Subgroups — C₂×Dic₆×C₂₅ #11924949

Order 1200.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₂₅	C₂	1	2	yes	maximal
3	Dic₆×C₂₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₈×C₂₅	—	3	1	no	maximal, Hall
5	C₂²×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₂₅	C₂²	1	2	yes	—
7	Dic₃×C₂₅	C₂²	1	4	yes	—
8	C₂×C₅×Dic₆	C₅	1	1	yes	maximal, characteristic
9	Q₈×C₂₅	—	3	4	no	—
10	C₂×C₄×C₂₅	—	3	2	no	—
11	C₂×C₄×C₂₅	D₃	1	1	yes	characteristic
12	C₂×C₃×C₂₅	Q₈	1	2	yes	complemented
13	C₂×C₃×C₂₅	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
15	C₂×C₅×Dic₃	C₂×C₅	1	2	yes	—
16	C₅×Dic₆	C₂×C₅	1	4	yes	—
17	C₂²×C₂₅	C₂×D₃	1	1	yes	characteristic
18	C₄×C₂₅	—	3	4	no	—
19	C₄×C₂₅	C₂×D₃	1	2	yes	—
20	C₂×C₅×Q₈	—	3	1	no	—
21	C₃×C₂₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
23	C₃×C₄×C₅	C₂²×C₅	1	2	yes	—
24	C₅×Dic₃	C₂²×C₅	1	4	yes	—
25	C₂×C₂₅	Dic₆	1	2	yes	direct product factor
26	C₂×C₂₅	C₂²×D₃	1	1	yes	characteristic
27	C₂×Dic₆	C₂₅	1	1	yes	characteristic, direct product factor, Hall
28	C₅×Q₈	—	3	4	no	—
29	C₂×C₄×C₅	—	3	2	no	—
30	C₂×C₄×C₅	C₅×D₃	1	1	yes	characteristic
31	C₂×C₃×C₅	C₅×Q₈	1	2	yes	—
32	C₂×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
33	C₂₅	C₂×Dic₆	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃×C₄	C₂×C₂₅	1	1	yes	characteristic
35	C₂×Dic₃	C₂×C₂₅	1	2	yes	—
36	Dic₆	C₂×C₂₅	1	4	yes	direct product factor
37	C₂²×C₅	C₂×C₅×D₃	1	1	yes	characteristic
38	C₄×C₅	—	3	4	no	—
39	C₄×C₅	C₂×C₅×D₃	1	2	yes	—
40	C₂×Q₈	—	3	1	no	Sylow
41	C₃×C₅	C₂×C₅×Q₈	1	1	yes	characteristic
42	C₂²×C₃	C₂²×C₂₅	1	1	yes	characteristic
43	C₃×C₄	C₂²×C₂₅	1	2	yes	—
44	Dic₃	C₂²×C₂₅	1	4	yes	—
45	C₂×C₅	C₅×Dic₆	1	2	yes	—
46	C₂×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
47	Q₈	—	3	4	no	—
48	C₂×C₄	—	3	2	no	—
49	C₂×C₄	D₃×C₂₅	1	1	yes	characteristic
50	C₂×C₃	Q₈×C₂₅	1	2	yes	complemented
51	C₂×C₃	C₂³×C₂₅	1	1	yes	characteristic
52	C₅	C₂×C₅×Dic₆	1	1	yes	characteristic
53	C₂²	C₂×D₃×C₂₅	1	1	yes	characteristic
54	C₄	—	3	4	no	—
55	C₄	C₂×D₃×C₂₅	1	2	yes	—
56	C₃	C₂×Q₈×C₂₅	1	1	yes	characteristic, complemented, Sylow
57	C₂	Dic₆×C₂₅	1	2	yes	direct product factor
58	C₂	C₂²×D₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₂₅	C₂×D₃
commutator	C₂×C₃	C₂³×C₂₅
Frattini	C₂×C₅	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₂₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂²×C₅
cosocle	C₂×C₃×C₅	C₂³×C₅
hypercenter	C₂×C₄×C₂₅	D₃
hypocenter	C₃	C₂×Q₈×C₂₅
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₂₅ ◁ C₂×C₄×C₂₅

Complements

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

N	H ≅ G/N	type
3. Dic₆×C₂₅	C₂	direct (N × H)
12. C₂×C₃×C₂₅	Q₈	semidirect
21. C₃×C₂₅	C₂×Q₈	semidirect
25. C₂×C₂₅	Dic₆	direct (N × H)
27. C₂×Dic₆	C₂₅	direct (N × H)
33. C₂₅	C₂×Dic₆	direct (N × H)
36. Dic₆	C₂×C₂₅	direct (N × H)
50. C₂×C₃	Q₈×C₂₅	semidirect
56. C₃	C₂×Q₈×C₂₅	semidirect
57. C₂	Dic₆×C₂₅	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×C₃×C₄×C₂₅	2
C₂×Dic₃×C₂₅	2
Dic₆×C₂₅	2
C₂×Q₈×C₂₅	3
C₂×C₅×Dic₆	5

Subgroups — C2×Dic6×C25 #11924949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₆×C₂₅ #11924949