Subgroups — C₁₃×#24766 #15711105

Order 3328.

960 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊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×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#468	—	2	4	no	—
27	C₁₃×#465	—	2	4	no	—
28	C₁₃×#461	—	2	4	no	—
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₁₃×#424	—	2	4	no	—
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	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×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₁₃×#398	—	2	1	no	—
45	C₁₃×#398	—	2	1	no	—
46	C₁₃×#397	—	2	1	no	—
47	C₁₃×#397	—	2	1	no	—
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#390	—	2	1	no	—
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#385	—	2	1	no	—
56	C₁₃×#382	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	2	no	—
73	C₂×C₁₃×SD₁₆	—	4	1	no	—
74	C₂×C₁₃×SD₁₆	—	4	1	no	—
75	C₂×C₁₃×M₁₆	—	2	2	no	—
76	C₂×C₁₃×M₁₆	—	2	2	no	—
77	C₂×C₁₃×M₁₆	—	4	1	no	—
78	C₂²×C₈×C₁₃	—	2	2	no	—
79	C₂²×C₈×C₁₃	—	2	2	no	—
80	C₂²×C₈×C₁₃	—	4	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊Q₈	—	2	2	no	—
86	C₁₃×C₄⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	D₄	1	4	yes	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₁₃×#117	—	2	2	no	—
96	C₁₃×#117	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	—	2	2	no	—
122	C₁₃×#106	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	2	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
127	C₁₃×#103	—	2	2	no	—
128	C₁₃×#103	—	2	2	no	—
129	C₁₃×#103	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	4	1	no	—
132	C₁₃×#103	—	4	1	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	C₁₃×#95	—	2	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	#24766	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	8	1	no	—
166	C₂×D₄×C₁₃	—	8	1	no	—
167	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	8	1	no	—
181	C₂²×C₄×C₁₃	—	8	1	no	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	#41	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₁₃×SD₁₆	—	4	4	no	—
191	C₁₃×SD₁₆	—	4	4	no	—
192	C₁₃×M₁₆	—	4	4	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	4	4	no	—
204	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₄⋊C₄	—	4	2	no	—
219	C₁₃×C₄⋊C₄	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	8	1	no	—
222	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	2	no	—
226	C₁₃×C₂²⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	4	2	no	—
228	C₁₃×C₂²⋊C₄	—	4	2	no	—
229	C₁₃×C₂²⋊C₄	—	8	1	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	8	1	no	—
235	C₄²×C₁₃	C₂×D₄	1	2	yes	—
236	C₄²×C₁₃	#41	1	2	yes	—
237	C₂×#468	C₂×C₁₃	1	1	yes	characteristic
238	C₂×#465	C₂×C₁₃	1	1	yes	characteristic
239	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2621	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2324	C₂×C₁₃	1	1	yes	characteristic
243	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1892	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	#121	1	2	yes	—
266	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₁₃	—	4	1	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	Q₈×C₁₃	—	4	1	no	—
272	Q₈×C₁₃	—	4	1	no	—
273	Q₈×C₁₃	—	4	1	no	—
274	Q₈×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	2	2	no	—
276	D₄×C₁₃	—	2	2	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	8	4	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	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	#121	1	2	yes	—
319	C₂×C₄×C₁₃	#121	1	2	yes	—
320	C₂×C₄×C₁₃	#121	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
327	C₈×C₁₃	—	2	2	no	—
328	C₈×C₁₃	—	2	2	no	—
329	C₈×C₁₃	—	4	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
334	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
341	#468	—	2	4	no	—
342	#465	—	2	4	no	—
343	#461	—	2	4	no	—
344	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
346	#424	—	2	4	no	—
347	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
359	#398	—	2	1	no	—
360	#398	—	2	1	no	—
361	#397	—	2	1	no	—
362	#397	—	2	1	no	—
363	#391	C₂²×C₁₃	1	1	yes	characteristic
364	#391	C₂²×C₁₃	1	1	yes	characteristic
365	#390	—	2	1	no	—
366	#390	C₂²×C₁₃	1	1	yes	characteristic
367	#389	C₂²×C₁₃	1	1	yes	characteristic
368	#388	—	2	1	no	—
369	#386	—	2	1	no	—
370	#385	—	2	1	no	—
371	#382	C₂²×C₁₃	1	1	yes	characteristic
372	#380	C₂²×C₁₃	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
374	#340	C₂²×C₁₃	1	1	yes	characteristic
375	#340	C₂²×C₁₃	1	1	yes	characteristic
376	#340	C₂²×C₁₃	1	1	yes	characteristic
377	#340	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	4	1	no	—
382	C₂²×C₁₃	—	4	1	no	—
383	C₂²×C₁₃	—	4	1	no	—
384	C₂²×C₁₃	—	4	1	no	—
385	C₂²×C₁₃	—	4	2	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	—	8	1	no	—
390	C₂²×C₁₃	—	8	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
393	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
394	C₂²×C₁₃	#537	1	1	yes	characteristic
395	C₂²×C₁₃	#577	1	1	yes	characteristic
396	C₂²×C₁₃	#577	1	1	yes	characteristic
397	C₂²×C₁₃	#577	1	1	yes	characteristic
398	C₂²×C₁₃	#578	1	1	yes	characteristic
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	1	no	—
404	C₄×C₁₃	—	4	1	no	—
405	C₄×C₁₃	—	8	1	no	—
406	C₄×C₁₃	—	8	1	no	—
407	C₄×C₁₃	—	8	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	—	8	1	no	—
411	C₄×C₁₃	D₄²	1	1	yes	characteristic
412	C₄×C₁₃	#547	1	1	yes	characteristic
413	C₄×C₁₃	#548	1	1	yes	characteristic
414	C₄×C₁₃	#553	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×SD₁₆	—	2	2	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	2	2	no	—
425	C₂×SD₁₆	—	4	1	no	—
426	C₂×SD₁₆	—	4	1	no	—
427	C₂×M₁₆	—	2	2	no	—
428	C₂×M₁₆	—	2	2	no	—
429	C₂×M₁₆	—	4	1	no	—
430	C₂²×C₈	—	2	2	no	—
431	C₂²×C₈	—	2	2	no	—
432	C₂²×C₈	—	4	1	no	—
433	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄⋊Q₈	—	2	2	no	—
438	C₄⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	#121	—	2	2	no	—
444	#121	D₄×C₁₃	1	4	yes	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	#107	—	2	2	no	—
474	#106	—	2	2	no	—
475	C₄⋊C₈	—	2	2	no	—
476	C₄⋊C₈	—	2	2	no	—
477	C₄⋊C₈	—	2	2	no	—
478	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	#103	—	4	1	no	—
484	#103	—	4	1	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	—	2	1	no	—
496	C₂×C₁₃	—	4	2	no	—
497	C₂×C₁₃	—	8	2	no	—
498	C₂×C₁₃	#2416	1	1	yes	characteristic
499	C₂×C₁₃	#3042	1	1	yes	characteristic
500	C₂×C₁₃	#3046	1	1	yes	characteristic
501	C₂×C₁₃	#3057	1	1	yes	characteristic
502	C₂×C₁₃	#3063	1	1	yes	characteristic
503	C₂×C₁₃	#3258	1	1	yes	characteristic
504	C₂×C₁₃	#3260	1	1	yes	characteristic
505	C₂⁴	—	2	1	no	—
506	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	8	1	no	—
526	C₂×D₄	—	8	1	no	—
527	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	8	1	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
548	C₂²×C₄	C₁₃×#41	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	SD₁₆	—	4	4	no	—
551	SD₁₆	—	4	4	no	—
552	M₁₆	—	4	4	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	4	4	no	—
564	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
565	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	8	1	no	—
582	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	8	1	no	—
590	C₂²⋊C₄	—	8	1	no	—
591	C₂²⋊C₄	—	8	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	8	1	no	—
595	C₄²	C₂×D₄×C₁₃	1	2	yes	—
596	C₄²	C₁₃×#41	1	2	yes	—
597	C₁₃	#24766	1	1	yes	characteristic, direct product factor, Sylow
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	C₁₃×#121	1	2	yes	—
612	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	8	4	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	C₁₃×#121	1	2	yes	—
665	C₂×C₄	C₁₃×#121	1	2	yes	—
666	C₂×C₄	C₁₃×#121	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
670	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
671	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
692	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
693	C₂²	C₁₃×#537	1	1	yes	characteristic
694	C₂²	C₁₃×#577	1	1	yes	characteristic
695	C₂²	C₁₃×#577	1	1	yes	characteristic
696	C₂²	C₁₃×#577	1	1	yes	characteristic
697	C₂²	C₁₃×#578	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	D₄²×C₁₃	1	1	yes	characteristic
711	C₄	C₁₃×#547	1	1	yes	characteristic
712	C₄	C₁₃×#548	1	1	yes	characteristic
713	C₄	C₁₃×#553	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₁₃×#2416	1	1	yes	characteristic
717	C₂	C₁₃×#3042	1	1	yes	characteristic
718	C₂	C₁₃×#3046	1	1	yes	characteristic
719	C₂	C₁₃×#3057	1	1	yes	characteristic
720	C₂	C₁₃×#3063	1	1	yes	characteristic
721	C₂	C₁₃×#3258	1	1	yes	characteristic
722	C₂	C₁₃×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#461	C₂	semidirect
4. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#2621	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2066	C₂	semidirect
9. C₁₃×#2055	C₂	semidirect
10. C₁₃×#2055	C₂	semidirect
11. C₁₃×#1981	C₂	semidirect
12. C₁₃×#1949	C₂	semidirect
13. C₁₃×#1894	C₂	semidirect
14. C₁₃×#1892	C₂	semidirect
15. C₁₃×#1804	C₂	semidirect
126. C₁₃×C₄⋊C₈	D₄	semidirect
144. #24766	C₁₃	direct (N × H)
239. C₂×#461	C₂×C₁₃	semidirect
240. C₂×#424	C₂×C₁₃	semidirect
241. #2621	C₂×C₁₃	semidirect
243. #2068	C₂×C₁₃	semidirect
244. #2066	C₂×C₁₃	semidirect
245. #2055	C₂×C₁₃	semidirect
246. #2055	C₂×C₁₃	semidirect
247. #1981	C₂×C₁₃	semidirect
248. #1949	C₂×C₁₃	semidirect
249. #1894	C₂×C₁₃	semidirect
250. #1892	C₂×C₁₃	semidirect
251. #1804	C₂×C₁₃	semidirect
478. C₄⋊C₈	D₄×C₁₃	semidirect
597. C₁₃	#24766	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×#468	2
C₂×C₁₃×#465	2
C₂×C₁₃×#461	2
C₂×C₁₃×#424	2
C₁₃×#2621	2
C₁₃×#2324	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#2055	2
C₁₃×#1981	2
C₁₃×#1949	2
C₁₃×#1894	2
C₁₃×#1892	2
C₁₃×#1804	2
#24766	13

Subgroups — C13×#24766 #15711105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24766 #15711105