Subgroups — C₁₃×#17925 #15704264

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1584	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1579	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1491	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1485	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#484	C₄	1	2	yes	—
15	C₁₃×#477	C₄	1	2	yes	—
16	C₁₃×#462	C₄	1	2	yes	—
17	C₁₃×#451	C₄	1	2	yes	—
18	C₁₃×#446	—	2	2	no	—
19	C₁₃×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₁₃	—	2	2	no	—
21	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
25	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
26	C₁₃×#433	—	2	2	no	—
27	C₁₃×#432	C₂²	1	1	yes	characteristic
28	C₁₃×#431	—	2	2	no	—
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#335	C₂²	1	2	yes	—
34	C₁₃×#334	C₂²	1	2	yes	—
35	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	1	yes	characteristic
40	C₁₃×#322	C₂²	1	1	yes	characteristic
41	C₁₃×#322	C₂²	1	1	yes	characteristic
42	C₈²×C₁₃	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
45	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×M₁₆	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₃×#125	—	2	1	no	—
50	C₁₃×C₂²⋊Q₈	—	2	1	no	—
51	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	—	2	1	no	—
55	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#117	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#107	C₂×C₄	1	2	yes	—
64	C₁₃×#107	C₂×C₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	—	2	2	no	—
66	C₁₃×C₄⋊C₈	—	2	2	no	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×#103	C₂×C₄	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#103	C₂×C₄	1	2	yes	—
76	C₁₃×#103	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
81	C₁₃×#97	—	2	2	no	—
82	C₁₃×#97	—	2	1	no	—
83	C₁₃×#97	—	2	1	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	1	no	—
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#17925	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
105	C₁₃×Q₁₆	—	2	4	no	—
106	C₁₃×Q₁₆	—	2	4	no	—
107	C₁₃×M₁₆	—	4	2	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	2	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	#41	1	1	yes	characteristic
133	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
134	#3104	C₂×C₁₃	1	1	yes	characteristic
135	#2985	C₂×C₁₃	1	1	yes	characteristic
136	#2982	C₂×C₁₃	1	1	yes	characteristic
137	#1587	C₂×C₁₃	1	2	yes	complemented
138	#1584	C₂×C₁₃	1	2	yes	complemented
139	#1579	C₂×C₁₃	1	2	yes	complemented
140	C₈×Q₁₆	C₂×C₁₃	1	2	yes	complemented
141	#1572	C₂×C₁₃	1	1	yes	characteristic
142	#1491	C₂×C₁₃	1	1	yes	characteristic
143	#1485	C₂×C₁₃	1	1	yes	characteristic
144	#1453	C₂×C₁₃	1	1	yes	characteristic
145	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	4	no	—
147	Q₈×C₁₃	—	2	2	no	—
148	Q₈×C₁₃	—	2	2	no	—
149	Q₈×C₁₃	—	2	2	no	—
150	Q₈×C₁₃	—	8	1	no	—
151	Q₈×C₁₃	#131	1	4	yes	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	8	1	no	—
161	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	—	2	2	no	—
172	C₈×C₁₃	—	4	1	no	—
173	C₈×C₁₃	—	4	2	no	—
174	C₈×C₁₃	—	4	2	no	—
175	#533	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
177	#484	C₄×C₁₃	1	2	yes	—
178	#477	C₄×C₁₃	1	2	yes	—
179	#462	C₄×C₁₃	1	2	yes	—
180	#451	C₄×C₁₃	1	2	yes	—
181	#446	—	2	2	no	—
182	#446	C₂²×C₁₃	1	2	yes	—
183	C₈×Q₈	—	2	2	no	—
184	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
185	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
186	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
187	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
188	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
189	#433	—	2	2	no	—
190	#432	C₂²×C₁₃	1	1	yes	characteristic
191	#431	—	2	2	no	—
192	#431	C₂²×C₁₃	1	1	yes	characteristic
193	#431	C₂²×C₁₃	1	1	yes	characteristic
194	#431	C₂²×C₁₃	1	1	yes	characteristic
195	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	#335	C₂²×C₁₃	1	2	yes	—
197	#334	C₂²×C₁₃	1	2	yes	—
198	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
199	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
200	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
201	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
202	#322	C₂²×C₁₃	1	1	yes	characteristic
203	#322	C₂²×C₁₃	1	1	yes	characteristic
204	#322	C₂²×C₁₃	1	1	yes	characteristic
205	C₈²	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₁₃	—	2	4	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	4	2	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	2	no	—
218	C₄×C₁₃	C₂×#131	1	2	yes	—
219	C₄×C₁₃	#578	1	2	yes	—
220	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
222	C₂×Q₁₆	C₂×C₄×C₁₃	1	2	yes	—
223	C₂×M₁₆	—	2	1	no	—
224	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
225	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
226	#125	—	2	1	no	—
227	C₂²⋊Q₈	—	2	1	no	—
228	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
233	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
234	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
235	#117	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
240	#107	C₂×C₄×C₁₃	1	2	yes	—
241	#107	C₂×C₄×C₁₃	1	2	yes	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
247	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
248	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
249	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
250	#103	C₂×C₄×C₁₃	1	2	yes	—
251	#103	C₂×C₄×C₁₃	1	2	yes	—
252	#103	C₂×C₄×C₁₃	1	2	yes	—
253	#103	C₂×C₄×C₁₃	1	2	yes	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	—	2	1	no	—
256	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
257	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
258	#97	—	2	2	no	—
259	#97	—	2	1	no	—
260	#97	—	2	1	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×C₁₃	—	4	1	no	—
272	C₂×C₁₃	#2929	1	1	yes	characteristic
273	C₂×C₁₃	#2950	1	1	yes	characteristic
274	C₂×C₁₃	#2956	1	1	yes	characteristic
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
279	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
285	Q₁₆	—	2	4	no	—
286	Q₁₆	—	2	4	no	—
287	M₁₆	—	4	2	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
294	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
305	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₄²	C₁₃×#41	1	1	yes	characteristic
313	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
314	C₁₃	#17925	1	1	yes	characteristic, direct product factor, Sylow
315	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
316	Q₈	—	2	4	no	—
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	8	1	no	—
321	Q₈	C₁₃×#131	1	4	yes	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	—	4	1	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	C₂×C₁₃×#131	1	2	yes	—
358	C₄	C₁₃×#578	1	2	yes	—
359	C₂	—	4	1	no	—
360	C₂	C₁₃×#2929	1	1	yes	characteristic
361	C₂	C₁₃×#2950	1	1	yes	characteristic
362	C₂	C₁₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×C₁₃	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1587	C₂	semidirect
5. C₁₃×#1584	C₂	semidirect
6. C₁₃×#1579	C₂	semidirect
7. C₈×C₁₃×Q₁₆	C₂	semidirect
94. #17925	C₁₃	direct (N × H)
137. #1587	C₂×C₁₃	semidirect
138. #1584	C₂×C₁₃	semidirect
139. #1579	C₂×C₁₃	semidirect
140. C₈×Q₁₆	C₂×C₁₃	semidirect
314. C₁₃	#17925	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×#3104	2
C₁₃×#2985	2
C₁₃×#2982	2
C₁₃×#1587	2
C₁₃×#1584	2
C₁₃×#1579	2
C₈×C₁₃×Q₁₆	2
C₁₃×#1572	2
C₁₃×#1491	2
C₁₃×#1485	2
C₁₃×#1453	2
#17925	13

Subgroups — C13×#17925 #15704264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17925 #15704264