Subgroups — C₂×C₄×C₁₆×D₁₃ #16015540

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×D₁₃	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6090	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₄	1	1	yes	characteristic
16	C₂×C₁₆×D₁₃	C₄	1	16	yes	direct product factor
17	C₂×C₁₆×D₁₃	C₂²	1	8	yes	—
18	C₄×C₈×D₁₃	C₄	1	4	yes	—
19	C₄×C₈×D₁₃	C₂²	1	4	yes	—
20	C₄×C₁₃×C₁₆	C₂²	1	4	yes	complemented
21	C₁₆×Dic₁₃	C₂²	1	8	yes	complemented
22	C₄×#6090	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₃	C₈	1	2	yes	—
24	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₁₃	C₈	1	8	yes	—
33	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
35	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
36	C₂×C₈×D₁₃	C₂³	1	2	yes	—
37	C₄²×D₁₃	C₈	1	4	yes	—
38	C₄²×D₁₃	C₂×C₄	1	4	yes	—
39	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	complemented
40	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
41	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	2	yes	—
43	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
44	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
45	C₈×Dic₁₃	C₂³	1	2	yes	—
46	C₂×#6090	C₂×C₄	1	8	yes	complemented
47	C₂×#6090	C₂³	1	4	yes	—
48	C₄×#1055	C₂×C₄	1	4	yes	—
49	C₁₆×D₁₃	C₂×C₄	1	32	yes	direct product factor
50	C₂²×C₄×C₁₆	—	13	1	no	maximal, Sylow
51	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
56	C₂×C₄×D₁₃	C₁₆	1	16	yes	direct product factor
57	C₂×C₄×D₁₃	C₄²	1	4	yes	—
58	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
59	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
60	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
61	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
63	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
66	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×C₈	1	2	yes	—
68	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
69	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
70	C₄×Dic₁₃	C₂×C₈	1	8	yes	—
71	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
72	C₂×#1055	C₄²	1	4	yes	—
73	C₂×#1055	C₂×C₈	1	4	yes	—
74	C₂×#1055	C₂²×C₄	1	2	yes	—
75	C₂×#1055	C₂²×C₄	1	2	yes	—
76	C₈×D₁₃	C₄²	1	8	yes	—
77	C₈×D₁₃	C₂×C₈	1	16	yes	—
78	C₈×D₁₃	C₂²×C₄	1	8	yes	—
79	C₁₃×C₁₆	C₂²×C₄	1	8	yes	complemented
80	#6090	C₂²×C₄	1	8	yes	complemented
81	C₂³×C₁₆	—	13	2	no	—
82	C₂²×C₄×C₈	—	13	1	no	—
83	C₂×C₄×C₁₆	—	13	2	no	—
84	C₂×C₄×C₁₆	—	13	1	no	—
85	C₂×C₄×C₁₆	—	13	8	no	—
86	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic, direct product factor
87	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
88	C₂²×D₁₃	C₄×C₈	1	4	yes	—
89	C₂²×D₁₃	C₂×C₁₆	1	8	yes	—
90	C₂²×D₁₃	C₂²×C₈	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×C₁₆	1	8	yes	complemented
92	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
93	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
94	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
96	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
97	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
98	C₂×Dic₁₃	C₂×C₁₆	1	8	yes	complemented
99	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
100	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
101	C₄×D₁₃	C₄×C₈	1	8	yes	—
102	C₄×D₁₃	C₂×C₁₆	1	32	yes	direct product factor
103	C₄×D₁₃	C₂×C₄²	1	4	yes	—
104	C₄×D₁₃	C₂²×C₈	1	4	yes	—
105	C₈×C₁₃	C₂×C₄²	1	2	yes	—
106	C₈×C₁₃	C₂²×C₈	1	4	yes	—
107	C₈×C₁₃	C₂³×C₄	1	2	yes	—
108	#1055	C₂×C₄²	1	4	yes	—
109	#1055	C₂²×C₈	1	4	yes	—
110	C₂³×C₈	—	13	1	no	—
111	C₂³×C₈	—	13	1	no	—
112	C₂²×C₄²	—	13	1	no	—
113	C₂²×C₁₆	—	13	2	no	—
114	C₂²×C₁₆	—	13	16	no	—
115	C₂²×C₁₆	—	13	8	no	—
116	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
117	C₂×C₄×C₈	—	13	1	no	—
118	C₂×C₄×C₈	—	13	1	no	—
119	C₂×C₄×C₈	—	13	1	no	—
120	C₂×C₄×C₈	—	13	4	no	—
121	C₂×C₄×C₈	—	13	4	no	—
122	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
123	C₄×C₁₆	—	13	8	no	—
124	C₄×C₁₆	—	13	4	no	—
125	C₄×C₁₆	C₂×D₁₃	1	4	yes	direct product factor
126	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
127	C₂²×C₁₃	C₂²×C₁₆	1	4	yes	—
128	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
129	C₂×D₁₃	C₄×C₁₆	1	16	yes	direct product factor
130	C₂×D₁₃	C₂×C₄×C₈	1	4	yes	—
131	C₂×D₁₃	C₂²×C₁₆	1	8	yes	—
132	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
133	C₄×C₁₃	C₂²×C₁₆	1	8	yes	complemented
134	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
135	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
136	Dic₁₃	C₂×C₄×C₈	1	4	yes	—
137	Dic₁₃	C₂²×C₁₆	1	8	yes	complemented
138	C₂³×C₄	—	13	2	no	—
139	C₂³×C₄	—	13	1	no	—
140	C₂²×C₈	—	13	1	no	—
141	C₂²×C₈	—	13	1	no	—
142	C₂²×C₈	—	13	8	no	—
143	C₂²×C₈	—	13	2	no	—
144	C₂²×C₈	—	13	4	no	—
145	C₂²×C₈	—	13	8	no	—
146	C₂²×C₈	—	13	2	no	—
147	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
148	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
149	C₂×C₄²	—	13	2	no	—
150	C₂×C₄²	—	13	1	no	—
151	C₂×C₄²	—	13	4	no	—
152	C₂×C₄²	—	13	4	no	—
153	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
154	C₂×C₁₆	—	13	8	no	—
155	C₂×C₁₆	—	13	4	no	—
156	C₂×C₁₆	—	13	32	no	—
157	C₂×C₁₆	C₄×D₁₃	1	8	yes	direct product factor
158	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
159	C₄×C₈	—	13	2	no	—
160	C₄×C₈	—	13	4	no	—
161	C₄×C₈	—	13	2	no	—
162	C₄×C₈	—	13	4	no	—
163	C₄×C₈	C₄×D₁₃	1	2	yes	—
164	C₄×C₈	C₂²×D₁₃	1	2	yes	—
165	C₂×C₁₃	C₂×C₄×C₁₆	1	4	yes	complemented
166	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
167	C₂×C₁₃	C₂³×C₁₆	1	2	yes	—
168	D₁₃	C₂×C₄×C₁₆	1	8	yes	direct product factor
169	C₂⁴	—	13	1	no	—
170	C₂²×C₄	—	13	2	no	—
171	C₂²×C₄	—	13	1	no	—
172	C₂²×C₄	—	13	4	no	—
173	C₂²×C₄	—	13	8	no	—
174	C₂²×C₄	—	13	2	no	—
175	C₂²×C₄	—	13	4	no	—
176	C₂²×C₄	—	13	2	no	—
177	C₂²×C₄	—	13	16	no	—
178	C₂²×C₄	C₈×D₁₃	1	2	yes	—
179	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
180	C₂×C₈	—	13	4	no	—
181	C₂×C₈	—	13	4	no	—
182	C₂×C₈	—	13	2	no	—
183	C₂×C₈	—	13	2	no	—
184	C₂×C₈	—	13	8	no	—
185	C₂×C₈	—	13	16	no	—
186	C₂×C₈	—	13	8	no	—
187	C₂×C₈	C₈×D₁₃	1	4	yes	—
188	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
189	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
190	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
191	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
192	C₄²	—	13	8	no	—
193	C₄²	—	13	2	no	—
194	C₄²	—	13	2	no	—
195	C₄²	C₈×D₁₃	1	2	yes	—
196	C₄²	C₂×C₄×D₁₃	1	2	yes	—
197	C₁₆	—	13	8	no	—
198	C₁₆	C₂×C₄×D₁₃	1	8	yes	direct product factor
199	C₁₃	C₂²×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
200	C₂³	—	13	2	no	—
201	C₂³	—	13	8	no	—
202	C₂³	—	13	4	no	—
203	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
204	C₂×C₄	—	13	2	no	—
205	C₂×C₄	—	13	4	no	—
206	C₂×C₄	—	13	8	no	—
207	C₂×C₄	—	13	4	no	—
208	C₂×C₄	—	13	4	no	—
209	C₂×C₄	—	13	4	no	—
210	C₂×C₄	—	13	32	no	—
211	C₂×C₄	—	13	8	no	—
212	C₂×C₄	C₁₆×D₁₃	1	8	yes	direct product factor
213	C₂×C₄	C₄²×D₁₃	1	2	yes	—
214	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
215	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
216	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
217	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
218	C₈	—	13	4	no	—
219	C₈	—	13	4	no	—
220	C₈	C₄²×D₁₃	1	2	yes	—
221	C₈	C₂×C₈×D₁₃	1	4	yes	—
222	C₈	C₂²×C₄×D₁₃	1	2	yes	—
223	C₂²	—	13	16	no	—
224	C₂²	—	13	4	no	—
225	C₂²	—	13	8	no	—
226	C₂²	C₄×C₈×D₁₃	1	2	yes	—
227	C₂²	C₂×C₁₆×D₁₃	1	4	yes	—
228	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
229	C₄	—	13	4	no	—
230	C₄	—	13	8	no	—
231	C₄	C₄×C₈×D₁₃	1	2	yes	—
232	C₄	C₂×C₁₆×D₁₃	1	8	yes	direct product factor
233	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
234	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
235	C₂	—	13	8	no	—
236	C₂	C₄×C₁₆×D₁₃	1	4	yes	direct product factor
237	C₂	C₂×C₄×C₈×D₁₃	1	1	yes	characteristic
238	C₂	C₂²×C₁₆×D₁₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₆	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₄×C₁₆
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#6090	C₂	semidirect
4. C₂×C₁₆×Dic₁₃	C₂	semidirect
5. C₄×C₁₆×D₁₃	C₂	direct (N × H)
6. C₂×C₄×C₁₃×C₁₆	C₂	semidirect
16. C₂×C₁₆×D₁₃	C₄	direct (N × H)
20. C₄×C₁₃×C₁₆	C₂²	semidirect
21. C₁₆×Dic₁₃	C₂²	semidirect
22. C₄×#6090	C₂²	semidirect
39. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
46. C₂×#6090	C₂×C₄	semidirect
49. C₁₆×D₁₃	C₂×C₄	direct (N × H)
56. C₂×C₄×D₁₃	C₁₆	direct (N × H)
79. C₁₃×C₁₆	C₂²×C₄	semidirect
80. #6090	C₂²×C₄	semidirect
86. C₂×C₄×C₁₆	D₁₃	direct (N × H)
91. C₂×C₄×C₁₃	C₂×C₁₆	semidirect
98. C₂×Dic₁₃	C₂×C₁₆	semidirect
102. C₄×D₁₃	C₂×C₁₆	direct (N × H)
125. C₄×C₁₆	C₂×D₁₃	direct (N × H)
129. C₂×D₁₃	C₄×C₁₆	direct (N × H)
133. C₄×C₁₃	C₂²×C₁₆	semidirect
137. Dic₁₃	C₂²×C₁₆	semidirect
157. C₂×C₁₆	C₄×D₁₃	direct (N × H)
165. C₂×C₁₃	C₂×C₄×C₁₆	semidirect
168. D₁₃	C₂×C₄×C₁₆	direct (N × H)
198. C₁₆	C₂×C₄×D₁₃	direct (N × H)
199. C₁₃	C₂²×C₄×C₁₆	semidirect
212. C₂×C₄	C₁₆×D₁₃	direct (N × H)
232. C₄	C₂×C₁₆×D₁₃	direct (N × H)
236. C₂	C₄×C₁₆×D₁₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₆×D₁₃	2
C₂×C₄×C₈×D₁₃	2
C₂×C₄×#6090	2
C₂×C₁₆×Dic₁₃	2
C₄×C₁₆×D₁₃	2
C₂×C₄×C₁₃×C₁₆	2
C₂²×C₄×C₁₆	13

Subgroups — C2×C4×C16×D13 #16015540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₆×D₁₃ #16015540