Subgroups — C₂×#13123231 #16069013

Order 3328.

8094 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88128	C₂	1	14	yes	maximal, complemented
2	#13123231	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₅₂	C₂²	1	28	yes	—
5	C₂²×C₄²×C₁₃	C₂²	1	7	yes	—
6	C₂×#88128	—	2	112	no	—
7	C₂×#88128	C₂²	1	112	yes	complemented
8	C₄³×C₁₃	C₂²	1	8	yes	complemented
9	C₂⁴×D₁₃	C₂³	1	8	yes	—
10	C₂³×C₄×C₁₃	C₂³	1	7	yes	—
11	C₂²×D₅₂	—	2	336	no	—
12	C₂²×D₅₂	C₂³	1	112	yes	—
13	C₂×C₄²×C₁₃	D₄	1	56	yes	complemented
14	C₂×C₄²×C₁₃	C₂³	1	28	yes	—
15	#88128	—	2	448	no	—
16	C₂×#2867	—	13	1	no	maximal, Sylow
17	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
18	C₂³×D₁₃	—	2	112	no	—
19	C₂³×D₁₃	C₂⁴	1	16	yes	—
20	C₂²×C₄×C₁₃	C₂×D₄	1	84	yes	—
21	C₂²×C₄×C₁₃	C₂⁴	1	14	yes	—
22	C₂×D₅₂	—	2	672	no	—
23	C₂×D₅₂	—	4	448	no	—
24	C₄²×C₁₃	C₂×D₄	1	112	yes	complemented
25	C₂²×#127	—	13	14	no	—
26	#2867	—	13	16	no	—
27	C₂×C₄³	D₁₃	1	1	yes	characteristic, complemented
28	C₂³×C₁₃	C₂²×D₄	1	14	yes	—
29	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
30	C₂²×D₁₃	—	2	112	no	—
31	C₂²×D₁₃	—	4	224	no	—
32	C₂×C₄×C₁₃	#127	1	112	yes	complemented
33	C₂×C₄×C₁₃	C₂²×D₄	1	84	yes	—
34	D₅₂	—	4	448	no	—
35	C₂³×D₄	—	13	28	no	—
36	C₂×#127	—	13	112	no	—
37	C₂×#127	—	26	112	no	—
38	C₂²×C₄²	C₂×D₁₃	1	7	yes	—
39	C₄³	C₂×D₁₃	1	8	yes	complemented
40	C₂²×C₁₃	C₂×#127	1	28	yes	—
41	C₂²×C₁₃	C₂³×D₄	1	7	yes	—
42	C₂×D₁₃	—	4	112	no	—
43	C₂×D₁₃	—	8	64	no	—
44	C₄×C₁₃	C₂×#127	1	56	yes	complemented
45	C₂⁵	—	13	8	no	—
46	C₂²×D₄	—	13	112	no	—
47	C₂²×D₄	—	26	336	no	—
48	C₂³×C₄	C₂²×D₁₃	1	7	yes	—
49	#127	—	26	448	no	—
50	C₂×C₄²	D₅₂	1	56	yes	complemented
51	C₂×C₄²	C₂²×D₁₃	1	28	yes	—
52	C₂×C₁₃	#2867	1	8	yes	complemented
53	C₂×C₁₃	C₂²×#127	1	7	yes	—
54	D₁₃	—	8	16	no	—
55	C₂⁴	—	13	16	no	—
56	C₂⁴	—	26	112	no	—
57	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
58	C₂×D₄	—	26	672	no	—
59	C₂×D₄	—	52	448	no	—
60	C₂²×C₄	C₂×D₅₂	1	84	yes	—
61	C₂²×C₄	C₂³×D₁₃	1	14	yes	—
62	C₄²	C₂×D₅₂	1	112	yes	complemented
63	C₁₃	C₂×#2867	1	1	yes	characteristic, complemented, Sylow
64	C₂³	—	26	112	no	—
65	C₂³	—	52	224	no	—
66	C₂³	C₂²×D₅₂	1	14	yes	—
67	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
68	D₄	—	52	448	no	—
69	C₂×C₄	#88128	1	112	yes	complemented
70	C₂×C₄	C₂²×D₅₂	1	84	yes	—
71	C₂²	—	52	112	no	—
72	C₂²	—	104	64	no	—
73	C₂²	C₂×#88128	1	28	yes	—
74	C₂²	C₂³×D₅₂	1	7	yes	—
75	C₄	C₂×#88128	1	56	yes	complemented
76	C₂	—	104	16	no	—
77	C₂	#13123231	1	8	yes	direct product factor
78	C₂	C₂²×#88128	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂³×C₁₃	C₂⁵
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂×C₄³×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	C₂×#2867
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
1. C₂²×#88128	C₂	semidirect
2. #13123231	C₂	direct (N × H)
3. C₂×C₄³×C₁₃	C₂	semidirect
7. C₂×#88128	C₂²	semidirect
8. C₄³×C₁₃	C₂²	semidirect
13. C₂×C₄²×C₁₃	D₄	semidirect
24. C₄²×C₁₃	C₂×D₄	semidirect
27. C₂×C₄³	D₁₃	semidirect
32. C₂×C₄×C₁₃	#127	semidirect
39. C₄³	C₂×D₁₃	semidirect
44. C₄×C₁₃	C₂×#127	semidirect
50. C₂×C₄²	D₅₂	semidirect
52. C₂×C₁₃	#2867	semidirect
62. C₄²	C₂×D₅₂	semidirect
63. C₁₃	C₂×#2867	semidirect
69. C₂×C₄	#88128	semidirect
75. C₄	C₂×#88128	semidirect
77. C₂	#13123231	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×#88128	2
#13123231	2
C₂×C₄³×C₁₃	2
C₂×#2867	13

Subgroups — C2×#13123231 #16069013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123231 #16069013