Subgroups — C₇²×D₁₉₅ #34062189

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₆₅	—	3	1	no	maximal, Hall
3	C₇²×D₃₉	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₇×D₁₉₅	C₇	1	8	yes	maximal, direct product factor
6	C₃×C₇²×C₁₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₇²×D₁₅	—	13	1	no	maximal, Hall
8	C₃×C₅×C₇×C₁₃	C₂×C₇	1	8	yes	complemented
9	C₇²×D₁₃	—	15	1	no	Hall
10	C₇×D₆₅	—	3	8	no	—
11	C₃×C₅×C₇²	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₃	D₁₅	1	1	yes	characteristic, complemented, Hall
13	C₇×D₃₉	—	5	8	no	—
14	C₇²×D₅	—	39	1	no	Hall
15	C₅×C₇×C₁₃	D₃×C₇	1	8	yes	complemented
16	D₁₉₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	D₃×C₇²	—	65	1	no	Hall
18	C₃×C₇×C₁₃	C₇×D₅	1	8	yes	complemented
19	C₅×C₇²	D₃₉	1	1	yes	characteristic, complemented, Hall
20	C₇×D₁₅	—	13	8	no	—
21	C₃×C₅×C₁₃	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
22	C₇×D₁₃	—	15	8	no	—
23	C₃×C₇²	D₆₅	1	1	yes	characteristic, complemented, Hall
24	D₆₅	—	3	1	no	Hall
25	C₃×C₅×C₇	C₇×D₁₃	1	8	yes	complemented
26	C₂×C₇²	—	195	1	no	Hall
27	C₇×C₁₃	C₇×D₁₅	1	8	yes	complemented
28	D₃₉	—	5	1	no	Hall
29	C₇×D₅	—	39	8	no	—
30	C₅×C₁₃	D₃×C₇²	1	1	yes	characteristic, complemented, Hall
31	C₇²	D₁₉₅	1	1	yes	characteristic, direct product factor, Sylow
32	D₃×C₇	—	65	8	no	—
33	C₃×C₁₃	C₇²×D₅	1	1	yes	characteristic, complemented, Hall
34	C₅×C₇	C₇×D₃₉	1	8	yes	complemented
35	D₁₅	—	13	1	no	Hall
36	D₁₃	—	15	1	no	Hall
37	C₃×C₇	C₇×D₆₅	1	8	yes	complemented
38	C₃×C₅	C₇²×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	—	195	8	no	—
40	C₁₃	C₇²×D₁₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	39	1	no	Hall
42	C₇	C₇×D₁₉₅	1	8	yes	direct product factor
43	D₃	—	65	1	no	Hall
44	C₅	C₇²×D₃₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇²×D₆₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	195	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₁₉₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₃	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₃	C₂	semidirect
4. C₅×C₇²×C₁₃	D₃	semidirect
5. C₇×D₁₉₅	C₇	direct (N × H)
6. C₃×C₇²×C₁₃	D₅	semidirect
8. C₃×C₅×C₇×C₁₃	C₂×C₇	semidirect
11. C₃×C₅×C₇²	D₁₃	semidirect
12. C₇²×C₁₃	D₁₅	semidirect
15. C₅×C₇×C₁₃	D₃×C₇	semidirect
16. D₁₉₅	C₇²	direct (N × H)
18. C₃×C₇×C₁₃	C₇×D₅	semidirect
19. C₅×C₇²	D₃₉	semidirect
21. C₃×C₅×C₁₃	C₂×C₇²	semidirect
23. C₃×C₇²	D₆₅	semidirect
25. C₃×C₅×C₇	C₇×D₁₃	semidirect
27. C₇×C₁₃	C₇×D₁₅	semidirect
30. C₅×C₁₃	D₃×C₇²	semidirect
31. C₇²	D₁₉₅	direct (N × H)
33. C₃×C₁₃	C₇²×D₅	semidirect
34. C₅×C₇	C₇×D₃₉	semidirect
37. C₃×C₇	C₇×D₆₅	semidirect
38. C₃×C₅	C₇²×D₁₃	semidirect
40. C₁₃	C₇²×D₁₅	semidirect
42. C₇	C₇×D₁₉₅	direct (N × H)
44. C₅	C₇²×D₃₉	semidirect
45. C₃	C₇²×D₆₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₃	2
C₇²×D₆₅	3
C₇²×D₃₉	5
C₇×D₁₉₅	7
C₇²×D₁₅	13

Subgroups — C72×D195 #34062189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×D₁₉₅ #34062189