Subgroups — C₂×#13112752 #15771893

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
3	#13112752	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	2	yes	—
8	C₂×C₄×#1055	C₄	1	2	yes	—
9	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
10	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₄×#6090	C₄	1	2	yes	—
12	C₄×#6090	C₂²	1	2	yes	—
13	C₈×#1055	C₄	1	2	yes	—
14	C₈×#1055	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×#1055	C₈	1	4	yes	—
19	C₂×C₁₃×C₁₆	C₈	1	8	yes	complemented
20	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×#6090	C₈	1	8	yes	complemented
26	C₂×#6090	C₂×C₄	1	4	yes	—
27	C₄×#1055	C₈	1	4	yes	—
28	C₄×#1055	C₂×C₄	1	4	yes	—
29	C₂×#1311	—	13	1	no	maximal, Sylow
30	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
36	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₃	C₄²	1	1	yes	characteristic
39	C₄²×C₁₃	C₂×C₈	1	2	yes	—
40	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×#1055	—	2	8	no	—
42	C₂×#1055	C₂×C₈	1	8	yes	—
43	C₁₃×C₁₆	C₂×C₈	1	8	yes	complemented
44	#6090	C₂×C₈	1	8	yes	complemented
45	C₂×C₄×C₁₆	—	13	1	no	—
46	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
47	C₂×C₈²	—	13	1	no	—
48	#1311	—	13	4	no	—
49	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
52	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
53	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
54	C₂×C₄×C₁₃	M₃₂	1	8	yes	—
55	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
57	C₈×C₁₃	C₄×C₈	1	2	yes	—
58	C₈×C₁₃	C₄×C₈	1	2	yes	—
59	C₈×C₁₃	C₂²×C₈	1	2	yes	—
60	C₈×C₁₃	C₂²×C₈	1	2	yes	—
61	#1055	—	2	8	no	—
62	C₂²×C₁₆	—	13	2	no	—
63	C₂²×C₁₆	Dic₁₃	1	2	yes	—
64	C₂×C₄×C₈	—	13	2	no	—
65	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
66	C₄×C₁₆	—	13	2	no	—
67	C₄×C₁₆	—	13	2	no	—
68	C₄×C₁₆	Dic₁₃	1	2	yes	—
69	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
70	C₈²	—	13	2	no	—
71	C₈²	—	13	2	no	—
72	C₂²×C₁₃	C₈²	1	2	yes	—
73	C₂²×C₁₃	#346	1	4	yes	—
74	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
75	C₄×C₁₃	C₈²	1	2	yes	—
76	C₄×C₁₃	#346	1	4	yes	—
77	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
78	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
79	C₄×C₁₃	C₂×M₃₂	1	4	yes	—
80	C₂²×C₈	—	13	4	no	—
81	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
82	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
83	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
84	C₂×C₁₆	—	13	8	no	—
85	C₂×C₁₆	—	13	4	no	—
86	C₂×C₁₆	#1055	1	8	yes	complemented
87	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
88	C₄×C₈	—	13	4	no	—
89	C₄×C₈	—	13	4	no	—
90	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
91	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
92	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
93	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
94	C₂×C₁₃	#1311	1	4	yes	complemented
95	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
96	C₂×C₁₃	C₂×#346	1	2	yes	—
97	C₂²×C₄	C₈×D₁₃	1	2	yes	—
98	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
99	C₂×C₈	—	13	8	no	—
100	C₂×C₈	—	26	8	no	—
101	C₂×C₈	C₈×D₁₃	1	4	yes	—
102	C₂×C₈	C₂×#1055	1	4	yes	—
103	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
104	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
105	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
106	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
107	C₄²	C₈×D₁₃	1	2	yes	—
108	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
109	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
110	C₁₆	—	13	8	no	—
111	C₁₆	C₂×#1055	1	8	yes	complemented
112	C₁₃	C₂×#1311	1	1	yes	characteristic, complemented, Sylow
113	C₂³	C₈×Dic₁₃	1	1	yes	characteristic
114	C₂×C₄	#88038	1	8	yes	—
115	C₂×C₄	C₄×#1055	1	2	yes	—
116	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
117	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
118	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
119	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
120	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
121	C₈	—	26	8	no	—
122	C₈	C₄×#1055	1	2	yes	—
123	C₈	C₈×Dic₁₃	1	2	yes	—
124	C₈	C₂×C₈×D₁₃	1	2	yes	—
125	C₈	C₂²×#1055	1	2	yes	—
126	C₂²	C₈×#1055	1	2	yes	—
127	C₂²	#11718094	1	4	yes	—
128	C₂²	C₂×C₈×Dic₁₃	1	1	yes	characteristic
129	C₄	C₈×#1055	1	2	yes	—
130	C₄	#11718094	1	4	yes	—
131	C₄	C₂×#88038	1	4	yes	—
132	C₄	C₂×C₄×#1055	1	1	yes	characteristic
133	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
134	C₂	#13112752	1	4	yes	direct product factor
135	C₂	C₂×C₈×#1055	1	1	yes	characteristic
136	C₂	C₂×#11718094	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₈²
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1311
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. #13112752	C₂	direct (N × H)
19. C₂×C₁₃×C₁₆	C₈	semidirect
25. C₂×#6090	C₈	semidirect
43. C₁₃×C₁₆	C₂×C₈	semidirect
44. #6090	C₂×C₈	semidirect
86. C₂×C₁₆	#1055	semidirect
94. C₂×C₁₃	#1311	semidirect
111. C₁₆	C₂×#1055	semidirect
112. C₁₃	C₂×#1311	semidirect
134. C₂	#13112752	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×C₄×#6090	2
C₂×C₈×#1055	2
#13112752	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#1311	13

Subgroups — C2×#13112752 #15771893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112752 #15771893