Subgroups — C₂×C₃₁×#135 #14520753

Order 1984.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×C₃₁	C₂	1	2	yes	maximal, complemented
2	C₃₁×#135	C₂	1	8	yes	maximal, direct product factor
3	C₂×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
5	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×C₃₁	—	2	4	no	—
8	#41×C₃₁	C₂²	1	8	yes	complemented
9	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
10	C₂×D₄×C₃₁	—	2	2	no	—
11	C₂×D₄×C₃₁	C₂²	1	2	yes	—
12	C₂²×C₄×C₃₁	—	2	2	no	—
13	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
14	Q₁₆×C₃₁	C₂²	1	4	yes	complemented
15	SD₁₆×C₃₁	C₂²	1	8	yes	complemented
16	D₈×C₃₁	C₂²	1	4	yes	complemented
17	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₃₁	C₂²	1	4	yes	complemented
20	C₂³×C₃₁	—	2	2	no	—
21	C₂³×C₃₁	D₄	1	1	yes	characteristic
22	Q₈×C₃₁	—	2	2	no	—
23	Q₈×C₃₁	C₂³	1	4	yes	—
24	D₄×C₃₁	—	2	8	no	—
25	D₄×C₃₁	—	2	2	no	—
26	D₄×C₃₁	C₂³	1	4	yes	—
27	C₂×C₄×C₃₁	—	2	2	no	—
28	C₂×C₄×C₃₁	—	2	8	no	—
29	C₂×C₄×C₃₁	D₄	1	2	yes	—
30	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
32	C₂×C₄×C₃₁	C₂³	1	2	yes	—
33	C₈×C₃₁	C₂³	1	2	yes	—
34	C₈×C₃₁	C₂³	1	2	yes	—
35	C₂²×C₃₁	—	2	2	no	—
36	C₂²×C₃₁	—	2	4	no	—
37	C₂²×C₃₁	—	4	4	no	—
38	C₂²×C₃₁	C₂×D₄	1	2	yes	—
39	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
40	C₄×C₃₁	—	2	4	no	—
41	C₄×C₃₁	C₂×D₄	1	2	yes	—
42	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
43	C₄×C₃₁	C₂⁴	1	1	yes	characteristic
44	C₂×#135	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₃₁	—	2	2	no	—
46	C₂×C₃₁	—	4	4	no	—
47	C₂×C₃₁	#135	1	2	yes	direct product factor
48	C₂×C₃₁	C₂²×D₄	1	1	yes	characteristic
49	C₂×#41	C₂×C₃₁	1	2	yes	complemented
50	#135	C₂×C₃₁	1	8	yes	direct product factor
51	C₂×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	C₂×C₃₁	1	2	yes	complemented
53	C₂×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
54	C₂²×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
55	C₃₁	C₂×#135	1	1	yes	characteristic, direct product factor, Sylow
56	#41	—	2	4	no	—
57	#41	C₂²×C₃₁	1	8	yes	complemented
58	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
59	C₂×D₄	—	2	2	no	—
60	C₂×D₄	C₂²×C₃₁	1	2	yes	—
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
63	Q₁₆	C₂²×C₃₁	1	4	yes	complemented
64	SD₁₆	C₂²×C₃₁	1	8	yes	complemented
65	D₈	C₂²×C₃₁	1	4	yes	complemented
66	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
67	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
68	C₂×C₈	C₂²×C₃₁	1	4	yes	complemented
69	C₂³	—	2	2	no	—
70	C₂³	D₄×C₃₁	1	1	yes	characteristic
71	Q₈	—	2	2	no	—
72	Q₈	C₂³×C₃₁	1	4	yes	—
73	D₄	—	2	8	no	—
74	D₄	—	2	2	no	—
75	D₄	C₂³×C₃₁	1	4	yes	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	8	no	—
78	C₂×C₄	D₄×C₃₁	1	2	yes	—
79	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
80	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
81	C₂×C₄	C₂³×C₃₁	1	2	yes	—
82	C₈	C₂³×C₃₁	1	2	yes	—
83	C₈	C₂³×C₃₁	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	2	4	no	—
86	C₂²	—	4	4	no	—
87	C₂²	C₂×D₄×C₃₁	1	2	yes	—
88	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
89	C₄	—	2	4	no	—
90	C₄	C₂×D₄×C₃₁	1	2	yes	—
91	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
92	C₄	C₂⁴×C₃₁	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	4	4	no	—
95	C₂	C₃₁×#135	1	2	yes	direct product factor
96	C₂	C₂²×D₄×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#41×C₃₁	C₂	semidirect
2. C₃₁×#135	C₂	direct (N × H)
3. C₂×Q₁₆×C₃₁	C₂	semidirect
4. C₂×SD₁₆×C₃₁	C₂	semidirect
5. C₂×D₈×C₃₁	C₂	semidirect
6. C₂²×C₈×C₃₁	C₂	semidirect
8. #41×C₃₁	C₂²	semidirect
14. Q₁₆×C₃₁	C₂²	semidirect
15. SD₁₆×C₃₁	C₂²	semidirect
16. D₈×C₃₁	C₂²	semidirect
19. C₂×C₈×C₃₁	C₂²	semidirect
44. C₂×#135	C₃₁	direct (N × H)
47. C₂×C₃₁	#135	direct (N × H)
49. C₂×#41	C₂×C₃₁	semidirect
50. #135	C₂×C₃₁	direct (N × H)
51. C₂×Q₁₆	C₂×C₃₁	semidirect
52. C₂×SD₁₆	C₂×C₃₁	semidirect
53. C₂×D₈	C₂×C₃₁	semidirect
54. C₂²×C₈	C₂×C₃₁	semidirect
55. C₃₁	C₂×#135	direct (N × H)
57. #41	C₂²×C₃₁	semidirect
63. Q₁₆	C₂²×C₃₁	semidirect
64. SD₁₆	C₂²×C₃₁	semidirect
65. D₈	C₂²×C₃₁	semidirect
68. C₂×C₈	C₂²×C₃₁	semidirect
95. C₂	C₃₁×#135	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×C₃₁	2
C₃₁×#135	2
C₂×Q₁₆×C₃₁	2
C₂×SD₁₆×C₃₁	2
C₂×D₈×C₃₁	2
C₂²×C₈×C₃₁	2
C₂×#135	31

Subgroups — C2×C31×#135 #14520753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#135 #14520753