Subgroups — C₁₃×#26188 #15712527

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1862	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	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₁₃×#463	—	2	4	no	—
25	C₁₃×#440	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₁₃×#399	—	2	1	no	—
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#385	—	2	1	no	—
50	C₁₃×#384	C₂²	1	1	yes	characteristic
51	C₁₃×#380	—	2	1	no	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
70	C₂×C₁₃×D₈	—	2	2	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂×C₁₃×D₈	—	2	2	no	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	4	1	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	4	1	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	4	1	no	—
86	C₄×D₄×C₁₃	—	4	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#107	—	2	2	no	—
115	C₁₃×#107	—	4	1	no	—
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	4	1	no	—
125	C₁₃×#97	—	2	2	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	C₁₃×#95	D₄	1	1	yes	characteristic
133	#26188	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₁₃	#41	1	2	yes	—
153	C₂×D₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	8	1	no	—
168	C₂²×C₄×C₁₃	—	8	1	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₁₃×SD₁₆	—	2	8	no	—
177	C₁₃×D₈	—	4	4	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	4	2	no	—
203	C₁₃×C₄⋊C₄	—	4	2	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	8	1	no	—
206	C₁₃×C₄⋊C₄	—	8	1	no	—
207	C₁₃×C₄⋊C₄	#41	1	2	yes	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	—	4	2	no	—
212	C₁₃×C₂²⋊C₄	—	4	2	no	—
213	C₁₃×C₂²⋊C₄	—	4	2	no	—
214	C₁₃×C₂²⋊C₄	—	4	2	no	—
215	C₁₃×C₂²⋊C₄	—	8	1	no	—
216	C₁₃×C₂²⋊C₄	—	8	1	no	—
217	C₄²×C₁₃	—	2	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	2	1	no	—
223	C₄²×C₁₃	—	4	2	no	—
224	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
225	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2448	C₂×C₁₃	1	1	yes	characteristic, complemented
227	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1917	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1879	C₂×C₁₃	1	1	yes	characteristic
235	#1879	C₂×C₁₃	1	1	yes	characteristic
236	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	4	1	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	2	no	—
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	4	1	no	—
257	Q₈×C₁₃	—	4	1	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	2	no	—
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	1	no	—
265	D₄×C₁₃	#123	1	4	yes	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	4	8	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	8	4	no	—
303	C₂×C₄×C₁₃	—	8	4	no	—
304	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
311	C₈×C₁₃	—	2	2	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₈×C₁₃	—	4	1	no	—
315	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	—	2	1	no	—
323	#463	—	2	4	no	—
324	#440	—	2	4	no	—
325	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
337	#399	—	2	1	no	—
338	#397	—	2	1	no	—
339	#391	C₂²×C₁₃	1	1	yes	characteristic
340	#390	C₂²×C₁₃	1	1	yes	characteristic
341	#390	C₂²×C₁₃	1	1	yes	characteristic
342	#389	C₂²×C₁₃	1	1	yes	characteristic
343	#389	C₂²×C₁₃	1	1	yes	characteristic
344	#389	C₂²×C₁₃	1	1	yes	characteristic
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#385	—	2	1	no	—
348	#385	—	2	1	no	—
349	#384	C₂²×C₁₃	1	1	yes	characteristic
350	#380	—	2	1	no	—
351	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
352	#340	C₂²×C₁₃	1	1	yes	characteristic
353	#340	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#340	C₂²×C₁₃	1	1	yes	characteristic
356	#336	C₂²×C₁₃	1	1	yes	characteristic
357	#336	C₂²×C₁₃	1	1	yes	characteristic
358	#336	C₂²×C₁₃	1	1	yes	characteristic
359	#336	C₂²×C₁₃	1	1	yes	characteristic
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	2	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	8	1	no	—
371	C₂²×C₁₃	—	8	1	no	—
372	C₂²×C₁₃	—	8	1	no	—
373	C₂²×C₁₃	—	8	1	no	—
374	C₂²×C₁₃	#525	1	1	yes	characteristic
375	C₂²×C₁₃	D₄²	1	1	yes	characteristic
376	C₂²×C₁₃	#548	1	1	yes	characteristic
377	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂²×C₁₃	#575	1	1	yes	characteristic
379	C₂²×C₁₃	#576	1	1	yes	characteristic
380	C₂²×C₁₃	#578	1	1	yes	characteristic
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	2	no	—
385	C₄×C₁₃	—	4	1	no	—
386	C₄×C₁₃	—	4	1	no	—
387	C₄×C₁₃	—	4	1	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	8	1	no	—
390	C₄×C₁₃	—	8	1	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
394	C₄×C₁₃	#539	1	1	yes	characteristic
395	C₄×C₁₃	#547	1	1	yes	characteristic
396	C₄×C₁₃	#553	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
406	C₂×D₈	—	2	2	no	—
407	C₂×D₈	—	2	2	no	—
408	C₂×D₈	—	2	2	no	—
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	#124	—	2	2	no	—
414	#124	—	4	1	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	4	1	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	4	1	no	—
422	C₄×D₄	—	4	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	4	4	no	—
430	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
450	#107	—	2	2	no	—
451	#107	—	4	1	no	—
452	C₄⋊C₈	—	2	2	no	—
453	#103	—	2	2	no	—
454	#103	—	2	2	no	—
455	#103	—	2	2	no	—
456	#102	—	2	2	no	—
457	#102	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	—	4	1	no	—
461	#97	—	2	2	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	D₄×C₁₃	1	1	yes	characteristic
468	#95	D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₁₃	—	4	4	no	—
470	C₂×C₁₃	—	16	1	no	—
471	C₂×C₁₃	#2443	1	1	yes	characteristic
472	C₂×C₁₃	#3114	1	1	yes	characteristic
473	C₂×C₁₃	#3124	1	1	yes	characteristic
474	C₂×C₁₃	#3269	1	1	yes	characteristic
475	C₂×C₁₃	#3274	1	1	yes	characteristic
476	C₂×C₁₃	#3367	1	1	yes	characteristic
477	C₂×C₁₃	#3370	1	1	yes	characteristic
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
496	C₂×D₄	C₁₃×#41	1	2	yes	—
497	C₂×D₄	C₁₃×#41	1	2	yes	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	8	1	no	—
512	C₂²×C₄	—	8	1	no	—
513	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
520	SD₁₆	—	2	8	no	—
521	D₈	—	4	4	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	8	1	no	—
550	C₄⋊C₄	—	8	1	no	—
551	C₄⋊C₄	C₁₃×#41	1	2	yes	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	4	2	no	—
568	C₁₃	#26188	1	1	yes	characteristic, direct product factor, Sylow
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	C₁₃×#123	1	4	yes	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	—	8	4	no	—
634	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
635	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
637	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
638	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
639	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	C₁₃×#525	1	1	yes	characteristic
660	C₂²	D₄²×C₁₃	1	1	yes	characteristic
661	C₂²	C₁₃×#548	1	1	yes	characteristic
662	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
663	C₂²	C₁₃×#575	1	1	yes	characteristic
664	C₂²	C₁₃×#576	1	1	yes	characteristic
665	C₂²	C₁₃×#578	1	1	yes	characteristic
666	C₄	—	2	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
679	C₄	C₁₃×#539	1	1	yes	characteristic
680	C₄	C₁₃×#547	1	1	yes	characteristic
681	C₄	C₁₃×#553	1	1	yes	characteristic
682	C₂	—	4	4	no	—
683	C₂	—	16	1	no	—
684	C₂	C₁₃×#2443	1	1	yes	characteristic
685	C₂	C₁₃×#3114	1	1	yes	characteristic
686	C₂	C₁₃×#3124	1	1	yes	characteristic
687	C₂	C₁₃×#3269	1	1	yes	characteristic
688	C₂	C₁₃×#3274	1	1	yes	characteristic
689	C₂	C₁₃×#3367	1	1	yes	characteristic
690	C₂	C₁₃×#3370	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#440	C₂	semidirect
3. C₁₃×#2448	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2093	C₂	semidirect
6. C₁₃×#2087	C₂	semidirect
7. C₁₃×#2072	C₂	semidirect
8. C₁₃×#2042	C₂	semidirect
9. C₁₃×#1936	C₂	semidirect
10. C₁₃×#1917	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1863	C₂	semidirect
15. C₁₃×#1862	C₂	semidirect
133. #26188	C₁₃	direct (N × H)
225. C₂×#440	C₂×C₁₃	semidirect
226. #2448	C₂×C₁₃	semidirect
227. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
228. #2093	C₂×C₁₃	semidirect
229. #2087	C₂×C₁₃	semidirect
230. #2072	C₂×C₁₃	semidirect
231. #2042	C₂×C₁₃	semidirect
232. #1936	C₂×C₁₃	semidirect
233. #1917	C₂×C₁₃	semidirect
236. #1877	C₂×C₁₃	semidirect
237. #1863	C₂×C₁₃	semidirect
238. #1862	C₂×C₁₃	semidirect
568. C₁₃	#26188	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×#463	2
C₂×C₁₃×#440	2
C₁₃×#2448	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2093	2
C₁₃×#2087	2
C₁₃×#2072	2
C₁₃×#2042	2
C₁₃×#1936	2
C₁₃×#1917	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1863	2
C₁₃×#1862	2
#26188	13

Subgroups — C13×#26188 #15712527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26188 #15712527