Subgroups — C₁₃×#33787 #15720126

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2208	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#540	—	2	1	no	—
16	C₁₃×#536	—	2	1	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
21	C₁₃×#499	C₂²	1	1	yes	characteristic
22	C₁₃×#497	—	2	1	no	—
23	C₁₃×#497	—	2	1	no	—
24	C₁₃×#495	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	1	yes	characteristic
26	C₁₃×#494	C₂²	1	1	yes	characteristic
27	C₁₃×#494	C₂²	1	1	yes	characteristic
28	C₁₃×#493	C₂²	1	1	yes	characteristic
29	C₁₃×#490	—	2	1	no	—
30	C₁₃×#469	—	2	1	no	—
31	C₁₃×#466	C₂²	1	2	yes	—
32	C₁₃×#442	—	2	1	no	—
33	C₄×C₁₃×D₈	C₂²	1	2	yes	—
34	C₁₃×#405	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₁₃×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₁₃×#137	—	4	4	no	—
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×SD₁₆	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×SD₁₆	—	2	1	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×D₈	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×#127	—	2	1	no	—
65	C₁₃×#125	—	2	1	no	—
66	C₁₃×#124	—	2	1	no	—
67	C₁₃×#124	—	2	1	no	—
68	C₁₃×#123	—	4	2	no	—
69	C₁₃×#123	—	4	2	no	—
70	C₁₃×C₂²⋊Q₈	—	4	2	no	—
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	4	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₁₃×SD₃₂	—	4	2	no	—
76	C₁₃×SD₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	—	4	2	no	—
78	C₁₃×D₁₆	—	4	2	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₁₃×#107	C₂³	1	2	yes	—
82	C₁₃×#106	—	2	1	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#97	D₄	1	1	yes	characteristic
86	C₁₃×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33787	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	4	2	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₁₃×Q₁₆	—	2	2	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	4	2	no	—
111	C₁₃×Q₁₆	—	4	2	no	—
112	C₁₃×Q₁₆	—	4	2	no	—
113	C₁₃×SD₁₆	—	4	2	no	—
114	C₁₃×SD₁₆	—	4	2	no	—
115	C₁₃×SD₁₆	—	4	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	—	4	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	#3176	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2248	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2245	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2242	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2210	C₂×C₁₃	1	2	yes	complemented
147	#2208	C₂×C₁₃	1	2	yes	complemented
148	#2186	C₂×C₁₃	1	2	yes	complemented
149	#2185	C₂×C₁₃	1	2	yes	complemented
150	#2164	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	no	—
157	Q₈×C₁₃	—	4	1	no	—
158	Q₈×C₁₃	—	4	1	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	1	no	—
165	D₄×C₁₃	—	8	2	no	—
166	D₄×C₁₃	—	16	2	no	—
167	D₄×C₁₃	—	16	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	8	2	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	16	2	no	—
177	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₁₃	—	2	1	no	—
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
185	C₂×#137	—	2	1	no	—
186	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
188	#540	—	2	1	no	—
189	#536	—	2	1	no	—
190	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
191	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
192	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
193	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
194	#499	C₂²×C₁₃	1	1	yes	characteristic
195	#497	—	2	1	no	—
196	#497	—	2	1	no	—
197	#495	C₂²×C₁₃	1	1	yes	characteristic
198	#495	C₂²×C₁₃	1	1	yes	characteristic
199	#494	C₂²×C₁₃	1	1	yes	characteristic
200	#494	C₂²×C₁₃	1	1	yes	characteristic
201	#493	C₂²×C₁₃	1	1	yes	characteristic
202	#490	—	2	1	no	—
203	#469	—	2	1	no	—
204	#466	C₂²×C₁₃	1	2	yes	—
205	#442	—	2	1	no	—
206	C₄×D₈	C₂²×C₁₃	1	2	yes	—
207	#405	C₂²×C₁₃	1	1	yes	characteristic
208	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
209	#358	C₂²×C₁₃	1	2	yes	—
210	#358	C₂²×C₁₃	1	2	yes	—
211	#358	C₂²×C₁₃	1	2	yes	—
212	#357	C₂²×C₁₃	1	2	yes	—
213	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
214	#346	C₂²×C₁₃	1	1	yes	characteristic
215	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	1	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	—	8	1	no	—
229	C₄×C₁₃	—	8	1	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	#535	1	1	yes	characteristic
232	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×#41	—	2	1	no	—
234	C₂²×Q₈	—	2	1	no	—
235	#137	—	4	4	no	—
236	#135	—	4	2	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	4	2	no	—
241	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×D₈	C₂³×C₁₃	1	2	yes	—
250	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	#127	—	2	1	no	—
255	#125	—	2	1	no	—
256	#124	—	2	1	no	—
257	#124	—	2	1	no	—
258	#123	—	4	2	no	—
259	#123	—	4	2	no	—
260	C₂²⋊Q₈	—	4	2	no	—
261	#121	—	2	2	no	—
262	#121	—	4	2	no	—
263	C₄×D₄	—	2	2	no	—
264	#117	D₄×C₁₃	1	1	yes	characteristic
265	SD₃₂	—	4	2	no	—
266	SD₃₂	—	4	2	no	—
267	SD₃₂	—	4	2	no	—
268	D₁₆	—	4	2	no	—
269	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
270	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
271	#107	C₂³×C₁₃	1	2	yes	—
272	#106	—	2	1	no	—
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#97	D₄×C₁₃	1	1	yes	characteristic
276	#97	D₄×C₁₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₁₃	—	4	1	no	—
280	C₂×C₁₃	—	16	2	no	—
281	C₂×C₁₃	—	16	1	no	—
282	C₂×C₁₃	#3205	1	1	yes	characteristic
283	C₂×C₁₃	#3416	1	2	yes	—
284	#41	—	4	2	no	—
285	#41	—	4	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
301	Q₁₆	—	2	2	no	—
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	4	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	4	2	no	—
314	M₁₆	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
330	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₁₆	—	2	2	no	—
333	C₁₆	—	2	2	no	—
334	C₁₃	#33787	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	4	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	8	2	no	—
350	D₄	—	16	2	no	—
351	D₄	—	16	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
363	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
368	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	C₁₃×#535	1	1	yes	characteristic
385	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	16	2	no	—
388	C₂	—	16	1	no	—
389	C₂	C₁₃×#3205	1	1	yes	characteristic
390	C₂	C₁₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3176	C₂	semidirect
2. C₁₃×#3156	C₂	semidirect
3. C₁₃×#2250	C₂	semidirect
4. C₁₃×#2248	C₂	semidirect
5. C₁₃×#2245	C₂	semidirect
6. C₁₃×#2242	C₂	semidirect
7. C₁₃×#2210	C₂	semidirect
8. C₁₃×#2208	C₂	semidirect
9. C₁₃×#2186	C₂	semidirect
10. C₁₃×#2185	C₂	semidirect
11. C₁₃×#2164	C₂	semidirect
89. #33787	C₁₃	direct (N × H)
140. #3176	C₂×C₁₃	semidirect
141. #3156	C₂×C₁₃	semidirect
142. #2250	C₂×C₁₃	semidirect
143. #2248	C₂×C₁₃	semidirect
144. #2245	C₂×C₁₃	semidirect
145. #2242	C₂×C₁₃	semidirect
146. #2210	C₂×C₁₃	semidirect
147. #2208	C₂×C₁₃	semidirect
148. #2186	C₂×C₁₃	semidirect
149. #2185	C₂×C₁₃	semidirect
150. #2164	C₂×C₁₃	semidirect
334. C₁₃	#33787	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×#3176	2
C₁₃×#3156	2
C₁₃×#2250	2
C₁₃×#2248	2
C₁₃×#2245	2
C₁₃×#2242	2
C₁₃×#2210	2
C₁₃×#2208	2
C₁₃×#2186	2
C₁₃×#2185	2
C₁₃×#2164	2
#33787	13

Subgroups — C13×#33787 #15720126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33787 #15720126