Subgroups — C₂×#32914861 #49149409

Order 36972.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#32914861	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22604455	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₃×C₇₉	C₃	1	1	yes	maximal, characteristic
4	#22604455	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₃×C₇₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic
7	C₂×D₁₃×C₇₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₇₉⋊C₉	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₇₉	C₂×C₉	1	1	yes	characteristic, complemented
11	D₁₃×C₇₉	C₂×C₉	1	2	yes	complemented
12	C₂×C₇₉⋊C₉	—	13	2	no	—
13	C₂×C₇₉⋊C₉	—	13	1	no	—
14	C₁₃×C₇₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₇₉	—	13	1	no	—
16	C₇₉⋊C₉	—	13	1	no	Hall
17	C₂×C₃×C₇₉	—	13	2	no	—
18	C₂×C₃×C₇₉	D₁₃⋊C₃	1	1	yes	characteristic
19	C₂×D₁₃⋊C₉	—	79	1	no	maximal, Hall
20	C₂²×C₇₉	—	13	1	no	Hall
21	C₃×C₇₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic
22	C₂×C₁₃⋊C₉	—	79	1	no	—
23	D₁₃⋊C₉	—	79	2	no	—
24	C₂×C₇₉	—	13	2	no	—
25	C₂×C₇₉	D₁₃⋊C₉	1	1	yes	characteristic, complemented
26	C₂×C₃×D₁₃	C₇₉⋊C₃	1	1	yes	characteristic
27	C₁₃⋊C₉	—	79	1	no	Hall
28	C₇₉	C₂×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×C₁₃	C₂×C₇₉⋊C₃	1	1	yes	characteristic
30	C₃×D₁₃	C₂×C₇₉⋊C₃	1	2	yes	—
31	C₂×D₁₃	C₇₉⋊C₉	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	C₂²×C₇₉⋊C₃	1	1	yes	characteristic
33	C₂²×C₉	—	1027	1	no	Hall
34	C₂×C₁₃	C₂×C₇₉⋊C₉	1	1	yes	characteristic, complemented
35	D₁₃	C₂×C₇₉⋊C₉	1	2	yes	complemented
36	C₂×C₉	—	1027	2	no	—
37	C₂×C₉	—	1027	1	no	—
38	C₁₃	C₂²×C₇₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	1	no	—
40	C₉	—	1027	1	no	Sylow
41	C₂×C₃	—	13	2	no	—
42	C₂×C₃	#20259717	1	1	yes	characteristic
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×#20259717	1	1	yes	characteristic
45	C₂	—	13	2	no	—
46	C₂	#32914861	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#20259717
commutator, hypocenter	C₁₃×C₇₉	C₂²×C₉
Frattini	C₃	C₂×#20259717
Fitting, socle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₂×C₃×D₁₃×C₇₉	C₃
cosocle	C₃×C₁₃×C₇₉	C₂²×C₃
LCS	G ▷ C₁₃×C₇₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #32914861	C₂	direct (N × H)
2. C₂×#22604455	C₂	semidirect
4. #22604455	C₂²	semidirect
7. C₂×D₁₃×C₇₉	C₉	semidirect
10. C₂×C₁₃×C₇₉	C₂×C₉	semidirect
11. D₁₃×C₇₉	C₂×C₉	semidirect
14. C₁₃×C₇₉	C₂²×C₉	semidirect
25. C₂×C₇₉	D₁₃⋊C₉	semidirect
28. C₇₉	C₂×D₁₃⋊C₉	semidirect
31. C₂×D₁₃	C₇₉⋊C₉	semidirect
34. C₂×C₁₃	C₂×C₇₉⋊C₉	semidirect
35. D₁₃	C₂×C₇₉⋊C₉	semidirect
38. C₁₃	C₂²×C₇₉⋊C₉	semidirect
46. C₂	#32914861	direct (N × H)

Maximal subgroups

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

subgroup	index
#32914861	2
C₂×#22604455	2
C₂×C₃×D₁₃×C₇₉	3
C₂²×C₇₉⋊C₉	13
C₂×D₁₃⋊C₉	79

Subgroups — C2×#32914861 #49149409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#32914861 #49149409