Subgroups — #31798061⋊C₂ #47975151

Order 35076.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31798069	C₂	1	1	yes	maximal, characteristic, complemented
2	#31798065	C₂	1	1	yes	maximal, characteristic, complemented
3	#31798061	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₇×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#22578530	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₉₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₇×D₇₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃₇×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃₇×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₇₉⋊C₃	—	37	1	no	maximal, Hall
11	C₂×C₇₉⋊C₃	—	37	1	no	—
12	D₇₉⋊C₃	—	37	1	no	—
13	D₇₉⋊C₃	—	37	1	no	—
14	C₂×D₃₇⋊C₃	—	79	1	no	maximal, Hall
15	C₂×D₇₉	—	37	1	no	Hall
16	C₇₉⋊C₃	—	37	1	no	Hall
17	C₂×C₃₇⋊C₃	—	79	1	no	—
18	D₃₇⋊C₃	—	79	1	no	—
19	D₃₇⋊C₃	—	79	1	no	—
20	C₂×C₇₉	—	37	1	no	—
21	D₇₉	—	37	1	no	—
22	D₇₉	D₃₇⋊C₃	1	1	yes	characteristic, complemented
23	C₂×D₃₇	—	79	1	no	Hall
24	C₃₇⋊C₃	—	79	1	no	Hall
25	C₇₉	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃₇	—	79	1	no	—
27	D₃₇	—	79	1	no	—
28	D₃₇	D₇₉⋊C₃	1	1	yes	characteristic, complemented
29	C₃₇	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2923	1	no	Hall
31	C₂×C₃	—	2923	1	no	—
32	C₂×C₃	—	2923	1	no	—
33	C₂×C₃	—	2923	1	no	—
34	C₂²	—	2923	1	no	Sylow
35	C₃	—	2923	1	no	Sylow
36	C₂	—	37	1	no	—
37	C₂	—	79	1	no	—
38	C₂	—	2923	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₇×C₇₉	C₂²×C₃
LCS	G ▷ C₃₇×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #31798069	C₂	semidirect
2. #31798065	C₂	semidirect
3. #31798061	C₂	semidirect
4. D₃₇×D₇₉	C₃	semidirect
5. #22578530	C₂²	semidirect
6. D₂₉₂₃	C₂×C₃	semidirect
7. C₃₇×D₇₉	C₂×C₃	semidirect
8. D₃₇×C₇₉	C₂×C₃	semidirect
9. C₃₇×C₇₉	C₂²×C₃	semidirect
22. D₇₉	D₃₇⋊C₃	semidirect
25. C₇₉	C₂×D₃₇⋊C₃	semidirect
28. D₃₇	D₇₉⋊C₃	semidirect
29. C₃₇	C₂×D₇₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#31798069	2
#31798065	2
#31798061	2
D₃₇×D₇₉	3
C₂×D₇₉⋊C₃	37
C₂×D₃₇⋊C₃	79

Subgroups — #31798061⋊C2 #47975151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #31798061⋊C₂ #47975151