Subgroups — C₂×C₂₅×D₂₃₇ #37557155

Order 23700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×D₂₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₂₅×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₅×D₇₉	—	3	1	no	maximal, Hall
4	C₃×C₂₅×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₂₃₇	C₅	1	1	yes	maximal, characteristic
6	C₂₅×D₇₉	—	3	2	no	—
7	C₂×C₂₅×C₇₉	D₃	1	1	yes	characteristic, complemented
8	C₅×D₂₃₇	C₂×C₅	1	2	yes	—
9	C₂×C₃×C₅×C₇₉	C₂×C₅	1	1	yes	characteristic
10	C₂₅×C₇₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₇₉	—	3	1	no	—
12	C₃×C₅×C₇₉	C₂²×C₅	1	1	yes	characteristic
13	C₂×D₂₃₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₇₉	C₅×D₃	1	1	yes	characteristic
15	C₅×D₇₉	—	3	2	no	—
16	C₂×C₃×C₇₉	C₂×C₂₅	1	1	yes	characteristic, complemented
17	D₂₃₇	C₂×C₂₅	1	2	yes	direct product factor
18	C₅×C₇₉	C₂×C₅×D₃	1	1	yes	characteristic
19	C₂×D₇₉	—	3	1	no	Hall
20	C₂×D₃×C₂₅	—	79	1	no	maximal, Hall
21	C₃×C₇₉	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇₉	D₃×C₂₅	1	1	yes	characteristic, complemented
23	D₇₉	—	3	2	no	—
24	C₂×C₃×C₂₅	D₇₉	1	1	yes	characteristic, complemented
25	D₃×C₂₅	—	79	2	no	—
26	C₂²×C₂₅	—	237	1	no	Hall
27	C₇₉	C₂×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₂₅	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×D₃	—	79	1	no	—
30	C₂×C₂₅	—	237	2	no	—
31	C₂×C₂₅	D₂₃₇	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₅	C₅×D₇₉	1	1	yes	characteristic
33	C₅×D₃	—	79	2	no	—
34	C₂₅	C₂×D₂₃₇	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₅	—	237	1	no	—
36	C₃×C₅	C₂×C₅×D₇₉	1	1	yes	characteristic
37	C₂×D₃	—	79	1	no	Hall
38	C₂×C₅	—	237	2	no	—
39	C₂×C₅	C₅×D₂₃₇	1	1	yes	characteristic
40	C₂×C₃	C₂₅×D₇₉	1	1	yes	characteristic, complemented
41	D₃	—	79	2	no	—
42	C₅	C₂×C₅×D₂₃₇	1	1	yes	characteristic
43	C₂²	—	237	1	no	Sylow
44	C₃	C₂×C₂₅×D₇₉	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	237	2	no	—
46	C₂	C₂₅×D₂₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₂₃₇
commutator, hypocenter	C₃×C₇₉	C₂²×C₂₅
Frattini	C₅	C₂×C₅×D₂₃₇
Fitting	C₂×C₃×C₂₅×C₇₉	C₂
socle	C₂×C₃×C₅×C₇₉	C₂×C₅
prime radical	C₂×C₅×D₂₃₇	C₅
cosocle	C₃×C₅×C₇₉	C₂²×C₅
LCS	G ▷ C₃×C₇₉
UCS	C₁ ◁ C₂×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×D₂₃₇	C₂	direct (N × H)
2. C₂×C₃×C₂₅×C₇₉	C₂	semidirect
4. C₃×C₂₅×C₇₉	C₂²	semidirect
7. C₂×C₂₅×C₇₉	D₃	semidirect
10. C₂₅×C₇₉	C₂×D₃	semidirect
13. C₂×D₂₃₇	C₂₅	direct (N × H)
16. C₂×C₃×C₇₉	C₂×C₂₅	semidirect
17. D₂₃₇	C₂×C₂₅	direct (N × H)
21. C₃×C₇₉	C₂²×C₂₅	semidirect
22. C₂×C₇₉	D₃×C₂₅	semidirect
24. C₂×C₃×C₂₅	D₇₉	semidirect
27. C₇₉	C₂×D₃×C₂₅	semidirect
28. C₃×C₂₅	C₂×D₇₉	semidirect
31. C₂×C₂₅	D₂₃₇	direct (N × H)
34. C₂₅	C₂×D₂₃₇	direct (N × H)
40. C₂×C₃	C₂₅×D₇₉	semidirect
44. C₃	C₂×C₂₅×D₇₉	semidirect
46. C₂	C₂₅×D₂₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×D₂₃₇	2
C₂×C₃×C₂₅×C₇₉	2
C₂×C₂₅×D₇₉	3
C₂×C₅×D₂₃₇	5
C₂×D₃×C₂₅	79

Subgroups — C2×C25×D237 #37557155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×D₂₃₇ #37557155