Subgroups — C₇×C₃⋊#13091735 #44501426

Order 30660.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇×#13091735	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₃⋊#64408	—	5	1	no	maximal, Hall
5	C₅×C₇×D₇₃	D₃	1	1	yes	characteristic
6	C₃⋊#13091735	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×D₇₃	D₅	1	1	yes	characteristic
8	C₅×C₇×C₇₃	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₇₃	C₂×C₇	1	1	yes	characteristic
10	C₇×#64408	—	15	1	no	Hall
11	C₃×C₇×C₇₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	#13091735	—	3	1	no	Hall
13	C₃×C₅×C₇₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×D₇₃	D₁₅	1	1	yes	characteristic
15	C₃⋊#64408	—	5	1	no	Hall
16	C₅×D₇₃	D₃×C₇	1	1	yes	characteristic
17	C₇×C₇₃	Dic₁₅	1	1	yes	characteristic, complemented, Hall
18	C₃×D₇₃	C₇×D₅	1	1	yes	characteristic
19	C₇×Dic₁₅	—	73	1	no	maximal, Hall
20	C₅×C₇₃	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
21	#64408	—	15	1	no	Hall
22	C₃×C₇₃	C₇×Dic₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	—	73	1	no	—
24	D₇₃	C₇×D₁₅	1	1	yes	characteristic
25	C₇×Dic₅	—	219	1	no	Hall
26	C₃×C₅×C₇	#64408	1	1	yes	characteristic, complemented, Hall
27	C₇×Dic₃	—	365	1	no	Hall
28	C₇₃	C₇×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	—	73	1	no	—
30	Dic₁₅	—	73	1	no	Hall
31	C₂×C₃×C₇	—	73	1	no	—
32	C₅×C₇	C₃⋊#64408	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	—	73	1	no	—
34	C₄×C₇	—	1095	1	no	Hall
35	C₃×C₇	#13091735	1	1	yes	characteristic, complemented, Hall
36	Dic₅	—	219	1	no	Hall
37	C₃×C₅	C₇×#64408	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	73	1	no	—
39	Dic₃	—	365	1	no	Hall
40	C₂×C₅	—	73	1	no	—
41	C₇	C₃⋊#13091735	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	—	73	1	no	—
43	C₅	C₇×C₃⋊#64408	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	1095	1	no	Sylow
45	C₃	C₇×#13091735	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	73	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊#13091735
commutator, hypocenter	C₃×C₅×C₇₃	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₄
prime radical	C₃×C₅×C₇×D₇₃	C₂
cosocle	C₃×C₅×D₇₃	C₂×C₇
LCS	G ▷ C₃×C₅×C₇₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₇₃	C₄	semidirect
6. C₃⋊#13091735	C₇	direct (N × H)
8. C₅×C₇×C₇₃	Dic₃	semidirect
11. C₃×C₇×C₇₃	Dic₅	semidirect
13. C₃×C₅×C₇₃	C₄×C₇	semidirect
17. C₇×C₇₃	Dic₁₅	semidirect
20. C₅×C₇₃	C₇×Dic₃	semidirect
22. C₃×C₇₃	C₇×Dic₅	semidirect
26. C₃×C₅×C₇	#64408	semidirect
28. C₇₃	C₇×Dic₁₅	semidirect
32. C₅×C₇	C₃⋊#64408	semidirect
35. C₃×C₇	#13091735	semidirect
37. C₃×C₅	C₇×#64408	semidirect
41. C₇	C₃⋊#13091735	direct (N × H)
43. C₅	C₇×C₃⋊#64408	semidirect
45. C₃	C₇×#13091735	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×D₇₃	2
C₇×#13091735	3
C₇×C₃⋊#64408	5
C₃⋊#13091735	7
C₇×Dic₁₅	73

Subgroups — C7×C3⋊#13091735 #44501426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊#13091735 #44501426