Subgroups — C₁₃×#24876 #15711215

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2407	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₁₃×#485	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₁₃×#416	—	2	4	no	—
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×#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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×#394	—	2	1	no	—
41	C₁₃×#392	—	2	1	no	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#390	—	2	1	no	—
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₄×C₁₃×C₄⋊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	C₂×C₁₃×#41	—	2	2	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	4	1	no	—
66	C₂×C₁₃×#41	—	4	1	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	—	2	2	no	—
76	C₂²×C₈×C₁₃	—	2	2	no	—
77	C₂²×C₈×C₁₃	—	4	1	no	—
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	4	1	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	4	1	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₁₃×#117	—	2	2	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	—	4	1	no	—
91	C₁₃×#117	—	4	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	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	—	2	1	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#107	—	2	2	no	—
118	C₁₃×#106	—	2	2	no	—
119	C₁₃×#106	—	4	1	no	—
120	C₁₃×#106	—	4	1	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	2	2	no	—
123	C₁₃×#103	—	4	1	no	—
124	C₁₃×#103	D₄	1	4	yes	complemented
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	2	2	no	—
128	C₁₃×#102	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	—	2	2	no	—
131	C₁₃×C₂²⋊C₈	—	4	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	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	#24876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	—	2	1	no	—
140	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×#41	—	2	8	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	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	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	—	4	2	no	—
161	C₂×D₄×C₁₃	—	4	2	no	—
162	C₂×D₄×C₁₃	—	4	2	no	—
163	C₂×D₄×C₁₃	—	4	2	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	—	8	1	no	—
166	C₂×D₄×C₁₃	#41	1	2	yes	—
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	—	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	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	#41	1	2	yes	—
192	C₂²×C₄×C₁₃	#41	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	4	4	no	—
206	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	4	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	—	4	2	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₁₃×C₂²⋊C₄	—	8	1	no	—
232	C₁₃×C₂²⋊C₄	—	8	1	no	—
233	C₁₃×C₂²⋊C₄	—	8	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	4	2	no	—
237	C₄²×C₁₃	—	4	2	no	—
238	C₄²×C₁₃	—	4	2	no	—
239	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2407	C₂×C₁₃	1	1	yes	characteristic
242	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1869	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
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	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	#123	1	2	yes	—
275	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₁₃	—	2	2	no	—
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	—	4	1	no	—
279	Q₈×C₁₃	—	4	1	no	—
280	D₄×C₁₃	—	2	2	no	—
281	D₄×C₁₃	—	2	2	no	—
282	D₄×C₁₃	—	4	4	no	—
283	D₄×C₁₃	—	4	8	no	—
284	D₄×C₁₃	—	4	1	no	—
285	D₄×C₁₃	—	4	1	no	—
286	D₄×C₁₃	—	8	4	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	4	8	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	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	#123	1	2	yes	—
328	C₂×C₄×C₁₃	#135	1	2	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
335	C₈×C₁₃	—	2	2	no	—
336	C₈×C₁₃	—	4	1	no	—
337	C₈×C₁₃	—	4	1	no	—
338	C₈×C₁₃	—	4	1	no	—
339	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
340	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
346	#485	—	2	4	no	—
347	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
351	#416	—	2	4	no	—
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×#102	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	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
363	#394	—	2	1	no	—
364	#392	—	2	1	no	—
365	#391	C₂²×C₁₃	1	1	yes	characteristic
366	#390	—	2	1	no	—
367	#390	C₂²×C₁₃	1	1	yes	characteristic
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#386	—	2	1	no	—
371	#385	—	2	1	no	—
372	#384	C₂²×C₁₃	1	1	yes	characteristic
373	#380	C₂²×C₁₃	1	1	yes	characteristic
374	#380	C₂²×C₁₃	1	1	yes	characteristic
375	#380	C₂²×C₁₃	1	1	yes	characteristic
376	C₄×C₄⋊C₄	—	2	1	no	—
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	#340	C₂²×C₁₃	1	1	yes	characteristic
379	#340	C₂²×C₁₃	1	1	yes	characteristic
380	#340	C₂²×C₁₃	1	1	yes	characteristic
381	#340	C₂²×C₁₃	1	1	yes	characteristic
382	#336	C₂²×C₁₃	1	1	yes	characteristic
383	#336	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	2	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	—	4	1	no	—
391	C₂²×C₁₃	—	4	1	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	1	no	—
397	C₂²×C₁₃	—	4	1	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	1	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	8	1	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
406	C₂²×C₁₃	D₄²	1	1	yes	characteristic
407	C₂²×C₁₃	#546	1	1	yes	characteristic
408	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
409	C₂²×C₁₃	#575	1	1	yes	characteristic
410	C₂²×C₁₃	#577	1	1	yes	characteristic
411	C₂²×C₁₃	#577	1	1	yes	characteristic
412	C₄×C₁₃	—	2	2	no	—
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	4	1	no	—
415	C₄×C₁₃	—	4	1	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	8	1	no	—
419	C₄×C₁₃	—	8	1	no	—
420	C₄×C₁₃	—	8	1	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	—	8	1	no	—
423	C₄×C₁₃	#525	1	1	yes	characteristic
424	C₄×C₁₃	#538	1	1	yes	characteristic
425	C₄×C₁₃	#546	1	1	yes	characteristic
426	C₄×C₁₃	#551	1	1	yes	characteristic
427	C₂×#41	—	2	2	no	—
428	C₂×#41	—	2	2	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	2	2	no	—
431	C₂×#41	—	4	1	no	—
432	C₂×#41	—	4	1	no	—
433	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×C₈	—	2	2	no	—
442	C₂²×C₈	—	2	2	no	—
443	C₂²×C₈	—	4	1	no	—
444	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	4	1	no	—
450	#121	—	2	2	no	—
451	#121	—	4	1	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	#117	—	2	2	no	—
455	#117	—	2	2	no	—
456	#117	—	4	1	no	—
457	#117	—	4	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄²	—	2	1	no	—
480	C₂×C₄²	—	2	1	no	—
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
483	#107	—	2	2	no	—
484	#106	—	2	2	no	—
485	#106	—	4	1	no	—
486	#106	—	4	1	no	—
487	#103	—	2	2	no	—
488	#103	—	2	2	no	—
489	#103	—	4	1	no	—
490	#103	D₄×C₁₃	1	4	yes	complemented
491	#102	—	2	2	no	—
492	#102	—	2	2	no	—
493	#102	—	2	2	no	—
494	#102	—	4	1	no	—
495	C₂²⋊C₈	—	2	2	no	—
496	C₂²⋊C₈	—	2	2	no	—
497	C₂²⋊C₈	—	4	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	C₂×C₁₃	—	4	2	no	—
505	C₂×C₁₃	—	8	1	no	—
506	C₂×C₁₃	—	8	2	no	—
507	C₂×C₁₃	#2418	1	1	yes	characteristic
508	C₂×C₁₃	#3091	1	1	yes	characteristic
509	C₂×C₁₃	#3099	1	1	yes	characteristic
510	C₂×C₁₃	#3271	1	1	yes	characteristic
511	C₂×C₁₃	#3284	1	1	yes	characteristic
512	C₂×C₁₃	#3303	1	1	yes	characteristic
513	C₂×C₁₃	#3311	1	1	yes	characteristic
514	C₂⁴	—	2	1	no	—
515	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
517	#41	—	2	8	no	—
518	#41	—	4	4	no	—
519	#41	—	4	4	no	—
520	#41	—	4	4	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	4	1	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	8	1	no	—
541	C₂×D₄	C₁₃×#41	1	2	yes	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₁₃×#41	1	2	yes	—
567	C₂²×C₄	C₁₃×#41	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	4	4	no	—
581	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	8	1	no	—
597	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₂²⋊C₄	—	4	2	no	—
605	C₂²⋊C₄	—	8	1	no	—
606	C₂²⋊C₄	—	8	1	no	—
607	C₂²⋊C₄	—	8	1	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	4	2	no	—
612	C₄²	—	4	2	no	—
613	C₄²	—	4	2	no	—
614	C₁₃	#24876	1	1	yes	characteristic, direct product factor, Sylow
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	C₁₃×#123	1	2	yes	—
636	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	2	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	8	4	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	4	8	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	C₁₃×#123	1	2	yes	—
689	C₂×C₄	C₁₃×#135	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
692	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
693	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
694	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
722	C₂²	D₄²×C₁₃	1	1	yes	characteristic
723	C₂²	C₁₃×#546	1	1	yes	characteristic
724	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
725	C₂²	C₁₃×#575	1	1	yes	characteristic
726	C₂²	C₁₃×#577	1	1	yes	characteristic
727	C₂²	C₁₃×#577	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	8	1	no	—
735	C₄	—	8	1	no	—
736	C₄	—	8	1	no	—
737	C₄	—	8	1	no	—
738	C₄	—	8	1	no	—
739	C₄	C₁₃×#525	1	1	yes	characteristic
740	C₄	C₁₃×#538	1	1	yes	characteristic
741	C₄	C₁₃×#546	1	1	yes	characteristic
742	C₄	C₁₃×#551	1	1	yes	characteristic
743	C₂	—	4	2	no	—
744	C₂	—	8	1	no	—
745	C₂	—	8	2	no	—
746	C₂	C₁₃×#2418	1	1	yes	characteristic
747	C₂	C₁₃×#3091	1	1	yes	characteristic
748	C₂	C₁₃×#3099	1	1	yes	characteristic
749	C₂	C₁₃×#3271	1	1	yes	characteristic
750	C₂	C₁₃×#3284	1	1	yes	characteristic
751	C₂	C₁₃×#3303	1	1	yes	characteristic
752	C₂	C₁₃×#3311	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2407	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#485	C₂	semidirect
2. C₂×C₁₃×#416	C₂	semidirect
4. C₁₃×#2354	C₂	semidirect
5. C₁₃×#2094	C₂	semidirect
6. C₁₃×#2072	C₂	semidirect
7. C₁₃×#2035	C₂	semidirect
8. C₁₃×#2034	C₂	semidirect
9. C₁₃×#1927	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1875	C₂	semidirect
12. C₁₃×#1869	C₂	semidirect
13. C₁₃×#1854	C₂	semidirect
14. C₁₃×#1807	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
124. C₁₃×#103	D₄	semidirect
138. #24876	C₁₃	direct (N × H)
239. C₂×#485	C₂×C₁₃	semidirect
240. C₂×#416	C₂×C₁₃	semidirect
242. #2354	C₂×C₁₃	semidirect
243. #2094	C₂×C₁₃	semidirect
244. #2072	C₂×C₁₃	semidirect
245. #2035	C₂×C₁₃	semidirect
246. #2034	C₂×C₁₃	semidirect
247. #1927	C₂×C₁₃	semidirect
248. #1925	C₂×C₁₃	semidirect
249. #1875	C₂×C₁₃	semidirect
250. #1869	C₂×C₁₃	semidirect
251. #1854	C₂×C₁₃	semidirect
252. #1807	C₂×C₁₃	semidirect
253. #1788	C₂×C₁₃	semidirect
490. #103	D₄×C₁₃	semidirect
614. C₁₃	#24876	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×#485	2
C₂×C₁₃×#416	2
C₁₃×#2407	2
C₁₃×#2354	2
C₁₃×#2094	2
C₁₃×#2072	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#1927	2
C₁₃×#1925	2
C₁₃×#1875	2
C₁₃×#1869	2
C₁₃×#1854	2
C₁₃×#1807	2
C₁₃×#1788	2
#24876	13

Subgroups — C13×#24876 #15711215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24876 #15711215