Subgroups — C₁₃×#22669 #15709008

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#430	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1950	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1855	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1811	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×M₁₆	C₂²	1	4	yes	—
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#436	—	2	2	no	—
13	C₁₃×#436	C₄	1	4	yes	—
14	C₁₃×#436	C₄	1	4	yes	—
15	C₁₃×#435	—	2	4	no	—
16	C₈×D₄×C₁₃	—	2	2	no	—
17	C₁₃×#430	—	2	8	no	—
18	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#108	C₂²	1	2	yes	—
20	C₂×C₁₃×#108	C₂²	1	4	yes	—
21	C₂×C₁₃×#108	C₂²	1	2	yes	—
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₃×#407	C₂²	1	4	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#341	C₂²	1	2	yes	—
30	C₁₃×#341	C₂²	1	4	yes	—
31	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂×C₁₃×M₁₆	—	2	4	no	—
34	C₂×C₁₃×M₁₆	—	2	4	no	—
35	C₂×C₁₃×M₁₆	—	2	4	no	—
36	C₂×C₁₃×M₁₆	—	2	8	no	—
37	C₂×C₁₃×M₁₆	—	4	4	no	—
38	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
39	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
40	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
41	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₃	D₄	1	2	yes	—
49	C₄×D₄×C₁₃	D₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#108	—	2	8	no	—
54	C₁₃×#108	—	2	4	no	—
55	C₁₃×#108	—	2	2	no	—
56	C₁₃×#108	—	4	2	no	—
57	C₁₃×#108	D₄	1	4	yes	complemented
58	C₁₃×C₄⋊C₈	—	2	2	no	—
59	C₁₃×C₄⋊C₈	—	2	2	no	—
60	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₁₃×C₂²⋊C₈	—	2	4	no	—
63	C₁₃×C₂²⋊C₈	—	2	4	no	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₁₃×#97	—	2	2	no	—
66	C₄×C₈×C₁₃	—	2	2	no	—
67	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
69	#22669	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
71	C₂×D₄×C₁₃	—	4	2	no	—
72	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
73	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
84	C₁₃×M₁₆	—	2	2	no	—
85	C₁₃×M₁₆	—	2	16	no	—
86	C₁₃×M₁₆	—	2	4	no	—
87	C₁₃×M₁₆	—	2	2	no	—
88	C₁₃×M₁₆	—	2	4	no	—
89	C₁₃×M₁₆	—	2	2	no	—
90	C₁₃×M₁₆	—	4	8	no	—
91	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	1	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	4	8	no	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₁₃	#41	1	2	yes	—
105	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
106	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
107	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
108	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
113	D₄×M₁₆	C₂×C₁₃	1	2	yes	—
114	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
115	C₂×#430	C₂×C₁₃	1	2	yes	complemented
116	#1950	C₂×C₁₃	1	2	yes	complemented
117	#1855	C₂×C₁₃	1	4	yes	complemented
118	#1848	C₂×C₁₃	1	1	yes	characteristic, complemented
119	#1811	C₂×C₁₃	1	2	yes	complemented
120	C₄×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂³×C₁₃	—	2	2	no	—
122	C₂³×C₁₃	—	2	2	no	—
123	C₂³×C₁₃	—	4	2	no	—
124	C₂³×C₁₃	—	4	2	no	—
125	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
126	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
127	D₄×C₁₃	—	2	4	no	—
128	D₄×C₁₃	—	4	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	4	1	no	—
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
148	C₈×C₁₃	—	2	4	no	—
149	C₈×C₁₃	—	2	2	no	—
150	C₈×C₁₃	—	2	4	no	—
151	C₈×C₁₃	—	4	4	no	—
152	C₈×C₁₃	—	4	2	no	—
153	C₈×C₁₃	C₄×D₄	1	4	yes	—
154	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	—
155	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
156	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
157	#436	—	2	2	no	—
158	#436	C₄×C₁₃	1	4	yes	—
159	#436	C₄×C₁₃	1	4	yes	—
160	#435	—	2	4	no	—
161	C₈×D₄	—	2	2	no	—
162	#430	—	2	8	no	—
163	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
164	C₂×#108	C₂²×C₁₃	1	2	yes	—
165	C₂×#108	C₂²×C₁₃	1	4	yes	—
166	C₂×#108	C₂²×C₁₃	1	2	yes	—
167	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
168	#423	C₂²×C₁₃	1	2	yes	—
169	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
170	#407	C₂²×C₁₃	1	4	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
172	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
174	#341	C₂²×C₁₃	1	4	yes	—
175	#341	C₂²×C₁₃	1	2	yes	—
176	C₂²×C₁₃	—	2	1	no	—
177	C₂²×C₁₃	—	2	1	no	—
178	C₂²×C₁₃	—	2	4	no	—
179	C₂²×C₁₃	—	2	4	no	—
180	C₂²×C₁₃	—	2	4	no	—
181	C₂²×C₁₃	—	8	2	no	—
182	C₂²×C₁₃	—	8	2	no	—
183	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
185	C₂²×C₁₃	#554	1	1	yes	characteristic
186	C₄×C₁₃	—	2	4	no	—
187	C₄×C₁₃	—	2	1	no	—
188	C₄×C₁₃	—	2	1	no	—
189	C₄×C₁₃	—	2	1	no	—
190	C₄×C₁₃	#430	1	2	yes	complemented
191	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₁₃	#520	1	1	yes	characteristic
193	C₄×C₁₃	D₄²	1	1	yes	characteristic
194	C₄×C₁₃	#547	1	1	yes	characteristic
195	C₂²×D₄	Q₈×C₁₃	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	—	2	4	no	—
199	C₂×M₁₆	—	2	4	no	—
200	C₂×M₁₆	—	2	8	no	—
201	C₂×M₁₆	—	4	4	no	—
202	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
203	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
204	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
205	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
208	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
210	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
211	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
212	C₄×D₄	D₄×C₁₃	1	2	yes	—
213	C₄×D₄	D₄×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₄	Q₈×C₁₃	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	Q₈×C₁₃	1	2	yes	—
216	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
217	#108	—	2	8	no	—
218	#108	—	2	4	no	—
219	#108	—	2	2	no	—
220	#108	—	4	2	no	—
221	#108	D₄×C₁₃	1	4	yes	complemented
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
225	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
226	C₂²⋊C₈	—	2	4	no	—
227	C₂²⋊C₈	—	2	4	no	—
228	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
229	#97	—	2	2	no	—
230	C₄×C₈	—	2	2	no	—
231	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
232	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×C₁₃	—	2	1	no	—
234	C₂×C₁₃	—	2	1	no	—
235	C₂×C₁₃	—	4	4	no	—
236	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
238	C₂×C₁₃	#2916	1	1	yes	characteristic
239	C₂⁴	C₂×Q₈×C₁₃	1	2	yes	—
240	C₂×D₄	—	4	2	no	—
241	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
242	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
248	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
249	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
251	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
253	M₁₆	—	2	2	no	—
254	M₁₆	—	2	16	no	—
255	M₁₆	—	2	4	no	—
256	M₁₆	—	2	2	no	—
257	M₁₆	—	2	4	no	—
258	M₁₆	—	2	2	no	—
259	M₁₆	—	4	8	no	—
260	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	4	8	no	—
269	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
270	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
272	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
273	C₂×C₈	C₁₃×#41	1	2	yes	—
274	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
275	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
276	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
277	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
278	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
279	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
281	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₁₃	#22669	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
288	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
289	D₄	—	2	4	no	—
290	D₄	—	4	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
301	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
303	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
308	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
310	C₈	—	2	4	no	—
311	C₈	—	2	2	no	—
312	C₈	—	2	4	no	—
313	C₈	—	4	4	no	—
314	C₈	—	4	2	no	—
315	C₈	C₄×D₄×C₁₃	1	4	yes	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	4	no	—
321	C₂²	—	8	2	no	—
322	C₂²	—	8	2	no	—
323	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
324	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
325	C₂²	C₁₃×#554	1	1	yes	characteristic
326	C₄	—	2	4	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	C₁₃×#430	1	2	yes	complemented
331	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
332	C₄	C₁₃×#520	1	1	yes	characteristic
333	C₄	D₄²×C₁₃	1	1	yes	characteristic
334	C₄	C₁₃×#547	1	1	yes	characteristic
335	C₂	—	2	1	no	—
336	C₂	—	2	1	no	—
337	C₂	—	4	4	no	—
338	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
339	C₂	C₂×C₁₃×#430	1	1	yes	characteristic
340	C₂	C₁₃×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#430	C₂	semidirect
4. C₁₃×#1950	C₂	semidirect
5. C₁₃×#1855	C₂	semidirect
6. C₁₃×#1848	C₂	semidirect
7. C₁₃×#1811	C₂	semidirect
8. C₄×C₁₃×#108	C₂	semidirect
57. C₁₃×#108	D₄	semidirect
69. #22669	C₁₃	direct (N × H)
115. C₂×#430	C₂×C₁₃	semidirect
116. #1950	C₂×C₁₃	semidirect
117. #1855	C₂×C₁₃	semidirect
118. #1848	C₂×C₁₃	semidirect
119. #1811	C₂×C₁₃	semidirect
120. C₄×#108	C₂×C₁₃	semidirect
190. C₄×C₁₃	#430	semidirect
221. #108	D₄×C₁₃	semidirect
282. C₁₃	#22669	direct (N × H)
330. C₄	C₁₃×#430	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#436	2
C₂×C₁₃×#430	2
C₁₃×#1950	2
C₁₃×#1855	2
C₁₃×#1848	2
C₁₃×#1811	2
C₄×C₁₃×#108	2
#22669	13

Subgroups — C13×#22669 #15709008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22669 #15709008