Subgroups — C₁₃×#33799 #15720138

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2253	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2242	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2234	C₂	1	2	yes	maximal
7	C₁₃×#2227	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2226	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2225	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2224	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	—	2	1	no	—
13	C₁₃×#529	—	2	1	no	—
14	C₁₃×#500	C₂²	1	1	yes	characteristic
15	C₁₃×#500	C₂²	1	1	yes	characteristic
16	C₁₃×#499	—	2	1	no	—
17	C₁₃×#499	C₂²	1	2	yes	—
18	C₁₃×#499	C₂²	1	1	yes	characteristic
19	C₁₃×#498	—	2	1	no	—
20	C₁₃×#495	C₂²	1	1	yes	characteristic
21	C₁₃×#488	—	2	1	no	—
22	C₁₃×#467	C₂²	1	1	yes	characteristic
23	C₁₃×#466	C₂²	1	1	yes	characteristic
24	C₁₃×#465	—	2	1	no	—
25	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×SD₁₆	—	2	1	no	—
27	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
28	C₁₃×#427	—	2	1	no	—
29	C₁₃×#427	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#367	C₂²	1	2	yes	—
32	C₁₃×#367	C₂²	1	2	yes	—
33	C₁₃×#366	C₂²	1	2	yes	—
34	C₁₃×#366	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×SD₁₆	—	2	1	no	—
45	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×#126	—	4	1	no	—
51	C₁₃×#125	—	2	1	no	—
52	C₁₃×#125	—	2	2	no	—
53	C₁₃×#124	—	2	1	no	—
54	C₁₃×#123	—	4	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	—	4	1	no	—
57	C₁₃×C₂²⋊Q₈	—	4	1	no	—
58	C₁₃×#121	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×Q₈×C₁₃	—	4	1	no	—
61	C₄×Q₈×C₁₃	—	4	1	no	—
62	C₄×D₄×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	4	1	no	—
64	C₁₃×#117	—	2	2	no	—
65	C₁₃×#117	—	4	1	no	—
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
69	C₁₃×#107	—	2	1	no	—
70	C₁₃×#107	—	2	1	no	—
71	C₁₃×#107	C₂³	1	2	yes	—
72	C₁₃×#107	C₂³	1	2	yes	—
73	C₁₃×#107	C₂³	1	1	yes	characteristic
74	C₁₃×#107	C₂³	1	1	yes	characteristic
75	C₁₃×#106	—	2	2	no	—
76	C₁₃×#106	—	2	2	no	—
77	C₁₃×#106	—	2	1	no	—
78	C₁₃×#103	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#102	—	2	1	no	—
81	C₁₃×#102	—	2	1	no	—
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#33799	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	4	1	no	—
89	C₂×Q₈×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	1	no	—
93	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₁₃×Q₁₆	—	2	1	no	—
97	C₁₃×Q₁₆	—	2	1	no	—
98	C₁₃×SD₁₆	—	4	2	no	—
99	C₁₃×D₈	—	2	1	no	—
100	C₁₃×D₈	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₂²⋊C₄	—	4	2	no	—
121	C₁₃×C₂²⋊C₄	—	4	1	no	—
122	C₁₃×C₂²⋊C₄	—	4	1	no	—
123	C₁₃×C₂²⋊C₄	—	4	1	no	—
124	C₁₃×C₂²⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₄²×C₁₃	—	4	2	no	—
127	C₄²×C₁₃	—	4	1	no	—
128	C₄²×C₁₃	D₈	1	1	yes	characteristic
129	C₄²×C₁₃	D₈	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₁₃×C₁₆	—	2	2	no	—
133	C₁₃×C₁₆	—	2	2	no	—
134	#3168	C₂×C₁₃	1	1	yes	characteristic
135	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2253	C₂×C₁₃	1	2	yes	complemented
137	#2242	C₂×C₁₃	1	2	yes	complemented
138	#2237	C₂×C₁₃	1	2	yes	complemented
139	#2234	C₂×C₁₃	1	2	yes	—
140	#2227	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2226	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2225	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2224	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
147	Q₈×C₁₃	—	4	1	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	Q₈×C₁₃	—	8	2	no	—
150	Q₈×C₁₃	—	8	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	8	2	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	8	2	no	—
164	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	#137	1	2	yes	—
173	C₈×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₈×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
175	#533	—	2	1	no	—
176	#529	—	2	1	no	—
177	#500	C₂²×C₁₃	1	1	yes	characteristic
178	#500	C₂²×C₁₃	1	1	yes	characteristic
179	#499	—	2	1	no	—
180	#499	C₂²×C₁₃	1	2	yes	—
181	#499	C₂²×C₁₃	1	1	yes	characteristic
182	#498	—	2	1	no	—
183	#495	C₂²×C₁₃	1	1	yes	characteristic
184	#488	—	2	1	no	—
185	#467	C₂²×C₁₃	1	1	yes	characteristic
186	#466	C₂²×C₁₃	1	1	yes	characteristic
187	#465	—	2	1	no	—
188	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
189	C₄×SD₁₆	—	2	1	no	—
190	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
191	#427	—	2	1	no	—
192	#427	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	#367	C₂²×C₁₃	1	2	yes	—
195	#367	C₂²×C₁₃	1	2	yes	—
196	#366	C₂²×C₁₃	1	2	yes	—
197	#366	C₂²×C₁₃	1	2	yes	—
198	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
199	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
200	#358	C₂²×C₁₃	1	2	yes	—
201	#358	C₂²×C₁₃	1	2	yes	—
202	#357	C₂²×C₁₃	1	2	yes	—
203	#357	C₂²×C₁₃	1	2	yes	—
204	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
205	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	8	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	—	8	1	no	—
212	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	8	1	no	—
218	C₄×C₁₃	—	8	2	no	—
219	C₄×C₁₃	—	8	1	no	—
220	C₄×C₁₃	—	8	2	no	—
221	C₄×C₁₃	—	8	1	no	—
222	C₄×C₁₃	#508	1	2	yes	—
223	C₄×C₁₃	#536	1	1	yes	characteristic
224	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
225	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×SD₁₆	—	2	1	no	—
227	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	#126	—	4	1	no	—
233	#125	—	2	1	no	—
234	#125	—	2	2	no	—
235	#124	—	2	1	no	—
236	#123	—	4	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	4	1	no	—
239	C₂²⋊Q₈	—	4	1	no	—
240	#121	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	—	4	1	no	—
243	C₄×Q₈	—	4	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	4	1	no	—
246	#117	—	2	2	no	—
247	#117	—	4	1	no	—
248	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
249	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
250	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
251	#107	—	2	1	no	—
252	#107	—	2	1	no	—
253	#107	C₂³×C₁₃	1	2	yes	—
254	#107	C₂³×C₁₃	1	2	yes	—
255	#107	C₂³×C₁₃	1	1	yes	characteristic
256	#107	C₂³×C₁₃	1	1	yes	characteristic
257	#106	—	2	2	no	—
258	#106	—	2	2	no	—
259	#106	—	2	1	no	—
260	#103	—	2	1	no	—
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	1	no	—
264	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
265	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₁₃	—	4	1	no	—
269	C₂×C₁₃	—	16	1	no	—
270	C₂×C₁₃	#3226	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
272	C₂×C₁₃	#3414	1	1	yes	characteristic
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
280	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	Q₁₆	—	2	1	no	—
283	Q₁₆	—	2	1	no	—
284	SD₁₆	—	4	2	no	—
285	D₈	—	2	1	no	—
286	D₈	—	2	1	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	1	no	—
314	C₄²	C₁₃×D₈	1	1	yes	characteristic
315	C₄²	C₁₃×D₈	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₁₆	—	2	2	no	—
319	C₁₆	—	2	2	no	—
320	C₁₃	#33799	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	4	1	no	—
322	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
323	Q₈	—	4	1	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	8	2	no	—
326	Q₈	—	8	2	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	1	no	—
329	D₄	—	8	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
341	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
342	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
343	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	2	1	no	—
348	C₈	C₁₃×#137	1	2	yes	—
349	C₈	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
350	C₈	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	1	no	—
367	C₄	C₁₃×#508	1	2	yes	—
368	C₄	C₁₃×#536	1	1	yes	characteristic
369	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
370	C₂	—	4	1	no	—
371	C₂	—	16	1	no	—
372	C₂	C₁₃×#3226	1	1	yes	characteristic
373	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
374	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#466	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3160	C₂	semidirect
3. C₁₃×#2253	C₂	semidirect
4. C₁₃×#2242	C₂	semidirect
5. C₁₃×#2237	C₂	semidirect
7. C₁₃×#2227	C₂	semidirect
8. C₁₃×#2226	C₂	semidirect
9. C₁₃×#2225	C₂	semidirect
10. C₁₃×#2224	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
86. #33799	C₁₃	direct (N × H)
135. #3160	C₂×C₁₃	semidirect
136. #2253	C₂×C₁₃	semidirect
137. #2242	C₂×C₁₃	semidirect
138. #2237	C₂×C₁₃	semidirect
140. #2227	C₂×C₁₃	semidirect
141. #2226	C₂×C₁₃	semidirect
142. #2225	C₂×C₁₃	semidirect
143. #2224	C₂×C₁₃	semidirect
144. #2162	C₂×C₁₃	semidirect
320. C₁₃	#33799	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×#3168	2
C₁₃×#3160	2
C₁₃×#2253	2
C₁₃×#2242	2
C₁₃×#2237	2
C₁₃×#2234	2
C₁₃×#2227	2
C₁₃×#2226	2
C₁₃×#2225	2
C₁₃×#2224	2
C₁₃×#2162	2
#33799	13

Subgroups — C13×#33799 #15720138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33799 #15720138