Subgroups — C₁₃×#19189 #15705528

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3245	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1689	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1687	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1665	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	1	no	—
11	C₂×C₁₃×#131	—	2	1	no	—
12	C₁₃×#532	C₂²	1	2	yes	—
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#495	—	2	1	no	—
15	C₁₃×#495	—	2	1	no	—
16	C₁₃×#494	C₂²	1	1	yes	characteristic
17	C₁₃×#493	C₂²	1	1	yes	characteristic
18	C₁₃×#492	C₂²	1	2	yes	—
19	C₁₃×#474	—	2	2	no	—
20	C₁₃×#474	C₂²	1	4	yes	—
21	C₁₃×#466	—	2	4	no	—
22	C₁₃×#459	—	2	2	no	—
23	C₁₃×#459	C₂²	1	4	yes	—
24	C₁₃×#436	—	2	1	no	—
25	C₁₃×#436	C₂²	1	2	yes	—
26	C₈×D₄×C₁₃	—	2	1	no	—
27	C₈×D₄×C₁₃	C₂²	1	2	yes	—
28	C₁₃×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₃×#408	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#334	C₂²	1	2	yes	—
33	C₁₃×#334	C₂²	1	2	yes	—
34	C₁₃×#332	C₂²	1	4	yes	—
35	C₁₃×#331	C₂²	1	4	yes	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₁₃×#135	—	4	4	no	—
39	C₁₃×#135	—	4	4	no	—
40	C₂×C₁₃×Q₁₆	—	2	1	no	—
41	C₂×C₁₃×Q₁₆	—	2	1	no	—
42	C₂×C₁₃×SD₁₆	—	2	2	no	—
43	C₂×C₁₃×SD₁₆	—	2	2	no	—
44	C₂×C₁₃×D₈	—	2	4	no	—
45	C₂×C₁₃×D₈	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₁₃×#131	—	4	4	no	—
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
55	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₁₃×#127	D₄	1	1	yes	characteristic
57	C₁₃×#127	C₂³	1	2	yes	—
58	C₁₃×#124	—	2	2	no	—
59	C₁₃×#124	—	2	1	no	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₁₃×#121	D₄	1	2	yes	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#107	—	2	4	no	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×C₄⋊C₈	—	2	1	no	—
72	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#102	—	2	4	no	—
76	C₁₃×C₂²⋊C₈	—	2	2	no	—
77	C₁₃×C₂²⋊C₈	—	2	2	no	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#19189	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₁₃×#41	—	4	2	no	—
84	C₁₃×#41	—	4	2	no	—
85	C₁₃×#41	—	4	4	no	—
86	C₁₃×#41	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	2	1	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
102	C₁₃×Q₁₆	—	4	2	no	—
103	C₁₃×Q₁₆	—	4	2	no	—
104	C₁₃×SD₁₆	—	4	4	no	—
105	C₁₃×SD₁₆	—	4	4	no	—
106	C₁₃×D₈	—	4	2	no	—
107	C₁₃×D₈	—	4	2	no	—
108	C₁₃×D₈	—	8	4	no	—
109	C₁₃×M₁₆	—	4	2	no	—
110	C₁₃×M₁₆	—	4	4	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	4	no	—
114	C₂×C₈×C₁₃	—	4	4	no	—
115	C₂×C₈×C₁₃	—	8	2	no	—
116	C₂×C₈×C₁₃	D₈	1	4	yes	complemented
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
125	C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	4	2	no	—
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	#41	1	1	yes	characteristic
132	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
133	#3245	C₂×C₁₃	1	2	yes	complemented
134	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1689	C₂×C₁₃	1	2	yes	complemented
137	#1687	C₂×C₁₃	1	2	yes	complemented
138	#1665	C₂×C₁₃	1	4	yes	complemented
139	C₂×#334	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1547	C₂×C₁₃	1	2	yes	complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	#121	1	1	yes	characteristic
144	Q₈×C₁₃	—	4	2	no	—
145	Q₈×C₁₃	—	4	2	no	—
146	Q₈×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	2	4	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	4	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	8	2	no	—
156	D₄×C₁₃	—	8	4	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	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	8	4	no	—
164	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₈×C₁₃	—	2	1	no	—
173	C₈×C₁₃	—	2	1	no	—
174	C₈×C₁₃	—	4	2	no	—
175	C₈×C₁₃	—	4	4	no	—
176	C₈×C₁₃	C₂×D₈	1	2	yes	—
177	C₈×C₁₃	C₂×D₈	1	2	yes	—
178	C₂×#135	—	2	1	no	—
179	C₂×#135	—	2	1	no	—
180	C₂×#131	—	2	1	no	—
181	#532	C₂²×C₁₃	1	2	yes	—
182	#532	C₂²×C₁₃	1	1	yes	characteristic
183	#495	—	2	1	no	—
184	#495	—	2	1	no	—
185	#494	C₂²×C₁₃	1	1	yes	characteristic
186	#493	C₂²×C₁₃	1	1	yes	characteristic
187	#492	C₂²×C₁₃	1	2	yes	—
188	#474	—	2	2	no	—
189	#474	C₂²×C₁₃	1	4	yes	—
190	#466	—	2	4	no	—
191	#459	—	2	2	no	—
192	#459	C₂²×C₁₃	1	4	yes	—
193	#436	—	2	1	no	—
194	#436	C₂²×C₁₃	1	2	yes	—
195	C₈×D₄	—	2	1	no	—
196	C₈×D₄	C₂²×C₁₃	1	2	yes	—
197	#423	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
199	#408	—	2	1	no	—
200	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
201	#334	C₂²×C₁₃	1	2	yes	—
202	#334	C₂²×C₁₃	1	2	yes	—
203	#332	C₂²×C₁₃	1	4	yes	—
204	#331	C₂²×C₁₃	1	4	yes	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	4	2	no	—
208	C₂²×C₁₃	—	4	2	no	—
209	C₂²×C₁₃	—	4	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	#459	1	2	yes	—
214	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	4	2	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	#459	1	2	yes	—
221	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₁₃	#577	1	2	yes	—
224	C₂×#41	—	2	1	no	—
225	C₂×#41	—	2	2	no	—
226	#135	—	4	4	no	—
227	#135	—	4	4	no	—
228	C₂×Q₁₆	—	2	1	no	—
229	C₂×Q₁₆	—	2	1	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	—	2	1	no	—
235	#131	—	4	4	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
242	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
244	#127	D₄×C₁₃	1	1	yes	characteristic
245	#127	C₂³×C₁₃	1	2	yes	—
246	#124	—	2	2	no	—
247	#124	—	2	1	no	—
248	#121	—	2	1	no	—
249	#121	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	D₄×C₁₃	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
257	#107	—	2	4	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
261	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
262	#102	—	2	4	no	—
263	#102	—	2	4	no	—
264	C₂²⋊C₈	—	2	2	no	—
265	C₂²⋊C₈	—	2	2	no	—
266	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
267	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₁₃	—	2	2	no	—
271	C₂×C₁₃	—	8	2	no	—
272	C₂×C₁₃	—	16	2	no	—
273	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
274	C₂×C₁₃	#3060	1	1	yes	characteristic
275	C₂×C₁₃	#3067	1	1	yes	characteristic
276	#41	—	4	2	no	—
277	#41	—	4	2	no	—
278	#41	—	4	4	no	—
279	#41	—	4	4	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
295	Q₁₆	—	4	2	no	—
296	Q₁₆	—	4	2	no	—
297	SD₁₆	—	4	4	no	—
298	SD₁₆	—	4	4	no	—
299	D₈	—	4	2	no	—
300	D₈	—	4	2	no	—
301	D₈	—	8	4	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	—	4	4	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₂×C₈	—	8	2	no	—
309	C₂×C₈	C₁₃×D₈	1	4	yes	complemented
310	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₄²	C₁₃×#41	1	1	yes	characteristic
325	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₁₃	#19189	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	C₁₃×#121	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
351	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
352	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
354	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	4	2	no	—
361	C₈	—	4	4	no	—
362	C₈	C₂×C₁₃×D₈	1	2	yes	—
363	C₈	C₂×C₁₃×D₈	1	2	yes	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	C₁₃×#459	1	2	yes	—
373	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₁₃×#459	1	2	yes	—
380	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
381	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₄	C₁₃×#577	1	2	yes	—
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
387	C₂	C₁₃×#3060	1	1	yes	characteristic
388	C₂	C₁₃×#3067	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3245	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₁₃×#2931	C₂	semidirect
4. C₁₃×#1689	C₂	semidirect
5. C₁₃×#1687	C₂	semidirect
6. C₁₃×#1665	C₂	semidirect
7. C₂×C₁₃×#334	C₂	semidirect
8. C₁₃×#1547	C₂	semidirect
82. #19189	C₁₃	direct (N × H)
116. C₂×C₈×C₁₃	D₈	semidirect
133. #3245	C₂×C₁₃	semidirect
134. #3147	C₂×C₁₃	semidirect
135. #2931	C₂×C₁₃	semidirect
136. #1689	C₂×C₁₃	semidirect
137. #1687	C₂×C₁₃	semidirect
138. #1665	C₂×C₁₃	semidirect
139. C₂×#334	C₂×C₁₃	semidirect
140. #1547	C₂×C₁₃	semidirect
309. C₂×C₈	C₁₃×D₈	semidirect
326. C₁₃	#19189	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×#3245	2
C₁₃×#3147	2
C₁₃×#2931	2
C₁₃×#1689	2
C₁₃×#1687	2
C₁₃×#1665	2
C₂×C₁₃×#334	2
C₁₃×#1547	2
#19189	13

Subgroups — C13×#19189 #15705528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19189 #15705528