Subgroups — C₂×#13130030 #16792564

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₃⋊C₈	C₂	1	2	yes	maximal
2	#13130030	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718251	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₁₃⋊C₈	C₄	1	4	yes	—
6	C₂²×C₈×D₁₃	C₄	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×#1057	C₄	1	4	yes	—
9	C₂×C₄×#1057	C₂²	1	4	yes	—
10	C₄×D₁₃⋊C₈	C₄	1	8	yes	—
11	C₄×D₁₃⋊C₈	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	#11718251	C₂²	1	16	yes	complemented
18	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
20	C₂²×#1057	C₂×C₄	1	8	yes	—
21	C₂×D₁₃⋊C₈	—	2	16	no	—
22	C₂×D₁₃⋊C₈	C₂×C₄	1	16	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
27	C₂²×#1055	C₂×C₄	1	2	yes	—
28	C₂×C₈×D₁₃	C₈	1	16	yes	complemented
29	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
30	C₄²×D₁₃	C₂×C₄	1	2	yes	—
31	C₄²×D₁₃	C₂×C₄	1	4	yes	—
32	C₄²×D₁₃	C₂³	1	2	yes	—
33	C₄×#1057	C₂×C₄	1	8	yes	—
34	C₄×#1057	C₂×C₄	1	16	yes	—
35	C₄×#1057	C₂³	1	8	yes	—
36	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
37	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
38	C₈×Dic₁₃	C₂³	1	4	yes	—
39	C₄×#1055	C₂×C₄	1	4	yes	—
40	C₂²×#322	—	13	1	no	maximal, Sylow
41	C₂³×D₁₃	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
45	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
46	C₂×C₄×D₁₃	C₄²	1	2	yes	—
47	C₂×C₄×D₁₃	C₄²	1	4	yes	—
48	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
49	C₂×C₄×D₁₃	M₁₆	1	16	yes	—
50	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
51	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
52	C₂×#1057	—	2	16	no	—
53	C₂×#1057	C₂²×C₄	1	16	yes	—
54	D₁₃⋊C₈	—	2	32	no	—
55	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	complemented
56	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
57	C₄²×C₁₃	C₄²	1	2	yes	—
58	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
59	C₄×Dic₁₃	C₄²	1	4	yes	—
60	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
62	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
63	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
64	C₂×#1055	C₂×C₈	1	8	yes	complemented
65	C₂×#1055	C₂²×C₄	1	4	yes	—
66	C₈×D₁₃	C₂×C₈	1	32	yes	complemented
67	C₂²×C₄×C₈	—	13	2	no	—
68	C₂²×C₄×C₈	—	13	1	no	—
69	C₂×#322	—	13	4	no	—
70	C₂×#322	—	13	8	no	—
71	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
72	C₂²×D₁₃	C₄×C₈	1	4	yes	—
73	C₂²×D₁₃	#97	1	8	yes	—
74	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
75	C₂×C₄×C₁₃	#97	1	8	yes	—
76	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
78	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
79	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
80	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
81	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
82	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
83	C₂×Dic₁₃	C₂×M₁₆	1	8	yes	—
84	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
85	C₄×D₁₃	C₄×C₈	1	8	yes	—
86	C₄×D₁₃	#97	1	16	yes	—
87	C₄×D₁₃	C₂²×C₈	1	8	yes	—
88	C₄×D₁₃	C₂×M₁₆	1	16	yes	—
89	#1057	—	2	16	no	—
90	C₈×C₁₃	C₂²×C₈	1	8	yes	complemented
91	#1055	C₂²×C₈	1	8	yes	complemented
92	C₂³×C₈	—	13	2	no	—
93	C₂³×C₈	—	13	4	no	—
94	C₂²×C₄²	—	13	1	no	—
95	C₂×C₄×C₈	—	13	8	no	—
96	C₂×C₄×C₈	—	13	8	no	—
97	C₂×C₄×C₈	—	13	4	no	—
98	C₂×C₄×C₈	—	13	4	no	—
99	C₂×C₄×C₈	—	13	2	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	C₂×C₄×C₈	—	13	4	no	—
102	C₂×C₄×C₈	—	13	4	no	—
103	C₂×C₄×C₈	#261	1	1	yes	characteristic
104	#322	—	13	16	no	—
105	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
106	C₂²×C₁₃	C₂×#97	1	4	yes	—
107	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
108	C₂×D₁₃	#322	1	16	yes	complemented
109	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	—
110	C₂×D₁₃	C₂×#97	1	8	yes	—
111	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
112	C₄×C₁₃	C₂×#97	1	8	yes	—
113	C₄×C₁₃	C₂³×C₈	1	2	yes	—
114	Dic₁₃	C₂×C₄×C₈	1	4	yes	—
115	Dic₁₃	C₂×#97	1	4	yes	—
116	Dic₁₃	C₂²×M₁₆	1	4	yes	—
117	C₂³×C₄	—	13	2	no	—
118	C₂³×C₄	—	13	1	no	—
119	C₂²×C₈	—	13	2	no	—
120	C₂²×C₈	—	13	16	no	—
121	C₂²×C₈	—	13	8	no	—
122	C₂²×C₈	—	13	16	no	—
123	C₂²×C₈	—	13	8	no	—
124	C₂²×C₈	—	26	16	no	—
125	C₂²×C₈	C₂×#261	1	2	yes	—
126	C₂×C₄²	—	13	2	no	—
127	C₂×C₄²	—	13	1	no	—
128	C₂×C₄²	—	13	4	no	—
129	C₂×C₄²	—	13	2	no	—
130	C₂×C₄²	—	13	2	no	—
131	C₂×C₄²	C₂×#261	1	1	yes	characteristic
132	C₄×C₈	—	13	8	no	—
133	C₄×C₈	—	13	16	no	—
134	C₄×C₈	—	13	8	no	—
135	C₄×C₈	—	13	4	no	—
136	C₄×C₈	—	13	4	no	—
137	C₄×C₈	—	13	4	no	—
138	C₄×C₈	C₂×#261	1	4	yes	—
139	C₂×C₁₃	C₂×#322	1	4	yes	complemented
140	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
141	C₂×C₁₃	C₂²×#97	1	2	yes	—
142	D₁₃	C₂×#322	1	8	yes	complemented
143	C₂⁴	—	13	1	no	—
144	C₂²×C₄	—	13	2	no	—
145	C₂²×C₄	—	13	1	no	—
146	C₂²×C₄	—	13	16	no	—
147	C₂²×C₄	—	13	8	no	—
148	C₂²×C₄	—	13	4	no	—
149	C₂²×C₄	—	13	2	no	—
150	C₂²×C₄	—	13	4	no	—
151	C₂²×C₄	—	13	2	no	—
152	C₂²×C₄	C₄×#261	1	2	yes	—
153	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
154	C₂×C₈	—	13	8	no	—
155	C₂×C₈	—	13	4	no	—
156	C₂×C₈	—	13	32	no	—
157	C₂×C₈	—	13	16	no	—
158	C₂×C₈	—	26	32	no	—
159	C₂×C₈	—	26	16	no	—
160	C₂×C₈	D₁₃⋊C₈	1	8	yes	complemented
161	C₂×C₈	C₂²×#261	1	4	yes	—
162	C₄²	—	13	2	no	—
163	C₄²	—	13	4	no	—
164	C₄²	—	13	4	no	—
165	C₄²	—	13	1	no	—
166	C₄²	—	13	1	no	—
167	C₄²	C₄×#261	1	2	yes	—
168	C₄²	C₂²×#261	1	2	yes	—
169	C₁₃	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
170	C₂³	—	13	4	no	—
171	C₂³	—	13	8	no	—
172	C₂³	—	13	2	no	—
173	C₂³	C₂×C₄×#261	1	1	yes	characteristic
174	C₂×C₄	—	13	4	no	—
175	C₂×C₄	—	13	8	no	—
176	C₂×C₄	—	13	2	no	—
177	C₂×C₄	—	13	2	no	—
178	C₂×C₄	—	13	2	no	—
179	C₂×C₄	—	13	8	no	—
180	C₂×C₄	—	13	16	no	—
181	C₂×C₄	—	13	16	no	—
182	C₂×C₄	—	13	8	no	—
183	C₂×C₄	#88100	1	8	yes	—
184	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
185	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
186	C₂×C₄	C₂×C₄×#261	1	4	yes	—
187	C₂×C₄	C₂³×#261	1	1	yes	characteristic
188	C₈	—	13	8	no	—
189	C₈	—	26	16	no	—
190	C₈	C₂×D₁₃⋊C₈	1	8	yes	complemented
191	C₂²	—	13	16	no	—
192	C₂²	—	13	4	no	—
193	C₂²	—	13	8	no	—
194	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
195	C₂²	C₂×#88100	1	4	yes	—
196	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
197	C₄	—	13	4	no	—
198	C₄	—	13	4	no	—
199	C₄	—	13	4	no	—
200	C₄	C₄×D₁₃⋊C₈	1	2	yes	—
201	C₄	C₂×#88100	1	8	yes	—
202	C₄	C₂²×D₁₃⋊C₈	1	2	yes	—
203	C₂	—	13	8	no	—
204	C₂	#13130030	1	4	yes	direct product factor
205	C₂	C₂×C₄×D₁₃⋊C₈	1	1	yes	characteristic
206	C₂	C₂²×#88100	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
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	C₂²×#322
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130030	C₂	direct (N × H)
3. C₂×#11718251	C₂	semidirect
17. #11718251	C₂²	semidirect
28. C₂×C₈×D₁₃	C₈	semidirect
55. C₂×C₈×C₁₃	C₂×C₈	semidirect
64. C₂×#1055	C₂×C₈	semidirect
66. C₈×D₁₃	C₂×C₈	semidirect
90. C₈×C₁₃	C₂²×C₈	semidirect
91. #1055	C₂²×C₈	semidirect
108. C₂×D₁₃	#322	semidirect
139. C₂×C₁₃	C₂×#322	semidirect
142. D₁₃	C₂×#322	semidirect
160. C₂×C₈	D₁₃⋊C₈	semidirect
169. C₁₃	C₂²×#322	semidirect
190. C₈	C₂×D₁₃⋊C₈	semidirect
204. C₂	#13130030	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×D₁₃⋊C₈	2
#13130030	2
C₂×#11718251	2
C₂×C₄×C₈×D₁₃	2
C₂²×#322	13

Subgroups — C2×#13130030 #16792564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130030 #16792564