Subgroups — C₁₃×#26923 #15713262

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2046	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1931	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1922	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1887	C₂	1	2	yes	maximal
9	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	C₁₃×#544	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₁₃×#519	C₂²	1	1	yes	characteristic
14	C₁₃×#518	C₂²	1	2	yes	—
15	C₁₃×#478	—	2	2	no	—
16	C₁₃×#478	—	2	2	no	—
17	C₁₃×#476	—	2	2	no	—
18	C₁₃×#474	—	2	2	no	—
19	C₁₃×#440	—	2	2	no	—
20	C₁₃×#440	—	2	2	no	—
21	C₄×C₁₃×SD₁₆	—	2	2	no	—
22	C₄×C₁₃×SD₁₆	—	2	2	no	—
23	C₁₃×#428	C₂²	1	2	yes	—
24	C₁₃×#427	C₂²	1	2	yes	—
25	C₁₃×#424	C₂²	1	2	yes	—
26	C₁₃×#419	C₂²	1	2	yes	—
27	C₁₃×#418	C₂²	1	2	yes	—
28	C₁₃×#418	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#100	C₂²	1	2	yes	—
32	C₁₃×#405	C₂²	1	2	yes	—
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#343	C₂²	1	1	yes	characteristic
35	C₁₃×#341	C₂²	1	2	yes	—
36	C₁₃×#339	C₂²	1	2	yes	—
37	C₁₃×#339	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	4	1	no	—
41	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
42	C₂×C₁₃×SD₁₆	—	2	4	no	—
43	C₂×C₁₃×SD₁₆	—	2	4	no	—
44	C₂×C₁₃×SD₁₆	—	2	2	no	—
45	C₂×C₁₃×SD₁₆	—	2	2	no	—
46	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
47	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×#127	—	2	4	no	—
51	C₁₃×#125	—	2	2	no	—
52	C₁₃×C₂²⋊Q₈	—	4	1	no	—
53	C₄×Q₈×C₁₃	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	2	2	no	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₁₃×#117	—	4	1	no	—
60	C₁₃×#117	C₂³	1	2	yes	—
61	C₁₃×#117	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#107	—	2	2	no	—
66	C₁₃×#107	D₄	1	2	yes	complemented
67	C₁₃×#107	D₄	1	2	yes	complemented
68	C₁₃×#106	—	2	2	no	—
69	C₁₃×#106	D₄	1	2	yes	complemented
70	C₁₃×#106	D₄	1	2	yes	complemented
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×#103	—	2	2	no	—
74	C₁₃×#103	—	2	2	no	—
75	C₁₃×#102	—	2	2	no	—
76	C₁₃×#102	—	2	2	no	—
77	C₁₃×#102	—	2	2	no	—
78	C₁₃×#102	—	2	2	no	—
79	C₁₃×#102	—	2	2	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#101	—	2	2	no	—
82	C₁₃×#100	—	2	4	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	4	1	no	—
86	#26923	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	1	no	—
92	C₂×Q₈×C₁₃	#41	1	2	yes	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	8	2	no	—
100	C₂×D₄×C₁₃	—	8	2	no	—
101	C₂×D₄×C₁₃	#41	1	4	yes	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×SD₁₆	—	2	8	no	—
109	C₁₃×SD₁₆	—	2	8	no	—
110	C₁₃×M₁₆	—	2	2	no	—
111	C₁₃×M₁₆	—	2	2	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	4	2	no	—
137	#3081	C₂×C₁₃	1	2	yes	complemented
138	#2949	C₂×C₁₃	1	2	yes	complemented
139	#2046	C₂×C₁₃	1	2	yes	complemented
140	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2014	C₂×C₁₃	1	1	yes	characteristic
142	#1931	C₂×C₁₃	1	2	yes	complemented
143	#1922	C₂×C₁₃	1	2	yes	complemented
144	#1887	C₂×C₁₃	1	2	yes	—
145	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₁₃	—	2	4	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	8	2	no	—
150	C₂³×C₁₃	—	8	2	no	—
151	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	4	no	—
153	Q₈×C₁₃	—	4	2	no	—
154	Q₈×C₁₃	—	16	1	no	—
155	D₄×C₁₃	—	2	4	no	—
156	D₄×C₁₃	—	2	4	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	8	8	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	8	1	no	—
172	C₂×C₄×C₁₃	—	16	2	no	—
173	C₂×C₄×C₁₃	—	16	2	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
177	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	—	2	2	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	2	no	—
182	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
183	#544	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
185	#519	C₂²×C₁₃	1	1	yes	characteristic
186	#518	C₂²×C₁₃	1	2	yes	—
187	#478	—	2	2	no	—
188	#478	—	2	2	no	—
189	#476	—	2	2	no	—
190	#474	—	2	2	no	—
191	#440	—	2	2	no	—
192	#440	—	2	2	no	—
193	C₄×SD₁₆	—	2	2	no	—
194	C₄×SD₁₆	—	2	2	no	—
195	#428	C₂²×C₁₃	1	2	yes	—
196	#427	C₂²×C₁₃	1	2	yes	—
197	#424	C₂²×C₁₃	1	2	yes	—
198	#419	C₂²×C₁₃	1	2	yes	—
199	#418	C₂²×C₁₃	1	2	yes	—
200	#418	C₂²×C₁₃	1	2	yes	—
201	C₂×#102	C₂²×C₁₃	1	2	yes	—
202	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#100	C₂²×C₁₃	1	2	yes	—
204	#405	C₂²×C₁₃	1	2	yes	—
205	#391	C₂²×C₁₃	1	1	yes	characteristic
206	#343	C₂²×C₁₃	1	1	yes	characteristic
207	#341	C₂²×C₁₃	1	2	yes	—
208	#339	C₂²×C₁₃	1	2	yes	—
209	#339	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	4	4	no	—
214	C₂²×C₁₃	—	8	4	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	16	2	no	—
218	C₂²×C₁₃	#539	1	1	yes	characteristic
219	C₂²×C₁₃	D₄²	1	1	yes	characteristic
220	C₂²×C₁₃	#551	1	1	yes	characteristic
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	8	1	no	—
228	C₄×C₁₃	#525	1	2	yes	—
229	C₄×C₁₃	#548	1	2	yes	—
230	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×D₄	—	4	1	no	—
232	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
238	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
240	C₄⋊Q₈	—	2	2	no	—
241	#127	—	2	4	no	—
242	#125	—	2	2	no	—
243	C₂²⋊Q₈	—	4	1	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	#117	—	4	1	no	—
251	#117	C₂³×C₁₃	1	2	yes	—
252	#117	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	4	2	no	—
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	#107	—	2	2	no	—
257	#107	D₄×C₁₃	1	2	yes	complemented
258	#107	D₄×C₁₃	1	2	yes	complemented
259	#106	—	2	2	no	—
260	#106	D₄×C₁₃	1	2	yes	complemented
261	#106	D₄×C₁₃	1	2	yes	complemented
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	#103	—	2	2	no	—
265	#103	—	2	2	no	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#101	—	2	2	no	—
273	#100	—	2	4	no	—
274	#97	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	#95	—	4	1	no	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	8	4	no	—
280	C₂×C₁₃	#2463	1	1	yes	characteristic
281	C₂×C₁₃	#3288	1	1	yes	characteristic
282	C₂×C₁₃	#3291	1	1	yes	characteristic
283	C₂⁴	—	2	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	C₁₃×#41	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	C₁₃×#41	1	4	yes	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
304	SD₁₆	—	2	8	no	—
305	SD₁₆	—	2	8	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
322	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	4	2	no	—
333	C₁₃	#26923	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	2	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
340	Q₈	—	2	4	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	16	1	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	—	16	2	no	—
362	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
363	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
365	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	16	2	no	—
377	C₂²	C₁₃×#539	1	1	yes	characteristic
378	C₂²	D₄²×C₁₃	1	1	yes	characteristic
379	C₂²	C₁₃×#551	1	1	yes	characteristic
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	1	no	—
387	C₄	C₁₃×#525	1	2	yes	—
388	C₄	C₁₃×#548	1	2	yes	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	8	4	no	—
392	C₂	C₁₃×#2463	1	1	yes	characteristic
393	C₂	C₁₃×#3288	1	1	yes	characteristic
394	C₂	C₁₃×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3081	C₂	semidirect
2. C₁₃×#2949	C₂	semidirect
3. C₁₃×#2046	C₂	semidirect
4. C₁₃×#2028	C₂	semidirect
6. C₁₃×#1931	C₂	semidirect
7. C₁₃×#1922	C₂	semidirect
9. C₁₃×#1857	C₂	semidirect
66. C₁₃×#107	D₄	semidirect
67. C₁₃×#107	D₄	semidirect
69. C₁₃×#106	D₄	semidirect
70. C₁₃×#106	D₄	semidirect
86. #26923	C₁₃	direct (N × H)
137. #3081	C₂×C₁₃	semidirect
138. #2949	C₂×C₁₃	semidirect
139. #2046	C₂×C₁₃	semidirect
140. #2028	C₂×C₁₃	semidirect
142. #1931	C₂×C₁₃	semidirect
143. #1922	C₂×C₁₃	semidirect
145. #1857	C₂×C₁₃	semidirect
257. #107	D₄×C₁₃	semidirect
258. #107	D₄×C₁₃	semidirect
260. #106	D₄×C₁₃	semidirect
261. #106	D₄×C₁₃	semidirect
333. C₁₃	#26923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3081	2
C₁₃×#2949	2
C₁₃×#2046	2
C₁₃×#2028	2
C₁₃×#2014	2
C₁₃×#1931	2
C₁₃×#1922	2
C₁₃×#1887	2
C₁₃×#1857	2
#26923	13

Subgroups — C13×#26923 #15713262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26923 #15713262