Subgroups — C₁₃×#3055 #13112113

Order 1664.

548 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#469	C₂	1	2	yes	maximal, complemented
6	C₁₃×#468	C₂	1	2	yes	maximal, complemented
7	C₁₃×#466	C₂	1	2	yes	maximal, complemented
8	C₁₃×#465	C₂	1	2	yes	maximal, complemented
9	C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₃	—	2	1	no	—
14	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
17	C₂×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₁₃×D₈	C₂²	1	2	yes	complemented
19	C₂×C₁₃×M₁₆	—	2	4	no	—
20	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₁₆	C₂²	1	2	yes	complemented
23	C₂²×C₈×C₁₃	C₂²	1	2	yes	complemented
24	C₁₃×#123	—	2	1	no	—
25	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#121	—	2	1	no	—
28	C₁₃×#121	—	2	1	no	—
29	C₁₃×#121	C₂²	1	2	yes	—
30	C₁₃×#121	C₂²	1	2	yes	—
31	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#120	—	2	1	no	—
34	C₄×D₄×C₁₃	—	2	1	no	—
35	C₄×D₄×C₁₃	—	2	1	no	—
36	C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₁₃×#107	C₂²	1	2	yes	complemented
40	C₁₃×#106	C₂²	1	2	yes	complemented
41	C₁₃×#103	C₂²	1	2	yes	complemented
42	C₁₃×#102	C₂²	1	2	yes	complemented
43	C₁₃×#102	C₂²	1	2	yes	complemented
44	C₁₃×#102	C₂²	1	2	yes	complemented
45	C₂⁴×C₁₃	—	2	1	no	—
46	C₂⁴×C₁₃	D₄	1	1	yes	characteristic
47	C₁₃×#41	—	2	2	no	—
48	C₁₃×#41	—	2	2	no	—
49	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×D₄×C₁₃	—	2	1	no	—
51	C₂×D₄×C₁₃	—	2	1	no	—
52	C₂×D₄×C₁₃	—	2	1	no	—
53	C₂×D₄×C₁₃	—	2	2	no	—
54	C₂×D₄×C₁₃	—	2	2	no	—
55	C₂×D₄×C₁₃	—	2	2	no	—
56	C₂×D₄×C₁₃	—	2	1	no	—
57	C₂×D₄×C₁₃	—	2	2	no	—
58	C₂×D₄×C₁₃	—	4	4	no	—
59	C₂×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×SD₁₆	—	2	4	no	—
72	C₁₃×D₈	—	2	4	no	—
73	C₁₃×M₁₆	—	2	2	no	—
74	C₁₃×M₁₆	—	2	4	no	—
75	C₁₃×M₁₆	D₄	1	4	yes	complemented
76	C₂×C₈×C₁₃	—	2	4	no	—
77	C₂×C₈×C₁₃	C₂³	1	2	yes	—
78	C₂×C₈×C₁₃	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₄²×C₁₃	—	2	1	no	—
93	#3055	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂³×C₁₃	—	2	2	no	—
95	C₂³×C₁₃	—	2	2	no	—
96	C₂³×C₁₃	—	2	1	no	—
97	C₂³×C₁₃	—	2	2	no	—
98	C₂³×C₁₃	—	4	1	no	—
99	C₂³×C₁₃	—	4	2	no	—
100	C₂³×C₁₃	—	4	2	no	—
101	C₂³×C₁₃	—	4	2	no	—
102	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
105	Q₈×C₁₃	—	2	1	no	—
106	Q₈×C₁₃	—	2	1	no	—
107	D₄×C₁₃	—	2	1	no	—
108	D₄×C₁₃	—	2	2	no	—
109	D₄×C₁₃	—	2	2	no	—
110	D₄×C₁₃	—	2	1	no	—
111	D₄×C₁₃	—	4	2	no	—
112	D₄×C₁₃	—	4	4	no	—
113	D₄×C₁₃	—	4	2	no	—
114	D₄×C₁₃	—	4	2	no	—
115	D₄×C₁₃	—	4	4	no	—
116	D₄×C₁₃	—	4	2	no	—
117	C₂×C₄×C₁₃	—	2	2	no	—
118	C₂×C₄×C₁₃	—	2	2	no	—
119	C₂×C₄×C₁₃	—	2	2	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	1	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	1	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	4	2	no	—
129	C₂×C₄×C₁₃	—	4	2	no	—
130	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₁₃	#41	1	2	yes	—
135	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₈×C₁₃	—	2	2	no	—
137	C₈×C₁₃	C₂×D₄	1	4	yes	complemented
138	C₂×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂²×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#525	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#469	C₂×C₁₃	1	2	yes	complemented
143	#468	C₂×C₁₃	1	2	yes	complemented
144	#466	C₂×C₁₃	1	2	yes	complemented
145	#465	C₂×C₁₃	1	2	yes	complemented
146	#428	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#418	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#417	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂²×C₁₃	—	2	1	no	—
150	C₂²×C₁₃	—	2	1	no	—
151	C₂²×C₁₃	—	2	1	no	—
152	C₂²×C₁₃	—	2	1	no	—
153	C₂²×C₁₃	—	2	1	no	—
154	C₂²×C₁₃	—	2	1	no	—
155	C₂²×C₁₃	—	2	1	no	—
156	C₂²×C₁₃	—	4	4	no	—
157	C₂²×C₁₃	—	4	1	no	—
158	C₂²×C₁₃	—	4	2	no	—
159	C₂²×C₁₃	—	4	2	no	—
160	C₂²×C₁₃	—	4	1	no	—
161	C₂²×C₁₃	—	4	1	no	—
162	C₂²×C₁₃	—	4	2	no	—
163	C₂²×C₁₃	—	8	4	no	—
164	C₂²×C₁₃	#121	1	2	yes	—
165	C₂²×C₁₃	AGL(1,ℤ/8)	1	2	yes	complemented
166	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₄×C₁₃	—	2	1	no	—
168	C₄×C₁₃	—	2	1	no	—
169	C₄×C₁₃	—	4	1	no	—
170	C₄×C₁₃	—	4	2	no	—
171	C₄×C₁₃	—	4	1	no	—
172	C₄×C₁₃	—	4	1	no	—
173	C₄×C₁₃	#121	1	2	yes	—
174	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
177	C₂²×D₄	—	2	1	no	—
178	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
179	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
180	AGL(1,ℤ/8)	—	2	4	no	—
181	C₂×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
182	C₂×D₈	C₂²×C₁₃	1	2	yes	complemented
183	C₂×M₁₆	—	2	4	no	—
184	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×M₁₆	C₂²×C₁₃	1	2	yes	complemented
187	C₂²×C₈	C₂²×C₁₃	1	2	yes	complemented
188	#123	—	2	1	no	—
189	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
190	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
191	#121	—	2	1	no	—
192	#121	—	2	1	no	—
193	#121	C₂²×C₁₃	1	2	yes	—
194	#121	C₂²×C₁₃	1	2	yes	—
195	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
196	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
197	#120	—	2	1	no	—
198	C₄×D₄	—	2	1	no	—
199	C₄×D₄	—	2	1	no	—
200	#117	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	—	2	1	no	—
203	#107	C₂²×C₁₃	1	2	yes	complemented
204	#106	C₂²×C₁₃	1	2	yes	complemented
205	#103	C₂²×C₁₃	1	2	yes	complemented
206	#102	C₂²×C₁₃	1	2	yes	complemented
207	#102	C₂²×C₁₃	1	2	yes	complemented
208	#102	C₂²×C₁₃	1	2	yes	complemented
209	C₂×C₁₃	—	2	2	no	—
210	C₂×C₁₃	—	2	2	no	—
211	C₂×C₁₃	—	4	1	no	—
212	C₂×C₁₃	—	8	1	no	—
213	C₂×C₁₃	—	8	2	no	—
214	C₂×C₁₃	C₂×#121	1	1	yes	characteristic
215	C₂×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂×C₁₃	#575	1	1	yes	characteristic
217	C₂⁴	—	2	1	no	—
218	C₂⁴	D₄×C₁₃	1	1	yes	characteristic
219	#41	—	2	2	no	—
220	#41	—	2	2	no	—
221	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×D₄	—	2	1	no	—
223	C₂×D₄	—	2	1	no	—
224	C₂×D₄	—	2	1	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	—	2	1	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	4	4	no	—
231	C₂×D₄	C₂³×C₁₃	1	2	yes	—
232	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	1	no	—
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
238	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
243	SD₁₆	—	2	4	no	—
244	D₈	—	2	4	no	—
245	M₁₆	—	2	2	no	—
246	M₁₆	—	2	4	no	—
247	M₁₆	D₄×C₁₃	1	4	yes	complemented
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	C₂³×C₁₃	1	2	yes	—
250	C₂×C₈	C₂³×C₁₃	1	2	yes	—
251	C₄⋊C₄	—	2	1	no	—
252	C₄⋊C₄	—	2	1	no	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
255	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
257	C₂²⋊C₄	—	2	1	no	—
258	C₂²⋊C₄	—	2	1	no	—
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₂²⋊C₄	—	2	2	no	—
262	C₂²⋊C₄	—	2	1	no	—
263	C₂²⋊C₄	—	2	1	no	—
264	C₄²	—	2	1	no	—
265	C₁₃	#3055	1	1	yes	characteristic, direct product factor, Sylow
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	1	no	—
269	C₂³	—	2	2	no	—
270	C₂³	—	4	1	no	—
271	C₂³	—	4	2	no	—
272	C₂³	—	4	2	no	—
273	C₂³	—	4	2	no	—
274	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
277	Q₈	—	2	1	no	—
278	Q₈	—	2	1	no	—
279	D₄	—	2	1	no	—
280	D₄	—	2	2	no	—
281	D₄	—	2	2	no	—
282	D₄	—	2	1	no	—
283	D₄	—	4	4	no	—
284	D₄	—	4	2	no	—
285	D₄	—	4	2	no	—
286	D₄	—	4	4	no	—
287	D₄	—	4	2	no	—
288	D₄	—	4	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂×C₄	C₁₃×#41	1	2	yes	—
307	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₈	—	2	2	no	—
309	C₈	C₂×D₄×C₁₃	1	4	yes	complemented
310	C₂²	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	1	no	—
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	4	4	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	1	no	—
322	C₂²	—	4	1	no	—
323	C₂²	—	4	2	no	—
324	C₂²	—	8	4	no	—
325	C₂²	C₁₃×#121	1	2	yes	—
326	C₂²	C₁₃×AGL(1,ℤ/8)	1	2	yes	complemented
327	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	4	1	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	1	no	—
333	C₄	—	4	1	no	—
334	C₄	C₁₃×#121	1	2	yes	—
335	C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
337	C₂	—	2	2	no	—
338	C₂	—	2	2	no	—
339	C₂	—	4	1	no	—
340	C₂	—	8	2	no	—
341	C₂	—	8	1	no	—
342	C₂	C₂×C₁₃×#121	1	1	yes	characteristic
343	C₂	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂	C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₁₃×M₁₆	C₂	semidirect
3. C₁₃×#525	C₂	semidirect
4. C₂×C₁₃×#121	C₂	semidirect
5. C₁₃×#469	C₂	semidirect
6. C₁₃×#468	C₂	semidirect
7. C₁₃×#466	C₂	semidirect
8. C₁₃×#465	C₂	semidirect
9. C₁₃×#428	C₂	semidirect
10. C₁₃×#418	C₂	semidirect
11. C₁₃×#417	C₂	semidirect
17. C₂×C₁₃×SD₁₆	C₂²	semidirect
18. C₂×C₁₃×D₈	C₂²	semidirect
22. C₂×C₁₃×M₁₆	C₂²	semidirect
23. C₂²×C₈×C₁₃	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₁₃×#121	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
39. C₁₃×#107	C₂²	semidirect
40. C₁₃×#106	C₂²	semidirect
41. C₁₃×#103	C₂²	semidirect
42. C₁₃×#102	C₂²	semidirect
43. C₁₃×#102	C₂²	semidirect
44. C₁₃×#102	C₂²	semidirect
75. C₁₃×M₁₆	D₄	semidirect
93. #3055	C₁₃	direct (N × H)
137. C₈×C₁₃	C₂×D₄	semidirect
138. C₂×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
139. C₂²×M₁₆	C₂×C₁₃	semidirect
140. #525	C₂×C₁₃	semidirect
141. C₂×#121	C₂×C₁₃	semidirect
142. #469	C₂×C₁₃	semidirect
143. #468	C₂×C₁₃	semidirect
144. #466	C₂×C₁₃	semidirect
145. #465	C₂×C₁₃	semidirect
146. #428	C₂×C₁₃	semidirect
147. #418	C₂×C₁₃	semidirect
148. #417	C₂×C₁₃	semidirect
165. C₂²×C₁₃	AGL(1,ℤ/8)	semidirect
181. C₂×SD₁₆	C₂²×C₁₃	semidirect
182. C₂×D₈	C₂²×C₁₃	semidirect
186. C₂×M₁₆	C₂²×C₁₃	semidirect
187. C₂²×C₈	C₂²×C₁₃	semidirect
189. C₂²⋊Q₈	C₂²×C₁₃	semidirect
190. C₂²⋊Q₈	C₂²×C₁₃	semidirect
195. #121	C₂²×C₁₃	semidirect
196. #121	C₂²×C₁₃	semidirect
203. #107	C₂²×C₁₃	semidirect
204. #106	C₂²×C₁₃	semidirect
205. #103	C₂²×C₁₃	semidirect
206. #102	C₂²×C₁₃	semidirect
207. #102	C₂²×C₁₃	semidirect
208. #102	C₂²×C₁₃	semidirect
247. M₁₆	D₄×C₁₃	semidirect
265. C₁₃	#3055	direct (N × H)
309. C₈	C₂×D₄×C₁₃	semidirect
326. C₂²	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×AGL(1,ℤ/8)	2
C₂²×C₁₃×M₁₆	2
C₁₃×#525	2
C₂×C₁₃×#121	2
C₁₃×#469	2
C₁₃×#468	2
C₁₃×#466	2
C₁₃×#465	2
C₁₃×#428	2
C₁₃×#418	2
C₁₃×#417	2
#3055	13

Subgroups — C13×#3055 #13112113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3055 #13112113