Subgroups — C₃×C₅×Dic₄₉₇ #44447121

Order 29820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₄₉₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇×C₇₁	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅×Dic₇₁	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₇₁	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇×C₇₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅×C₇₁	D₇	1	1	yes	characteristic
10	Dic₄₉₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₅×Dic₇₁	—	7	1	no	Hall
13	C₃×C₅×C₇₁	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×Dic₇₁	—	7	1	no	Hall
16	C₂×C₅×C₇₁	C₃×D₇	1	1	yes	characteristic
17	C₇×C₇₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇₁	C₅×D₇	1	1	yes	characteristic
19	C₃×C₅×Dic₇	—	71	1	no	maximal, Hall
20	C₅×C₇₁	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
21	Dic₇₁	—	7	1	no	Hall
22	C₃×C₇₁	C₅×Dic₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	D₇₁	1	1	yes	characteristic
24	C₂×C₇₁	C₃×C₅×D₇	1	1	yes	characteristic
25	C₅×Dic₇	—	71	1	no	Hall
26	C₃×C₅×C₇	Dic₇₁	1	1	yes	characteristic, complemented, Hall
27	C₃×Dic₇	—	71	1	no	Hall
28	C₇₁	C₃×C₅×Dic₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	C₃×D₇₁	1	1	yes	characteristic
30	C₃×C₄×C₅	—	497	1	no	Hall
31	C₂×C₃×C₇	C₅×D₇₁	1	1	yes	characteristic
32	C₅×C₇	C₃×Dic₇₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	D₄₉₇	1	1	yes	characteristic
34	Dic₇	—	71	1	no	Hall
35	C₃×C₇	C₅×Dic₇₁	1	1	yes	characteristic, complemented, Hall
36	C₄×C₅	—	497	1	no	Hall
37	C₃×C₅	Dic₄₉₇	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₇	C₃×C₅×D₇₁	1	1	yes	characteristic
39	C₃×C₄	—	497	1	no	Hall
40	C₂×C₅	C₃×D₄₉₇	1	1	yes	characteristic
41	C₇	C₃×C₅×Dic₇₁	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	C₅×D₄₉₇	1	1	yes	characteristic
43	C₅	C₃×Dic₄₉₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	497	1	no	Sylow
45	C₃	C₅×Dic₄₉₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₅×D₄₉₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₄₉₇
commutator, hypocenter	C₇×C₇₁	C₃×C₄×C₅
Frattini	C₂	C₃×C₅×D₄₉₇
Fitting, socle, prime radical	C₂×C₃×C₅×C₇×C₇₁	C₂
cosocle	C₂×C₇×C₇₁	C₂×C₃×C₅
LCS	G ▷ C₇×C₇₁
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₄₉₇	C₃	direct (N × H)
3. C₃×C₅×C₇×C₇₁	C₄	semidirect
4. C₃×Dic₄₉₇	C₅	direct (N × H)
8. C₅×C₇×C₇₁	C₃×C₄	semidirect
10. Dic₄₉₇	C₃×C₅	direct (N × H)
11. C₃×C₇×C₇₁	C₄×C₅	semidirect
13. C₃×C₅×C₇₁	Dic₇	semidirect
17. C₇×C₇₁	C₃×C₄×C₅	semidirect
20. C₅×C₇₁	C₃×Dic₇	semidirect
22. C₃×C₇₁	C₅×Dic₇	semidirect
26. C₃×C₅×C₇	Dic₇₁	semidirect
28. C₇₁	C₃×C₅×Dic₇	semidirect
32. C₅×C₇	C₃×Dic₇₁	semidirect
35. C₃×C₇	C₅×Dic₇₁	semidirect
37. C₃×C₅	Dic₄₉₇	direct (N × H)
41. C₇	C₃×C₅×Dic₇₁	semidirect
43. C₅	C₃×Dic₄₉₇	direct (N × H)
45. C₃	C₅×Dic₄₉₇	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×C₅×C₇×C₇₁	2
C₅×Dic₄₉₇	3
C₃×Dic₄₉₇	5
C₃×C₅×Dic₇₁	7
C₃×C₅×Dic₇	71

Subgroups — C3×C5×Dic497 #44447121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×Dic₄₉₇ #44447121