Subgroups — C₂²×C₅×A₅ #11925735

Order 1200.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×A₅	C₂	1	3	yes	maximal, direct product factor
2	C₅×A₅	C₂²	1	1	yes	characteristic, direct product factor
3	C₂²×C₅×A₄	—	5	1	no	maximal
4	C₂²×A₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₅×D₅	—	6	1	no	maximal
6	C₂²×C₅×D₃	—	10	1	no	maximal
7	C₂×C₅×A₄	—	5	3	no	—
8	C₂×A₅	C₂×C₅	1	3	yes	direct product factor
9	C₂²×C₅²	—	6	1	no	—
10	C₂×C₅×D₅	—	6	3	no	—
11	C₂×C₅×D₅	—	6	3	no	—
12	C₂⁴×C₅	—	5	1	no	—
13	C₂²×C₃×C₅	—	10	1	no	—
14	C₂×C₅×D₃	—	10	3	no	—
15	C₂×C₅×D₃	—	10	3	no	—
16	C₅×A₄	—	5	1	no	—
17	A₅	C₂²×C₅	1	1	yes	characteristic, direct product factor
18	C₂×C₅²	—	6	3	no	—
19	C₅×D₅	—	6	3	no	—
20	C₅×D₅	—	6	1	no	—
21	C₂²×A₄	—	5	1	no	Hall
22	C₂³×C₅	—	5	3	no	—
23	C₂³×C₅	—	15	3	no	—
24	C₂³×C₅	—	15	1	no	—
25	C₂²×D₅	—	6	1	no	—
26	C₂×C₃×C₅	—	10	3	no	—
27	C₅×D₃	—	10	3	no	—
28	C₅×D₃	—	10	1	no	—
29	C₅²	—	6	1	no	Sylow
30	C₂²×D₃	—	10	1	no	—
31	C₂×A₄	—	5	3	no	—
32	C₂²×C₅	—	5	1	no	—
33	C₂²×C₅	—	6	1	no	—
34	C₂²×C₅	—	12	2	no	—
35	C₂²×C₅	—	15	3	no	—
36	C₂²×C₅	—	15	2	no	—
37	C₂²×C₅	—	15	3	no	—
38	C₂²×C₅	—	15	3	no	—
39	C₂²×C₅	A₅	1	1	yes	maximal normal, characteristic, direct product factor
40	C₂×D₅	—	6	3	no	—
41	C₂×D₅	—	6	3	no	—
42	C₂⁴	—	5	1	no	Sylow
43	C₃×C₅	—	10	1	no	—
44	C₂²×C₃	—	10	1	no	—
45	C₂×D₃	—	10	3	no	—
46	C₂×D₃	—	10	3	no	—
47	A₄	—	5	1	no	—
48	C₂×C₅	—	6	3	no	—
49	C₂×C₅	—	12	6	no	—
50	C₂×C₅	—	15	1	no	—
51	C₂×C₅	—	15	3	no	—
52	C₂×C₅	C₂×A₅	1	3	yes	direct product factor
53	D₅	—	6	1	no	—
54	D₅	—	6	3	no	—
55	C₂³	—	5	3	no	—
56	C₂³	—	15	3	no	—
57	C₂³	—	15	1	no	—
58	C₂×C₃	—	10	3	no	—
59	D₃	—	10	1	no	—
60	D₃	—	10	3	no	—
61	C₅	—	6	1	no	—
62	C₅	—	12	2	no	—
63	C₅	C₂²×A₅	1	1	yes	characteristic, direct product factor
64	C₂²	—	5	1	no	—
65	C₂²	—	15	3	no	—
66	C₂²	—	15	2	no	—
67	C₂²	—	15	3	no	—
68	C₂²	—	15	3	no	—
69	C₂²	C₅×A₅	1	1	yes	characteristic, direct product factor
70	C₃	—	10	1	no	Sylow
71	C₂	—	15	1	no	—
72	C₂	—	15	3	no	—
73	C₂	C₂×C₅×A₅	1	3	yes	direct product factor

	subgroup	G/H
center, Fitting, hypercenter	C₂²×C₅	A₅
commutator, hypocenter	A₅	C₂²×C₅
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×A₅	C₂	direct (N × H)
2. C₅×A₅	C₂²	direct (N × H)
4. C₂²×A₅	C₅	direct (N × H)
8. C₂×A₅	C₂×C₅	direct (N × H)
17. A₅	C₂²×C₅	direct (N × H)
39. C₂²×C₅	A₅	direct (N × H)
52. C₂×C₅	C₂×A₅	direct (N × H)
63. C₅	C₂²×A₅	direct (N × H)
69. C₂²	C₅×A₅	direct (N × H)
73. C₂	C₂×C₅×A₅	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×A₅	2
C₂²×C₅×A₄	5
C₂²×A₅	5
C₂²×C₅×D₅	6
C₂²×C₅×D₃	10

Subgroups — C22×C5×A5 #11925735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×A₅ #11925735