Subgroups — C₂²×C₅×#672 #13102357

Order 1600.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#672	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₅²	C₄	1	1	yes	characteristic
4	C₂×C₅²×C₈	C₄	1	3	yes	—
5	C₂×C₅²×C₈	C₂²	1	3	yes	—
6	C₅×#672	C₂²	1	4	yes	direct product factor
7	C₂²×C₅×C₁₆	—	5	1	no	maximal
8	C₂²×#672	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₅²	C₈	1	1	yes	characteristic
10	C₂×C₄×C₅²	C₈	1	3	yes	—
11	C₂×C₄×C₅²	C₂×C₄	1	3	yes	—
12	C₅²×C₈	C₂×C₄	1	3	yes	—
13	C₅²×C₈	C₂³	1	1	yes	characteristic
14	C₂²×C₅×C₈	—	2	2	no	—
15	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
16	C₂²×C₅×C₈	C₂×C₅	1	1	yes	characteristic
17	C₂×C₅×C₁₆	—	5	6	no	—
18	C₂×#672	C₂×C₅	1	6	yes	direct product factor
19	C₂²×C₅²	C₁₆	1	4	yes	complemented
20	C₂²×C₅²	C₂×C₈	1	3	yes	—
21	C₄×C₅²	C₂×C₈	1	3	yes	—
22	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₅	—	2	2	no	—
24	C₂²×C₄×C₅	Dic₅	1	1	yes	characteristic
25	C₂²×C₄×C₅	C₄×C₅	1	1	yes	characteristic
26	C₂×C₅×C₈	—	2	6	no	—
27	C₂×C₅×C₈	—	2	6	no	—
28	C₂×C₅×C₈	Dic₅	1	3	yes	—
29	C₂×C₅×C₈	C₄×C₅	1	3	yes	—
30	C₂×C₅×C₈	C₂×D₅	1	3	yes	—
31	C₂×C₅×C₈	C₂²×C₅	1	3	yes	—
32	C₅×C₁₆	—	5	4	no	—
33	#672	C₂²×C₅	1	4	yes	direct product factor
34	C₂²×C₁₆	—	5	1	no	Sylow
35	C₂×C₅²	C₂×C₁₆	1	6	yes	complemented
36	C₂×C₅²	C₂²×C₈	1	1	yes	characteristic
37	C₂³×C₅	—	2	2	no	—
38	C₂³×C₅	#168	1	1	yes	characteristic
39	C₂³×C₅	C₅×C₈	1	1	yes	characteristic
40	C₂×C₄×C₅	—	2	6	no	—
41	C₂×C₄×C₅	—	2	6	no	—
42	C₂×C₄×C₅	#168	1	3	yes	—
43	C₂×C₄×C₅	C₅×C₈	1	3	yes	—
44	C₂×C₄×C₅	C₂×Dic₅	1	3	yes	—
45	C₂×C₄×C₅	C₂×C₄×C₅	1	3	yes	—
46	C₅×C₈	—	2	6	no	—
47	C₅×C₈	—	2	2	no	—
48	C₅×C₈	C₂×Dic₅	1	3	yes	—
49	C₅×C₈	C₂×C₄×C₅	1	3	yes	—
50	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
51	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
52	C₂²×C₈	C₅×D₅	1	1	yes	characteristic
53	C₂×C₁₆	—	5	6	no	—
54	C₅²	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	—	2	8	no	—
56	C₂²×C₅	—	2	6	no	—
57	C₂²×C₅	#672	1	4	yes	direct product factor
58	C₂²×C₅	C₅×C₁₆	1	4	yes	complemented
59	C₂²×C₅	C₂×#168	1	3	yes	—
60	C₂²×C₅	C₂×C₅×C₈	1	3	yes	—
61	C₄×C₅	—	2	2	no	—
62	C₄×C₅	—	2	6	no	—
63	C₄×C₅	C₂×#168	1	3	yes	—
64	C₄×C₅	C₂×C₅×C₈	1	3	yes	—
65	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
66	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
67	C₂²×C₄	C₅×Dic₅	1	1	yes	characteristic
68	C₂×C₈	C₅×Dic₅	1	3	yes	—
69	C₂×C₈	C₂×C₅×D₅	1	3	yes	—
70	C₁₆	—	5	4	no	—
71	C₂×C₅	—	2	12	no	—
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	C₂×#672	1	6	yes	direct product factor
74	C₂×C₅	C₂×C₅×C₁₆	1	6	yes	complemented
75	C₂×C₅	C₂²×#168	1	1	yes	characteristic
76	C₂×C₅	C₂²×C₅×C₈	1	1	yes	characteristic
77	C₂³	C₅×#168	1	1	yes	characteristic
78	C₂×C₄	C₅×#168	1	3	yes	—
79	C₂×C₄	C₂×C₅×Dic₅	1	3	yes	—
80	C₈	C₂×C₅×Dic₅	1	3	yes	—
81	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
82	C₅	—	2	2	no	—
83	C₅	C₂²×#672	1	1	yes	characteristic, direct product factor
84	C₅	C₂²×C₅×C₁₆	1	1	yes	characteristic, complemented
85	C₂²	C₅×#672	1	4	yes	direct product factor
86	C₂²	C₂×C₅×#168	1	3	yes	—
87	C₄	C₂×C₅×#168	1	3	yes	—
88	C₄	C₂²×C₅×Dic₅	1	1	yes	characteristic
89	C₂	C₂×C₅×#672	1	6	yes	direct product factor
90	C₂	C₂²×C₅×#168	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₈	D₅
commutator, hypocenter	C₅	C₂²×C₅×C₁₆
Frattini	C₈	C₂²×C₅×D₅
Fitting	C₂²×C₅²×C₈	C₂
socle, prime radical	C₂³×C₅²	C₈
cosocle	C₅×C₈	C₂³×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₂²×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#672	C₂	direct (N × H)
6. C₅×#672	C₂²	direct (N × H)
8. C₂²×#672	C₅	direct (N × H)
18. C₂×#672	C₂×C₅	direct (N × H)
19. C₂²×C₅²	C₁₆	semidirect
33. #672	C₂²×C₅	direct (N × H)
35. C₂×C₅²	C₂×C₁₆	semidirect
54. C₅²	C₂²×C₁₆	semidirect
57. C₂²×C₅	#672	direct (N × H)
58. C₂²×C₅	C₅×C₁₆	semidirect
73. C₂×C₅	C₂×#672	direct (N × H)
74. C₂×C₅	C₂×C₅×C₁₆	semidirect
83. C₅	C₂²×#672	direct (N × H)
84. C₅	C₂²×C₅×C₁₆	semidirect
85. C₂²	C₅×#672	direct (N × H)
89. C₂	C₂×C₅×#672	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×C₅²×C₈	2
C₂×C₅×#672	2
C₂²×C₅×C₁₆	5
C₂²×#672	5

Subgroups — C22×C5×#672 #13102357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#672 #13102357