Subgroups — C₁₃×#33690 #15720029

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3183	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2956	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2239	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2231	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2212	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2191	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2190	C₂	1	1	yes	maximal, characteristic
9	C₁₃×AGL(1,ℤ/16)	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2180	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#575	C₂²	1	1	yes	characteristic
13	C₁₃×#568	—	2	1	no	—
14	C₁₃×#529	—	2	1	no	—
15	C₁₃×#510	C₂²	1	2	yes	—
16	C₁₃×#509	C₂²	1	2	yes	—
17	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#488	—	2	1	no	—
20	C₁₃×#470	C₂²	1	1	yes	characteristic
21	C₁₃×#469	C₂²	1	1	yes	characteristic
22	C₁₃×#468	—	2	1	no	—
23	C₁₃×#444	—	2	1	no	—
24	C₁₃×#444	C₂²	1	2	yes	—
25	C₁₃×#443	—	2	1	no	—
26	C₁₃×#443	C₂²	1	2	yes	—
27	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#440	—	2	1	no	—
30	C₁₃×#430	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#104	—	2	1	no	—
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#365	C₂²	1	2	yes	complemented
34	C₁₃×#365	C₂²	1	2	yes	complemented
35	C₁₃×#364	C₂²	1	2	yes	complemented
36	C₁₃×#362	C₂²	1	2	yes	complemented
37	C₁₃×#361	C₂²	1	2	yes	complemented
38	C₁₃×#360	C₂²	1	2	yes	—
39	C₁₃×#360	C₂²	1	2	yes	—
40	C₁₃×#349	C₂²	1	1	yes	characteristic
41	C₁₃×#349	C₂²	1	1	yes	characteristic
42	C₁₃×#347	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₁₃×#137	—	2	2	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₃×#135	—	2	1	no	—
47	C₁₃×#135	C₂³	1	2	yes	—
48	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
51	C₁₃×#131	—	2	2	no	—
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	—	4	2	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	4	2	no	—
56	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₁₃×#126	—	4	1	no	—
59	C₁₃×#125	—	2	1	no	—
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#123	—	4	1	no	—
62	C₁₃×C₂²⋊Q₈	—	2	1	no	—
63	C₁₃×#121	—	2	1	no	—
64	C₄×Q₈×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	1	no	—
66	C₄×D₄×C₁₃	—	4	1	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₁₃×Q₃₂	—	2	2	no	—
70	C₁₃×SD₃₂	—	2	2	no	—
71	C₁₃×SD₃₂	—	2	2	no	—
72	C₁₃×D₁₆	—	2	2	no	—
73	C₁₃×M₃₂	C₂³	1	2	yes	—
74	C₁₃×M₃₂	C₂³	1	2	yes	—
75	C₁₃×#108	—	2	1	no	—
76	C₁₃×#108	C₂³	1	2	yes	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#106	C₂³	1	1	yes	characteristic
79	C₁₃×#106	C₂³	1	1	yes	characteristic
80	C₁₃×#104	—	2	2	no	—
81	C₁₃×#104	—	2	2	no	—
82	C₁₃×#103	—	2	1	no	—
83	C₁₃×#103	—	2	1	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₁₃×#102	—	2	1	no	—
86	C₁₃×#97	D₄	1	1	yes	characteristic
87	C₁₃×#97	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	#33690	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₁₃×#41	—	2	2	no	—
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	4	1	no	—
94	C₁₃×#41	—	4	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	#41	1	2	yes	—
108	C₁₃×SD₁₆	—	2	2	no	—
109	C₁₃×SD₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×D₈	—	2	1	no	—
112	C₁₃×D₈	—	2	2	no	—
113	C₁₃×D₈	#41	1	2	yes	—
114	C₁₃×M₁₆	—	2	2	no	—
115	C₁₃×M₁₆	—	2	2	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	—	4	2	no	—
118	C₁₃×M₁₆	—	4	1	no	—
119	C₁₃×M₁₆	—	4	2	no	—
120	C₂×C₈×C₁₃	—	4	2	no	—
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	2	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	1	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×C₁₆	—	2	2	no	—
143	C₁₃×C₁₆	—	2	2	no	—
144	#3183	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2956	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2239	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2238	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2231	C₂×C₁₃	1	2	yes	complemented
149	#2212	C₂×C₁₃	1	2	yes	complemented
150	#2191	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2190	C₂×C₁₃	1	1	yes	characteristic
152	AGL(1,ℤ/16)	C₂×C₁₃	1	2	yes	complemented
153	#2180	C₂×C₁₃	1	2	yes	complemented
154	#2165	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	Q₈×C₁₃	—	2	2	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	4	1	no	—
161	Q₈×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	8	1	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
187	C₈×C₁₃	C₂×#41	1	2	yes	—
188	#575	C₂²×C₁₃	1	1	yes	characteristic
189	#568	—	2	1	no	—
190	#529	—	2	1	no	—
191	#510	C₂²×C₁₃	1	2	yes	—
192	#509	C₂²×C₁₃	1	2	yes	—
193	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
194	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	#488	—	2	1	no	—
196	#470	C₂²×C₁₃	1	1	yes	characteristic
197	#469	C₂²×C₁₃	1	1	yes	characteristic
198	#468	—	2	1	no	—
199	#444	—	2	1	no	—
200	#444	C₂²×C₁₃	1	2	yes	—
201	#443	—	2	1	no	—
202	#443	C₂²×C₁₃	1	2	yes	—
203	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
204	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	#440	—	2	1	no	—
206	#430	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×#104	—	2	1	no	—
208	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
209	#365	C₂²×C₁₃	1	2	yes	complemented
210	#365	C₂²×C₁₃	1	2	yes	complemented
211	#364	C₂²×C₁₃	1	2	yes	complemented
212	#362	C₂²×C₁₃	1	2	yes	complemented
213	#361	C₂²×C₁₃	1	2	yes	complemented
214	#360	C₂²×C₁₃	1	2	yes	—
215	#360	C₂²×C₁₃	1	2	yes	—
216	#349	C₂²×C₁₃	1	1	yes	characteristic
217	#349	C₂²×C₁₃	1	1	yes	characteristic
218	#347	C₂²×C₁₃	1	2	yes	complemented
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	4	1	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	—	8	1	no	—
225	C₂²×C₁₃	—	16	1	no	—
226	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	8	1	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	1	no	—
234	C₄×C₁₃	#525	1	1	yes	characteristic
235	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂×#41	—	2	1	no	—
237	#137	—	2	2	no	—
238	AGL(1,ℤ/8)	—	2	2	no	—
239	#135	—	2	1	no	—
240	#135	C₂³×C₁₃	1	2	yes	—
241	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
244	#131	—	2	2	no	—
245	#131	—	2	2	no	—
246	#131	—	4	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
250	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
251	#126	—	4	1	no	—
252	#125	—	2	1	no	—
253	#124	—	2	1	no	—
254	#123	—	4	1	no	—
255	C₂²⋊Q₈	—	2	1	no	—
256	#121	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	4	1	no	—
260	#117	—	4	1	no	—
261	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
262	Q₃₂	—	2	2	no	—
263	SD₃₂	—	2	2	no	—
264	SD₃₂	—	2	2	no	—
265	D₁₆	—	2	2	no	—
266	M₃₂	C₂³×C₁₃	1	2	yes	—
267	M₃₂	C₂³×C₁₃	1	2	yes	—
268	#108	—	2	1	no	—
269	#108	C₂³×C₁₃	1	2	yes	—
270	#107	—	2	1	no	—
271	#106	C₂³×C₁₃	1	1	yes	characteristic
272	#106	C₂³×C₁₃	1	1	yes	characteristic
273	#104	—	2	2	no	—
274	#104	—	2	2	no	—
275	#103	—	2	1	no	—
276	#103	—	2	1	no	—
277	#102	—	2	1	no	—
278	#102	—	2	1	no	—
279	#97	D₄×C₁₃	1	1	yes	characteristic
280	#97	C₂³×C₁₃	1	1	yes	characteristic
281	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₁₃	—	2	1	no	—
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	—	8	2	no	—
286	C₂×C₁₃	—	16	1	no	—
287	C₂×C₁₃	#3109	1	1	yes	characteristic
288	#41	—	2	2	no	—
289	#41	—	2	2	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	C₁₃×#41	1	2	yes	—
305	SD₁₆	—	2	2	no	—
306	SD₁₆	—	2	2	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	2	1	no	—
309	D₈	—	2	2	no	—
310	D₈	C₁₃×#41	1	2	yes	—
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₁₆	—	2	2	no	—
340	C₁₆	—	2	2	no	—
341	C₁₃	#33690	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	8	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
374	C₈	C₂×C₁₃×#41	1	2	yes	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	16	1	no	—
382	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	8	1	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₁₃×#525	1	1	yes	characteristic
391	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	4	1	no	—
394	C₂	—	8	2	no	—
395	C₂	—	16	1	no	—
396	C₂	C₁₃×#3109	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#3109
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#2190	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3183	C₂	semidirect
2. C₁₃×#2956	C₂	semidirect
3. C₁₃×#2239	C₂	semidirect
4. C₁₃×#2238	C₂	semidirect
5. C₁₃×#2231	C₂	semidirect
6. C₁₃×#2212	C₂	semidirect
7. C₁₃×#2191	C₂	semidirect
9. C₁₃×AGL(1,ℤ/16)	C₂	semidirect
10. C₁₃×#2180	C₂	semidirect
11. C₁₃×#2165	C₂	semidirect
17. C₁₃×#499	C₂²	semidirect
18. C₁₃×#495	C₂²	semidirect
27. C₁₃×#442	C₂²	semidirect
28. C₁₃×#441	C₂²	semidirect
33. C₁₃×#365	C₂²	semidirect
34. C₁₃×#365	C₂²	semidirect
35. C₁₃×#364	C₂²	semidirect
36. C₁₃×#362	C₂²	semidirect
37. C₁₃×#361	C₂²	semidirect
42. C₁₃×#347	C₂²	semidirect
90. #33690	C₁₃	direct (N × H)
144. #3183	C₂×C₁₃	semidirect
145. #2956	C₂×C₁₃	semidirect
146. #2239	C₂×C₁₃	semidirect
147. #2238	C₂×C₁₃	semidirect
148. #2231	C₂×C₁₃	semidirect
149. #2212	C₂×C₁₃	semidirect
150. #2191	C₂×C₁₃	semidirect
152. AGL(1,ℤ/16)	C₂×C₁₃	semidirect
153. #2180	C₂×C₁₃	semidirect
154. #2165	C₂×C₁₃	semidirect
193. #499	C₂²×C₁₃	semidirect
194. #495	C₂²×C₁₃	semidirect
203. #442	C₂²×C₁₃	semidirect
204. #441	C₂²×C₁₃	semidirect
209. #365	C₂²×C₁₃	semidirect
210. #365	C₂²×C₁₃	semidirect
211. #364	C₂²×C₁₃	semidirect
212. #362	C₂²×C₁₃	semidirect
213. #361	C₂²×C₁₃	semidirect
218. #347	C₂²×C₁₃	semidirect
341. C₁₃	#33690	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×#3183	2
C₁₃×#2956	2
C₁₃×#2239	2
C₁₃×#2238	2
C₁₃×#2231	2
C₁₃×#2212	2
C₁₃×#2191	2
C₁₃×#2190	2
C₁₃×AGL(1,ℤ/16)	2
C₁₃×#2180	2
C₁₃×#2165	2
#33690	13

Subgroups — C13×#33690 #15720029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33690 #15720029