Subgroups — C₂×C₁₃×#2867 #15722981

Order 3328.

8094 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	14	yes	maximal, complemented
2	C₁₃×#2867	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄×C₁₃	C₂²	1	28	yes	—
5	C₂×C₁₃×#127	—	2	112	no	—
6	C₂×C₁₃×#127	C₂²	1	112	yes	complemented
7	C₂²×C₄²×C₁₃	C₂²	1	7	yes	—
8	C₄³×C₁₃	C₂²	1	8	yes	complemented
9	C₂⁵×C₁₃	C₂³	1	8	yes	—
10	C₂²×D₄×C₁₃	—	2	336	no	—
11	C₂²×D₄×C₁₃	C₂³	1	112	yes	—
12	C₂³×C₄×C₁₃	C₂³	1	7	yes	—
13	C₁₃×#127	—	2	448	no	—
14	C₂×C₄²×C₁₃	D₄	1	56	yes	complemented
15	C₂×C₄²×C₁₃	C₂³	1	28	yes	—
16	C₂×#2867	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂⁴×C₁₃	—	2	112	no	—
18	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
19	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
20	C₂×D₄×C₁₃	—	2	672	no	—
21	C₂×D₄×C₁₃	—	4	448	no	—
22	C₂²×C₄×C₁₃	C₂×D₄	1	84	yes	—
23	C₂²×C₄×C₁₃	C₂⁴	1	14	yes	—
24	C₄²×C₁₃	C₂×D₄	1	112	yes	complemented
25	C₂²×#127	C₂×C₁₃	1	14	yes	complemented
26	#2867	C₂×C₁₃	1	16	yes	direct product factor
27	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₂³×C₁₃	—	2	112	no	—
29	C₂³×C₁₃	—	4	224	no	—
30	C₂³×C₁₃	C₂²×D₄	1	14	yes	—
31	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
32	D₄×C₁₃	—	4	448	no	—
33	C₂×C₄×C₁₃	#127	1	112	yes	complemented
34	C₂×C₄×C₁₃	C₂²×D₄	1	84	yes	—
35	C₂³×D₄	C₂²×C₁₃	1	28	yes	—
36	C₂×#127	—	2	112	no	—
37	C₂×#127	C₂²×C₁₃	1	112	yes	complemented
38	C₂²×C₄²	C₂²×C₁₃	1	7	yes	—
39	C₄³	C₂²×C₁₃	1	8	yes	complemented
40	C₂²×C₁₃	—	4	112	no	—
41	C₂²×C₁₃	—	8	64	no	—
42	C₂²×C₁₃	C₂×#127	1	28	yes	—
43	C₂²×C₁₃	C₂³×D₄	1	7	yes	—
44	C₄×C₁₃	C₂×#127	1	56	yes	complemented
45	C₂⁵	C₂³×C₁₃	1	8	yes	—
46	C₂²×D₄	—	2	336	no	—
47	C₂²×D₄	C₂³×C₁₃	1	112	yes	—
48	C₂³×C₄	C₂³×C₁₃	1	7	yes	—
49	#127	—	2	448	no	—
50	C₂×C₄²	D₄×C₁₃	1	56	yes	complemented
51	C₂×C₄²	C₂³×C₁₃	1	28	yes	—
52	C₂×C₁₃	—	8	16	no	—
53	C₂×C₁₃	#2867	1	8	yes	direct product factor
54	C₂×C₁₃	C₂²×#127	1	7	yes	—
55	C₂⁴	—	2	112	no	—
56	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
57	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
58	C₂×D₄	—	2	672	no	—
59	C₂×D₄	—	4	448	no	—
60	C₂²×C₄	C₂×D₄×C₁₃	1	84	yes	—
61	C₂²×C₄	C₂⁴×C₁₃	1	14	yes	—
62	C₄²	C₂×D₄×C₁₃	1	112	yes	complemented
63	C₁₃	C₂×#2867	1	1	yes	characteristic, direct product factor, Sylow
64	C₂³	—	2	112	no	—
65	C₂³	—	4	224	no	—
66	C₂³	C₂²×D₄×C₁₃	1	14	yes	—
67	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
68	D₄	—	4	448	no	—
69	C₂×C₄	C₁₃×#127	1	112	yes	complemented
70	C₂×C₄	C₂²×D₄×C₁₃	1	84	yes	—
71	C₂²	—	4	112	no	—
72	C₂²	—	8	64	no	—
73	C₂²	C₂×C₁₃×#127	1	28	yes	—
74	C₂²	C₂³×D₄×C₁₃	1	7	yes	—
75	C₄	C₂×C₁₃×#127	1	56	yes	complemented
76	C₂	—	8	16	no	—
77	C₂	C₁₃×#2867	1	8	yes	direct product factor
78	C₂	C₂²×C₁₃×#127	1	7	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#127	C₂	semidirect
2. C₁₃×#2867	C₂	direct (N × H)
3. C₂×C₄³×C₁₃	C₂	semidirect
6. C₂×C₁₃×#127	C₂²	semidirect
8. C₄³×C₁₃	C₂²	semidirect
14. C₂×C₄²×C₁₃	D₄	semidirect
16. C₂×#2867	C₁₃	direct (N × H)
24. C₄²×C₁₃	C₂×D₄	semidirect
25. C₂²×#127	C₂×C₁₃	semidirect
26. #2867	C₂×C₁₃	direct (N × H)
27. C₂×C₄³	C₂×C₁₃	semidirect
33. C₂×C₄×C₁₃	#127	semidirect
37. C₂×#127	C₂²×C₁₃	semidirect
39. C₄³	C₂²×C₁₃	semidirect
44. C₄×C₁₃	C₂×#127	semidirect
50. C₂×C₄²	D₄×C₁₃	semidirect
53. C₂×C₁₃	#2867	direct (N × H)
62. C₄²	C₂×D₄×C₁₃	semidirect
63. C₁₃	C₂×#2867	direct (N × H)
69. C₂×C₄	C₁₃×#127	semidirect
75. C₄	C₂×C₁₃×#127	semidirect
77. C₂	C₁₃×#2867	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×C₁₃×#127	2
C₁₃×#2867	2
C₂×C₄³×C₁₃	2
C₂×#2867	13

Subgroups — C2×C13×#2867 #15722981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2867 #15722981