Subgroups — D₃₁×#4294⋊C₂ #35234331

Order 21204.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4294⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#4294⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₁×#4294	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×D₃₁	C₃	1	1	yes	maximal, characteristic
5	C₃₁×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅₈₉	C₂×C₃	1	1	yes	characteristic
7	C₃×C₃₁×D₁₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₉×D₃₁	C₂×C₃	1	1	yes	characteristic
9	D₁₉×D₃₁	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₉×C₃₁	C₂²×C₃	1	1	yes	characteristic
11	D₅₈₉	C₂×C₉	1	1	yes	characteristic, complemented
12	C₁₉×D₃₁	C₂×C₉	1	1	yes	characteristic, complemented
13	C₃₁×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
14	C₂×C₉×D₃₁	—	19	1	no	maximal, Hall
15	C₂×#4294⋊C₂	—	31	1	no	maximal, Hall
16	C₁₉×C₃₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₉×C₃₁	—	19	1	no	—
18	C₉×D₃₁	—	19	1	no	—
19	C₉×D₃₁	—	19	1	no	—
20	C₂×C₃×D₃₁	—	57	1	no	—
21	C₂×#4294	—	31	1	no	—
22	#4294⋊C₂	—	31	1	no	—
23	#4294⋊C₂	D₃₁	1	1	yes	characteristic, direct product factor
24	C₉×C₃₁	—	19	1	no	Hall
25	C₂×C₃×D₁₉	—	31	1	no	—
26	C₂×C₃×C₃₁	—	57	1	no	—
27	C₃×D₃₁	—	57	1	no	—
28	C₃×D₃₁	D₁₉⋊C₃	1	1	yes	characteristic
29	#4294	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃₁	—	57	1	no	Hall
31	C₂×C₃×C₁₉	—	31	1	no	—
32	C₃×D₁₉	—	31	1	no	—
33	C₃×D₁₉	C₃×D₃₁	1	1	yes	characteristic
34	C₃×C₃₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic
35	C₂×D₁₉	—	31	1	no	Hall
36	C₂×C₃₁	—	57	1	no	—
37	D₃₁	—	57	1	no	—
38	D₃₁	#4294⋊C₂	1	1	yes	characteristic, direct product factor
39	C₃×C₁₉	C₂×C₃×D₃₁	1	1	yes	characteristic
40	C₂×C₁₉	—	31	1	no	—
41	D₁₉	—	31	1	no	—
42	D₁₉	C₉×D₃₁	1	1	yes	characteristic, complemented
43	C₂²×C₉	—	589	1	no	Hall
44	C₃₁	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
45	C₁₉	C₂×C₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	19	1	no	—
47	C₂×C₉	—	589	1	no	—
48	C₂×C₉	—	589	1	no	—
49	C₂²×C₃	—	1767	1	no	—
50	C₉	—	19	1	no	Sylow
51	C₂×C₃	—	31	1	no	—
52	C₂×C₃	—	57	1	no	—
53	C₂×C₃	—	1767	1	no	—
54	C₂²	—	1767	1	no	Sylow
55	C₃	D₃₁×D₁₉⋊C₃	1	1	yes	characteristic
56	C₂	—	31	1	no	—
57	C₂	—	57	1	no	—
58	C₂	—	1767	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₃₁×D₁₉⋊C₃
commutator, hypocenter	C₁₉×C₃₁	C₂²×C₉
Fitting, socle, cosocle	C₃×C₁₉×C₃₁	C₂²×C₃
prime radical	C₃×D₁₉×D₃₁	C₃
LCS	G ▷ C₁₉×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #4294⋊D₃₁	C₂	semidirect
2. C₃₁×#4294⋊C₂	C₂	semidirect
3. D₃₁×#4294	C₂	semidirect
5. C₃₁×#4294	C₂²	semidirect
9. D₁₉×D₃₁	C₉	semidirect
11. D₅₈₉	C₂×C₉	semidirect
12. C₁₉×D₃₁	C₂×C₉	semidirect
13. C₃₁×D₁₉	C₂×C₉	semidirect
16. C₁₉×C₃₁	C₂²×C₉	semidirect
23. #4294⋊C₂	D₃₁	direct (N × H)
29. #4294	C₂×D₃₁	semidirect
38. D₃₁	#4294⋊C₂	direct (N × H)
42. D₁₉	C₉×D₃₁	semidirect
44. C₃₁	C₂×#4294⋊C₂	semidirect
45. C₁₉	C₂×C₉×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
#4294⋊D₃₁	2
C₃₁×#4294⋊C₂	2
D₃₁×#4294	2
C₃×D₁₉×D₃₁	3
C₂×C₉×D₃₁	19
C₂×#4294⋊C₂	31

Subgroups — D31×#4294⋊C2 #35234331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×#4294⋊C₂ #35234331