Subgroups — C₂²×C₅×C₂⁴⋊C₅ #13107921

Order 1600.

1206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂⁴⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₂⁴⋊C₅	C₂²	1	1	yes	characteristic, direct product factor
3	C₂⁶×C₅	C₅	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂⁴⋊C₅	C₅	1	5	yes	maximal, direct product factor
5	C₂⁵×C₅	—	5	3	no	—
6	C₂⁵×C₅	—	5	9	no	—
7	C₂⁵×C₅	C₂×C₅	1	3	yes	complemented
8	C₂×C₂⁴⋊C₅	C₂×C₅	1	15	yes	direct product factor
9	C₂²×C₅²	—	16	1	no	maximal
10	C₂⁴×C₅	—	5	9	no	—
11	C₂⁴×C₅	—	5	9	no	—
12	C₂⁴×C₅	—	5	6	no	—
13	C₂⁴×C₅	—	5	18	no	—
14	C₂⁴×C₅	—	5	36	no	—
15	C₂⁴×C₅	—	5	9	no	—
16	C₂⁴×C₅	—	5	36	no	—
17	C₂⁴×C₅	—	5	6	no	—
18	C₂⁴×C₅	—	5	1	no	—
19	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₂⁴⋊C₅	C₂²×C₅	1	5	yes	direct product factor
21	C₂⁶	C₅²	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₅²	—	16	3	no	—
23	C₂³×C₅	—	5	3	no	—
24	C₂³×C₅	—	5	18	no	—
25	C₂³×C₅	—	5	18	no	—
26	C₂³×C₅	—	5	18	no	—
27	C₂³×C₅	—	5	36	no	—
28	C₂³×C₅	—	5	9	no	—
29	C₂³×C₅	—	5	18	no	—
30	C₂³×C₅	—	5	72	no	—
31	C₂³×C₅	—	5	36	no	—
32	C₂³×C₅	—	5	3	no	—
33	C₂³×C₅	—	5	36	no	—
34	C₂³×C₅	—	5	9	no	—
35	C₂³×C₅	—	5	3	no	—
36	C₂⁵	—	5	3	no	—
37	C₂⁵	—	5	9	no	—
38	C₂⁵	C₂×C₅²	1	3	yes	complemented
39	C₅²	—	16	1	no	Sylow
40	C₂²×C₅	—	5	6	no	—
41	C₂²×C₅	—	5	18	no	—
42	C₂²×C₅	—	5	1	no	—
43	C₂²×C₅	—	5	9	no	—
44	C₂²×C₅	—	5	36	no	—
45	C₂²×C₅	—	5	36	no	—
46	C₂²×C₅	—	5	6	no	—
47	C₂²×C₅	—	5	9	no	—
48	C₂²×C₅	—	5	9	no	—
49	C₂²×C₅	—	16	5	no	—
50	C₂²×C₅	C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor
51	C₂⁴	—	5	9	no	—
52	C₂⁴	—	5	9	no	—
53	C₂⁴	—	5	6	no	—
54	C₂⁴	—	5	18	no	—
55	C₂⁴	—	5	36	no	—
56	C₂⁴	—	5	9	no	—
57	C₂⁴	—	5	36	no	—
58	C₂⁴	—	5	6	no	—
59	C₂⁴	—	5	1	no	—
60	C₂⁴	C₂²×C₅²	1	1	yes	characteristic, complemented
61	C₂×C₅	—	5	3	no	—
62	C₂×C₅	—	5	9	no	—
63	C₂×C₅	—	16	15	no	—
64	C₂×C₅	C₂×C₂⁴⋊C₅	1	3	yes	direct product factor
65	C₂³	—	5	3	no	—
66	C₂³	—	5	18	no	—
67	C₂³	—	5	18	no	—
68	C₂³	—	5	18	no	—
69	C₂³	—	5	36	no	—
70	C₂³	—	5	9	no	—
71	C₂³	—	5	18	no	—
72	C₂³	—	5	72	no	—
73	C₂³	—	5	36	no	—
74	C₂³	—	5	3	no	—
75	C₂³	—	5	36	no	—
76	C₂³	—	5	9	no	—
77	C₂³	—	5	3	no	—
78	C₅	—	16	5	no	—
79	C₅	C₂²×C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor
80	C₂²	—	5	6	no	—
81	C₂²	—	5	18	no	—
82	C₂²	—	5	1	no	—
83	C₂²	—	5	9	no	—
84	C₂²	—	5	36	no	—
85	C₂²	—	5	36	no	—
86	C₂²	—	5	6	no	—
87	C₂²	—	5	9	no	—
88	C₂²	—	5	9	no	—
89	C₂²	C₅×C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor
90	C₂	—	5	3	no	—
91	C₂	—	5	9	no	—
92	C₂	C₂×C₅×C₂⁴⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂⁶×C₅	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₂⁴⋊C₅	C₂	direct (N × H)
2. C₅×C₂⁴⋊C₅	C₂²	direct (N × H)
3. C₂⁶×C₅	C₅	semidirect
4. C₂²×C₂⁴⋊C₅	C₅	direct (N × H)
7. C₂⁵×C₅	C₂×C₅	semidirect
8. C₂×C₂⁴⋊C₅	C₂×C₅	direct (N × H)
19. C₂⁴×C₅	C₂²×C₅	semidirect
20. C₂⁴⋊C₅	C₂²×C₅	direct (N × H)
21. C₂⁶	C₅²	semidirect
38. C₂⁵	C₂×C₅²	semidirect
50. C₂²×C₅	C₂⁴⋊C₅	direct (N × H)
60. C₂⁴	C₂²×C₅²	semidirect
64. C₂×C₅	C₂×C₂⁴⋊C₅	direct (N × H)
79. C₅	C₂²×C₂⁴⋊C₅	direct (N × H)
89. C₂²	C₅×C₂⁴⋊C₅	direct (N × H)
92. C₂	C₂×C₅×C₂⁴⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₂⁴⋊C₅	2
C₂⁶×C₅	5
C₂²×C₂⁴⋊C₅	5
C₂²×C₅²	16

Subgroups — C22×C5×C24⋊C5 #13107921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₂⁴⋊C₅ #13107921