂	direct (N × H)
87. C₅	C₂³×Q₃₂	direct (N × H)
88. C₂²	C₂×C₅×Q₃₂	direct (N × H)
93. C₂	C₂²×C₅×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×C₅×Q₁₆	2
C₂²×C₅×Q₃₂	2
C₂³×C₅×C₁₆	2
C₂³×Q₃₂	5

Subgroups — C23×C5×Q32 #11985347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×Q₃₂ #11985347