Subgroups — C₂×Dic₃×D₂₅ #11924924

Order 1200.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₇₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×D₂₅	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₂₅	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₂₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₂₅	C₄	1	4	yes	complemented
8	C₂×C₃×D₂₅	C₂²	1	2	yes	—
9	Dic₇₅	C₂²	1	2	yes	complemented
10	Dic₃×C₂₅	C₂²	1	2	yes	complemented
11	C₂×D₅×Dic₃	—	5	1	no	maximal
12	C₂²×D₂₅	D₃	1	1	yes	characteristic
13	C₂×C₄×C₂₅	—	3	1	no	—
14	C₂×Dic₂₅	—	3	1	no	—
15	C₄×D₂₅	—	3	4	no	—
16	C₂×C₃×C₂₅	C₂×C₄	1	2	yes	complemented
17	C₂×C₃×C₂₅	C₂³	1	1	yes	characteristic
18	C₃×D₂₅	C₂×C₄	1	4	yes	complemented
19	C₂²×C₃×D₅	—	5	1	no	—
20	C₂×Dic₁₅	—	5	1	no	—
21	C₂×C₅×Dic₃	D₅	1	1	yes	characteristic
22	D₅×Dic₃	—	5	4	no	—
23	C₂²×C₂₅	C₂×D₃	1	1	yes	characteristic
24	C₂×D₂₅	Dic₃	1	4	yes	direct product factor
25	C₂×D₂₅	C₂×D₃	1	2	yes	—
26	C₄×C₂₅	—	3	2	no	—
27	Dic₂₅	—	3	2	no	—
28	C₂×C₄×D₅	—	15	1	no	—
29	C₃×C₂₅	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃×C₅	C₂×D₅	1	1	yes	characteristic
31	C₂×C₃×D₅	—	5	4	no	—
32	C₂×C₃×D₅	—	5	2	no	—
33	Dic₁₅	—	5	2	no	—
34	C₅×Dic₃	C₂×D₅	1	2	yes	—
35	C₂×C₂₅	C₂×Dic₃	1	2	yes	complemented
36	C₂×C₂₅	C₂²×D₃	1	1	yes	characteristic
37	D₂₅	C₂×Dic₃	1	4	yes	direct product factor
38	C₂²×Dic₃	—	25	1	no	Hall
39	C₂²×D₅	—	5	1	no	—
40	C₂×C₄×C₅	—	3	1	no	—
41	C₂×Dic₅	—	15	1	no	—
42	C₄×D₅	—	15	4	no	—
43	C₂×C₃×C₅	C₄×D₅	1	2	yes	—
44	C₂×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
45	C₃×D₅	—	5	4	no	—
46	C₂₅	C₂²×Dic₃	1	1	yes	characteristic, complemented, Sylow
47	C₂³×C₃	—	25	1	no	—
48	C₂×Dic₃	—	25	1	no	—
49	C₂×Dic₃	—	25	4	no	—
50	C₂×Dic₃	D₂₅	1	1	yes	characteristic, direct product factor
51	C₂²×C₅	D₃×D₅	1	1	yes	characteristic
52	C₂×D₅	—	5	4	no	—
53	C₂×D₅	—	5	2	no	—
54	C₄×C₅	—	3	2	no	—
55	Dic₅	—	15	2	no	—
56	C₂²×C₄	—	75	1	no	Sylow
57	C₃×C₅	C₂×C₄×D₅	1	1	yes	characteristic
58	C₂²×C₃	—	25	4	no	—
59	C₂²×C₃	—	25	2	no	—
60	C₂²×C₃	C₂×D₂₅	1	1	yes	characteristic
61	Dic₃	—	25	2	no	—
62	Dic₃	C₂×D₂₅	1	2	yes	direct product factor
63	C₂×C₅	D₅×Dic₃	1	2	yes	—
64	C₂×C₅	C₂×D₃×D₅	1	1	yes	characteristic
65	D₅	—	5	4	no	—
66	C₂³	—	25	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	75	4	no	—
69	C₂×C₄	—	75	1	no	—
70	C₂×C₃	—	25	4	no	—
71	C₂×C₃	C₄×D₂₅	1	2	yes	complemented
72	C₂×C₃	C₂²×D₂₅	1	1	yes	characteristic
73	C₅	C₂×D₅×Dic₃	1	1	yes	characteristic
74	C₂²	—	25	4	no	—
75	C₂²	—	25	2	no	—
76	C₂²	D₃×D₂₅	1	1	yes	characteristic
77	C₄	—	3	2	no	—
78	C₄	—	75	2	no	—
79	C₃	C₂×C₄×D₂₅	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	25	4	no	—
81	C₂	Dic₃×D₂₅	1	2	yes	direct product factor
82	C₂	C₂×D₃×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₂₅
commutator, hypocenter	C₃×C₂₅	C₂²×C₄
Frattini	C₂×C₅	C₂×D₃×D₅
Fitting	C₂²×C₃×C₂₅	C₂²
socle	C₂²×C₃×C₅	C₂×D₅
prime radical	C₂²×C₃×D₂₅	C₂
cosocle	C₂×C₃×C₂₅	C₂³
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₇₅	C₂	semidirect
3. C₂×Dic₃×C₂₅	C₂	semidirect
4. Dic₃×D₂₅	C₂	direct (N × H)
7. C₂×C₃×D₂₅	C₄	semidirect
9. Dic₇₅	C₂²	semidirect
10. Dic₃×C₂₅	C₂²	semidirect
16. C₂×C₃×C₂₅	C₂×C₄	semidirect
18. C₃×D₂₅	C₂×C₄	semidirect
24. C₂×D₂₅	Dic₃	direct (N × H)
29. C₃×C₂₅	C₂²×C₄	semidirect
35. C₂×C₂₅	C₂×Dic₃	semidirect
37. D₂₅	C₂×Dic₃	direct (N × H)
46. C₂₅	C₂²×Dic₃	semidirect
50. C₂×Dic₃	D₂₅	direct (N × H)
62. Dic₃	C₂×D₂₅	direct (N × H)
71. C₂×C₃	C₄×D₂₅	semidirect
79. C₃	C₂×C₄×D₂₅	semidirect
81. C₂	Dic₃×D₂₅	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×C₃×D₂₅	2
C₂×Dic₇₅	2
C₂×Dic₃×C₂₅	2
Dic₃×D₂₅	2
C₂×C₄×D₂₅	3
C₂×D₅×Dic₃	5

Subgroups — C2×Dic3×D25 #11924924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃×D₂₅ #11924924