Subgroups — C₁₃×#19267 #15705606

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
3	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1668	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1667	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1545	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
9	C₂²×C₁₃×D₈	—	2	2	no	—
10	C₂×C₁₃×#127	C₂²	1	2	yes	—
11	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₁₃×#493	—	2	1	no	—
13	C₁₃×#493	—	2	1	no	—
14	C₁₃×#493	C₂²	1	4	yes	—
15	C₁₃×#460	—	2	2	no	—
16	C₁₃×#460	C₂²	1	4	yes	complemented
17	C₁₃×#459	—	2	2	no	—
18	C₁₃×#459	C₂²	1	4	yes	complemented
19	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
20	C₈×D₄×C₁₃	—	2	2	no	—
21	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
22	C₁₃×#431	—	2	1	no	—
23	C₁₃×#431	C₂²	1	1	yes	characteristic
24	C₁₃×#423	C₂²	1	2	yes	—
25	C₁₃×#418	—	2	2	no	—
26	C₂×C₄×C₈×C₁₃	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#335	C₂²	1	4	yes	complemented
29	C₁₃×#331	C₂²	1	8	yes	complemented
30	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
31	C₂²×D₄×C₁₃	—	2	2	no	—
32	C₂²×D₄×C₁₃	—	2	2	no	—
33	C₂²×D₄×C₁₃	—	2	2	no	—
34	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
35	C₂×C₁₃×SD₁₆	—	2	4	no	—
36	C₂×C₁₃×D₈	—	2	4	no	—
37	C₂×C₁₃×D₈	—	2	4	no	—
38	C₂×C₁₃×D₈	—	2	4	no	—
39	C₂×C₁₃×D₈	—	4	8	no	—
40	C₂×C₁₃×M₁₆	—	2	2	no	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₃	D₄	1	2	yes	—
43	C₁₃×#127	—	2	2	no	—
44	C₁₃×#127	—	2	2	no	—
45	C₁₃×#127	—	2	2	no	—
46	C₁₃×#127	C₂³	1	4	yes	—
47	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₄×D₄×C₁₃	—	2	1	no	—
50	C₄×D₄×C₁₃	—	2	1	no	—
51	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#117	—	2	1	no	—
54	C₁₃×#117	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	—	2	1	no	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	—	2	2	no	—
58	C₁₃×C₄⋊C₈	—	2	2	no	—
59	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
60	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
61	C₁₃×#102	—	2	4	no	—
62	C₁₃×#102	—	2	4	no	—
63	C₁₃×C₂²⋊C₈	—	2	1	no	—
64	C₁₃×C₂²⋊C₈	—	2	2	no	—
65	C₄×C₈×C₁₃	—	2	2	no	—
66	C₄×C₈×C₁₃	—	2	1	no	—
67	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
68	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₄×C₈×C₁₃	C₂³	1	2	yes	—
70	#19267	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	4	2	no	—
72	C₁₃×#41	—	2	2	no	—
73	C₁₃×#41	D₈	1	4	yes	complemented
74	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂×D₄×C₁₃	—	2	1	no	—
76	C₂×D₄×C₁₃	—	2	4	no	—
77	C₂×D₄×C₁₃	—	2	4	no	—
78	C₂×D₄×C₁₃	—	2	4	no	—
79	C₂×D₄×C₁₃	—	4	8	no	—
80	C₂×D₄×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	4	no	—
84	C₂×D₄×C₁₃	—	4	4	no	—
85	C₂×D₄×C₁₃	—	8	4	no	—
86	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
93	C₁₃×SD₁₆	—	4	8	no	—
94	C₁₃×D₈	—	4	8	no	—
95	C₁₃×D₈	—	4	8	no	—
96	C₁₃×D₈	—	4	8	no	—
97	C₁₃×M₁₆	—	4	4	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	—	4	4	no	—
102	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₄²×C₁₃	—	2	1	no	—
112	C₄²×C₁₃	—	2	1	no	—
113	C₄²×C₁₃	—	2	1	no	—
114	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₃	#41	1	1	yes	characteristic
117	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
119	#3038	C₂×C₁₃	1	2	yes	complemented
120	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#1668	C₂×C₁₃	1	4	yes	complemented
122	#1667	C₂×C₁₃	1	4	yes	complemented
123	#1567	C₂×C₁₃	1	1	yes	characteristic, complemented
124	#1545	C₂×C₁₃	1	2	yes	complemented
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	4	4	no	—
127	C₂³×C₁₃	—	8	4	no	—
128	C₂³×C₁₃	—	8	4	no	—
129	C₂³×C₁₃	—	8	4	no	—
130	C₂³×C₁₃	#121	1	1	yes	characteristic
131	Q₈×C₁₃	—	2	1	no	—
132	Q₈×C₁₃	C₂×D₈	1	2	yes	complemented
133	D₄×C₁₃	—	2	4	no	—
134	D₄×C₁₃	—	2	1	no	—
135	D₄×C₁₃	—	4	4	no	—
136	D₄×C₁₃	—	4	4	no	—
137	D₄×C₁₃	—	4	8	no	—
138	D₄×C₁₃	—	8	4	no	—
139	D₄×C₁₃	—	8	4	no	—
140	D₄×C₁₃	—	8	4	no	—
141	D₄×C₁₃	—	8	4	no	—
142	D₄×C₁₃	C₂×D₈	1	2	yes	complemented
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃	#135	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
159	C₈×C₁₃	—	2	2	no	—
160	C₈×C₁₃	—	4	4	no	—
161	C₈×C₁₃	—	4	2	no	—
162	C₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
163	C₂×AGL(1,ℤ/8)	—	2	2	no	—
164	C₂²×D₈	—	2	2	no	—
165	C₂×#127	C₂²×C₁₃	1	2	yes	—
166	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
167	#493	—	2	1	no	—
168	#493	—	2	1	no	—
169	#493	C₂²×C₁₃	1	4	yes	—
170	#460	—	2	2	no	—
171	#460	C₂²×C₁₃	1	4	yes	complemented
172	#459	—	2	2	no	—
173	#459	C₂²×C₁₃	1	4	yes	complemented
174	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
175	C₈×D₄	—	2	2	no	—
176	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
177	#431	—	2	1	no	—
178	#431	C₂²×C₁₃	1	1	yes	characteristic
179	#423	C₂²×C₁₃	1	2	yes	—
180	#418	—	2	2	no	—
181	C₂×C₄×C₈	—	2	1	no	—
182	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
183	#335	C₂²×C₁₃	1	4	yes	complemented
184	#331	C₂²×C₁₃	1	8	yes	complemented
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	4	1	no	—
189	C₂²×C₁₃	—	4	1	no	—
190	C₂²×C₁₃	—	8	4	no	—
191	C₂²×C₁₃	—	8	4	no	—
192	C₂²×C₁₃	—	8	4	no	—
193	C₂²×C₁₃	—	16	8	no	—
194	C₂²×C₁₃	#466	1	2	yes	—
195	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	4	1	no	—
200	C₄×C₁₃	—	4	1	no	—
201	C₄×C₁₃	#466	1	2	yes	—
202	C₄×C₁₃	#472	1	2	yes	—
203	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
204	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
205	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
206	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	—	2	2	no	—
209	C₂²×D₄	—	2	2	no	—
210	AGL(1,ℤ/8)	—	4	8	no	—
211	C₂×SD₁₆	—	2	4	no	—
212	C₂×D₈	—	2	4	no	—
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	—	2	4	no	—
215	C₂×D₈	—	4	8	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	D₄×C₁₃	1	2	yes	—
219	#127	—	2	2	no	—
220	#127	—	2	2	no	—
221	#127	—	2	2	no	—
222	#127	C₂³×C₁₃	1	4	yes	—
223	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
224	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
228	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
229	#117	—	2	1	no	—
230	#117	D₄×C₁₃	1	1	yes	characteristic
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
236	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
237	#102	—	2	4	no	—
238	#102	—	2	4	no	—
239	C₂²⋊C₈	—	2	1	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
244	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₁₃	1	2	yes	—
246	C₂×C₁₃	—	2	2	no	—
247	C₂×C₁₃	—	4	2	no	—
248	C₂×C₁₃	—	16	4	no	—
249	C₂×C₁₃	#3038	1	1	yes	characteristic
250	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
251	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
252	C₂⁴	—	4	2	no	—
253	#41	—	2	2	no	—
254	#41	C₁₃×D₈	1	4	yes	complemented
255	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	4	8	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂×D₄	—	8	4	no	—
267	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
274	SD₁₆	—	4	8	no	—
275	D₈	—	4	8	no	—
276	D₈	—	4	8	no	—
277	D₈	—	4	8	no	—
278	M₁₆	—	4	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₄²	C₁₃×#41	1	1	yes	characteristic
298	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
299	C₁₃	#19267	1	1	yes	characteristic, direct product factor, Sylow
300	C₂³	—	2	1	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	8	4	no	—
303	C₂³	—	8	4	no	—
304	C₂³	—	8	4	no	—
305	C₂³	C₁₃×#121	1	1	yes	characteristic
306	Q₈	—	2	1	no	—
307	Q₈	C₂×C₁₃×D₈	1	2	yes	complemented
308	D₄	—	2	4	no	—
309	D₄	—	2	1	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	8	no	—
313	D₄	—	8	4	no	—
314	D₄	—	8	4	no	—
315	D₄	—	8	4	no	—
316	D₄	—	8	4	no	—
317	D₄	C₂×C₁₃×D₈	1	2	yes	complemented
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
327	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
328	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
329	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
330	C₂×C₄	C₁₃×#135	1	2	yes	—
331	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
334	C₈	—	2	2	no	—
335	C₈	—	4	4	no	—
336	C₈	—	4	2	no	—
337	C₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	8	4	no	—
344	C₂²	—	8	4	no	—
345	C₂²	—	8	4	no	—
346	C₂²	—	16	8	no	—
347	C₂²	C₁₃×#466	1	2	yes	—
348	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	C₁₃×#466	1	2	yes	—
355	C₄	C₁₃×#472	1	2	yes	—
356	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
357	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
358	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	2	no	—
361	C₂	—	16	4	no	—
362	C₂	C₁₃×#3038	1	1	yes	characteristic
363	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
364	C₂	C₂×C₁₃×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#493	C₂	semidirect
2. C₁₃×#3038	C₂	semidirect
3. C₈×C₁₃×#41	C₂	semidirect
4. C₁₃×#1668	C₂	semidirect
5. C₁₃×#1667	C₂	semidirect
6. C₁₃×#1567	C₂	semidirect
7. C₁₃×#1545	C₂	semidirect
16. C₁₃×#460	C₂²	semidirect
18. C₁₃×#459	C₂²	semidirect
19. C₈×Q₈×C₁₃	C₂²	semidirect
21. C₈×D₄×C₁₃	C₂²	semidirect
28. C₁₃×#335	C₂²	semidirect
29. C₁₃×#331	C₂²	semidirect
70. #19267	C₁₃	direct (N × H)
73. C₁₃×#41	D₈	semidirect
118. C₂×#493	C₂×C₁₃	semidirect
119. #3038	C₂×C₁₃	semidirect
120. C₈×#41	C₂×C₁₃	semidirect
121. #1668	C₂×C₁₃	semidirect
122. #1667	C₂×C₁₃	semidirect
123. #1567	C₂×C₁₃	semidirect
124. #1545	C₂×C₁₃	semidirect
132. Q₈×C₁₃	C₂×D₈	semidirect
142. D₄×C₁₃	C₂×D₈	semidirect
162. C₈×C₁₃	AGL(1,ℤ/8)	semidirect
171. #460	C₂²×C₁₃	semidirect
173. #459	C₂²×C₁₃	semidirect
174. C₈×Q₈	C₂²×C₁₃	semidirect
176. C₈×D₄	C₂²×C₁₃	semidirect
183. #335	C₂²×C₁₃	semidirect
184. #331	C₂²×C₁₃	semidirect
254. #41	C₁₃×D₈	semidirect
299. C₁₃	#19267	direct (N × H)
307. Q₈	C₂×C₁₃×D₈	semidirect
317. D₄	C₂×C₁₃×D₈	semidirect
337. C₈	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#493	2
C₁₃×#3038	2
C₈×C₁₃×#41	2
C₁₃×#1668	2
C₁₃×#1667	2
C₁₃×#1567	2
C₁₃×#1545	2
#19267	13

Subgroups — C13×#19267 #15705606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19267 #15705606