Subgroups — C₁₃×#24204 #15710543

Order 3328.

1208 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2011	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₁₃×#559	—	2	4	no	—
20	C₁₃×#559	—	2	4	no	—
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#463	—	2	4	no	—
35	C₁₃×#442	—	2	4	no	—
36	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
49	C₁₃×#396	—	2	1	no	—
50	C₁₃×#396	—	2	1	no	—
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#384	C₂²	1	1	yes	characteristic
56	C₁₃×#380	—	2	1	no	—
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×SD₁₆	—	4	1	no	—
76	C₂×C₁₃×D₈	—	2	2	no	—
77	C₂×C₁₃×D₈	—	2	2	no	—
78	C₂×C₁₃×D₈	—	2	2	no	—
79	C₂×C₁₃×D₈	—	2	2	no	—
80	C₂×C₁₃×D₈	—	2	2	no	—
81	C₂×C₁₃×D₈	—	4	1	no	—
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	—	2	2	no	—
88	C₁₃×#124	—	2	8	no	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	D₄	1	4	yes	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×#123	—	2	8	no	—
95	C₁₃×C₂²⋊Q₈	—	4	4	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	D₄	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×#106	—	2	2	no	—
135	C₁₃×C₄⋊C₈	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	4	1	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	2	2	no	—
143	C₁₃×#102	—	4	1	no	—
144	C₁₃×#102	—	4	1	no	—
145	C₁₃×#102	—	4	1	no	—
146	C₁₃×#97	—	2	2	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	—	2	1	no	—
149	#24204	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	—	2	1	no	—
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	2	no	—
154	C₂×Q₈×C₁₃	—	2	2	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	4	1	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	—	4	2	no	—
181	C₂×D₄×C₁₃	—	8	1	no	—
182	C₂×D₄×C₁₃	—	8	1	no	—
183	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₁₃	#41	1	2	yes	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	1	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	4	2	no	—
195	C₂²×C₄×C₁₃	—	4	2	no	—
196	C₂²×C₄×C₁₃	—	8	1	no	—
197	C₂²×C₄×C₁₃	—	8	1	no	—
198	C₂²×C₄×C₁₃	—	8	1	no	—
199	C₂²×C₄×C₁₃	—	8	1	no	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×SD₁₆	—	4	4	no	—
208	C₁₃×D₈	—	2	8	no	—
209	C₁₃×D₈	—	4	4	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	#41	1	2	yes	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	4	2	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	—	4	2	no	—
236	C₁₃×C₄⋊C₄	—	8	1	no	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	4	2	no	—
245	C₁₃×C₂²⋊C₄	—	4	2	no	—
246	C₁₃×C₂²⋊C₄	—	4	2	no	—
247	C₁₃×C₂²⋊C₄	—	8	1	no	—
248	C₁₃×C₂²⋊C₄	—	8	1	no	—
249	C₄²×C₁₃	—	2	4	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	C₂×D₄	1	2	yes	—
255	C₄²×C₁₃	C₂×D₄	1	2	yes	—
256	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2538	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2012	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2011	C₂×C₁₃	1	1	yes	characteristic
264	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1959	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	—	4	1	no	—
280	C₂³×C₁₃	—	4	1	no	—
281	C₂³×C₁₃	—	4	1	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₁₃	—	2	2	no	—
294	Q₈×C₁₃	—	2	2	no	—
295	Q₈×C₁₃	—	4	4	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	D₄×C₁₃	—	2	2	no	—
299	D₄×C₁₃	—	2	2	no	—
300	D₄×C₁₃	—	2	2	no	—
301	D₄×C₁₃	—	2	2	no	—
302	D₄×C₁₃	—	2	2	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	4	8	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	8	4	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	8	4	no	—
343	C₂×C₄×C₁₃	—	8	4	no	—
344	C₂×C₄×C₁₃	—	8	4	no	—
345	C₂×C₄×C₁₃	#120	1	2	yes	—
346	C₂×C₄×C₁₃	#120	1	2	yes	—
347	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
354	C₈×C₁₃	—	2	2	no	—
355	C₈×C₁₃	—	4	1	no	—
356	C₈×C₁₃	—	4	1	no	—
357	C₈×C₁₃	—	4	1	no	—
358	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
361	#559	—	2	4	no	—
362	#559	—	2	4	no	—
363	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#124	—	2	1	no	—
365	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#123	—	2	1	no	—
368	C₂×#123	—	2	1	no	—
369	C₂×C₂²⋊Q₈	—	2	1	no	—
370	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄×D₄	—	2	1	no	—
373	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
376	#463	—	2	4	no	—
377	#442	—	2	4	no	—
378	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
391	#396	—	2	1	no	—
392	#396	—	2	1	no	—
393	#390	C₂²×C₁₃	1	1	yes	characteristic
394	#390	C₂²×C₁₃	1	1	yes	characteristic
395	#389	C₂²×C₁₃	1	1	yes	characteristic
396	#389	C₂²×C₁₃	1	1	yes	characteristic
397	#384	C₂²×C₁₃	1	1	yes	characteristic
398	#380	—	2	1	no	—
399	#340	C₂²×C₁₃	1	1	yes	characteristic
400	#340	C₂²×C₁₃	1	1	yes	characteristic
401	#336	C₂²×C₁₃	1	1	yes	characteristic
402	#336	C₂²×C₁₃	1	1	yes	characteristic
403	#336	C₂²×C₁₃	1	1	yes	characteristic
404	#336	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	2	no	—
407	C₂²×C₁₃	—	4	2	no	—
408	C₂²×C₁₃	—	4	2	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	2	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	8	1	no	—
415	C₂²×C₁₃	—	8	1	no	—
416	C₂²×C₁₃	—	8	1	no	—
417	C₂²×C₁₃	—	8	1	no	—
418	C₂²×C₁₃	—	8	1	no	—
419	C₂²×C₁₃	—	8	1	no	—
420	C₂²×C₁₃	—	8	1	no	—
421	C₂²×C₁₃	—	8	1	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	—	8	1	no	—
424	C₂²×C₁₃	—	8	1	no	—
425	C₂²×C₁₃	—	8	1	no	—
426	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
427	C₂²×C₁₃	#548	1	1	yes	characteristic
428	C₂²×C₁₃	#550	1	1	yes	characteristic
429	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
430	C₂²×C₁₃	#575	1	1	yes	characteristic
431	C₂²×C₁₃	#576	1	1	yes	characteristic
432	C₂²×C₁₃	#577	1	1	yes	characteristic
433	C₄×C₁₃	—	2	2	no	—
434	C₄×C₁₃	—	2	2	no	—
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	4	2	no	—
437	C₄×C₁₃	—	4	1	no	—
438	C₄×C₁₃	—	4	1	no	—
439	C₄×C₁₃	—	4	1	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	8	1	no	—
442	C₄×C₁₃	—	8	1	no	—
443	C₄×C₁₃	—	8	1	no	—
444	C₄×C₁₃	#525	1	1	yes	characteristic
445	C₄×C₁₃	#537	1	1	yes	characteristic
446	C₄×C₁₃	#546	1	1	yes	characteristic
447	C₄×C₁₃	#547	1	1	yes	characteristic
448	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂×SD₁₆	—	2	2	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×D₈	—	2	2	no	—
462	C₂×D₈	—	2	2	no	—
463	C₂×D₈	—	2	2	no	—
464	C₂×D₈	—	2	2	no	—
465	C₂×D₈	—	2	2	no	—
466	C₂×D₈	—	4	1	no	—
467	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
471	#127	—	2	2	no	—
472	#127	—	2	2	no	—
473	#124	—	2	8	no	—
474	#124	—	2	2	no	—
475	#124	—	2	2	no	—
476	#124	—	2	2	no	—
477	#124	D₄×C₁₃	1	4	yes	—
478	#123	—	2	8	no	—
479	#123	—	2	8	no	—
480	C₂²⋊Q₈	—	4	4	no	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×D₄	—	2	8	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	D₄×C₁₃	1	4	yes	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	#106	—	2	2	no	—
520	C₄⋊C₈	—	2	2	no	—
521	#103	—	2	2	no	—
522	#103	—	2	2	no	—
523	#103	—	4	1	no	—
524	#102	—	2	2	no	—
525	#102	—	2	2	no	—
526	#102	—	2	2	no	—
527	#102	—	2	2	no	—
528	#102	—	4	1	no	—
529	#102	—	4	1	no	—
530	#102	—	4	1	no	—
531	#97	—	2	2	no	—
532	#95	—	2	1	no	—
533	#95	—	2	1	no	—
534	C₂×C₁₃	—	8	2	no	—
535	C₂×C₁₃	—	8	2	no	—
536	C₂×C₁₃	—	8	2	no	—
537	C₂×C₁₃	#2407	1	1	yes	characteristic
538	C₂×C₁₃	#3006	1	1	yes	characteristic
539	C₂×C₁₃	#3012	1	1	yes	characteristic
540	C₂×C₁₃	#3370	1	1	yes	characteristic
541	C₂×C₁₃	#3373	1	1	yes	characteristic
542	C₂×C₁₃	#3399	1	1	yes	characteristic
543	C₂×C₁₃	#3401	1	1	yes	characteristic
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	1	no	—
546	C₂⁴	—	2	1	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	8	1	no	—
576	C₂×D₄	—	8	1	no	—
577	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
578	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₂×D₄	C₁₃×#41	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	8	1	no	—
591	C₂²×C₄	—	8	1	no	—
592	C₂²×C₄	—	8	1	no	—
593	C₂²×C₄	—	8	1	no	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
601	SD₁₆	—	4	4	no	—
602	D₈	—	2	8	no	—
603	D₈	—	4	4	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	C₁₃×#41	1	2	yes	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	8	1	no	—
631	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	—	8	1	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	C₂×D₄×C₁₃	1	2	yes	—
649	C₄²	C₂×D₄×C₁₃	1	2	yes	—
650	C₁₃	#24204	1	1	yes	characteristic, direct product factor, Sylow
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	4	no	—
676	Q₈	—	4	1	no	—
677	Q₈	—	4	1	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	4	1	no	—
691	D₄	—	8	4	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	C₁₃×#120	1	2	yes	—
726	C₂×C₄	C₁₃×#120	1	2	yes	—
727	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
731	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
732	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	4	1	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	—	8	1	no	—
758	C₂²	—	8	1	no	—
759	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
760	C₂²	C₁₃×#548	1	1	yes	characteristic
761	C₂²	C₁₃×#550	1	1	yes	characteristic
762	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
763	C₂²	C₁₃×#575	1	1	yes	characteristic
764	C₂²	C₁₃×#576	1	1	yes	characteristic
765	C₂²	C₁₃×#577	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	8	1	no	—
775	C₄	—	8	1	no	—
776	C₄	—	8	1	no	—
777	C₄	C₁₃×#525	1	1	yes	characteristic
778	C₄	C₁₃×#537	1	1	yes	characteristic
779	C₄	C₁₃×#546	1	1	yes	characteristic
780	C₄	C₁₃×#547	1	1	yes	characteristic
781	C₂	—	8	2	no	—
782	C₂	—	8	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₁₃×#2407	1	1	yes	characteristic
785	C₂	C₁₃×#3006	1	1	yes	characteristic
786	C₂	C₁₃×#3012	1	1	yes	characteristic
787	C₂	C₁₃×#3370	1	1	yes	characteristic
788	C₂	C₁₃×#3373	1	1	yes	characteristic
789	C₂	C₁₃×#3399	1	1	yes	characteristic
790	C₂	C₁₃×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#559	C₂	semidirect
2. C₂×C₁₃×#463	C₂	semidirect
3. C₂×C₁₃×#442	C₂	semidirect
4. C₁₃×#2538	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
6. C₁₃×#2041	C₂	semidirect
7. C₁₃×#2012	C₂	semidirect
9. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1959	C₂	semidirect
11. C₁₃×#1880	C₂	semidirect
12. C₁₃×#1879	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
14. C₁₃×#1864	C₂	semidirect
15. C₁₃×#1802	C₂	semidirect
149. #24204	C₁₃	direct (N × H)
256. C₂×#559	C₂×C₁₃	semidirect
257. C₂×#463	C₂×C₁₃	semidirect
258. C₂×#442	C₂×C₁₃	semidirect
259. #2538	C₂×C₁₃	semidirect
260. #2042	C₂×C₁₃	semidirect
261. #2041	C₂×C₁₃	semidirect
262. #2012	C₂×C₁₃	semidirect
264. #1985	C₂×C₁₃	semidirect
265. #1959	C₂×C₁₃	semidirect
266. #1880	C₂×C₁₃	semidirect
267. #1879	C₂×C₁₃	semidirect
268. #1865	C₂×C₁₃	semidirect
269. #1864	C₂×C₁₃	semidirect
270. #1802	C₂×C₁₃	semidirect
650. C₁₃	#24204	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#559	2
C₂×C₁₃×#463	2
C₂×C₁₃×#442	2
C₁₃×#2538	2
C₁₃×#2042	2
C₁₃×#2041	2
C₁₃×#2012	2
C₁₃×#2011	2
C₁₃×#1985	2
C₁₃×#1959	2
C₁₃×#1880	2
C₁₃×#1879	2
C₁₃×#1865	2
C₁₃×#1864	2
C₁₃×#1802	2
#24204	13

Subgroups — C13×#24204 #15710543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24204 #15710543