Subgroups — C₁₃×#32831 #15719170

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#2641	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2041	C₂	1	2	yes	maximal
11	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#107	C₂²	1	2	yes	—
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₁₃×#400	—	2	2	no	—
22	C₁₃×#398	—	2	2	no	—
23	C₁₃×#394	—	2	2	no	—
24	C₁₃×#394	—	2	2	no	—
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#390	C₂²	1	1	yes	characteristic
28	C₁₃×#390	C₂²	1	1	yes	characteristic
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#376	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×#127	—	4	2	no	—
46	C₁₃×#125	—	4	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	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	C₂³	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#107	—	4	2	no	—
64	C₁₃×#106	—	4	2	no	—
65	C₁₃×C₄⋊C₈	—	4	2	no	—
66	C₁₃×#102	—	4	2	no	—
67	C₁₃×#102	—	4	2	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₁₃×#102	—	4	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	D₄	1	2	yes	—
74	C₁₃×#95	D₄	1	2	yes	—
75	#32831	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	1	no	—
77	C₂⁴×C₁₃	—	2	1	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	8	2	no	—
89	C₂×D₄×C₁₃	—	8	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
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	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	4	2	no	—
112	C₁₃×C₄⋊C₄	—	4	2	no	—
113	C₁₃×C₄⋊C₄	—	8	2	no	—
114	C₁₃×C₄⋊C₄	—	8	2	no	—
115	C₁₃×C₄⋊C₄	—	8	2	no	—
116	C₁₃×C₂²⋊C₄	—	8	2	no	—
117	C₁₃×C₂²⋊C₄	—	8	2	no	—
118	C₁₃×C₂²⋊C₄	—	8	2	no	—
119	C₁₃×C₂²⋊C₄	—	8	2	no	—
120	C₄²×C₁₃	—	2	1	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	1	no	—
124	#2647	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#2641	C₂×C₁₃	1	1	yes	characteristic
126	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
127	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2067	C₂×C₁₃	1	2	yes	complemented
131	#2065	C₂×C₁₃	1	2	yes	complemented
132	#2059	C₂×C₁₃	1	2	yes	complemented
133	#2041	C₂×C₁₃	1	2	yes	—
134	#1832	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	—	4	1	no	—
137	C₂³×C₁₃	—	4	1	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	4	1	no	—
140	C₂³×C₁₃	—	4	1	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	D₄×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	4	2	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	8	4	no	—
151	D₄×C₁₃	—	8	4	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
175	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
176	C₈×C₁₃	—	4	2	no	—
177	C₈×C₁₃	—	4	2	no	—
178	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×#107	C₂²×C₁₃	1	2	yes	—
181	C₂×#106	C₂²×C₁₃	1	2	yes	—
182	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
183	C₂×#102	C₂²×C₁₃	1	2	yes	—
184	C₂×#102	C₂²×C₁₃	1	2	yes	—
185	C₂×#102	C₂²×C₁₃	1	2	yes	—
186	C₂×#102	C₂²×C₁₃	1	2	yes	—
187	#400	—	2	2	no	—
188	#398	—	2	2	no	—
189	#394	—	2	2	no	—
190	#394	—	2	2	no	—
191	#390	C₂²×C₁₃	1	1	yes	characteristic
192	#390	C₂²×C₁₃	1	1	yes	characteristic
193	#390	C₂²×C₁₃	1	1	yes	characteristic
194	#390	C₂²×C₁₃	1	1	yes	characteristic
195	#389	C₂²×C₁₃	1	2	yes	—
196	#389	C₂²×C₁₃	1	2	yes	—
197	#384	C₂²×C₁₃	1	1	yes	characteristic
198	#382	C₂²×C₁₃	1	1	yes	characteristic
199	#376	C₂²×C₁₃	1	1	yes	characteristic
200	#340	C₂²×C₁₃	1	2	yes	—
201	#340	C₂²×C₁₃	1	2	yes	—
202	#336	C₂²×C₁₃	1	2	yes	—
203	#336	C₂²×C₁₃	1	1	yes	characteristic
204	#336	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×C₁₃	—	8	1	no	—
206	C₂²×C₁₃	—	8	1	no	—
207	C₂²×C₁₃	—	8	1	no	—
208	C₂²×C₁₃	—	8	1	no	—
209	C₂²×C₁₃	—	8	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	#535	1	1	yes	characteristic
216	C₂²×C₁₃	#536	1	1	yes	characteristic
217	C₂²×C₁₃	#537	1	1	yes	characteristic
218	C₂²×C₁₃	#576	1	2	yes	—
219	C₂²×C₁₃	#577	1	2	yes	—
220	C₄×C₁₃	—	4	1	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	8	1	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	—	8	1	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	#562	1	2	yes	—
229	C₄×C₁₃	#563	1	2	yes	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	#127	—	4	2	no	—
237	#125	—	4	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
254	#107	—	4	2	no	—
255	#106	—	4	2	no	—
256	C₄⋊C₈	—	4	2	no	—
257	#102	—	4	2	no	—
258	#102	—	4	2	no	—
259	#102	—	4	2	no	—
260	#102	—	4	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	D₄×C₁₃	1	2	yes	—
265	#95	D₄×C₁₃	1	2	yes	—
266	C₂×C₁₃	—	16	1	no	—
267	C₂×C₁₃	—	16	1	no	—
268	C₂×C₁₃	#2820	1	1	yes	characteristic
269	C₂×C₁₃	#3220	1	1	yes	characteristic
270	C₂×C₁₃	#3222	1	1	yes	characteristic
271	C₂×C₁₃	#3241	1	2	yes	—
272	C₂×C₁₃	#3257	1	2	yes	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	8	2	no	—
286	C₂×D₄	—	8	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	8	2	no	—
311	C₄⋊C₄	—	8	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₂²⋊C₄	—	8	2	no	—
314	C₂²⋊C₄	—	8	2	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	1	no	—
321	C₁₃	#32831	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	4	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
362	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	8	1	no	—
366	C₂²	—	8	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₁₃×#535	1	1	yes	characteristic
376	C₂²	C₁₃×#536	1	1	yes	characteristic
377	C₂²	C₁₃×#537	1	1	yes	characteristic
378	C₂²	C₁₃×#576	1	2	yes	—
379	C₂²	C₁₃×#577	1	2	yes	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	2	no	—
388	C₄	C₁₃×#562	1	2	yes	—
389	C₄	C₁₃×#563	1	2	yes	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	C₁₃×#2820	1	1	yes	characteristic
393	C₂	C₁₃×#3220	1	1	yes	characteristic
394	C₂	C₁₃×#3222	1	1	yes	characteristic
395	C₂	C₁₃×#3241	1	2	yes	—
396	C₂	C₁₃×#3257	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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×#2094	C₂	semidirect
4. C₁₃×#2093	C₂	semidirect
5. C₁₃×#2073	C₂	semidirect
6. C₁₃×#2073	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#2059	C₂	semidirect
11. C₁₃×#1832	C₂	semidirect
75. #32831	C₁₃	direct (N × H)
124. #2647	C₂×C₁₃	semidirect
126. #2094	C₂×C₁₃	semidirect
127. #2093	C₂×C₁₃	semidirect
128. #2073	C₂×C₁₃	semidirect
129. #2073	C₂×C₁₃	semidirect
130. #2067	C₂×C₁₃	semidirect
131. #2065	C₂×C₁₃	semidirect
132. #2059	C₂×C₁₃	semidirect
134. #1832	C₂×C₁₃	semidirect
321. C₁₃	#32831	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×#2641	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2073	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#2059	2
C₁₃×#2041	2
C₁₃×#1832	2
#32831	13

Subgroups — C13×#32831 #15719170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32831 #15719170