Subgroups — C₁₃×#32817 #15719156

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2640	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2012	C₂	1	2	yes	maximal
9	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#124	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₁₃×#397	—	2	2	no	—
22	C₁₃×#397	—	2	2	no	—
23	C₁₃×#393	—	2	2	no	—
24	C₁₃×#393	—	2	2	no	—
25	C₁₃×#391	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#376	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	1	yes	characteristic
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	—	2	2	no	—
36	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×Q₁₆	—	4	2	no	—
39	C₂×C₁₃×Q₁₆	—	4	1	no	—
40	C₂×C₁₃×SD₁₆	—	4	2	no	—
41	C₂×C₁₃×SD₁₆	—	4	2	no	—
42	C₂×C₁₃×SD₁₆	—	4	2	no	—
43	C₂×C₁₃×D₈	—	4	2	no	—
44	C₂×C₁₃×D₈	—	4	1	no	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	4	2	no	—
49	C₁₃×C₄⋊Q₈	—	4	2	no	—
50	C₁₃×#124	—	4	2	no	—
51	C₁₃×#124	—	4	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₁₃×C₄⋊C₈	—	4	1	no	—
64	C₁₃×C₄⋊C₈	—	4	1	no	—
65	C₁₃×#103	—	4	2	no	—
66	C₁₃×#103	—	4	2	no	—
67	C₁₃×#102	—	4	2	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	D₄	1	1	yes	characteristic
74	C₁₃×#95	D₄	1	2	yes	—
75	C₁₃×#95	D₄	1	1	yes	characteristic
76	#32817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	4	4	no	—
85	C₂×Q₈×C₁₃	—	8	2	no	—
86	C₂×Q₈×C₁₃	—	8	2	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×Q₁₆	—	4	4	no	—
102	C₁₃×SD₁₆	—	4	8	no	—
103	C₁₃×D₈	—	4	4	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	4	4	no	—
116	C₁₃×C₂²⋊C₄	—	4	4	no	—
117	C₁₃×C₂²⋊C₄	—	4	4	no	—
118	C₁₃×C₂²⋊C₄	—	8	2	no	—
119	C₁₃×C₂²⋊C₄	—	8	2	no	—
120	C₁₃×C₂²⋊C₄	—	8	2	no	—
121	C₁₃×C₂²⋊C₄	—	8	2	no	—
122	C₄²×C₁₃	—	2	1	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	1	no	—
126	#2640	C₂×C₁₃	1	2	yes	complemented
127	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#2055	C₂×C₁₃	1	2	yes	complemented
129	#2054	C₂×C₁₃	1	1	yes	characteristic
130	#2024	C₂×C₁₃	1	2	yes	complemented
131	#2023	C₂×C₁₃	1	2	yes	complemented
132	#2015	C₂×C₁₃	1	2	yes	complemented
133	#2012	C₂×C₁₃	1	2	yes	—
134	#1832	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	4	2	no	—
145	Q₈×C₁₃	—	4	2	no	—
146	Q₈×C₁₃	—	4	2	no	—
147	Q₈×C₁₃	—	8	8	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
175	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
176	C₈×C₁₃	—	4	1	no	—
177	C₈×C₁₃	—	4	2	no	—
178	C₈×C₁₃	—	4	1	no	—
179	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
181	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
183	C₂×#124	C₂²×C₁₃	1	2	yes	—
184	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×#103	C₂²×C₁₃	1	2	yes	—
187	C₂×#103	C₂²×C₁₃	1	2	yes	—
188	C₂×#102	C₂²×C₁₃	1	2	yes	—
189	C₂×#102	C₂²×C₁₃	1	2	yes	—
190	#397	—	2	2	no	—
191	#397	—	2	2	no	—
192	#393	—	2	2	no	—
193	#393	—	2	2	no	—
194	#391	C₂²×C₁₃	1	2	yes	—
195	#391	C₂²×C₁₃	1	2	yes	—
196	#390	C₂²×C₁₃	1	2	yes	—
197	#390	C₂²×C₁₃	1	2	yes	—
198	#376	C₂²×C₁₃	1	1	yes	characteristic
199	#340	C₂²×C₁₃	1	1	yes	characteristic
200	#340	C₂²×C₁₃	1	2	yes	—
201	#340	C₂²×C₁₃	1	1	yes	characteristic
202	#336	C₂²×C₁₃	1	2	yes	—
203	#336	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	#535	1	2	yes	—
212	C₂²×C₁₃	#537	1	1	yes	characteristic
213	C₂²×C₁₃	#576	1	1	yes	characteristic
214	C₂²×C₁₃	#577	1	2	yes	—
215	C₂²×C₁₃	#578	1	1	yes	characteristic
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	2	no	—
218	C₄×C₁₃	—	4	1	no	—
219	C₄×C₁₃	—	4	1	no	—
220	C₄×C₁₃	—	8	2	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	—	8	2	no	—
223	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
224	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
225	C₄×C₁₃	#562	1	2	yes	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
228	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
229	C₂×Q₁₆	—	4	2	no	—
230	C₂×Q₁₆	—	4	1	no	—
231	C₂×SD₁₆	—	4	2	no	—
232	C₂×SD₁₆	—	4	2	no	—
233	C₂×SD₁₆	—	4	2	no	—
234	C₂×D₈	—	4	2	no	—
235	C₂×D₈	—	4	1	no	—
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₄⋊Q₈	—	4	2	no	—
240	C₄⋊Q₈	—	4	2	no	—
241	#124	—	4	2	no	—
242	#124	—	4	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
253	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
254	C₄⋊C₈	—	4	1	no	—
255	C₄⋊C₈	—	4	1	no	—
256	#103	—	4	2	no	—
257	#103	—	4	2	no	—
258	#102	—	4	2	no	—
259	#102	—	4	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	D₄×C₁₃	1	1	yes	characteristic
265	#95	D₄×C₁₃	1	2	yes	—
266	#95	D₄×C₁₃	1	1	yes	characteristic
267	C₂×C₁₃	—	16	2	no	—
268	C₂×C₁₃	#2819	1	1	yes	characteristic
269	C₂×C₁₃	#3224	1	2	yes	—
270	C₂×C₁₃	#3225	1	2	yes	—
271	C₂×C₁₃	#3262	1	1	yes	characteristic
272	C₂×C₁₃	#3263	1	1	yes	characteristic
273	C₂⁴	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	8	2	no	—
282	C₂×Q₈	—	8	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
297	Q₁₆	—	4	4	no	—
298	SD₁₆	—	4	8	no	—
299	D₈	—	4	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	8	2	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	1	no	—
322	C₁₃	#32817	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	8	8	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
363	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	C₁₃×#535	1	2	yes	—
375	C₂²	C₁₃×#537	1	1	yes	characteristic
376	C₂²	C₁₃×#576	1	1	yes	characteristic
377	C₂²	C₁₃×#577	1	2	yes	—
378	C₂²	C₁₃×#578	1	1	yes	characteristic
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
387	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
388	C₄	C₁₃×#562	1	2	yes	—
389	C₂	—	16	2	no	—
390	C₂	C₁₃×#2819	1	1	yes	characteristic
391	C₂	C₁₃×#3224	1	2	yes	—
392	C₂	C₁₃×#3225	1	2	yes	—
393	C₂	C₁₃×#3262	1	1	yes	characteristic
394	C₂	C₁₃×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2640	C₂	semidirect
2. C₁₃×#2056	C₂	semidirect
3. C₁₃×#2055	C₂	semidirect
5. C₁₃×#2024	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#2015	C₂	semidirect
9. C₁₃×#1832	C₂	semidirect
76. #32817	C₁₃	direct (N × H)
126. #2640	C₂×C₁₃	semidirect
127. #2056	C₂×C₁₃	semidirect
128. #2055	C₂×C₁₃	semidirect
130. #2024	C₂×C₁₃	semidirect
131. #2023	C₂×C₁₃	semidirect
132. #2015	C₂×C₁₃	semidirect
134. #1832	C₂×C₁₃	semidirect
322. C₁₃	#32817	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2640	2
C₁₃×#2056	2
C₁₃×#2055	2
C₁₃×#2054	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#2015	2
C₁₃×#2012	2
C₁₃×#1832	2
#32817	13

Subgroups — C13×#32817 #15719156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32817 #15719156