Subgroups — D₁₃×#2241 #16018205

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#494	C₂	1	1	yes	maximal, characteristic
3	#13117065	C₂	1	1	yes	maximal, characteristic, complemented
4	#13117064	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117063	C₂	1	1	yes	maximal, characteristic, complemented
6	#13117062	C₂	1	4	yes	maximal, complemented
7	D₁₃×#358	C₂	1	4	yes	maximal
8	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2241	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₁₆×D₁₃	—	2	1	no	—
11	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
12	D₁₃×C₄⋊Q₈	—	2	1	no	—
13	D₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₁₃×#500	C₂²	1	1	yes	characteristic
15	C₁₃×#494	C₂²	1	1	yes	characteristic
16	#11718842	—	2	1	no	—
17	#11718842	C₂²	1	2	yes	—
18	#11718753	—	2	1	no	—
19	#11718739	—	2	1	no	—
20	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
21	D₁₃×#107	—	2	1	no	—
22	D₁₃×#107	C₂²	1	2	yes	—
23	#11718535	—	2	1	no	—
24	#11718535	C₂²	1	2	yes	—
25	#11718360	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	#11718343	C₂²	1	1	yes	characteristic
28	C₁₃×#358	C₂²	1	4	yes	—
29	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
30	#11718156	C₂²	1	4	yes	—
31	#11718095	C₂²	1	4	yes	—
32	C₁₆×Dic₁₃	C₂²	1	2	yes	—
33	#11718084	C₂²	1	4	yes	—
34	C₄×#6090	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₁₃	—	2	2	no	—
36	C₂×Q₈×D₁₃	—	4	1	no	—
37	C₂×C₁₃×Q₁₆	—	2	1	no	—
38	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	#88198	—	2	2	no	—
42	#88198	—	4	1	no	—
43	C₂×#6107	—	2	2	no	—
44	C₂×#6107	—	2	2	no	—
45	Q₁₆×D₁₃	—	2	8	no	—
46	Q₁₆×D₁₃	—	4	4	no	—
47	C₂×Dic₅₂	—	2	1	no	—
48	C₂×Dic₅₂	C₂³	1	2	yes	—
49	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
51	C₄⋊C₄×D₁₃	—	2	2	no	—
52	C₄⋊C₄×D₁₃	—	4	1	no	—
53	C₄⋊C₄×D₁₃	—	4	1	no	—
54	C₄⋊C₄×D₁₃	—	4	1	no	—
55	#88142	—	2	2	no	—
56	#88142	—	4	1	no	—
57	#88142	—	4	1	no	—
58	#88142	—	4	1	no	—
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	#88123	—	2	1	no	—
61	#88123	—	2	1	no	—
62	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
63	C₁₃×#107	—	2	1	no	—
64	C₁₃×#107	C₂³	1	2	yes	—
65	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	#88058	—	2	1	no	—
67	#88058	C₂³	1	2	yes	—
68	C₈×Dic₁₃	D₄	1	1	yes	characteristic
69	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
70	C₂×#6090	C₂³	1	2	yes	—
71	#88047	—	2	2	no	—
72	#88047	—	2	2	no	—
73	C₄×#1055	D₄	1	1	yes	characteristic
74	C₁₆×D₁₃	—	2	4	no	—
75	C₂×#2241	—	13	1	no	maximal, Sylow
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	Q₈×D₁₃	—	4	4	no	—
79	Q₈×D₁₃	—	4	4	no	—
80	Q₈×D₁₃	—	8	4	no	—
81	C₂×C₄×D₁₃	—	4	2	no	—
82	C₂×C₄×D₁₃	—	4	2	no	—
83	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
84	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Dic₂₆	—	2	2	no	—
87	C₂×Dic₂₆	—	4	1	no	—
88	C₂×Dic₂₆	—	4	2	no	—
89	C₂×Dic₂₆	—	4	2	no	—
90	C₁₃×Q₁₆	—	2	4	no	—
91	C₁₃×Q₁₆	—	4	2	no	—
92	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₁₃×C₄⋊C₄	—	4	1	no	—
96	C₁₃×C₄⋊C₄	—	4	1	no	—
97	C₁₃×C₄⋊C₄	—	4	1	no	—
98	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
99	#6107	—	4	4	no	—
100	#6107	—	4	4	no	—
101	C₄⋊Dic₁₃	—	2	2	no	—
102	C₄⋊Dic₁₃	—	4	1	no	—
103	C₄⋊Dic₁₃	—	4	1	no	—
104	C₄⋊Dic₁₃	—	4	1	no	—
105	#6101	—	4	2	no	—
106	#6101	—	4	2	no	—
107	#6101	—	4	2	no	—
108	#6101	—	4	2	no	—
109	C₄×Dic₁₃	D₈	1	1	yes	characteristic
110	C₄×Dic₁₃	D₈	1	1	yes	characteristic
111	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×#1055	C₂×D₄	1	1	yes	characteristic
113	C₂×#1055	C₂×D₄	1	1	yes	characteristic
114	Dic₅₂	—	2	4	no	—
115	Dic₅₂	—	4	2	no	—
116	C₈×D₁₃	SD₁₆	1	4	yes	—
117	C₈×D₁₃	#41	1	4	yes	—
118	C₁₃×C₁₆	—	2	2	no	—
119	#6090	—	2	2	no	—
120	C₂×#500	—	13	1	no	—
121	C₂×#494	—	13	1	no	—
122	#2241	—	13	1	no	—
123	#2241	—	13	1	no	—
124	#2241	—	13	4	no	—
125	#2241	—	13	1	no	—
126	#2241	D₁₃	1	1	yes	characteristic, direct product factor
127	C₂×#358	—	13	4	no	—
128	C₂×C₄×C₁₆	—	13	1	no	—
129	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
130	Q₈×C₁₃	—	4	2	no	—
131	Q₈×C₁₃	—	4	2	no	—
132	Q₈×C₁₃	—	8	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×Dic₁₃	—	4	2	no	—
139	C₂×Dic₁₃	—	4	2	no	—
140	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
141	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
142	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
143	C₄×D₁₃	—	8	4	no	—
144	C₄×D₁₃	—	8	4	no	—
145	C₄×D₁₃	SD₃₂	1	4	yes	—
146	C₄×D₁₃	Q₃₂	1	4	yes	—
147	C₄×D₁₃	#124	1	2	yes	—
148	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
149	Dic₂₆	—	4	2	no	—
150	Dic₂₆	—	4	2	no	—
151	Dic₂₆	—	8	2	no	—
152	Dic₂₆	—	8	4	no	—
153	Dic₂₆	—	8	4	no	—
154	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
155	C₈×C₁₃	C₂×#41	1	2	yes	—
156	#1055	#124	1	2	yes	—
157	#1055	C₂×SD₁₆	1	2	yes	—
158	C₂²×Q₁₆	—	13	2	no	—
159	C₂²×Q₁₆	—	26	1	no	—
160	C₂×C₄⋊Q₈	—	26	1	no	—
161	C₂×C₄⋊Q₈	—	26	1	no	—
162	C₂²×C₁₆	—	13	2	no	—
163	#500	—	13	2	no	—
164	#500	—	13	1	no	—
165	#500	—	26	1	no	—
166	#500	—	26	1	no	—
167	#500	C₂×D₁₃	1	1	yes	characteristic
168	#494	—	13	2	no	—
169	#494	—	13	1	no	—
170	#494	—	26	1	no	—
171	#494	—	26	1	no	—
172	#494	C₂×D₁₃	1	1	yes	characteristic
173	C₂×#107	—	13	2	no	—
174	C₂×#107	—	26	1	no	—
175	C₂×C₄×C₈	—	13	1	no	—
176	#358	—	13	4	no	—
177	#358	—	13	4	no	—
178	#358	—	13	4	no	—
179	#358	C₂×D₁₃	1	4	yes	—
180	C₄×C₁₆	—	13	2	no	—
181	C₄×C₁₆	—	13	1	no	—
182	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
183	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
184	C₂×D₁₃	#486	1	2	yes	—
185	C₂×D₁₃	C₂×SD₃₂	1	2	yes	—
186	C₂×D₁₃	C₂×Q₃₂	1	2	yes	—
187	C₄×C₁₃	—	8	2	no	—
188	C₄×C₁₃	—	8	2	no	—
189	C₄×C₁₃	C₂×SD₃₂	1	2	yes	—
190	C₄×C₁₃	C₂×Q₃₂	1	2	yes	—
191	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
192	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
193	Dic₁₃	—	8	2	no	—
194	Dic₁₃	—	8	2	no	—
195	Dic₁₃	#486	1	2	yes	—
196	Dic₁₃	C₂×SD₃₂	1	2	yes	—
197	Dic₁₃	C₂×Q₃₂	1	2	yes	—
198	C₂²×Q₈	—	26	2	no	—
199	C₂²×Q₈	—	52	1	no	—
200	C₂×Q₁₆	—	2	1	no	—
201	C₂×Q₁₆	—	13	2	no	—
202	C₂×Q₁₆	—	26	8	no	—
203	C₂×Q₁₆	—	26	2	no	—
204	C₂×Q₁₆	—	26	2	no	—
205	C₂×Q₁₆	—	26	1	no	—
206	C₂×Q₁₆	—	52	4	no	—
207	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
208	C₂²×C₈	—	13	1	no	—
209	C₂²×C₈	—	13	1	no	—
210	C₄⋊Q₈	—	2	1	no	—
211	C₄⋊Q₈	—	2	1	no	—
212	C₄⋊Q₈	—	26	2	no	—
213	C₄⋊Q₈	—	26	2	no	—
214	C₄⋊Q₈	—	26	1	no	—
215	C₄⋊Q₈	—	26	1	no	—
216	C₄⋊Q₈	—	52	1	no	—
217	C₄⋊Q₈	—	52	1	no	—
218	C₄⋊Q₈	—	52	1	no	—
219	C₄⋊Q₈	—	52	1	no	—
220	C₂×C₄⋊C₄	—	26	2	no	—
221	C₂×C₄⋊C₄	—	52	1	no	—
222	C₂×C₄⋊C₄	—	52	1	no	—
223	C₂×C₄⋊C₄	—	52	1	no	—
224	C₂×C₄²	—	13	1	no	—
225	C₂×C₁₆	—	13	2	no	—
226	C₂×C₁₆	—	26	4	no	—
227	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
228	#107	—	2	1	no	—
229	#107	—	13	2	no	—
230	#107	—	26	2	no	—
231	#107	—	26	2	no	—
232	#107	—	26	1	no	—
233	#107	C₂²×D₁₃	1	2	yes	—
234	C₄×C₈	—	13	1	no	—
235	C₄×C₈	—	13	1	no	—
236	C₄×C₈	—	13	1	no	—
237	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
238	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
239	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
240	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
241	D₁₃	#2241	1	4	yes	direct product factor
242	C₂×Q₈	—	2	2	no	—
243	C₂×Q₈	—	4	1	no	—
244	C₂×Q₈	—	26	2	no	—
245	C₂×Q₈	—	52	2	no	—
246	C₂×Q₈	—	52	2	no	—
247	C₂×Q₈	—	52	4	no	—
248	C₂×Q₈	—	52	4	no	—
249	C₂×Q₈	—	52	1	no	—
250	C₂×Q₈	—	104	4	no	—
251	C₂²×C₄	—	13	1	no	—
252	C₂²×C₄	—	13	1	no	—
253	C₂²×C₄	—	13	1	no	—
254	C₂²×C₄	—	52	2	no	—
255	C₂²×C₄	—	52	2	no	—
256	Q₁₆	—	2	4	no	—
257	Q₁₆	—	4	2	no	—
258	Q₁₆	—	26	4	no	—
259	Q₁₆	—	52	4	no	—
260	Q₁₆	—	52	4	no	—
261	Q₁₆	—	52	2	no	—
262	C₂×C₈	—	13	1	no	—
263	C₂×C₈	—	13	1	no	—
264	C₂×C₈	—	13	4	no	—
265	C₂×C₈	—	13	4	no	—
266	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
267	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	4	1	no	—
270	C₄⋊C₄	—	4	1	no	—
271	C₄⋊C₄	—	4	1	no	—
272	C₄⋊C₄	—	26	2	no	—
273	C₄⋊C₄	—	52	2	no	—
274	C₄⋊C₄	—	52	2	no	—
275	C₄⋊C₄	—	52	2	no	—
276	C₄⋊C₄	—	52	2	no	—
277	C₄⋊C₄	—	52	1	no	—
278	C₄⋊C₄	—	52	1	no	—
279	C₄⋊C₄	—	52	1	no	—
280	C₄²	—	13	1	no	—
281	C₄²	—	13	1	no	—
282	C₄²	—	13	1	no	—
283	C₄²	D₄×D₁₃	1	1	yes	characteristic
284	C₁₆	—	2	2	no	—
285	C₁₆	—	26	2	no	—
286	C₁₃	C₂×#2241	1	1	yes	characteristic, complemented, Sylow
287	C₂³	—	13	1	no	—
288	Q₈	—	4	2	no	—
289	Q₈	—	4	2	no	—
290	Q₈	—	8	2	no	—
291	Q₈	—	52	2	no	—
292	Q₈	—	52	2	no	—
293	Q₈	—	104	4	no	—
294	Q₈	—	104	4	no	—
295	Q₈	—	104	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	13	1	no	—
299	C₂×C₄	—	13	1	no	—
300	C₂×C₄	—	13	1	no	—
301	C₂×C₄	—	13	2	no	—
302	C₂×C₄	—	13	4	no	—
303	C₂×C₄	—	13	4	no	—
304	C₂×C₄	—	13	2	no	—
305	C₂×C₄	—	52	2	no	—
306	C₂×C₄	—	52	2	no	—
307	C₂×C₄	—	104	4	no	—
308	C₂×C₄	—	104	4	no	—
309	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
310	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
312	C₈	—	13	2	no	—
313	C₈	—	13	2	no	—
314	C₈	SD₁₆×D₁₃	1	2	yes	—
315	C₈	#41×D₁₃	1	2	yes	—
316	C₂²	—	13	2	no	—
317	C₂²	—	13	2	no	—
318	C₂²	—	13	2	no	—
319	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
320	C₄	—	8	2	no	—
321	C₄	—	8	2	no	—
322	C₄	—	13	2	no	—
323	C₄	—	13	2	no	—
324	C₄	—	13	2	no	—
325	C₄	—	104	2	no	—
326	C₄	—	104	2	no	—
327	C₄	D₁₃×SD₃₂	1	2	yes	—
328	C₄	D₁₃×Q₃₂	1	2	yes	—
329	C₄	D₁₃×#124	1	1	yes	characteristic
330	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
331	C₂	—	13	4	no	—
332	C₂	D₁₃×#486	1	1	yes	characteristic
333	C₂	C₂×D₁₃×SD₃₂	1	1	yes	characteristic
334	C₂	C₂×D₁₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2241	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂²×D₁₃	C₂×D₈
hypercenter	#2241	D₁₃
hypocenter	C₁₃	C₂×#2241
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2241

Complements

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

N	H ≅ G/N	type
3. #13117065	C₂	semidirect
4. #13117064	C₂	semidirect
5. #13117063	C₂	semidirect
6. #13117062	C₂	semidirect
9. C₁₃×#2241	C₂	semidirect
126. #2241	D₁₃	direct (N × H)
241. D₁₃	#2241	direct (N × H)
286. C₁₃	C₂×#2241	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#500	2
D₁₃×#494	2
#13117065	2
#13117064	2
#13117063	2
#13117062	2
D₁₃×#358	2
C₄×C₁₆×D₁₃	2
C₁₃×#2241	2
C₂×#2241	13

Subgroups — D13×#2241 #16018205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2241 #16018205