Subgroups — C₁₃×#2416 #13111474

Order 1664.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#121	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#396	C₂	1	2	yes	maximal, complemented
7	C₁₃×#394	C₂	1	2	yes	maximal, complemented
8	C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#386	C₂	1	2	yes	maximal, complemented
11	C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#121	—	2	8	no	—
20	C₁₃×#121	—	2	4	no	—
21	C₁₃×#121	—	2	4	no	—
22	C₄×D₄×C₁₃	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#95	C₂²	1	2	yes	—
39	C₁₃×#95	C₂²	1	2	yes	—
40	C₂⁴×C₁₃	C₂³	1	2	yes	—
41	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
42	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×D₄×C₁₃	—	2	2	no	—
44	C₂×D₄×C₁₃	—	2	2	no	—
45	C₂×D₄×C₁₃	—	2	4	no	—
46	C₂×D₄×C₁₃	—	2	4	no	—
47	C₂×D₄×C₁₃	—	2	4	no	—
48	C₂×D₄×C₁₃	—	2	4	no	—
49	C₂×D₄×C₁₃	—	2	4	no	—
50	C₂×D₄×C₁₃	—	2	2	no	—
51	C₂×D₄×C₁₃	—	2	2	no	—
52	C₂×D₄×C₁₃	—	2	2	no	—
53	C₂×D₄×C₁₃	—	4	2	no	—
54	C₂×D₄×C₁₃	D₄	1	4	yes	complemented
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	4	no	—
58	C₂²×C₄×C₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	4	2	no	—
63	C₂²×C₄×C₁₃	D₄	1	4	yes	complemented
64	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₁₃×C₄⋊C₄	D₄	1	4	yes	complemented
78	C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₁₃×C₂²⋊C₄	—	2	4	no	—
82	C₁₃×C₂²⋊C₄	—	2	4	no	—
83	C₁₃×C₂²⋊C₄	—	2	4	no	—
84	C₁₃×C₂²⋊C₄	—	4	2	no	—
85	C₄²×C₁₃	—	2	2	no	—
86	#2416	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂³×C₁₃	—	2	1	no	—
88	C₂³×C₁₃	—	2	1	no	—
89	C₂³×C₁₃	—	2	1	no	—
90	C₂³×C₁₃	—	2	1	no	—
91	C₂³×C₁₃	—	2	1	no	—
92	C₂³×C₁₃	—	2	1	no	—
93	C₂³×C₁₃	—	2	1	no	—
94	C₂³×C₁₃	—	2	1	no	—
95	C₂³×C₁₃	—	2	1	no	—
96	C₂³×C₁₃	—	2	1	no	—
97	C₂³×C₁₃	—	2	2	no	—
98	C₂³×C₁₃	—	2	2	no	—
99	C₂³×C₁₃	—	2	2	no	—
100	C₂³×C₁₃	—	2	2	no	—
101	C₂³×C₁₃	—	2	2	no	—
102	C₂³×C₁₃	—	2	2	no	—
103	C₂³×C₁₃	—	2	2	no	—
104	C₂³×C₁₃	C₂×D₄	1	2	yes	—
105	C₂³×C₁₃	C₂×D₄	1	2	yes	—
106	C₂³×C₁₃	C₂×D₄	1	2	yes	—
107	C₂³×C₁₃	#41	1	2	yes	—
108	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
109	D₄×C₁₃	—	2	8	no	—
110	D₄×C₁₃	—	4	8	no	—
111	D₄×C₁₃	—	4	8	no	—
112	D₄×C₁₃	—	4	4	no	—
113	C₂×C₄×C₁₃	—	2	1	no	—
114	C₂×C₄×C₁₃	—	2	1	no	—
115	C₂×C₄×C₁₃	—	2	2	no	—
116	C₂×C₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	2	no	—
119	C₂×C₄×C₁₃	—	2	8	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	4	8	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
137	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₁₃	#41	1	2	yes	—
140	C₂×#121	C₂×C₁₃	1	2	yes	complemented
141	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂²×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#396	C₂×C₁₃	1	2	yes	complemented
146	#394	C₂×C₁₃	1	2	yes	complemented
147	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#389	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#386	C₂×C₁₃	1	2	yes	complemented
150	#380	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂²×C₁₃	—	2	2	no	—
152	C₂²×C₁₃	—	2	2	no	—
153	C₂²×C₁₃	—	2	2	no	—
154	C₂²×C₁₃	—	2	2	no	—
155	C₂²×C₁₃	—	2	2	no	—
156	C₂²×C₁₃	—	2	2	no	—
157	C₂²×C₁₃	—	2	2	no	—
158	C₂²×C₁₃	—	2	2	no	—
159	C₂²×C₁₃	—	2	2	no	—
160	C₂²×C₁₃	—	4	1	no	—
161	C₂²×C₁₃	—	4	1	no	—
162	C₂²×C₁₃	—	4	1	no	—
163	C₂²×C₁₃	—	4	1	no	—
164	C₂²×C₁₃	—	4	2	no	—
165	C₂²×C₁₃	—	4	2	no	—
166	C₂²×C₁₃	—	4	2	no	—
167	C₂²×C₁₃	—	4	2	no	—
168	C₂²×C₁₃	—	4	2	no	—
169	C₂²×C₁₃	—	4	2	no	—
170	C₂²×C₁₃	—	4	2	no	—
171	C₂²×C₁₃	#121	1	4	yes	complemented
172	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
179	C₄×C₁₃	—	2	2	no	—
180	C₄×C₁₃	—	2	2	no	—
181	C₄×C₁₃	—	2	4	no	—
182	C₄×C₁₃	—	4	1	no	—
183	C₄×C₁₃	—	4	2	no	—
184	C₄×C₁₃	—	4	1	no	—
185	C₄×C₁₃	—	4	2	no	—
186	C₄×C₁₃	#121	1	4	yes	complemented
187	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
188	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
189	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
190	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂³×C₄	C₂²×C₁₃	1	2	yes	—
193	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
194	#121	—	2	8	no	—
195	#121	—	2	4	no	—
196	#121	—	2	4	no	—
197	C₄×D₄	—	2	4	no	—
198	C₂×C₄⋊C₄	—	2	4	no	—
199	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
210	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
213	#95	C₂²×C₁₃	1	2	yes	—
214	#95	C₂²×C₁₃	1	2	yes	—
215	C₂×C₁₃	—	2	4	no	—
216	C₂×C₁₃	—	4	2	no	—
217	C₂×C₁₃	—	8	2	no	—
218	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
219	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
220	C₂×C₁₃	#537	1	1	yes	characteristic
221	C₂×C₁₃	D₄²	1	1	yes	characteristic
222	C₂×C₁₃	#547	1	1	yes	characteristic
223	C₂×C₁₃	#548	1	1	yes	characteristic
224	C₂×C₁₃	#553	1	1	yes	characteristic
225	C₂⁴	C₂³×C₁₃	1	2	yes	—
226	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
227	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×D₄	—	2	2	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	4	no	—
231	C₂×D₄	—	2	4	no	—
232	C₂×D₄	—	2	4	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	2	no	—
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	4	2	no	—
239	C₂×D₄	D₄×C₁₃	1	4	yes	complemented
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	D₄×C₁₃	1	4	yes	complemented
249	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
252	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
253	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
254	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	D₄×C₁₃	1	4	yes	complemented
263	C₂²⋊C₄	—	2	2	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₂²⋊C₄	—	2	2	no	—
266	C₂²⋊C₄	—	2	4	no	—
267	C₂²⋊C₄	—	2	4	no	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₄²	—	2	2	no	—
271	C₁₃	#2416	1	1	yes	characteristic, direct product factor, Sylow
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	1	no	—
278	C₂³	—	2	1	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	C₂×D₄×C₁₃	1	2	yes	—
290	C₂³	C₂×D₄×C₁₃	1	2	yes	—
291	C₂³	C₂×D₄×C₁₃	1	2	yes	—
292	C₂³	C₁₃×#41	1	2	yes	—
293	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
294	D₄	—	2	8	no	—
295	D₄	—	4	8	no	—
296	D₄	—	4	8	no	—
297	D₄	—	4	4	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
320	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
321	C₂×C₄	C₂×D₄×C₁₃	1	4	yes	—
322	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
323	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×C₄	C₁₃×#41	1	2	yes	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	C₁₃×#121	1	4	yes	complemented
346	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
349	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
350	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
351	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	4	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	2	no	—
360	C₄	C₁₃×#121	1	4	yes	complemented
361	C₂	—	2	4	no	—
362	C₂	—	4	2	no	—
363	C₂	—	8	2	no	—
364	C₂	C₂×C₁₃×#121	1	1	yes	characteristic
365	C₂	C₂×C₁₃×#121	1	1	yes	characteristic
366	C₂	C₁₃×#537	1	1	yes	characteristic
367	C₂	D₄²×C₁₃	1	1	yes	characteristic
368	C₂	C₁₃×#547	1	1	yes	characteristic
369	C₂	C₁₃×#548	1	1	yes	characteristic
370	C₂	C₁₃×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#121	C₂	semidirect
2. C₂×C₁₃×#121	C₂	semidirect
3. C₂×C₁₃×#121	C₂	semidirect
4. C₂×C₄×D₄×C₁₃	C₂	semidirect
5. C₂²×C₁₃×C₄⋊C₄	C₂	semidirect
6. C₁₃×#396	C₂	semidirect
7. C₁₃×#394	C₂	semidirect
8. C₁₃×#390	C₂	semidirect
9. C₁₃×#389	C₂	semidirect
10. C₁₃×#386	C₂	semidirect
11. C₁₃×#380	C₂	semidirect
54. C₂×D₄×C₁₃	D₄	semidirect
63. C₂²×C₄×C₁₃	D₄	semidirect
77. C₁₃×C₄⋊C₄	D₄	semidirect
86. #2416	C₁₃	direct (N × H)
140. C₂×#121	C₂×C₁₃	semidirect
141. C₂×#121	C₂×C₁₃	semidirect
142. C₂×#121	C₂×C₁₃	semidirect
143. C₂×C₄×D₄	C₂×C₁₃	semidirect
144. C₂²×C₄⋊C₄	C₂×C₁₃	semidirect
145. #396	C₂×C₁₃	semidirect
146. #394	C₂×C₁₃	semidirect
147. #390	C₂×C₁₃	semidirect
148. #389	C₂×C₁₃	semidirect
149. #386	C₂×C₁₃	semidirect
150. #380	C₂×C₁₃	semidirect
171. C₂²×C₁₃	#121	semidirect
186. C₄×C₁₃	#121	semidirect
239. C₂×D₄	D₄×C₁₃	semidirect
248. C₂²×C₄	D₄×C₁₃	semidirect
262. C₄⋊C₄	D₄×C₁₃	semidirect
271. C₁₃	#2416	direct (N × H)
345. C₂²	C₁₃×#121	semidirect
360. C₄	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#121	2
C₂×C₄×D₄×C₁₃	2
C₂²×C₁₃×C₄⋊C₄	2
C₁₃×#396	2
C₁₃×#394	2
C₁₃×#390	2
C₁₃×#389	2
C₁₃×#386	2
C₁₃×#380	2
#2416	13

Subgroups — C13×#2416 #13111474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2416 #13111474