Subgroups — C₁₃×#60626 #15746965

Order 3328.

2134 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	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3142	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3138	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3136	C₂	1	12	yes	maximal, complemented
6	C₁₃×#3135	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#490	C₂	1	3	yes	maximal, complemented
8	C₁₃×#2897	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
11	C₂×C₁₃×#131	C₂²	1	2	yes	—
12	C₁₃×#557	—	2	2	no	—
13	C₁₃×#554	—	2	6	no	—
14	C₁₃×#550	—	2	2	no	—
15	D₄²×C₁₃	—	2	6	no	—
16	C₁₃×#544	C₂²	1	6	yes	complemented
17	C₁₃×#535	C₂²	1	6	yes	—
18	C₁₃×#533	C₂²	1	3	yes	complemented
19	C₁₃×#532	C₂²	1	3	yes	—
20	C₂×C₁₃×#127	C₂²	1	3	yes	—
21	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
22	C₁₃×#520	C₂²	1	2	yes	—
23	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
24	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#491	C₂²	1	3	yes	complemented
26	C₁₃×#490	C₂²	1	3	yes	complemented
27	C₁₃×#490	C₂²	1	12	yes	complemented
28	C₁₃×#490	C₂²	1	6	yes	complemented
29	C₁₃×#490	C₂²	1	3	yes	complemented
30	C₁₃×#489	C₂²	1	12	yes	complemented
31	C₁₃×#488	C₂²	1	12	yes	complemented
32	C₁₃×#486	C₂²	1	12	yes	complemented
33	C₁₃×#418	C₂²	1	12	yes	complemented
34	C₁₃×#417	C₂²	1	12	yes	complemented
35	C₁₃×#416	C₂²	1	12	yes	complemented
36	C₂×C₁₃×#102	C₂²	1	12	yes	complemented
37	C₁₃×#405	C₂²	1	6	yes	complemented
38	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
39	C₂×C₁₃×#97	C₂²	1	3	yes	complemented
40	C₁₃×H(5,𝔽₂)	—	2	16	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	C₂³	1	6	yes	—
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	6	no	—
45	C₂²×D₄×C₁₃	—	2	6	no	—
46	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
47	C₁₃×#131	—	2	8	no	—
48	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
50	C₁₃×C₄⋊Q₈	—	2	6	no	—
51	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
53	C₁₃×#127	—	2	6	no	—
54	C₁₃×#127	C₂³	1	6	yes	—
55	C₁₃×#127	C₂³	1	3	yes	—
56	C₁₃×#125	—	2	6	no	—
57	C₁₃×#125	—	2	6	no	—
58	C₁₃×#125	C₂³	1	6	yes	—
59	C₁₃×#125	C₂³	1	3	yes	—
60	C₁₃×#125	C₂³	1	1	yes	characteristic
61	C₁₃×#124	C₂³	1	6	yes	—
62	C₁₃×C₂²⋊Q₈	—	2	6	no	—
63	C₁₃×C₂²⋊Q₈	—	2	12	no	—
64	C₁₃×#121	—	2	6	no	—
65	C₁₃×#121	—	2	12	no	—
66	C₁₃×#120	—	2	12	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	6	no	—
69	C₄×Q₈×C₁₃	D₄	1	2	yes	—
70	C₄×D₄×C₁₃	—	2	6	no	—
71	C₄×D₄×C₁₃	—	2	6	no	—
72	C₄×D₄×C₁₃	D₄	1	6	yes	—
73	C₁₃×#117	C₂³	1	6	yes	—
74	C₁₃×#117	C₂³	1	3	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
78	C₁₃×#103	C₂³	1	4	yes	—
79	C₁₃×#103	C₂³	1	12	yes	—
80	C₁₃×#102	C₂³	1	12	yes	—
81	C₁₃×#102	C₂³	1	24	yes	—
82	C₁₃×#102	C₂³	1	12	yes	—
83	C₁₃×#97	C₂³	1	1	yes	characteristic
84	C₁₃×#97	C₂³	1	3	yes	—
85	C₁₃×#97	C₂³	1	6	yes	—
86	C₄×C₈×C₁₃	C₂³	1	6	yes	—
87	#60626	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	6	no	—
89	C₁₃×#41	—	2	24	no	—
90	C₁₃×#41	—	4	8	no	—
91	C₁₃×#41	#41	1	8	yes	—
92	C₂×Q₈×C₁₃	—	2	6	no	—
93	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	6	no	—
96	C₂×D₄×C₁₃	—	2	6	no	—
97	C₂×D₄×C₁₃	—	2	6	no	—
98	C₂×D₄×C₁₃	—	2	12	no	—
99	C₂×D₄×C₁₃	—	2	24	no	—
100	C₂×D₄×C₁₃	—	4	24	no	—
101	C₂×D₄×C₁₃	—	8	12	no	—
102	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
103	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
104	C₂²×C₄×C₁₃	—	2	6	no	—
105	C₂²×C₄×C₁₃	—	2	6	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
108	C₁₃×M₁₆	—	2	12	no	—
109	C₂×C₈×C₁₃	—	2	12	no	—
110	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
111	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
112	C₁₃×C₄⋊C₄	—	2	6	no	—
113	C₁₃×C₄⋊C₄	—	2	12	no	—
114	C₁₃×C₄⋊C₄	—	2	6	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	6	no	—
118	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
119	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
120	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
121	C₁₃×C₂²⋊C₄	—	2	6	no	—
122	C₁₃×C₂²⋊C₄	—	2	12	no	—
123	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
124	C₄²×C₁₃	—	2	6	no	—
125	C₄²×C₁₃	C₂×D₄	1	6	yes	—
126	C₄²×C₁₃	C₂⁴	1	3	yes	—
127	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
128	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#3498	C₂×C₁₃	1	1	yes	characteristic
130	#3142	C₂×C₁₃	1	3	yes	complemented
131	#3138	C₂×C₁₃	1	3	yes	complemented
132	#3136	C₂×C₁₃	1	12	yes	complemented
133	#3135	C₂×C₁₃	1	3	yes	complemented
134	C₂×#490	C₂×C₁₃	1	3	yes	complemented
135	#2897	C₂×C₁₃	1	4	yes	complemented
136	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	2	6	no	—
138	C₂³×C₁₃	—	4	12	no	—
139	C₂³×C₁₃	—	8	12	no	—
140	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
141	Q₈×C₁₃	—	2	4	no	—
142	Q₈×C₁₃	—	8	6	no	—
143	Q₈×C₁₃	#124	1	4	yes	—
144	D₄×C₁₃	—	2	12	no	—
145	D₄×C₁₃	—	4	12	no	—
146	D₄×C₁₃	—	4	12	no	—
147	D₄×C₁₃	—	4	12	no	—
148	D₄×C₁₃	—	8	12	no	—
149	D₄×C₁₃	#124	1	12	yes	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	6	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	4	6	no	—
154	C₂×C₄×C₁₃	—	4	12	no	—
155	C₂×C₄×C₁₃	—	8	6	no	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
158	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
160	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
161	C₈×C₁₃	—	2	2	no	—
162	C₈×C₁₃	—	2	6	no	—
163	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
164	C₂×#131	C₂²×C₁₃	1	2	yes	—
165	#557	—	2	2	no	—
166	#554	—	2	6	no	—
167	#550	—	2	2	no	—
168	D₄²	—	2	6	no	—
169	#544	C₂²×C₁₃	1	6	yes	complemented
170	#535	C₂²×C₁₃	1	6	yes	—
171	#533	C₂²×C₁₃	1	3	yes	complemented
172	#532	C₂²×C₁₃	1	3	yes	—
173	C₂×#127	C₂²×C₁₃	1	3	yes	—
174	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
175	#520	C₂²×C₁₃	1	2	yes	—
176	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
177	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
178	#491	C₂²×C₁₃	1	3	yes	complemented
179	#490	C₂²×C₁₃	1	3	yes	complemented
180	#490	C₂²×C₁₃	1	12	yes	complemented
181	#490	C₂²×C₁₃	1	6	yes	complemented
182	#490	C₂²×C₁₃	1	3	yes	complemented
183	#489	C₂²×C₁₃	1	12	yes	complemented
184	#488	C₂²×C₁₃	1	12	yes	complemented
185	#486	C₂²×C₁₃	1	12	yes	complemented
186	#418	C₂²×C₁₃	1	12	yes	complemented
187	#417	C₂²×C₁₃	1	12	yes	complemented
188	#416	C₂²×C₁₃	1	12	yes	complemented
189	C₂×#102	C₂²×C₁₃	1	12	yes	complemented
190	#405	C₂²×C₁₃	1	6	yes	complemented
191	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
192	C₂×#97	C₂²×C₁₃	1	3	yes	complemented
193	C₂²×C₁₃	—	2	6	no	—
194	C₂²×C₁₃	—	4	12	no	—
195	C₂²×C₁₃	—	4	6	no	—
196	C₂²×C₁₃	—	16	12	no	—
197	C₂²×C₁₃	C₂×#124	1	6	yes	—
198	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	6	no	—
201	C₄×C₁₃	—	4	6	no	—
202	C₄×C₁₃	—	4	2	no	—
203	C₄×C₁₃	—	4	2	no	—
204	C₄×C₁₃	C₂×#124	1	6	yes	—
205	C₄×C₁₃	C₂²×#41	1	2	yes	—
206	H(5,𝔽₂)	—	2	16	no	—
207	C₂×#41	—	2	2	no	—
208	C₂×#41	C₂³×C₁₃	1	6	yes	—
209	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
210	C₂²×D₄	—	2	6	no	—
211	C₂²×D₄	—	2	6	no	—
212	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
213	#131	—	2	8	no	—
214	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
215	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
216	C₄⋊Q₈	—	2	6	no	—
217	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
218	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
219	#127	—	2	6	no	—
220	#127	C₂³×C₁₃	1	3	yes	—
221	#127	C₂³×C₁₃	1	6	yes	—
222	#125	—	2	6	no	—
223	#125	—	2	6	no	—
224	#125	C₂³×C₁₃	1	3	yes	—
225	#125	C₂³×C₁₃	1	6	yes	—
226	#125	C₂³×C₁₃	1	1	yes	characteristic
227	#124	C₂³×C₁₃	1	6	yes	—
228	C₂²⋊Q₈	—	2	6	no	—
229	C₂²⋊Q₈	—	2	12	no	—
230	#121	—	2	6	no	—
231	#121	—	2	12	no	—
232	#120	—	2	12	no	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	6	no	—
235	C₄×Q₈	D₄×C₁₃	1	2	yes	—
236	C₄×D₄	—	2	6	no	—
237	C₄×D₄	—	2	6	no	—
238	C₄×D₄	D₄×C₁₃	1	6	yes	—
239	#117	C₂³×C₁₃	1	6	yes	—
240	#117	C₂³×C₁₃	1	3	yes	—
241	C₂×C₄⋊C₄	—	2	6	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
243	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
244	#103	C₂³×C₁₃	1	4	yes	—
245	#103	C₂³×C₁₃	1	12	yes	—
246	#102	C₂³×C₁₃	1	12	yes	—
247	#102	C₂³×C₁₃	1	24	yes	—
248	#102	C₂³×C₁₃	1	12	yes	—
249	#97	C₂³×C₁₃	1	1	yes	characteristic
250	#97	C₂³×C₁₃	1	3	yes	—
251	#97	C₂³×C₁₃	1	6	yes	—
252	C₄×C₈	C₂³×C₁₃	1	6	yes	—
253	C₂×C₁₃	—	2	6	no	—
254	C₂×C₁₃	—	8	6	no	—
255	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
256	C₂×C₁₃	#3585	1	2	yes	—
257	C₂⁴	—	2	6	no	—
258	#41	—	2	24	no	—
259	#41	—	4	8	no	—
260	#41	C₁₃×#41	1	8	yes	—
261	C₂×Q₈	—	2	6	no	—
262	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
263	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
264	C₂×D₄	—	2	6	no	—
265	C₂×D₄	—	2	6	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	12	no	—
268	C₂×D₄	—	2	24	no	—
269	C₂×D₄	—	4	24	no	—
270	C₂×D₄	—	8	12	no	—
271	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
272	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
273	C₂²×C₄	—	2	6	no	—
274	C₂²×C₄	—	2	6	no	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
276	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
277	M₁₆	—	2	12	no	—
278	C₂×C₈	—	2	12	no	—
279	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
280	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
281	C₄⋊C₄	—	2	6	no	—
282	C₄⋊C₄	—	2	12	no	—
283	C₄⋊C₄	—	2	6	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	6	no	—
287	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
288	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
289	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
290	C₂²⋊C₄	—	2	6	no	—
291	C₂²⋊C₄	—	2	12	no	—
292	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
293	C₄²	—	2	6	no	—
294	C₄²	C₂×D₄×C₁₃	1	6	yes	—
295	C₄²	C₂⁴×C₁₃	1	3	yes	—
296	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
297	C₁₃	#60626	1	1	yes	characteristic, direct product factor, Sylow
298	C₂³	—	2	6	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	8	12	no	—
301	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
302	Q₈	—	2	4	no	—
303	Q₈	—	8	6	no	—
304	Q₈	C₁₃×#124	1	4	yes	—
305	D₄	—	2	12	no	—
306	D₄	—	4	12	no	—
307	D₄	—	4	12	no	—
308	D₄	—	4	12	no	—
309	D₄	—	8	12	no	—
310	D₄	C₁₃×#124	1	12	yes	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	6	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	6	no	—
315	C₂×C₄	—	4	12	no	—
316	C₂×C₄	—	8	6	no	—
317	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
319	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
320	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
321	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	6	no	—
324	C₂²	—	2	6	no	—
325	C₂²	—	4	12	no	—
326	C₂²	—	4	6	no	—
327	C₂²	—	16	12	no	—
328	C₂²	C₂×C₁₃×#124	1	6	yes	—
329	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	6	no	—
332	C₄	—	4	6	no	—
333	C₄	—	4	2	no	—
334	C₄	—	4	2	no	—
335	C₄	C₂×C₁₃×#124	1	6	yes	—
336	C₄	C₂²×C₁₃×#41	1	2	yes	—
337	C₂	—	2	6	no	—
338	C₂	—	8	6	no	—
339	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
340	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3142	C₂	semidirect
4. C₁₃×#3138	C₂	semidirect
5. C₁₃×#3136	C₂	semidirect
6. C₁₃×#3135	C₂	semidirect
7. C₂×C₁₃×#490	C₂	semidirect
8. C₁₃×#2897	C₂	semidirect
9. C₁₃×#2875	C₂	semidirect
16. C₁₃×#544	C₂²	semidirect
18. C₁₃×#533	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
24. C₁₃×#491	C₂²	semidirect
25. C₁₃×#491	C₂²	semidirect
26. C₁₃×#490	C₂²	semidirect
27. C₁₃×#490	C₂²	semidirect
28. C₁₃×#490	C₂²	semidirect
29. C₁₃×#490	C₂²	semidirect
30. C₁₃×#489	C₂²	semidirect
31. C₁₃×#488	C₂²	semidirect
32. C₁₃×#486	C₂²	semidirect
33. C₁₃×#418	C₂²	semidirect
34. C₁₃×#417	C₂²	semidirect
35. C₁₃×#416	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
37. C₁₃×#405	C₂²	semidirect
38. C₄×C₁₃×M₁₆	C₂²	semidirect
39. C₂×C₁₃×#97	C₂²	semidirect
87. #60626	C₁₃	direct (N × H)
128. #3504	C₂×C₁₃	semidirect
130. #3142	C₂×C₁₃	semidirect
131. #3138	C₂×C₁₃	semidirect
132. #3136	C₂×C₁₃	semidirect
133. #3135	C₂×C₁₃	semidirect
134. C₂×#490	C₂×C₁₃	semidirect
135. #2897	C₂×C₁₃	semidirect
136. #2875	C₂×C₁₃	semidirect
169. #544	C₂²×C₁₃	semidirect
171. #533	C₂²×C₁₃	semidirect
174. C₂×#125	C₂²×C₁₃	semidirect
177. #491	C₂²×C₁₃	semidirect
178. #491	C₂²×C₁₃	semidirect
179. #490	C₂²×C₁₃	semidirect
180. #490	C₂²×C₁₃	semidirect
181. #490	C₂²×C₁₃	semidirect
182. #490	C₂²×C₁₃	semidirect
183. #489	C₂²×C₁₃	semidirect
184. #488	C₂²×C₁₃	semidirect
185. #486	C₂²×C₁₃	semidirect
186. #418	C₂²×C₁₃	semidirect
187. #417	C₂²×C₁₃	semidirect
188. #416	C₂²×C₁₃	semidirect
189. C₂×#102	C₂²×C₁₃	semidirect
190. #405	C₂²×C₁₃	semidirect
191. C₄×M₁₆	C₂²×C₁₃	semidirect
192. C₂×#97	C₂²×C₁₃	semidirect
297. C₁₃	#60626	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×#3504	2
C₁₃×#3498	2
C₁₃×#3142	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#3135	2
C₂×C₁₃×#490	2
C₁₃×#2897	2
C₁₃×#2875	2
#60626	13

Subgroups — C13×#60626 #15746965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60626 #15746965