Subgroups — C₂×#107×C₃₅₉ #37526001

Order 22976.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₃₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₃₅₉	C₂	1	2	yes	maximal
3	#107×C₃₅₉	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₃₅₉	—	2	2	no	—
5	C₂²×C₄×C₃₅₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₅₉	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₅₉	C₂²	1	2	yes	—
8	C₄⋊C₄×C₃₅₉	—	2	2	no	—
9	C₄⋊C₄×C₃₅₉	C₂²	1	4	yes	—
10	C₂³×C₃₅₉	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₅₉	—	2	4	no	—
12	C₂×C₄×C₃₅₉	—	4	4	no	—
13	C₂×C₄×C₃₅₉	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₅₉	Q₈	1	2	yes	—
16	C₂×C₄×C₃₅₉	C₂³	1	1	yes	characteristic
17	C₈×C₃₅₉	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃₅₉	C₄⋊C₄	1	2	yes	—
19	C₂²×C₃₅₉	D₈	1	2	yes	—
20	C₂²×C₃₅₉	Q₁₆	1	2	yes	—
21	C₂²×C₃₅₉	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₅₉	—	4	4	no	—
23	C₄×C₃₅₉	C₄⋊C₄	1	2	yes	—
24	C₄×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₅₉	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₃₅₉	#107	1	4	yes	direct product factor
27	C₂×C₃₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₃₅₉	C₂×D₈	1	1	yes	characteristic
29	C₂×C₃₅₉	C₂×Q₁₆	1	1	yes	characteristic
30	C₃₅₉	C₂×#107	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×#107	C₃₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₈	C₂×C₃₅₉	1	1	yes	characteristic
33	C₂×C₄⋊C₄	C₂×C₃₅₉	1	2	yes	—
34	#107	C₂×C₃₅₉	1	4	yes	direct product factor
35	C₂²×C₄	—	2	2	no	—
36	C₂²×C₄	C₂²×C₃₅₉	1	1	yes	characteristic
37	C₂×C₈	C₄×C₃₅₉	1	4	yes	complemented
38	C₂×C₈	C₂²×C₃₅₉	1	2	yes	—
39	C₄⋊C₄	—	2	2	no	—
40	C₄⋊C₄	C₂²×C₃₅₉	1	4	yes	—
41	C₂³	D₄×C₃₅₉	1	1	yes	characteristic
42	C₂×C₄	—	2	4	no	—
43	C₂×C₄	—	4	4	no	—
44	C₂×C₄	C₂×C₄×C₃₅₉	1	2	yes	—
45	C₂×C₄	D₄×C₃₅₉	1	1	yes	characteristic
46	C₂×C₄	Q₈×C₃₅₉	1	2	yes	—
47	C₂×C₄	C₂³×C₃₅₉	1	1	yes	characteristic
48	C₈	C₂×C₄×C₃₅₉	1	4	yes	complemented
49	C₂²	C₄⋊C₄×C₃₅₉	1	2	yes	—
50	C₂²	D₈×C₃₅₉	1	2	yes	—
51	C₂²	Q₁₆×C₃₅₉	1	2	yes	—
52	C₂²	C₂×D₄×C₃₅₉	1	1	yes	characteristic
53	C₄	—	4	4	no	—
54	C₄	C₄⋊C₄×C₃₅₉	1	2	yes	—
55	C₄	C₂²×C₄×C₃₅₉	1	1	yes	characteristic
56	C₄	C₂×Q₈×C₃₅₉	1	1	yes	characteristic
57	C₂	#107×C₃₅₉	1	4	yes	direct product factor
58	C₂	C₂×C₄⋊C₄×C₃₅₉	1	1	yes	characteristic
59	C₂	C₂×D₈×C₃₅₉	1	1	yes	characteristic
60	C₂	C₂×Q₁₆×C₃₅₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₅₉	D₄
commutator	C₄	C₂²×C₄×C₃₅₉
Frattini, cosocle	C₂×C₄	C₂³×C₃₅₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₅₉ ◁ C₂²×C₄×C₃₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #107×C₃₅₉	C₂	direct (N × H)
6. C₂×C₈×C₃₅₉	C₄	semidirect
17. C₈×C₃₅₉	C₂×C₄	semidirect
26. C₂×C₃₅₉	#107	direct (N × H)
30. C₃₅₉	C₂×#107	direct (N × H)
31. C₂×#107	C₃₅₉	direct (N × H)
34. #107	C₂×C₃₅₉	direct (N × H)
37. C₂×C₈	C₄×C₃₅₉	semidirect
48. C₈	C₂×C₄×C₃₅₉	semidirect
57. C₂	#107×C₃₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₃₅₉	2
C₂×C₄⋊C₄×C₃₅₉	2
#107×C₃₅₉	2
C₂×#107	359

Subgroups — C2×#107×C359 #37526001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#107×C₃₅₉ #37526001