Subgroups — Dic₃₅×#4294 #37560909

Order 23940.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×Dic₃₅	C₃	1	1	yes	maximal, characteristic
3	C₅×C₇×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₇×#4294	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
6	Dic₅×#4294	—	7	1	no	maximal, Hall
7	C₁₉×Dic₃₅	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×#4294	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
10	C₂×C₅×#4294	D₇	1	1	yes	characteristic
11	C₃×C₁₉×Dic₇	—	5	1	no	—
12	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic
13	C₉×Dic₃₅	—	19	1	no	maximal, Hall
14	C₇×#4294	Dic₅	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₉×Dic₅	—	7	1	no	—
16	C₅×#4294	Dic₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic
18	C₄×#4294	—	35	1	no	Hall
19	C₅×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇×C₉	—	19	1	no	—
21	C₂×C₃×C₅×C₁₉	C₃×D₇	1	1	yes	characteristic
22	C₁₉×Dic₇	—	5	1	no	Hall
23	C₃×Dic₃₅	C₁₉⋊C₃	1	1	yes	characteristic
24	C₃×C₇×C₁₉	C₃×Dic₅	1	1	yes	characteristic
25	C₁₉×Dic₅	—	7	1	no	Hall
26	C₂×#4294	D₃₅	1	1	yes	characteristic
27	C₅×C₇×C₉	—	19	1	no	Hall
28	C₃×C₅×C₁₉	C₃×Dic₇	1	1	yes	characteristic
29	C₂×C₇×C₁₉	C₉×D₅	1	1	yes	characteristic
30	C₉×Dic₇	—	95	1	no	Hall
31	C₃×C₄×C₁₉	—	35	1	no	—
32	C₂×C₃×C₅×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic
33	C₂×C₅×C₁₉	C₉×D₇	1	1	yes	characteristic
34	C₉×Dic₅	—	133	1	no	Hall
35	#4294	Dic₃₅	1	1	yes	characteristic, direct product factor, Hall
36	Dic₃₅	#4294	1	1	yes	characteristic, direct product factor, Hall
37	C₇×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇×C₉	—	19	1	no	—
39	C₂×C₃×C₁₉	C₃×D₃₅	1	1	yes	characteristic
40	C₃×C₅×C₇	C₄×C₁₉⋊C₃	1	1	yes	characteristic
41	C₅×C₁₉	C₉×Dic₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₅×C₉	—	19	1	no	—
43	C₃×Dic₇	—	5	1	no	—
44	C₄×C₁₉	—	35	1	no	Hall
45	C₂×C₅×C₇	C₂×#4294	1	1	yes	characteristic
46	C₇×C₉	—	19	1	no	Hall
47	C₃×Dic₅	—	7	1	no	—
48	C₃×C₁₉	C₃×Dic₃₅	1	1	yes	characteristic
49	C₅×C₉	—	19	1	no	Hall
50	C₂×C₃×C₇	D₅×C₁₉⋊C₃	1	1	yes	characteristic
51	C₂×C₁₉	C₉×D₃₅	1	1	yes	characteristic
52	C₄×C₉	—	665	1	no	Hall
53	C₅×C₇	C₄×#4294	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	D₇×C₁₉⋊C₃	1	1	yes	characteristic
55	Dic₇	—	5	1	no	Hall
56	C₃×C₇	Dic₅×C₁₉⋊C₃	1	1	yes	characteristic
57	Dic₅	—	7	1	no	Hall
58	C₁₉	C₉×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₉	—	19	1	no	—
60	C₃×C₅	Dic₇×C₁₉⋊C₃	1	1	yes	characteristic
61	C₂×C₇	D₅×#4294	1	1	yes	characteristic
62	C₃×C₄	—	35	1	no	—
63	C₂×C₅	D₇×#4294	1	1	yes	characteristic
64	C₉	—	19	1	no	Sylow
65	C₇	Dic₅×#4294	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	C₁₉⋊C₃×D₃₅	1	1	yes	characteristic
67	C₅	Dic₇×#4294	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	35	1	no	Sylow
69	C₃	C₁₉⋊C₃×Dic₃₅	1	1	yes	characteristic
70	C₂	D₃₅×#4294	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₁₉⋊C₃×D₃₅
commutator, hypocenter	C₅×C₇×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×#4294	C₄	semidirect
7. C₁₉×Dic₃₅	C₉	semidirect
14. C₇×#4294	Dic₅	semidirect
16. C₅×#4294	Dic₇	semidirect
19. C₅×C₇×C₁₉	C₄×C₉	semidirect
35. #4294	Dic₃₅	direct (N × H)
36. Dic₃₅	#4294	direct (N × H)
37. C₇×C₁₉	C₉×Dic₅	semidirect
41. C₅×C₁₉	C₉×Dic₇	semidirect
53. C₅×C₇	C₄×#4294	semidirect
58. C₁₉	C₉×Dic₃₅	semidirect
65. C₇	Dic₅×#4294	semidirect
67. C₅	Dic₇×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×#4294	2
C₃×C₁₉×Dic₃₅	3
Dic₇×#4294	5
Dic₅×#4294	7
C₉×Dic₃₅	19

Subgroups — Dic35×#4294 #37560909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃₅×#4294 #37560909