Subgroups — C₁₃×#25907 #15712246

Order 3328.

1116 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2026	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1991	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1874	C₂	1	2	yes	maximal
8	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#125	—	2	8	no	—
11	C₂×C₁₃×#125	—	2	2	no	—
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#488	—	2	8	no	—
21	C₂×C₁₃×#103	C₂²	1	4	yes	—
22	C₂×C₁₃×#102	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#388	—	2	2	no	—
28	C₁₃×#386	—	2	2	no	—
29	C₁₃×#382	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	—	2	2	no	—
37	C₂³×C₄×C₁₃	D₄	1	2	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×#125	—	2	16	no	—
41	C₁₃×#125	—	2	8	no	—
42	C₁₃×#125	—	2	4	no	—
43	C₁₃×#125	D₄	1	8	yes	complemented
44	C₁₃×#124	—	2	4	no	—
45	C₁₃×C₂²⋊Q₈	—	2	4	no	—
46	C₁₃×#121	—	2	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#103	—	2	8	no	—
65	C₁₃×#102	—	2	8	no	—
66	C₁₃×C₂²⋊C₈	—	2	4	no	—
67	C₄×C₈×C₁₃	—	2	4	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	#25907	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	1	no	—
72	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	4	2	no	—
80	C₂×D₄×C₁₃	—	4	4	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	4	no	—
92	C₂²×C₄×C₁₃	—	4	4	no	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	#41	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₁₃×C₄⋊C₄	—	2	8	no	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	16	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	4	2	no	—
108	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
109	C₁₃×C₂²⋊C₄	—	4	4	no	—
110	C₁₃×C₂²⋊C₄	—	4	2	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	no	—
112	C₁₃×C₂²⋊C₄	—	4	2	no	—
113	C₄²×C₁₃	—	2	4	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	C₂×D₄	1	4	yes	—
116	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂×#488	C₂×C₁₃	1	2	yes	complemented
118	#2850	C₂×C₁₃	1	1	yes	characteristic
119	#2026	C₂×C₁₃	1	2	yes	complemented
120	#2025	C₂×C₁₃	1	2	yes	complemented
121	#1991	C₂×C₁₃	1	2	yes	complemented
122	#1874	C₂×C₁₃	1	2	yes	—
123	#1872	C₂×C₁₃	1	2	yes	complemented
124	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	4	1	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	#124	1	2	yes	—
134	C₂³×C₁₃	#135	1	4	yes	—
135	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₁₃	—	4	4	no	—
137	D₄×C₁₃	—	4	4	no	—
138	D₄×C₁₃	—	8	4	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	8	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	8	no	—
149	C₂×C₄×C₁₃	—	4	16	no	—
150	C₂×C₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	#120	1	4	yes	—
160	C₂×C₄×C₁₃	#124	1	2	yes	—
161	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
164	C₈×C₁₃	—	4	4	no	—
165	C₂×#125	—	2	8	no	—
166	C₂×#125	—	2	2	no	—
167	C₂×#125	C₂²×C₁₃	1	2	yes	—
168	C₂×#125	C₂²×C₁₃	1	2	yes	—
169	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
170	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
172	C₂²×C₄⋊C₄	—	2	2	no	—
173	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
174	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
175	#488	—	2	8	no	—
176	C₂×#103	C₂²×C₁₃	1	4	yes	—
177	C₂×#102	C₂²×C₁₃	1	4	yes	—
178	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
180	#391	C₂²×C₁₃	1	1	yes	characteristic
181	#390	C₂²×C₁₃	1	1	yes	characteristic
182	#388	—	2	2	no	—
183	#386	—	2	2	no	—
184	#382	C₂²×C₁₃	1	1	yes	characteristic
185	#340	C₂²×C₁₃	1	4	yes	—
186	#340	C₂²×C₁₃	1	4	yes	—
187	#336	C₂²×C₁₃	1	2	yes	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	8	1	no	—
193	C₂²×C₁₃	—	8	1	no	—
194	C₂²×C₁₃	—	8	1	no	—
195	C₂²×C₁₃	—	8	2	no	—
196	C₂²×C₁₃	—	8	2	no	—
197	C₂²×C₁₃	#488	1	4	yes	complemented
198	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
200	C₂²×C₁₃	#536	1	1	yes	characteristic
201	C₂²×C₁₃	C₂×#135	1	2	yes	—
202	C₂²×C₁₃	#575	1	2	yes	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	—	4	2	no	—
206	C₄×C₁₃	—	4	8	no	—
207	C₄×C₁₃	—	8	1	no	—
208	C₄×C₁₃	—	8	1	no	—
209	C₄×C₁₃	—	8	1	no	—
210	C₄×C₁₃	#548	1	4	yes	—
211	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	D₄×C₁₃	1	2	yes	—
216	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
218	#125	—	2	16	no	—
219	#125	—	2	8	no	—
220	#125	—	2	4	no	—
221	#125	D₄×C₁₃	1	8	yes	complemented
222	#124	—	2	4	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	#121	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	16	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	4	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	8	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	D₄×C₁₃	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
242	#103	—	2	8	no	—
243	#102	—	2	8	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	C₄×C₈	—	2	4	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	C₂×C₁₃	—	2	4	no	—
249	C₂×C₁₃	—	16	1	no	—
250	C₂×C₁₃	#2436	1	1	yes	characteristic
251	C₂×C₁₃	#3002	1	2	yes	—
252	C₂×C₁₃	C₂×#488	1	1	yes	characteristic
253	C₂×C₁₃	#3142	1	1	yes	characteristic
254	C₂×C₁₃	#3232	1	2	yes	—
255	C₂⁴	—	2	1	no	—
256	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₁₃×#41	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	C₂×D₄×C₁₃	1	4	yes	—
300	C₁₃	#25907	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	C₁₃×#124	1	2	yes	—
310	C₂³	C₁₃×#135	1	4	yes	—
311	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	Q₈	—	4	4	no	—
313	D₄	—	4	4	no	—
314	D₄	—	8	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	16	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	C₁₃×#120	1	4	yes	—
336	C₂×C₄	C₁₃×#124	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
338	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
339	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	8	1	no	—
346	C₂²	—	8	1	no	—
347	C₂²	—	8	1	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	C₁₃×#488	1	4	yes	complemented
351	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
352	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
353	C₂²	C₁₃×#536	1	1	yes	characteristic
354	C₂²	C₂×C₁₃×#135	1	2	yes	—
355	C₂²	C₁₃×#575	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	8	no	—
360	C₄	—	8	1	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	1	no	—
363	C₄	C₁₃×#548	1	4	yes	—
364	C₂	—	2	4	no	—
365	C₂	—	16	1	no	—
366	C₂	C₁₃×#2436	1	1	yes	characteristic
367	C₂	C₁₃×#3002	1	2	yes	—
368	C₂	C₂×C₁₃×#488	1	1	yes	characteristic
369	C₂	C₁₃×#3142	1	1	yes	characteristic
370	C₂	C₁₃×#3232	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#125	C₂	semidirect
2. C₂×C₁₃×#488	C₂	semidirect
4. C₁₃×#2026	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#1991	C₂	semidirect
8. C₁₃×#1872	C₂	semidirect
9. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
43. C₁₃×#125	D₄	semidirect
70. #25907	C₁₃	direct (N × H)
116. C₂²×#125	C₂×C₁₃	semidirect
117. C₂×#488	C₂×C₁₃	semidirect
119. #2026	C₂×C₁₃	semidirect
120. #2025	C₂×C₁₃	semidirect
121. #1991	C₂×C₁₃	semidirect
123. #1872	C₂×C₁₃	semidirect
124. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
197. C₂²×C₁₃	#488	semidirect
221. #125	D₄×C₁₃	semidirect
300. C₁₃	#25907	direct (N × H)
350. C₂²	C₁₃×#488	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#125	2
C₂×C₁₃×#488	2
C₁₃×#2850	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1991	2
C₁₃×#1874	2
C₁₃×#1872	2
C₄×C₁₃×C₂²⋊C₈	2
#25907	13

Subgroups — C13×#25907 #15712246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25907 #15712246