Subgroups — C₂×#13112754 #15771905

Order 3328.

350 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	2	yes	maximal
2	#13112754	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	4	yes	—
8	C₈²×C₁₃	C₄	1	2	yes	—
9	C₈²×C₁₃	C₂²	1	2	yes	—
10	C₄×#6090	C₄	1	4	yes	—
11	C₄×#6090	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	C₈	1	2	yes	—
13	C₂²×C₈×C₁₃	C₈	1	2	yes	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈×C₁₃	C₈	1	2	yes	—
17	C₄×C₈×C₁₃	C₈	1	2	yes	—
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×#6090	—	2	8	no	—
24	C₂×#6090	C₂×C₄	1	8	yes	—
25	C₂×#1312	—	13	1	no	maximal, Sylow
26	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈×C₁₃	—	2	4	no	—
30	C₂×C₈×C₁₃	C₁₆	1	8	yes	complemented
31	C₂×C₈×C₁₃	C₄²	1	2	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
36	C₄²×C₁₃	C₄²	1	1	yes	characteristic
37	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
38	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
39	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	#6090	—	2	8	no	—
41	C₂×C₄×C₁₆	—	13	2	no	—
42	C₂×C₈²	D₁₃	1	1	yes	characteristic
43	#1312	—	13	4	no	—
44	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₃	#97	1	4	yes	—
49	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
50	C₂×C₄×C₁₃	M₃₂	1	4	yes	—
51	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₁₃	—	2	4	no	—
55	C₈×C₁₃	#97	1	4	yes	—
56	C₈×C₁₃	C₂×C₁₆	1	8	yes	complemented
57	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
58	C₂²×C₁₆	—	13	4	no	—
59	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
60	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
61	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
62	C₄×C₁₆	—	13	4	no	—
63	C₄×C₁₆	—	13	4	no	—
64	C₈²	Dic₁₃	1	2	yes	—
65	C₈²	C₂×D₁₃	1	2	yes	—
66	C₂²×C₁₃	#322	1	2	yes	—
67	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
68	C₂²×C₁₃	#346	1	2	yes	—
69	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
70	C₄×C₁₃	#322	1	2	yes	—
71	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
72	C₄×C₁₃	#346	1	2	yes	—
73	C₄×C₁₃	C₂×#97	1	2	yes	—
74	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
75	C₄×C₁₃	C₂×M₃₂	1	2	yes	—
76	C₂²×C₈	#1055	1	2	yes	—
77	C₂²×C₈	#1055	1	2	yes	—
78	C₂²×C₈	C₄×D₁₃	1	2	yes	—
79	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
80	C₂×C₁₆	—	13	8	no	—
81	C₂×C₁₆	—	26	8	no	—
82	C₄×C₈	#1055	1	2	yes	—
83	C₄×C₈	#1055	1	2	yes	—
84	C₄×C₈	C₄×D₁₃	1	2	yes	—
85	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
86	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
87	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
88	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
89	C₂×C₁₃	#1312	1	4	yes	complemented
90	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
91	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
92	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
93	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
94	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
95	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
96	C₂×C₈	—	2	4	no	—
97	C₂×C₈	#6090	1	8	yes	complemented
98	C₂×C₈	#6094	1	8	yes	—
99	C₂×C₈	C₂×#1055	1	4	yes	—
100	C₂×C₈	C₂×#1055	1	4	yes	—
101	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
102	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
103	C₄²	C₂×#1055	1	1	yes	characteristic
104	C₄²	C₂×#1055	1	1	yes	characteristic
105	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
106	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
107	C₁₆	—	26	8	no	—
108	C₁₃	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
109	C₂³	C₄×#1055	1	1	yes	characteristic
110	C₂×C₄	C₄×#1055	1	1	yes	characteristic
111	C₂×C₄	C₄×#1055	1	1	yes	characteristic
112	C₂×C₄	C₄×#1055	1	1	yes	characteristic
113	C₂×C₄	C₂×#6090	1	4	yes	—
114	C₂×C₄	#88052	1	4	yes	—
115	C₂×C₄	#88055	1	4	yes	—
116	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
117	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
118	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
119	C₈	—	2	4	no	—
120	C₈	C₂×#6090	1	8	yes	complemented
121	C₈	#88055	1	4	yes	—
122	C₈	C₂×#6094	1	4	yes	—
123	C₂²	#11718047	1	2	yes	—
124	C₂²	C₄×#6090	1	2	yes	—
125	C₂²	#11718053	1	2	yes	—
126	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
127	C₄	#11718047	1	2	yes	—
128	C₄	C₄×#6090	1	2	yes	—
129	C₄	#11718053	1	2	yes	—
130	C₄	C₂²×#6090	1	2	yes	—
131	C₄	C₂×#88052	1	2	yes	—
132	C₄	C₂×#88055	1	2	yes	—
133	C₂	#13112754	1	4	yes	direct product factor
134	C₂	C₂×#11718047	1	1	yes	characteristic
135	C₂	C₂×C₄×#6090	1	1	yes	characteristic
136	C₂	C₂×#11718053	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	C₂×#1312
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
2. #13112754	C₂	direct (N × H)
30. C₂×C₈×C₁₃	C₁₆	semidirect
56. C₈×C₁₃	C₂×C₁₆	semidirect
89. C₂×C₁₃	#1312	semidirect
97. C₂×C₈	#6090	semidirect
108. C₁₃	C₂×#1312	semidirect
120. C₈	C₂×#6090	semidirect
133. C₂	#13112754	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
#13112754	2
C₂×C₈²×C₁₃	2
C₂×#1312	13

Subgroups — C2×#13112754 #15771905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112754 #15771905