Subgroups — C₁₃×#29200 #15715539

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2067	C₂	1	2	yes	maximal
5	C₁₃×#1959	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1958	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#400	—	2	2	no	—
25	C₁₃×#398	—	2	2	no	—
26	C₁₃×#391	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₂²	1	1	yes	characteristic
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#388	—	2	2	no	—
31	C₁₃×#385	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₁₃×#376	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₁₃×#124	—	2	2	no	—
45	C₁₃×#124	Q₈	1	4	yes	—
46	C₄×Q₈×C₁₃	—	4	2	no	—
47	C₄×D₄×C₁₃	—	4	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	—	4	2	no	—
65	C₁₃×#107	—	4	2	no	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×#103	—	2	4	no	—
68	C₁₃×#103	—	4	2	no	—
69	C₁₃×#102	—	2	4	no	—
70	C₁₃×#102	—	4	2	no	—
71	C₁₃×#97	—	2	2	no	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	D₄	1	2	yes	—
78	C₁₃×#95	D₄	1	2	yes	—
79	#29200	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	2	1	no	—
81	C₂×Q₈×C₁₃	—	2	1	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	—	8	2	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	#41	1	4	yes	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	4	2	no	—
114	C₁₃×C₄⋊C₄	—	8	2	no	—
115	C₁₃×C₄⋊C₄	—	8	2	no	—
116	C₁₃×C₄⋊C₄	—	8	2	no	—
117	C₁₃×C₄⋊C₄	—	8	2	no	—
118	C₁₃×C₂²⋊C₄	—	2	8	no	—
119	C₁₃×C₂²⋊C₄	—	4	2	no	—
120	C₁₃×C₂²⋊C₄	—	8	2	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	4	2	no	—
124	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
125	C₄²×C₁₃	#41	1	2	yes	—
126	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#2326	C₂×C₁₃	1	1	yes	characteristic
128	#2068	C₂×C₁₃	1	2	yes	complemented
129	#2067	C₂×C₁₃	1	2	yes	—
130	#1959	C₂×C₁₃	1	1	yes	characteristic
131	#1958	C₂×C₁₃	1	1	yes	characteristic
132	#1863	C₂×C₁₃	1	2	yes	complemented
133	#1862	C₂×C₁₃	1	2	yes	—
134	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1836	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	1	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₁₃	—	2	4	no	—
144	Q₈×C₁₃	—	4	2	no	—
145	D₄×C₁₃	—	2	4	no	—
146	D₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	8	4	no	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
171	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
174	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
175	C₈×C₁₃	—	2	4	no	—
176	C₈×C₁₃	—	4	2	no	—
177	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×#107	C₂²×C₁₃	1	2	yes	—
181	C₂×#107	C₂²×C₁₃	1	2	yes	—
182	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
183	C₂×#103	C₂²×C₁₃	1	2	yes	—
184	C₂×#103	C₂²×C₁₃	1	2	yes	—
185	C₂×#102	C₂²×C₁₃	1	2	yes	—
186	C₂×#102	C₂²×C₁₃	1	2	yes	—
187	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
189	#400	—	2	2	no	—
190	#398	—	2	2	no	—
191	#391	C₂²×C₁₃	1	1	yes	characteristic
192	#390	C₂²×C₁₃	1	1	yes	characteristic
193	#389	C₂²×C₁₃	1	2	yes	—
194	#389	C₂²×C₁₃	1	2	yes	—
195	#388	—	2	2	no	—
196	#385	—	2	2	no	—
197	#384	C₂²×C₁₃	1	1	yes	characteristic
198	#384	C₂²×C₁₃	1	1	yes	characteristic
199	#382	C₂²×C₁₃	1	1	yes	characteristic
200	#376	C₂²×C₁₃	1	1	yes	characteristic
201	#340	C₂²×C₁₃	1	2	yes	—
202	#340	C₂²×C₁₃	1	2	yes	—
203	#336	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	8	1	no	—
208	C₂²×C₁₃	—	8	1	no	—
209	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₂²×C₁₃	#532	1	1	yes	characteristic
211	C₂²×C₁₃	#535	1	1	yes	characteristic
212	C₂²×C₁₃	#576	1	2	yes	—
213	C₂²×C₁₃	#578	1	2	yes	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	4	2	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	1	no	—
218	C₄×C₁₃	—	4	1	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	—	8	1	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	—	8	1	no	—
223	C₄×C₁₃	#553	1	2	yes	—
224	C₄×C₁₃	#554	1	2	yes	—
225	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
226	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	—	2	1	no	—
228	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
229	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
230	#124	—	2	2	no	—
231	#124	Q₈×C₁₃	1	4	yes	—
232	C₄×Q₈	—	4	2	no	—
233	C₄×D₄	—	4	2	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
250	#107	—	4	2	no	—
251	#107	—	4	2	no	—
252	C₄⋊C₈	—	2	4	no	—
253	#103	—	2	4	no	—
254	#103	—	4	2	no	—
255	#102	—	2	4	no	—
256	#102	—	4	2	no	—
257	#97	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	D₄×C₁₃	1	2	yes	—
264	#95	D₄×C₁₃	1	2	yes	—
265	C₂×C₁₃	—	8	2	no	—
266	C₂×C₁₃	#2566	1	1	yes	characteristic
267	C₂×C₁₃	#3083	1	2	yes	—
268	C₂×C₁₃	#3175	1	2	yes	—
269	C₂×C₁₃	#3220	1	1	yes	characteristic
270	C₂×C₁₃	#3223	1	1	yes	characteristic
271	C₂⁴	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	8	2	no	—
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₁₃×#41	1	4	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	8	2	no	—
306	C₄⋊C₄	—	8	2	no	—
307	C₄⋊C₄	—	8	2	no	—
308	C₄⋊C₄	—	8	2	no	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	8	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	4	2	no	—
315	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
316	C₄²	C₁₃×#41	1	2	yes	—
317	C₁₃	#29200	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	2	2	no	—
319	C₂³	—	4	1	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	2	no	—
326	D₄	—	2	4	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
352	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
353	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
354	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
355	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	1	no	—
362	C₂²	—	8	1	no	—
363	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂²	C₁₃×#532	1	1	yes	characteristic
365	C₂²	C₁₃×#535	1	1	yes	characteristic
366	C₂²	C₁₃×#576	1	2	yes	—
367	C₂²	C₁₃×#578	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	C₁₃×#553	1	2	yes	—
378	C₄	C₁₃×#554	1	2	yes	—
379	C₂	—	8	2	no	—
380	C₂	C₁₃×#2566	1	1	yes	characteristic
381	C₂	C₁₃×#3083	1	2	yes	—
382	C₂	C₁₃×#3175	1	2	yes	—
383	C₂	C₁₃×#3220	1	1	yes	characteristic
384	C₂	C₁₃×#3223	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2647	C₂	semidirect
3. C₁₃×#2068	C₂	semidirect
7. C₁₃×#1863	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
10. C₁₃×#1836	C₂	semidirect
11. C₁₃×#1768	C₂	semidirect
79. #29200	C₁₃	direct (N × H)
126. #2647	C₂×C₁₃	semidirect
128. #2068	C₂×C₁₃	semidirect
132. #1863	C₂×C₁₃	semidirect
134. #1845	C₂×C₁₃	semidirect
135. #1836	C₂×C₁₃	semidirect
136. #1768	C₂×C₁₃	semidirect
317. C₁₃	#29200	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×#2647	2
C₁₃×#2326	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#1959	2
C₁₃×#1958	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1845	2
C₁₃×#1836	2
C₁₃×#1768	2
#29200	13

Subgroups — C13×#29200 #15715539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29200 #15715539