Subgroups — D₁₃×#2262 #16021043

Order 3328.

470 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#508	C₂	1	2	yes	maximal, complemented
2	#13117146	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117145	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117144	C₂	1	2	yes	maximal, complemented
5	#13117143	C₂	1	2	yes	maximal, complemented
6	#13117142	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₃×SD₆₄	C₂	1	2	yes	maximal, complemented
9	D₁₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2262	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#135	—	2	2	no	—
13	C₁₃×#508	C₂²	1	2	yes	complemented
14	#11718855	—	2	2	no	—
15	#11718580	C₂²	1	2	yes	complemented
16	D₁₃×Q₃₂	C₂²	1	2	yes	—
17	#11718577	—	2	2	no	—
18	D₁₃×SD₃₂	—	2	2	no	—
19	#11718573	C₂²	1	2	yes	complemented
20	D₁₃×D₁₆	C₂²	1	2	yes	—
21	#11718565	C₂²	1	2	yes	complemented
22	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×Q₆₄	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×SD₆₄	C₂²	1	2	yes	complemented
25	C₁₃×D₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic, complemented
27	#11718114	C₂²	1	2	yes	complemented
28	#11718113	C₂²	1	2	yes	complemented
29	#11718112	C₂²	1	2	yes	complemented
30	#11718111	C₂²	1	2	yes	complemented
31	C₂×#88034	C₂²	1	1	yes	characteristic, complemented
32	Dic₂₀₈	C₂²	1	1	yes	characteristic, complemented
33	#11718041	C₂²	1	2	yes	complemented
34	D₄₁₆	C₂²	1	1	yes	characteristic, complemented
35	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
36	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
37	D₁₃×C₃₂	C₂²	1	1	yes	characteristic, complemented
38	D₁₃×C₃₂	C₂²	1	1	yes	characteristic, complemented
39	#41×D₁₃	—	4	2	no	—
40	C₁₃×#135	—	2	2	no	—
41	#88204	—	4	2	no	—
42	#88173	—	2	2	no	—
43	Q₁₆×D₁₃	—	2	2	no	—
44	#88170	—	4	2	no	—
45	SD₁₆×D₁₃	—	4	2	no	—
46	#88166	—	2	2	no	—
47	D₈×D₁₃	—	2	2	no	—
48	#88158	—	2	2	no	—
49	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
50	C₁₃×Q₃₂	C₂³	1	2	yes	—
51	C₁₃×SD₃₂	—	2	2	no	—
52	C₁₃×D₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
54	#88069	—	2	2	no	—
55	#88068	—	2	2	no	—
56	#88067	—	2	2	no	—
57	#88066	—	2	2	no	—
58	C₂×#6090	D₄	1	1	yes	characteristic
59	Dic₁₀₄	C₂³	1	2	yes	—
60	#88040	—	2	2	no	—
61	D₂₀₈	C₂³	1	2	yes	—
62	C₁₆×D₁₃	D₄	1	1	yes	characteristic
63	C₁₆×D₁₃	D₄	1	1	yes	characteristic
64	C₁₆×D₁₃	C₂³	1	1	yes	characteristic
65	C₁₆×D₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₃₂	C₂³	1	1	yes	characteristic
67	C₁₃×C₃₂	C₂³	1	1	yes	characteristic
68	#88034	C₂³	1	1	yes	characteristic
69	#88034	C₂³	1	1	yes	characteristic
70	C₂×#2262	—	13	1	no	maximal, Sylow
71	C₁₃×#41	—	4	2	no	—
72	#6131	—	4	2	no	—
73	Q₈×D₁₃	—	4	2	no	—
74	#6129	—	4	2	no	—
75	#6129	—	8	2	no	—
76	D₄×D₁₃	—	4	2	no	—
77	D₄×D₁₃	—	8	2	no	—
78	#6127	—	4	2	no	—
79	#6127	—	8	2	no	—
80	C₂×C₄×D₁₃	—	8	2	no	—
81	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
82	C₁₃×Q₁₆	—	2	2	no	—
83	C₁₃×SD₁₆	—	4	2	no	—
84	C₁₃×D₈	—	2	2	no	—
85	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
86	#6107	—	4	2	no	—
87	#6106	—	4	2	no	—
88	#6105	—	4	2	no	—
89	#6104	—	4	2	no	—
90	C₂×#1055	D₈	1	1	yes	characteristic
91	Dic₅₂	—	2	2	no	—
92	D₁₀₄	—	2	2	no	—
93	#6095	—	4	2	no	—
94	C₈×D₁₃	D₈	1	1	yes	characteristic
95	C₈×D₁₃	D₈	1	1	yes	characteristic
96	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
97	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
98	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
99	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
100	#6090	C₂×D₄	1	1	yes	characteristic
101	#6090	C₂×D₄	1	1	yes	characteristic
102	C₂×#508	—	13	2	no	—
103	#2262	—	13	2	no	—
104	#2262	—	13	1	no	—
105	#2262	—	13	2	no	—
106	#2262	—	13	1	no	—
107	#2262	—	13	1	no	—
108	#2262	D₁₃	1	1	yes	characteristic, direct product factor
109	C₂×Q₆₄	—	13	1	no	—
110	C₂×SD₆₄	—	13	2	no	—
111	C₂×D₃₂	—	13	1	no	—
112	C₂²×C₃₂	—	13	1	no	—
113	C₂²×D₁₃	—	8	2	no	—
114	C₂²×D₁₃	D₁₆	1	1	yes	characteristic
115	Q₈×C₁₃	—	4	2	no	—
116	D₄×C₁₃	—	4	2	no	—
117	D₄×C₁₃	—	8	2	no	—
118	C₂×C₄×C₁₃	—	8	2	no	—
119	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
120	C₂²⋊D₁₃	—	8	2	no	—
121	C₂²⋊D₁₃	—	8	2	no	—
122	C₂²⋊D₁₃	—	8	2	no	—
123	C₂×Dic₁₃	—	8	2	no	—
124	C₂×Dic₁₃	D₁₆	1	1	yes	characteristic
125	D₅₂	—	4	2	no	—
126	D₅₂	—	8	2	no	—
127	C₄×D₁₃	—	8	2	no	—
128	C₄×D₁₃	—	8	2	no	—
129	C₄×D₁₃	—	8	2	no	—
130	C₄×D₁₃	D₁₆	1	1	yes	characteristic
131	C₄×D₁₃	D₁₆	1	1	yes	characteristic
132	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
133	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
134	Dic₂₆	—	4	2	no	—
135	Dic₂₆	—	8	2	no	—
136	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
137	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	#1055	C₂×D₈	1	1	yes	characteristic
139	#1055	C₂×D₈	1	1	yes	characteristic
140	C₂×#135	—	26	2	no	—
141	#508	—	13	2	no	—
142	#508	—	13	2	no	—
143	#508	—	13	2	no	—
144	#508	—	26	2	no	—
145	#508	—	26	2	no	—
146	#508	C₂×D₁₃	1	2	yes	complemented
147	C₂×Q₃₂	—	13	2	no	—
148	C₂×SD₃₂	—	26	2	no	—
149	C₂×D₁₆	—	13	2	no	—
150	C₂²×C₁₆	—	13	1	no	—
151	Q₆₄	—	13	2	no	—
152	Q₆₄	—	13	1	no	—
153	Q₆₄	C₂×D₁₃	1	1	yes	characteristic, complemented
154	SD₆₄	—	13	2	no	—
155	SD₆₄	—	13	2	no	—
156	SD₆₄	—	13	2	no	—
157	SD₆₄	C₂×D₁₃	1	2	yes	complemented
158	D₃₂	—	13	2	no	—
159	D₃₂	—	13	1	no	—
160	D₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
161	C₂×C₃₂	—	13	1	no	—
162	C₂×C₃₂	—	13	1	no	—
163	C₂×C₃₂	—	13	1	no	—
164	C₂×C₃₂	—	13	1	no	—
165	C₂×C₃₂	—	13	1	no	—
166	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
167	C₂²×C₁₃	—	8	2	no	—
168	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
169	C₂×D₁₃	—	2	2	no	—
170	C₂×D₁₃	—	8	2	no	—
171	C₂×D₁₃	—	16	4	no	—
172	C₂×D₁₃	C₂×D₁₆	1	1	yes	characteristic
173	C₂×D₁₃	C₂×D₁₆	1	1	yes	characteristic
174	C₄×C₁₃	—	8	2	no	—
175	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
176	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
177	Dic₁₃	—	8	2	no	—
178	Dic₁₃	C₂×D₁₆	1	1	yes	characteristic
179	Dic₁₃	C₂×D₁₆	1	1	yes	characteristic
180	C₂×#41	—	52	2	no	—
181	#135	—	2	2	no	—
182	#135	—	26	2	no	—
183	#135	—	26	2	no	—
184	#135	—	26	2	no	—
185	#135	—	52	2	no	—
186	#135	—	52	2	no	—
187	C₂×Q₁₆	—	26	2	no	—
188	C₂×SD₁₆	—	52	2	no	—
189	C₂×D₈	—	26	2	no	—
190	C₂²×C₈	—	13	1	no	—
191	Q₃₂	—	13	2	no	—
192	Q₃₂	—	26	2	no	—
193	Q₃₂	C₂²×D₁₃	1	2	yes	—
194	SD₃₂	—	2	2	no	—
195	SD₃₂	—	26	2	no	—
196	SD₃₂	—	26	2	no	—
197	SD₃₂	—	26	2	no	—
198	D₁₆	—	13	2	no	—
199	D₁₆	—	26	2	no	—
200	D₁₆	C₂²×D₁₃	1	2	yes	—
201	C₂×C₁₆	—	13	1	no	—
202	C₂×C₁₆	—	13	1	no	—
203	C₂×C₁₆	—	13	1	no	—
204	C₂×C₁₆	—	13	1	no	—
205	C₂×C₁₆	—	13	1	no	—
206	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
207	C₃₂	—	13	1	no	—
208	C₃₂	—	13	1	no	—
209	C₃₂	C₂²×D₁₃	1	1	yes	characteristic
210	C₃₂	C₂²×D₁₃	1	1	yes	characteristic
211	C₂×C₁₃	—	2	1	no	—
212	C₂×C₁₃	—	16	2	no	—
213	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
214	D₁₃	—	2	1	no	—
215	D₁₃	—	16	2	no	—
216	D₁₃	#2262	1	2	yes	direct product factor
217	#41	—	4	2	no	—
218	#41	—	52	2	no	—
219	#41	—	52	2	no	—
220	#41	—	52	2	no	—
221	#41	—	104	2	no	—
222	#41	—	104	2	no	—
223	C₂×Q₈	—	52	2	no	—
224	C₂×D₄	—	52	2	no	—
225	C₂×D₄	—	104	2	no	—
226	C₂²×C₄	—	13	1	no	—
227	C₂²×C₄	—	104	2	no	—
228	Q₁₆	—	2	2	no	—
229	Q₁₆	—	26	2	no	—
230	Q₁₆	—	52	2	no	—
231	SD₁₆	—	4	2	no	—
232	SD₁₆	—	52	2	no	—
233	SD₁₆	—	52	2	no	—
234	SD₁₆	—	52	2	no	—
235	D₈	—	2	2	no	—
236	D₈	—	26	2	no	—
237	D₈	—	52	2	no	—
238	C₂×C₈	—	13	1	no	—
239	C₂×C₈	—	13	1	no	—
240	C₂×C₈	—	13	1	no	—
241	C₂×C₈	—	13	1	no	—
242	C₂×C₈	—	13	1	no	—
243	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
244	C₁₆	—	13	1	no	—
245	C₁₆	—	13	1	no	—
246	C₁₆	D₄×D₁₃	1	1	yes	characteristic
247	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
248	C₁₃	C₂×#2262	1	1	yes	characteristic, complemented, Sylow
249	C₂³	—	13	1	no	—
250	C₂³	—	104	2	no	—
251	Q₈	—	4	2	no	—
252	Q₈	—	52	2	no	—
253	Q₈	—	104	2	no	—
254	D₄	—	4	2	no	—
255	D₄	—	8	2	no	—
256	D₄	—	52	2	no	—
257	D₄	—	104	2	no	—
258	D₄	—	104	2	no	—
259	D₄	—	104	2	no	—
260	D₄	—	104	2	no	—
261	C₂×C₄	—	8	2	no	—
262	C₂×C₄	—	13	1	no	—
263	C₂×C₄	—	13	1	no	—
264	C₂×C₄	—	13	1	no	—
265	C₂×C₄	—	13	1	no	—
266	C₂×C₄	—	13	1	no	—
267	C₂×C₄	—	104	2	no	—
268	C₂×C₄	—	104	2	no	—
269	C₂×C₄	—	104	2	no	—
270	C₂×C₄	—	104	2	no	—
271	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
272	C₈	—	13	1	no	—
273	C₈	—	13	1	no	—
274	C₈	D₈×D₁₃	1	1	yes	characteristic
275	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
276	C₂²	—	8	2	no	—
277	C₂²	—	13	1	no	—
278	C₂²	—	13	1	no	—
279	C₂²	—	26	2	no	—
280	C₂²	—	104	2	no	—
281	C₂²	—	208	4	no	—
282	C₂²	D₁₃×D₁₆	1	1	yes	characteristic
283	C₄	—	8	2	no	—
284	C₄	—	13	1	no	—
285	C₄	—	13	1	no	—
286	C₄	—	104	2	no	—
287	C₄	D₁₃×D₁₆	1	1	yes	characteristic
288	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
289	C₂	—	2	1	no	—
290	C₂	—	13	2	no	—
291	C₂	—	16	2	no	—
292	C₂	—	26	1	no	—
293	C₂	—	208	2	no	—
294	C₂	C₂×D₁₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×D₁₆
commutator, cosocle	C₁₃×C₁₆	C₂⁴
Frattini	C₁₆	C₂³×D₁₃
Fitting	C₁₃×#2262	C₂
socle	C₂×C₁₃	C₂²×D₁₆
hypercenter	#2262	D₁₃
hypocenter	C₁₃	C₂×#2262
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. D₁₃×#508	C₂	semidirect
2. #13117146	C₂	semidirect
3. #13117145	C₂	semidirect
4. #13117144	C₂	semidirect
5. #13117143	C₂	semidirect
6. #13117142	C₂	semidirect
7. D₁₃×Q₆₄	C₂	semidirect
8. D₁₃×SD₆₄	C₂	semidirect
9. D₁₃×D₃₂	C₂	semidirect
10. C₂×D₁₃×C₃₂	C₂	semidirect
11. C₁₃×#2262	C₂	semidirect
13. C₁₃×#508	C₂²	semidirect
15. #11718580	C₂²	semidirect
19. #11718573	C₂²	semidirect
21. #11718565	C₂²	semidirect
23. C₁₃×Q₆₄	C₂²	semidirect
24. C₁₃×SD₆₄	C₂²	semidirect
25. C₁₃×D₃₂	C₂²	semidirect
26. C₂×C₁₃×C₃₂	C₂²	semidirect
27. #11718114	C₂²	semidirect
28. #11718113	C₂²	semidirect
29. #11718112	C₂²	semidirect
30. #11718111	C₂²	semidirect
31. C₂×#88034	C₂²	semidirect
32. Dic₂₀₈	C₂²	semidirect
33. #11718041	C₂²	semidirect
34. D₄₁₆	C₂²	semidirect
37. D₁₃×C₃₂	C₂²	semidirect
38. D₁₃×C₃₂	C₂²	semidirect
108. #2262	D₁₃	direct (N × H)
146. #508	C₂×D₁₃	semidirect
153. Q₆₄	C₂×D₁₃	semidirect
157. SD₆₄	C₂×D₁₃	semidirect
160. D₃₂	C₂×D₁₃	semidirect
166. C₂×C₃₂	C₂×D₁₃	semidirect
216. D₁₃	#2262	direct (N × H)
248. C₁₃	C₂×#2262	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#508	2
#13117146	2
#13117145	2
#13117144	2
#13117143	2
#13117142	2
D₁₃×Q₆₄	2
D₁₃×SD₆₄	2
D₁₃×D₃₂	2
C₂×D₁₃×C₃₂	2
C₁₃×#2262	2
C₂×#2262	13

Subgroups — D13×#2262 #16021043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2262 #16021043