Subgroups — C₁₃×#2414 #13111472

Order 1664.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 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	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#394	C₂	1	2	yes	maximal, complemented
6	C₁₃×#392	C₂	1	2	yes	maximal, complemented
7	C₁₃×#390	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×#388	C₂	1	2	yes	maximal, complemented
11	C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#121	—	2	4	no	—
19	C₁₃×#121	—	2	4	no	—
20	C₄×D₄×C₁₃	—	2	4	no	—
21	C₁₃×#117	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#95	C₂²	1	2	yes	—
38	C₁₃×#95	C₂²	1	2	yes	—
39	C₂⁴×C₁₃	C₂³	1	2	yes	—
40	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
41	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
42	C₂×D₄×C₁₃	—	2	2	no	—
43	C₂×D₄×C₁₃	—	2	2	no	—
44	C₂×D₄×C₁₃	—	2	4	no	—
45	C₂×D₄×C₁₃	—	2	4	no	—
46	C₂×D₄×C₁₃	—	2	4	no	—
47	C₂×D₄×C₁₃	—	2	2	no	—
48	C₂×D₄×C₁₃	—	2	2	no	—
49	C₂×D₄×C₁₃	—	2	2	no	—
50	C₂×D₄×C₁₃	—	2	2	no	—
51	C₂×D₄×C₁₃	—	4	2	no	—
52	C₂×D₄×C₁₃	—	4	2	no	—
53	C₂×D₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	—	2	2	no	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	2	2	no	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	D₄	1	4	yes	complemented
60	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₁₃×C₄⋊C₄	D₄	1	4	yes	complemented
73	C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₁₃×C₂²⋊C₄	—	2	4	no	—
78	C₁₃×C₂²⋊C₄	—	2	4	no	—
79	C₁₃×C₂²⋊C₄	—	4	2	no	—
80	C₁₃×C₂²⋊C₄	—	4	2	no	—
81	C₄²×C₁₃	—	2	4	no	—
82	C₄²×C₁₃	—	2	2	no	—
83	#2414	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂³×C₁₃	—	2	1	no	—
85	C₂³×C₁₃	—	2	1	no	—
86	C₂³×C₁₃	—	2	1	no	—
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	2	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	C₂×D₄	1	2	yes	—
104	C₂³×C₁₃	#41	1	2	yes	—
105	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
106	D₄×C₁₃	—	2	8	no	—
107	D₄×C₁₃	—	4	8	no	—
108	D₄×C₁₃	—	4	8	no	—
109	D₄×C₁₃	—	4	4	no	—
110	C₂×C₄×C₁₃	—	2	1	no	—
111	C₂×C₄×C₁₃	—	2	1	no	—
112	C₂×C₄×C₁₃	—	2	1	no	—
113	C₂×C₄×C₁₃	—	2	1	no	—
114	C₂×C₄×C₁₃	—	2	2	no	—
115	C₂×C₄×C₁₃	—	2	2	no	—
116	C₂×C₄×C₁₃	—	2	8	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	2	no	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	2	no	—
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	1	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	—	4	4	no	—
130	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₁₃	#41	1	2	yes	—
135	C₂×C₄×C₁₃	#41	1	2	yes	—
136	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#394	C₂×C₁₃	1	2	yes	complemented
141	#392	C₂×C₁₃	1	2	yes	complemented
142	#390	C₂×C₁₃	1	2	yes	complemented
143	#390	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#389	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#388	C₂×C₁₃	1	2	yes	complemented
146	#380	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂²×C₁₃	—	2	2	no	—
148	C₂²×C₁₃	—	2	2	no	—
149	C₂²×C₁₃	—	2	2	no	—
150	C₂²×C₁₃	—	2	2	no	—
151	C₂²×C₁₃	—	2	2	no	—
152	C₂²×C₁₃	—	2	2	no	—
153	C₂²×C₁₃	—	4	1	no	—
154	C₂²×C₁₃	—	4	1	no	—
155	C₂²×C₁₃	—	4	1	no	—
156	C₂²×C₁₃	—	4	1	no	—
157	C₂²×C₁₃	—	4	1	no	—
158	C₂²×C₁₃	—	4	1	no	—
159	C₂²×C₁₃	—	4	1	no	—
160	C₂²×C₁₃	—	4	1	no	—
161	C₂²×C₁₃	—	4	2	no	—
162	C₂²×C₁₃	—	4	2	no	—
163	C₂²×C₁₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
169	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
171	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₄×C₁₃	—	2	2	no	—
176	C₄×C₁₃	—	2	2	no	—
177	C₄×C₁₃	—	2	4	no	—
178	C₄×C₁₃	—	4	1	no	—
179	C₄×C₁₃	—	4	1	no	—
180	C₄×C₁₃	—	4	2	no	—
181	C₄×C₁₃	—	4	2	no	—
182	C₄×C₁₃	#121	1	4	yes	—
183	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
186	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
187	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
188	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
189	#121	—	2	4	no	—
190	#121	—	2	4	no	—
191	C₄×D₄	—	2	4	no	—
192	#117	—	2	4	no	—
193	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
208	#95	C₂²×C₁₃	1	2	yes	—
209	#95	C₂²×C₁₃	1	2	yes	—
210	C₂×C₁₃	—	4	2	no	—
211	C₂×C₁₃	—	4	2	no	—
212	C₂×C₁₃	—	8	2	no	—
213	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
214	C₂×C₁₃	#525	1	1	yes	characteristic
215	C₂×C₁₃	#535	1	1	yes	characteristic
216	C₂×C₁₃	#546	1	1	yes	characteristic
217	C₂×C₁₃	#550	1	1	yes	characteristic
218	C₂×C₁₃	#553	1	1	yes	characteristic
219	C₂×C₁₃	#555	1	1	yes	characteristic
220	C₂⁴	C₂³×C₁₃	1	2	yes	—
221	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
222	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
223	C₂×D₄	—	2	2	no	—
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	2	4	no	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	—	2	2	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	2	2	no	—
231	C₂×D₄	—	2	2	no	—
232	C₂×D₄	—	4	2	no	—
233	C₂×D₄	—	4	2	no	—
234	C₂×D₄	—	4	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	D₄×C₁₃	1	4	yes	complemented
241	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
243	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
244	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
249	C₄⋊C₄	—	2	2	no	—
250	C₄⋊C₄	—	2	2	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	—	4	2	no	—
253	C₄⋊C₄	D₄×C₁₃	1	4	yes	complemented
254	C₂²⋊C₄	—	2	2	no	—
255	C₂²⋊C₄	—	2	4	no	—
256	C₂²⋊C₄	—	2	2	no	—
257	C₂²⋊C₄	—	2	4	no	—
258	C₂²⋊C₄	—	2	4	no	—
259	C₂²⋊C₄	—	2	4	no	—
260	C₂²⋊C₄	—	4	2	no	—
261	C₂²⋊C₄	—	4	2	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	2	no	—
264	C₁₃	#2414	1	1	yes	characteristic, direct product factor, Sylow
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	1	no	—
268	C₂³	—	2	1	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
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	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	C₂×D₄×C₁₃	1	2	yes	—
285	C₂³	C₁₃×#41	1	2	yes	—
286	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
287	D₄	—	2	8	no	—
288	D₄	—	4	8	no	—
289	D₄	—	4	8	no	—
290	D₄	—	4	4	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	C₂×D₄×C₁₃	1	4	yes	—
312	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×C₄	C₁₃×#41	1	2	yes	—
316	C₂×C₄	C₁₃×#41	1	2	yes	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	—	4	1	no	—
329	C₂²	—	4	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
339	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
341	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
342	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
343	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	C₁₃×#121	1	4	yes	—
353	C₂	—	4	2	no	—
354	C₂	—	4	2	no	—
355	C₂	—	8	2	no	—
356	C₂	C₂×C₁₃×#121	1	1	yes	characteristic
357	C₂	C₁₃×#525	1	1	yes	characteristic
358	C₂	C₁₃×#535	1	1	yes	characteristic
359	C₂	C₁₃×#546	1	1	yes	characteristic
360	C₂	C₁₃×#550	1	1	yes	characteristic
361	C₂	C₁₃×#553	1	1	yes	characteristic
362	C₂	C₁₃×#555	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×C₄×D₄×C₁₃	C₂	semidirect
4. C₂×C₁₃×#117	C₂	semidirect
5. C₁₃×#394	C₂	semidirect
6. C₁₃×#392	C₂	semidirect
7. C₁₃×#390	C₂	semidirect
8. C₁₃×#390	C₂	semidirect
9. C₁₃×#389	C₂	semidirect
10. C₁₃×#388	C₂	semidirect
11. C₁₃×#380	C₂	semidirect
59. C₂²×C₄×C₁₃	D₄	semidirect
72. C₁₃×C₄⋊C₄	D₄	semidirect
83. #2414	C₁₃	direct (N × H)
136. C₂×#121	C₂×C₁₃	semidirect
137. C₂×#121	C₂×C₁₃	semidirect
138. C₂×C₄×D₄	C₂×C₁₃	semidirect
139. C₂×#117	C₂×C₁₃	semidirect
140. #394	C₂×C₁₃	semidirect
141. #392	C₂×C₁₃	semidirect
142. #390	C₂×C₁₃	semidirect
143. #390	C₂×C₁₃	semidirect
144. #389	C₂×C₁₃	semidirect
145. #388	C₂×C₁₃	semidirect
146. #380	C₂×C₁₃	semidirect
240. C₂²×C₄	D₄×C₁₃	semidirect
253. C₄⋊C₄	D₄×C₁₃	semidirect
264. C₁₃	#2414	direct (N × H)

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
C₂×C₁₃×#117	2
C₁₃×#394	2
C₁₃×#392	2
C₁₃×#390	2
C₁₃×#389	2
C₁₃×#388	2
C₁₃×#380	2
#2414	13

Subgroups — C13×#2414 #13111472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2414 #13111472