Subgroups — C₂⁵×A₅ #14514913

Order 1920.

16634 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×A₅	C₂	1	31	yes	maximal, direct product factor
2	C₂³×A₅	C₂²	1	155	yes	direct product factor
3	C₂⁵×A₄	—	5	1	no	maximal, Hall
4	C₂⁵×D₅	—	6	1	no	maximal
5	C₂²×A₅	C₂³	1	155	yes	direct product factor
6	C₂⁵×D₃	—	10	1	no	maximal
7	C₂⁴×A₄	—	5	31	no	—
8	C₂⁵×C₅	—	6	1	no	—
9	C₂⁴×D₅	—	6	31	no	—
10	C₂⁴×D₅	—	6	31	no	—
11	C₂⁷	—	5	1	no	Sylow
12	C₂×A₅	C₂⁴	1	31	yes	direct product factor
13	C₂⁵×C₃	—	10	1	no	—
14	C₂⁴×D₃	—	10	31	no	—
15	C₂⁴×D₃	—	10	31	no	—
16	C₂³×A₄	—	5	155	no	—
17	C₂⁴×C₅	—	6	31	no	—
18	C₂³×D₅	—	6	465	no	—
19	C₂³×D₅	—	6	155	no	—
20	C₂⁶	—	5	31	no	—
21	C₂⁶	—	15	31	no	—
22	C₂⁶	—	15	1	no	—
23	A₅	C₂⁵	1	1	yes	characteristic, direct product factor
24	C₂⁴×C₃	—	10	31	no	—
25	C₂³×D₃	—	10	155	no	—
26	C₂³×D₃	—	10	465	no	—
27	C₂²×A₄	—	5	155	no	—
28	C₂³×C₅	—	6	155	no	—
29	C₂²×D₅	—	6	155	no	—
30	C₂²×D₅	—	6	1085	no	—
31	C₂⁵	—	5	155	no	—
32	C₂⁵	—	15	465	no	—
33	C₂⁵	—	15	310	no	—
34	C₂⁵	—	15	31	no	—
35	C₂⁵	—	15	31	no	—
36	C₂⁵	A₅	1	1	yes	maximal normal, characteristic, direct product factor
37	C₂³×C₃	—	10	155	no	—
38	C₂²×D₃	—	10	155	no	—
39	C₂²×D₃	—	10	1085	no	—
40	C₂×A₄	—	5	31	no	—
41	C₂²×C₅	—	6	155	no	—
42	C₂×D₅	—	6	465	no	—
43	C₂×D₅	—	6	31	no	—
44	C₂⁴	—	5	155	no	—
45	C₂⁴	—	15	1085	no	—
46	C₂⁴	—	15	2170	no	—
47	C₂⁴	—	15	155	no	—
48	C₂⁴	—	15	465	no	—
49	C₂⁴	C₂×A₅	1	31	yes	direct product factor
50	C₂²×C₃	—	10	155	no	—
51	C₂×D₃	—	10	465	no	—
52	C₂×D₃	—	10	31	no	—
53	A₄	—	5	1	no	—
54	C₂×C₅	—	6	31	no	—
55	D₅	—	6	1	no	—
56	D₅	—	6	31	no	—
57	C₂³	—	5	31	no	—
58	C₂³	—	15	465	no	—
59	C₂³	—	15	2170	no	—
60	C₂³	—	15	155	no	—
61	C₂³	—	15	1085	no	—
62	C₂³	C₂²×A₅	1	155	yes	direct product factor
63	C₂×C₃	—	10	31	no	—
64	D₃	—	10	31	no	—
65	D₃	—	10	1	no	—
66	C₅	—	6	1	no	Sylow
67	C₂²	—	5	1	no	—
68	C₂²	—	15	31	no	—
69	C₂²	—	15	310	no	—
70	C₂²	—	15	31	no	—
71	C₂²	—	15	465	no	—
72	C₂²	C₂³×A₅	1	155	yes	direct product factor
73	C₃	—	10	1	no	Sylow
74	C₂	—	15	1	no	—
75	C₂	—	15	31	no	—
76	C₂	C₂⁴×A₅	1	31	yes	direct product factor

	subgroup	G/H
center, Fitting, hypercenter	C₂⁵	A₅
commutator, hypocenter	A₅	C₂⁵
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁴×A₅	C₂	direct (N × H)
2. C₂³×A₅	C₂²	direct (N × H)
5. C₂²×A₅	C₂³	direct (N × H)
12. C₂×A₅	C₂⁴	direct (N × H)
23. A₅	C₂⁵	direct (N × H)
36. C₂⁵	A₅	direct (N × H)
49. C₂⁴	C₂×A₅	direct (N × H)
62. C₂³	C₂²×A₅	direct (N × H)
72. C₂²	C₂³×A₅	direct (N × H)
76. C₂	C₂⁴×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
C₂⁴×A₅	2
C₂⁵×A₄	5
C₂⁵×D₅	6
C₂⁵×D₃	10

Subgroups — C25×A5 #14514913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×A₅ #14514913