Subgroups — C₂×#13130050 #16792608

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719049	C₂	1	2	yes	maximal
2	#13130050	C₂	1	8	yes	maximal, direct product factor
3	C₂×#1057⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×D₁₃	C₄	1	2	yes	—
6	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88112	C₄	1	4	yes	—
8	C₂×#88111	C₄	1	4	yes	—
9	C₂×C₄×#1057	C₂²	1	4	yes	—
10	#11719049	C₄	1	8	yes	—
11	#11719049	C₂²	1	8	yes	—
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic
15	C₄×C₈×D₁₃	C₄	1	4	yes	—
16	C₄×C₈×D₁₃	C₂²	1	4	yes	—
17	#1057⋊C₈	C₂²	1	16	yes	complemented
18	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×#1057	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
25	C₂²×#1055	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₁₃	—	2	8	no	—
27	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
28	C₄²×D₁₃	C₂×C₄	1	2	yes	—
29	C₄²×D₁₃	C₂×C₄	1	4	yes	—
30	C₄²×D₁₃	C₂³	1	2	yes	—
31	#88112	C₂×C₄	1	16	yes	—
32	#88111	C₂×C₄	1	16	yes	—
33	C₄×#1057	C₂×C₄	1	8	yes	—
34	C₄×#1057	C₂³	1	8	yes	—
35	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
36	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
37	C₈×Dic₁₃	C₂³	1	4	yes	—
38	C₄×#1055	C₂×C₄	1	4	yes	—
39	C₂×#1452	—	13	1	no	maximal, Sylow
40	C₂³×D₁₃	C₄²	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
44	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
45	C₂×C₄×D₁₃	—	2	8	no	—
46	C₂×C₄×D₁₃	C₄²	1	4	yes	—
47	C₂×C₄×D₁₃	C₄²	1	2	yes	—
48	C₂×C₄×D₁₃	M₁₆	1	8	yes	—
49	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
50	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
51	C₂×#1057	—	2	16	no	—
52	C₂×#1057	C₂²×C₄	1	16	yes	—
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
55	C₄²×C₁₃	C₄²	1	2	yes	—
56	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
57	C₄×Dic₁₃	C₄²	1	4	yes	—
58	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
60	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
61	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
62	C₂×#1055	—	2	4	no	—
63	C₂×#1055	C₂²×C₄	1	4	yes	—
64	C₈×D₁₃	—	2	16	no	—
65	C₂×#431	—	13	2	no	—
66	C₂²×C₄×C₈	—	13	1	no	—
67	#1452	—	13	8	no	—
68	C₂×#322	—	13	4	no	—
69	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
70	C₂²×D₁₃	—	2	4	no	—
71	C₂²×D₁₃	#97	1	4	yes	—
72	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
75	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
77	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
78	C₂×Dic₁₃	#97	1	4	yes	—
79	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
80	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
81	C₂×Dic₁₃	#131	1	8	yes	—
82	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
83	C₄×D₁₃	—	2	8	no	—
84	C₄×D₁₃	—	2	8	no	—
85	C₄×D₁₃	#97	1	8	yes	—
86	C₄×D₁₃	C₂×M₁₆	1	8	yes	—
87	#1057	—	2	16	no	—
88	C₈×C₁₃	—	2	4	no	—
89	#1055	—	2	4	no	—
90	C₂³×C₈	—	13	2	no	—
91	C₂²×C₄²	—	13	1	no	—
92	#431	—	13	8	no	—
93	#431	—	13	8	no	—
94	C₂×C₄⋊C₈	—	13	4	no	—
95	C₂×C₂²⋊C₈	—	13	4	no	—
96	C₂×C₄×C₈	—	13	4	no	—
97	C₂×C₄×C₈	—	13	2	no	—
98	C₂×C₄×C₈	—	13	1	no	—
99	C₂×C₄×C₈	—	13	4	no	—
100	C₂×C₄×C₈	—	13	4	no	—
101	C₂×C₄×C₈	#261	1	1	yes	characteristic
102	#322	—	13	16	no	—
103	C₂²×C₁₃	C₂×#97	1	2	yes	—
104	C₂²×C₁₃	#405	1	4	yes	—
105	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
106	C₂×D₁₃	—	2	4	no	—
107	C₂×D₁₃	—	2	8	no	—
108	C₂×D₁₃	C₂×#97	1	4	yes	—
109	C₄×C₁₃	—	2	4	no	—
110	C₄×C₁₃	C₂×#97	1	2	yes	—
111	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
112	Dic₁₃	C₂×#97	1	4	yes	—
113	Dic₁₃	#405	1	4	yes	—
114	Dic₁₃	C₂×#131	1	4	yes	—
115	C₂³×C₄	—	13	1	no	—
116	C₂³×C₄	—	13	2	no	—
117	C₂²×C₈	—	13	8	no	—
118	C₂²×C₈	—	13	2	no	—
119	C₂²×C₈	—	13	8	no	—
120	C₂²×C₈	—	26	8	no	—
121	C₂²×C₈	C₂×#261	1	2	yes	—
122	C₂×C₄²	—	13	2	no	—
123	C₂×C₄²	—	13	1	no	—
124	C₂×C₄²	—	13	4	no	—
125	C₂×C₄²	—	13	2	no	—
126	C₂×C₄²	—	13	2	no	—
127	C₂×C₄²	C₂×#261	1	1	yes	characteristic
128	C₄⋊C₈	—	13	16	no	—
129	C₂²⋊C₈	—	13	16	no	—
130	C₄×C₈	—	13	8	no	—
131	C₄×C₈	—	13	8	no	—
132	C₄×C₈	—	13	4	no	—
133	C₄×C₈	—	13	4	no	—
134	C₄×C₈	—	13	4	no	—
135	C₄×C₈	C₂×#261	1	4	yes	—
136	C₂×C₁₃	#1452	1	4	yes	complemented
137	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
138	C₂×C₁₃	C₂×#405	1	2	yes	—
139	D₁₃	—	2	4	no	—
140	C₂⁴	—	13	1	no	—
141	C₂²×C₄	—	13	2	no	—
142	C₂²×C₄	—	13	1	no	—
143	C₂²×C₄	—	13	8	no	—
144	C₂²×C₄	—	13	2	no	—
145	C₂²×C₄	—	13	2	no	—
146	C₂²×C₄	—	13	4	no	—
147	C₂²×C₄	—	13	4	no	—
148	C₂²×C₄	—	26	8	no	—
149	C₂²×C₄	C₄×#261	1	2	yes	—
150	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	13	16	no	—
153	C₂×C₈	—	13	4	no	—
154	C₂×C₈	—	26	16	no	—
155	C₂×C₈	—	26	16	no	—
156	C₂×C₈	—	26	4	no	—
157	C₂×C₈	C₂²×#261	1	4	yes	—
158	C₄²	—	13	2	no	—
159	C₄²	—	13	4	no	—
160	C₄²	—	13	4	no	—
161	C₄²	—	13	1	no	—
162	C₄²	—	13	1	no	—
163	C₄²	C₄×#261	1	2	yes	—
164	C₄²	C₂²×#261	1	2	yes	—
165	C₁₃	C₂×#1452	1	1	yes	characteristic, complemented, Sylow
166	C₂³	—	13	4	no	—
167	C₂³	—	13	2	no	—
168	C₂³	—	26	4	no	—
169	C₂³	C₂×C₄×#261	1	1	yes	characteristic
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	13	4	no	—
172	C₂×C₄	—	13	8	no	—
173	C₂×C₄	—	13	2	no	—
174	C₂×C₄	—	13	2	no	—
175	C₂×C₄	—	13	2	no	—
176	C₂×C₄	—	13	8	no	—
177	C₂×C₄	—	13	8	no	—
178	C₂×C₄	—	26	8	no	—
179	C₂×C₄	—	26	8	no	—
180	C₂×C₄	D₁₃⋊M₁₆	1	4	yes	—
181	C₂×C₄	C₂×C₄×#261	1	4	yes	—
182	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
183	C₂×C₄	C₂³×#261	1	1	yes	characteristic
184	C₈	—	2	4	no	—
185	C₈	—	26	16	no	—
186	C₈	—	26	4	no	—
187	C₂²	—	13	4	no	—
188	C₂²	—	26	8	no	—
189	C₂²	—	26	4	no	—
190	C₂²	#11719047	1	2	yes	—
191	C₂²	#11719089	1	4	yes	—
192	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	13	4	no	—
195	C₄	—	13	4	no	—
196	C₄	—	13	4	no	—
197	C₄	#11719047	1	2	yes	—
198	C₄	C₂×D₁₃⋊M₁₆	1	2	yes	—
199	C₂	—	26	4	no	—
200	C₂	#13130050	1	4	yes	direct product factor
201	C₂	C₂×#11719047	1	1	yes	characteristic
202	C₂	C₂×#11719089	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1452
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130050	C₂	direct (N × H)
3. C₂×#1057⋊C₈	C₂	semidirect
17. #1057⋊C₈	C₂²	semidirect
136. C₂×C₁₃	#1452	semidirect
165. C₁₃	C₂×#1452	semidirect
200. C₂	#13130050	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×#11719049	2
#13130050	2
C₂×#1057⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂×#1452	13

Subgroups — C2×#13130050 #16792608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130050 #16792608