Subgroups — C₁₃×#3345 #13112403

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#41	—	2	1	no	—
17	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×#126	—	2	1	no	—
22	C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₁₃×#123	—	2	1	no	—
24	C₁₃×#123	—	2	1	no	—
25	C₁₃×#123	—	2	1	no	—
26	C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₁₃×#121	—	2	1	no	—
28	C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₃	—	2	1	no	—
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#107	C₂²	1	1	yes	characteristic
41	C₁₃×#107	C₂²	1	1	yes	characteristic
42	C₁₃×#107	C₂²	1	1	yes	characteristic
43	C₁₃×#106	C₂²	1	1	yes	characteristic
44	C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₁₃×#106	C₂²	1	1	yes	characteristic
48	C₁₃×#106	C₂²	1	1	yes	characteristic
49	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₁₃×#102	C₂²	1	1	yes	characteristic
56	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×#97	C₂²	1	1	yes	characteristic
59	C₁₃×#41	—	4	4	no	—
60	C₂×Q₈×C₁₃	—	2	1	no	—
61	C₂×D₄×C₁₃	—	2	1	no	—
62	C₂×D₄×C₁₃	—	2	1	no	—
63	C₂×D₄×C₁₃	—	2	1	no	—
64	C₂×D₄×C₁₃	—	2	1	no	—
65	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	1	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×D₈	—	2	2	no	—
76	C₁₃×M₁₆	—	2	2	no	—
77	C₂×C₈×C₁₃	—	2	2	no	—
78	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₄²×C₁₃	—	2	1	no	—
105	C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	#3345	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₁₃	—	2	1	no	—
108	C₂³×C₁₃	—	2	1	no	—
109	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
111	Q₈×C₁₃	—	4	2	no	—
112	D₄×C₁₃	—	2	2	no	—
113	D₄×C₁₃	—	2	1	no	—
114	D₄×C₁₃	—	2	1	no	—
115	D₄×C₁₃	—	2	1	no	—
116	D₄×C₁₃	—	2	1	no	—
117	D₄×C₁₃	—	4	2	no	—
118	D₄×C₁₃	—	4	2	no	—
119	D₄×C₁₃	—	4	2	no	—
120	D₄×C₁₃	—	8	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	1	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	4	2	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	8	1	no	—
135	C₂×C₄×C₁₃	—	8	1	no	—
136	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₈×C₁₃	—	2	1	no	—
142	C₈×C₁₃	—	2	1	no	—
143	C₈×C₁₃	—	2	1	no	—
144	C₈×C₁₃	#41	1	2	yes	complemented
145	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#501	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#482	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#481	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#481	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#480	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#478	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#476	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#469	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#466	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#442	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#435	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#428	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂²×C₁₃	—	2	1	no	—
161	C₂²×C₁₃	—	2	1	no	—
162	C₂²×C₁₃	—	2	1	no	—
163	C₂²×C₁₃	—	2	1	no	—
164	C₂²×C₁₃	—	2	1	no	—
165	C₂²×C₁₃	—	4	1	no	—
166	C₂²×C₁₃	—	4	1	no	—
167	C₂²×C₁₃	—	4	1	no	—
168	C₂²×C₁₃	—	4	1	no	—
169	C₂²×C₁₃	—	4	1	no	—
170	C₂²×C₁₃	—	4	1	no	—
171	C₂²×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
172	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₄×C₁₃	—	2	1	no	—
174	C₄×C₁₃	—	2	1	no	—
175	C₄×C₁₃	—	2	1	no	—
176	C₄×C₁₃	—	2	1	no	—
177	C₄×C₁₃	—	4	1	no	—
178	C₄×C₁₃	—	4	1	no	—
179	C₄×C₁₃	—	4	1	no	—
180	C₄×C₁₃	—	4	1	no	—
181	C₄×C₁₃	—	4	1	no	—
182	C₄×C₁₃	—	4	1	no	—
183	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×#41	—	2	1	no	—
186	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	#126	—	2	1	no	—
191	#125	C₂²×C₁₃	1	1	yes	characteristic
192	#123	—	2	1	no	—
193	#123	—	2	1	no	—
194	#123	—	2	1	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	#121	—	2	1	no	—
197	#121	C₂²×C₁₃	1	1	yes	characteristic
198	#121	C₂²×C₁₃	1	1	yes	characteristic
199	#121	C₂²×C₁₃	1	1	yes	characteristic
200	#121	C₂²×C₁₃	1	1	yes	characteristic
201	C₄×D₄	—	2	1	no	—
202	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
205	#117	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
209	#107	C₂²×C₁₃	1	1	yes	characteristic
210	#107	C₂²×C₁₃	1	1	yes	characteristic
211	#107	C₂²×C₁₃	1	1	yes	characteristic
212	#106	C₂²×C₁₃	1	1	yes	characteristic
213	#106	C₂²×C₁₃	1	1	yes	characteristic
214	#106	C₂²×C₁₃	1	1	yes	characteristic
215	#106	C₂²×C₁₃	1	1	yes	characteristic
216	#106	C₂²×C₁₃	1	1	yes	characteristic
217	#106	C₂²×C₁₃	1	1	yes	characteristic
218	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#102	C₂²×C₁₃	1	1	yes	characteristic
220	#102	C₂²×C₁₃	1	1	yes	characteristic
221	#102	C₂²×C₁₃	1	1	yes	characteristic
222	#102	C₂²×C₁₃	1	1	yes	characteristic
223	#102	C₂²×C₁₃	1	1	yes	characteristic
224	#102	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
227	#97	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₁₃	—	2	2	no	—
229	C₂×C₁₃	—	4	1	no	—
230	C₂×C₁₃	—	8	1	no	—
231	C₂×C₁₃	—	8	1	no	—
232	C₂×C₁₃	#547	1	1	yes	characteristic
233	C₂×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×C₁₃	#577	1	1	yes	characteristic
235	#41	—	4	4	no	—
236	C₂×Q₈	—	2	1	no	—
237	C₂×D₄	—	2	1	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	2	1	no	—
240	C₂×D₄	—	2	1	no	—
241	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
242	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
251	D₈	—	2	2	no	—
252	M₁₆	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊C₄	—	2	1	no	—
259	C₄⋊C₄	—	2	1	no	—
260	C₄⋊C₄	—	2	1	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	2	1	no	—
263	C₄⋊C₄	—	2	1	no	—
264	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
265	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²⋊C₄	—	2	1	no	—
272	C₂²⋊C₄	—	2	1	no	—
273	C₂²⋊C₄	—	2	1	no	—
274	C₂²⋊C₄	—	2	1	no	—
275	C₂²⋊C₄	—	2	1	no	—
276	C₂²⋊C₄	—	2	1	no	—
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
280	C₄²	—	2	1	no	—
281	C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	C₁₃	#3345	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	2	1	no	—
284	C₂³	—	2	1	no	—
285	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
287	Q₈	—	4	2	no	—
288	D₄	—	2	2	no	—
289	D₄	—	2	1	no	—
290	D₄	—	2	1	no	—
291	D₄	—	2	1	no	—
292	D₄	—	2	1	no	—
293	D₄	—	4	2	no	—
294	D₄	—	4	2	no	—
295	D₄	—	4	2	no	—
296	D₄	—	8	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	8	1	no	—
311	C₂×C₄	—	8	1	no	—
312	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
317	C₈	—	2	1	no	—
318	C₈	—	2	1	no	—
319	C₈	—	2	1	no	—
320	C₈	C₁₃×#41	1	2	yes	complemented
321	C₂²	—	2	1	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	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	1	no	—
332	C₂²	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
333	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
345	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
346	C₂	—	2	2	no	—
347	C₂	—	4	1	no	—
348	C₂	—	8	1	no	—
349	C₂	—	8	1	no	—
350	C₂	C₁₃×#547	1	1	yes	characteristic
351	C₂	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂	C₁₃×#577	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 ◁ C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. C₁₃×#547	C₂	semidirect
3. C₁₃×#501	C₂	semidirect
4. C₁₃×#482	C₂	semidirect
5. C₁₃×#481	C₂	semidirect
6. C₁₃×#481	C₂	semidirect
7. C₁₃×#480	C₂	semidirect
8. C₁₃×#478	C₂	semidirect
9. C₁₃×#476	C₂	semidirect
10. C₁₃×#469	C₂	semidirect
11. C₁₃×#466	C₂	semidirect
12. C₁₃×#442	C₂	semidirect
13. C₁₃×#435	C₂	semidirect
14. C₁₃×#428	C₂	semidirect
15. C₂×C₁₃×#106	C₂	semidirect
106. #3345	C₁₃	direct (N × H)
144. C₈×C₁₃	#41	semidirect
145. #553	C₂×C₁₃	semidirect
146. #547	C₂×C₁₃	semidirect
147. #501	C₂×C₁₃	semidirect
148. #482	C₂×C₁₃	semidirect
149. #481	C₂×C₁₃	semidirect
150. #481	C₂×C₁₃	semidirect
151. #480	C₂×C₁₃	semidirect
152. #478	C₂×C₁₃	semidirect
153. #476	C₂×C₁₃	semidirect
154. #469	C₂×C₁₃	semidirect
155. #466	C₂×C₁₃	semidirect
156. #442	C₂×C₁₃	semidirect
157. #435	C₂×C₁₃	semidirect
158. #428	C₂×C₁₃	semidirect
159. C₂×#106	C₂×C₁₃	semidirect
282. C₁₃	#3345	direct (N × H)
320. C₈	C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
C₁₃×#547	2
C₁₃×#501	2
C₁₃×#482	2
C₁₃×#481	2
C₁₃×#480	2
C₁₃×#478	2
C₁₃×#476	2
C₁₃×#469	2
C₁₃×#466	2
C₁₃×#442	2
C₁₃×#435	2
C₁₃×#428	2
C₂×C₁₃×#106	2
#3345	13

Subgroups — C13×#3345 #13112403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3345 #13112403