Subgroups — C₁₃×#26981 #15713320

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2429	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2421	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#467	—	2	4	no	—
26	C₁₃×#441	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	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×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
40	C₁₃×#400	—	2	1	no	—
41	C₁₃×#398	—	2	1	no	—
42	C₁₃×#397	—	2	1	no	—
43	C₁₃×#396	—	2	1	no	—
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#389	—	2	1	no	—
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#388	—	2	1	no	—
50	C₁₃×#388	—	2	1	no	—
51	C₁₃×#387	—	2	1	no	—
52	C₁₃×#382	C₂²	1	1	yes	characteristic
53	C₁₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×Q₁₆	—	2	2	no	—
66	C₂×C₁₃×Q₁₆	—	2	2	no	—
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	2	2	no	—
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×Q₁₆	—	4	1	no	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	4	1	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	4	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	4	1	no	—
84	C₁₃×C₂²⋊Q₈	—	4	1	no	—
85	C₁₃×C₂²⋊Q₈	—	4	1	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	4	1	no	—
89	C₄×Q₈×C₁₃	—	4	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	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
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×#106	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#103	—	4	1	no	—
123	C₁₃×#103	D₄	1	4	yes	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×#97	—	2	2	no	—
126	C₁₃×#97	—	4	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	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	D₄	1	1	yes	characteristic
137	C₁₃×#95	D₄	1	1	yes	characteristic
138	#26981	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×Q₁₆	—	2	8	no	—
179	C₁₃×Q₁₆	—	4	4	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	—	4	4	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	#41	1	2	yes	—
192	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	2	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
212	C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×C₂²⋊C₄	—	4	1	no	—
214	C₁₃×C₂²⋊C₄	—	4	2	no	—
215	C₁₃×C₂²⋊C₄	—	4	2	no	—
216	C₁₃×C₂²⋊C₄	—	4	2	no	—
217	C₁₃×C₂²⋊C₄	—	4	2	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	—	4	2	no	—
223	C₄²×C₁₃	—	4	2	no	—
224	C₂×#467	C₂×C₁₃	1	1	yes	characteristic
225	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2429	C₂×C₁₃	1	1	yes	characteristic
227	#2421	C₂×C₁₃	1	1	yes	characteristic
228	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2035	C₂×C₁₃	1	1	yes	characteristic
230	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2001	C₂×C₁₃	1	1	yes	characteristic
232	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1892	C₂×C₁₃	1	1	yes	characteristic
236	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1752	C₂×C₁₃	1	1	yes	characteristic
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	#137	1	2	yes	—
246	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₁₃	—	2	2	no	—
248	Q₈×C₁₃	—	2	2	no	—
249	Q₈×C₁₃	—	2	2	no	—
250	Q₈×C₁₃	—	2	2	no	—
251	Q₈×C₁₃	—	4	1	no	—
252	Q₈×C₁₃	—	4	1	no	—
253	Q₈×C₁₃	—	4	1	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	Q₈×C₁₃	—	4	1	no	—
256	Q₈×C₁₃	—	4	1	no	—
257	Q₈×C₁₃	—	4	1	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	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	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
308	C₈×C₁₃	—	2	2	no	—
309	C₈×C₁₃	—	2	2	no	—
310	C₈×C₁₃	—	2	2	no	—
311	C₈×C₁₃	—	4	1	no	—
312	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
314	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	#467	—	2	4	no	—
322	#441	—	2	4	no	—
323	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#103	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×#103	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
336	#400	—	2	1	no	—
337	#398	—	2	1	no	—
338	#397	—	2	1	no	—
339	#396	—	2	1	no	—
340	#391	C₂²×C₁₃	1	1	yes	characteristic
341	#391	C₂²×C₁₃	1	1	yes	characteristic
342	#389	—	2	1	no	—
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	#387	—	2	1	no	—
348	#382	C₂²×C₁₃	1	1	yes	characteristic
349	#380	C₂²×C₁₃	1	1	yes	characteristic
350	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
351	#340	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	#336	C₂²×C₁₃	1	1	yes	characteristic
356	#336	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	#532	1	1	yes	characteristic
365	C₂²×C₁₃	D₄²	1	1	yes	characteristic
366	C₂²×C₁₃	#546	1	1	yes	characteristic
367	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
368	C₂²×C₁₃	#575	1	1	yes	characteristic
369	C₂²×C₁₃	#578	1	1	yes	characteristic
370	C₂²×C₁₃	#578	1	1	yes	characteristic
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	2	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	1	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	—	8	1	no	—
381	C₄×C₁₃	—	8	1	no	—
382	C₄×C₁₃	—	8	1	no	—
383	C₄×C₁₃	—	8	1	no	—
384	C₄×C₁₃	#525	1	1	yes	characteristic
385	C₄×C₁₃	#540	1	1	yes	characteristic
386	C₄×C₁₃	#546	1	1	yes	characteristic
387	C₄×C₁₃	#553	1	1	yes	characteristic
388	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×Q₁₆	—	2	2	no	—
393	C₂×Q₁₆	—	2	2	no	—
394	C₂×Q₁₆	—	2	2	no	—
395	C₂×Q₁₆	—	2	2	no	—
396	C₂×Q₁₆	—	2	2	no	—
397	C₂×Q₁₆	—	4	1	no	—
398	C₂²×C₈	—	2	2	no	—
399	C₂²×C₈	—	2	2	no	—
400	C₂²×C₈	—	4	1	no	—
401	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊Q₈	—	2	2	no	—
406	C₄⋊Q₈	—	4	1	no	—
407	C₂²⋊Q₈	—	2	2	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	2	no	—
410	C₂²⋊Q₈	—	4	1	no	—
411	C₂²⋊Q₈	—	4	1	no	—
412	C₂²⋊Q₈	—	4	1	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	4	1	no	—
416	C₄×Q₈	—	4	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	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	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
441	#107	—	2	2	no	—
442	#106	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	4	1	no	—
448	#103	—	4	1	no	—
449	#103	—	4	1	no	—
450	#103	D₄×C₁₃	1	4	yes	—
451	C₂²⋊C₈	—	2	2	no	—
452	#97	—	2	2	no	—
453	#97	—	4	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	D₄×C₁₃	1	1	yes	characteristic
464	#95	D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₁₃	—	4	2	no	—
466	C₂×C₁₃	#2464	1	1	yes	characteristic
467	C₂×C₁₃	#3177	1	1	yes	characteristic
468	C₂×C₁₃	#3181	1	1	yes	characteristic
469	C₂×C₁₃	#3269	1	1	yes	characteristic
470	C₂×C₁₃	#3270	1	1	yes	characteristic
471	C₂×C₁₃	#3312	1	1	yes	characteristic
472	C₂×C₁₃	#3313	1	1	yes	characteristic
473	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	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	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
491	C₂×Q₈	C₁₃×#41	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	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	—	2	1	no	—
506	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
512	Q₁₆	—	2	8	no	—
513	Q₁₆	—	4	4	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	4	4	no	—
524	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
525	C₂×C₈	C₁₃×#41	1	2	yes	—
526	C₂×C₈	C₁₃×#41	1	2	yes	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	4	2	no	—
557	C₄²	—	4	2	no	—
558	C₁₃	#26981	1	1	yes	characteristic, direct product factor, Sylow
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	C₁₃×#137	1	2	yes	—
566	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	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	C₂²×D₄×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
624	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
625	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
626	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
628	C₈	—	2	2	no	—
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₈	—	4	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₁₃×#532	1	1	yes	characteristic
640	C₂²	D₄²×C₁₃	1	1	yes	characteristic
641	C₂²	C₁₃×#546	1	1	yes	characteristic
642	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
643	C₂²	C₁₃×#575	1	1	yes	characteristic
644	C₂²	C₁₃×#578	1	1	yes	characteristic
645	C₂²	C₁₃×#578	1	1	yes	characteristic
646	C₄	—	4	1	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	C₁₃×#525	1	1	yes	characteristic
660	C₄	C₁₃×#540	1	1	yes	characteristic
661	C₄	C₁₃×#546	1	1	yes	characteristic
662	C₄	C₁₃×#553	1	1	yes	characteristic
663	C₂	—	4	2	no	—
664	C₂	C₁₃×#2464	1	1	yes	characteristic
665	C₂	C₁₃×#3177	1	1	yes	characteristic
666	C₂	C₁₃×#3181	1	1	yes	characteristic
667	C₂	C₁₃×#3269	1	1	yes	characteristic
668	C₂	C₁₃×#3270	1	1	yes	characteristic
669	C₂	C₁₃×#3312	1	1	yes	characteristic
670	C₂	C₁₃×#3313	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#441	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
7. C₁₃×#2016	C₂	semidirect
9. C₁₃×#1960	C₂	semidirect
10. C₁₃×#1935	C₂	semidirect
11. C₁₃×#1935	C₂	semidirect
13. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1863	C₂	semidirect
138. #26981	C₁₃	direct (N × H)
225. C₂×#441	C₂×C₁₃	semidirect
228. #2085	C₂×C₁₃	semidirect
230. #2016	C₂×C₁₃	semidirect
232. #1960	C₂×C₁₃	semidirect
233. #1935	C₂×C₁₃	semidirect
234. #1935	C₂×C₁₃	semidirect
236. #1878	C₂×C₁₃	semidirect
237. #1863	C₂×C₁₃	semidirect
558. C₁₃	#26981	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×#467	2
C₂×C₁₃×#441	2
C₁₃×#2429	2
C₁₃×#2421	2
C₁₃×#2085	2
C₁₃×#2035	2
C₁₃×#2016	2
C₁₃×#2001	2
C₁₃×#1960	2
C₁₃×#1935	2
C₁₃×#1892	2
C₁₃×#1878	2
C₁₃×#1863	2
C₁₃×#1752	2
#26981	13

Subgroups — C13×#26981 #15713320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26981 #15713320