Subgroups — C₂×#13113140 #15828626

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6094	C₂	1	2	yes	maximal
3	#13113140	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718046	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6094	C₄	1	2	yes	—
8	C₂²×#6094	C₄	1	4	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
12	C₂×#88055	C₄	1	2	yes	—
13	C₂×#88055	C₄	1	4	yes	—
14	C₂×C₄×#1055	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₄×#6094	C₄	1	8	yes	—
17	C₄×#6094	C₄	1	4	yes	—
18	C₄×#6094	C₂²	1	4	yes	—
19	C₄×#6094	C₂²	1	8	yes	—
20	C₁₃×#322	C₂²	1	4	yes	complemented
21	#11718046	C₂²	1	8	yes	complemented
22	C₈×#1055	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
30	C₂²×#1055	C₂×C₄	1	2	yes	—
31	C₂²×#1055	C₂×C₄	1	4	yes	—
32	C₂×#6094	—	2	8	no	—
33	C₂×#6094	—	2	16	no	—
34	C₂×#6094	C₂×C₄	1	8	yes	—
35	C₂×#6094	C₂×C₄	1	16	yes	—
36	C₄²×D₁₃	C₂×C₄	1	4	yes	—
37	C₄²×D₁₃	C₂×C₄	1	2	yes	—
38	C₄²×D₁₃	C₂³	1	2	yes	—
39	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
40	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₃	C₂³	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	4	yes	—
43	#88055	C₂×C₄	1	8	yes	—
44	#88055	C₂×C₄	1	16	yes	—
45	C₄×#1055	C₂×C₄	1	2	yes	—
46	C₄×#1055	C₂×C₄	1	4	yes	—
47	C₄×#1055	C₂³	1	4	yes	—
48	C₄×#1055	C₂³	1	2	yes	—
49	C₂×#1455	—	13	1	no	maximal, Sylow
50	C₂³×D₁₃	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
53	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
54	C₂²×Dic₁₃	C₄²	1	2	yes	—
55	C₂×C₄×D₁₃	—	2	4	no	—
56	C₂×C₄×D₁₃	—	2	8	no	—
57	C₂×C₄×D₁₃	C₄²	1	2	yes	—
58	C₂×C₄×D₁₃	C₄²	1	4	yes	—
59	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
61	C₂×C₈×C₁₃	—	2	8	no	—
62	C₂×C₈×C₁₃	M₁₆	1	8	yes	complemented
63	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
64	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
66	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₄×Dic₁₃	C₄²	1	2	yes	—
69	C₄×Dic₁₃	C₄²	1	4	yes	—
70	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
71	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
72	C₂×#1055	—	2	4	no	—
73	C₂×#1055	M₁₆	1	16	yes	complemented
74	C₂×#1055	C₂²×C₄	1	4	yes	—
75	C₂×#1055	C₂²×C₄	1	8	yes	—
76	#6094	—	2	16	no	—
77	#6094	—	2	32	no	—
78	C₂×C₄×M₁₆	—	13	2	no	—
79	C₂×C₄×M₁₆	—	13	1	no	—
80	#1455	—	13	8	no	—
81	C₂×#322	—	13	2	no	—
82	C₂×#322	D₁₃	1	1	yes	characteristic, complemented
83	C₂×C₈²	—	13	1	no	—
84	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
85	C₂²×D₁₃	—	2	2	no	—
86	C₂²×D₁₃	—	2	4	no	—
87	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
92	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	—	2	4	no	—
96	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
97	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
98	C₄×D₁₃	—	2	4	no	—
99	C₄×D₁₃	—	2	8	no	—
100	C₄×D₁₃	—	2	4	no	—
101	C₄×D₁₃	—	2	8	no	—
102	C₈×C₁₃	—	2	8	no	—
103	C₈×C₁₃	C₂×M₁₆	1	8	yes	complemented
104	#1055	—	2	4	no	—
105	#1055	C₂×M₁₆	1	16	yes	complemented
106	C₂²×M₁₆	—	13	4	no	—
107	C₂²×M₁₆	—	13	2	no	—
108	C₂²×C₄²	—	13	1	no	—
109	C₄×M₁₆	—	13	8	no	—
110	C₄×M₁₆	—	13	4	no	—
111	C₄×M₁₆	—	13	8	no	—
112	C₄×M₁₆	—	13	4	no	—
113	C₂×#97	—	13	4	no	—
114	C₂×#97	—	13	2	no	—
115	C₂×C₄×C₈	—	13	2	no	—
116	C₂×C₄×C₈	—	13	1	no	—
117	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
119	#322	—	13	8	no	—
120	#322	C₂×D₁₃	1	4	yes	complemented
121	C₈²	—	13	4	no	—
122	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
123	C₂²×C₁₃	C₄×M₁₆	1	4	yes	—
124	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
125	C₂×D₁₃	—	2	2	no	—
126	C₂×D₁₃	—	2	4	no	—
127	C₂×D₁₃	—	4	4	no	—
128	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
129	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
130	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
131	C₄×C₁₃	C₂²×M₁₆	1	4	yes	—
132	Dic₁₃	—	2	2	no	—
133	Dic₁₃	—	2	4	no	—
134	C₂³×C₄	—	13	1	no	—
135	C₂³×C₄	—	13	2	no	—
136	C₂×M₁₆	—	13	16	no	—
137	C₂×M₁₆	—	13	8	no	—
138	C₂×M₁₆	—	26	16	no	—
139	C₂×M₁₆	—	26	8	no	—
140	C₂²×C₈	—	13	4	no	—
141	C₂²×C₈	—	13	2	no	—
142	C₂²×C₈	C₄×D₁₃	1	4	yes	—
143	C₂²×C₈	C₄×D₁₃	1	2	yes	—
144	C₂×C₄²	—	13	1	no	—
145	C₂×C₄²	—	13	2	no	—
146	C₂×C₄²	—	13	4	no	—
147	C₂×C₄²	—	13	2	no	—
148	C₂×C₄²	—	13	2	no	—
149	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
150	#97	—	13	16	no	—
151	#97	—	13	8	no	—
152	C₄×C₈	—	13	4	no	—
153	C₄×C₈	—	13	2	no	—
154	C₄×C₈	—	13	4	no	—
155	C₄×C₈	—	13	2	no	—
156	C₄×C₈	C₄×D₁₃	1	4	yes	—
157	C₄×C₈	C₄×D₁₃	1	2	yes	—
158	C₄×C₈	C₂²×D₁₃	1	2	yes	—
159	C₄×C₈	C₂²×D₁₃	1	4	yes	—
160	C₂×C₁₃	#1455	1	4	yes	complemented
161	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
162	C₂×C₁₃	C₂×C₄×M₁₆	1	2	yes	—
163	D₁₃	—	4	2	no	—
164	C₂⁴	—	13	1	no	—
165	C₂²×C₄	—	13	1	no	—
166	C₂²×C₄	—	13	2	no	—
167	C₂²×C₄	—	13	2	no	—
168	C₂²×C₄	—	13	4	no	—
169	C₂²×C₄	—	13	2	no	—
170	C₂²×C₄	—	13	4	no	—
171	C₂²×C₄	—	26	4	no	—
172	C₂²×C₄	—	26	8	no	—
173	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
175	M₁₆	—	26	32	no	—
176	M₁₆	—	26	16	no	—
177	C₂×C₈	—	2	8	no	—
178	C₂×C₈	—	13	16	no	—
179	C₂×C₈	—	13	8	no	—
180	C₂×C₈	—	13	4	no	—
181	C₂×C₈	—	26	4	no	—
182	C₂×C₈	#6094	1	8	yes	complemented
183	C₂×C₈	C₂×C₄×D₁₃	1	8	yes	—
184	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
185	C₄²	—	13	2	no	—
186	C₄²	—	13	4	no	—
187	C₄²	—	13	2	no	—
188	C₄²	—	13	4	no	—
189	C₄²	C₂×C₄×D₁₃	1	2	yes	—
190	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
191	C₄²	C₂³×D₁₃	1	1	yes	characteristic
192	C₁₃	C₂×#1455	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	13	2	no	—
194	C₂³	—	26	2	no	—
195	C₂³	—	26	4	no	—
196	C₂³	C₄²×D₁₃	1	1	yes	characteristic
197	C₂×C₄	—	13	2	no	—
198	C₂×C₄	—	13	4	no	—
199	C₂×C₄	—	26	2	no	—
200	C₂×C₄	—	26	4	no	—
201	C₂×C₄	—	26	4	no	—
202	C₂×C₄	—	26	8	no	—
203	C₂×C₄	—	26	4	no	—
204	C₂×C₄	—	26	8	no	—
205	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
206	C₂×C₄	C₄²×D₁₃	1	2	yes	—
207	C₂×C₄	C₂×#6094	1	4	yes	—
208	C₂×C₄	M₁₆×D₁₃	1	8	yes	—
209	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
211	C₈	—	2	8	no	—
212	C₈	—	13	16	no	—
213	C₈	—	26	4	no	—
214	C₈	C₂×#6094	1	8	yes	complemented
215	C₂²	—	26	2	no	—
216	C₂²	—	26	4	no	—
217	C₂²	—	52	4	no	—
218	C₂²	C₄×#6094	1	2	yes	—
219	C₂²	#11718368	1	4	yes	—
220	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
221	C₄	—	26	2	no	—
222	C₄	—	26	4	no	—
223	C₄	C₄×#6094	1	2	yes	—
224	C₄	#11718368	1	4	yes	—
225	C₄	C₂²×#6094	1	2	yes	—
226	C₄	C₂×M₁₆×D₁₃	1	4	yes	—
227	C₂	—	52	2	no	—
228	C₂	#13113140	1	4	yes	direct product factor
229	C₂	C₂×C₄×#6094	1	1	yes	characteristic
230	C₂	C₂×#11718368	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#322	C₂
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#322	D₁₃
hypocenter	C₁₃	C₂×#1455
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
3. #13113140	C₂	direct (N × H)
4. C₂×#11718046	C₂	semidirect
5. C₂×C₈×#1055	C₂	semidirect
6. C₂×C₁₃×#322	C₂	semidirect
20. C₁₃×#322	C₂²	semidirect
21. #11718046	C₂²	semidirect
22. C₈×#1055	C₂²	semidirect
62. C₂×C₈×C₁₃	M₁₆	semidirect
73. C₂×#1055	M₁₆	semidirect
82. C₂×#322	D₁₃	semidirect
103. C₈×C₁₃	C₂×M₁₆	semidirect
105. #1055	C₂×M₁₆	semidirect
120. #322	C₂×D₁₃	semidirect
160. C₂×C₁₃	#1455	semidirect
182. C₂×C₈	#6094	semidirect
192. C₁₃	C₂×#1455	semidirect
214. C₈	C₂×#6094	semidirect
228. C₂	#13113140	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×#6094	2
#13113140	2
C₂×#11718046	2
C₂×C₈×#1055	2
C₂×C₁₃×#322	2
C₂×#1455	13

Subgroups — C2×#13113140 #15828626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113140 #15828626