Subgroups — C₁₃×#24861 #15711200

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2408	C₂	1	1	yes	maximal, characteristic
4	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#120	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#480	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#102	—	2	4	no	—
31	C₂×C₁₃×#102	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×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#394	—	2	1	no	—
43	C₁₃×#392	—	2	1	no	—
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#379	—	2	1	no	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	4	1	no	—
70	C₂²×D₄×C₁₃	—	4	1	no	—
71	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	4	1	no	—
88	C₁₃×#121	—	4	1	no	—
89	C₁₃×#120	—	4	4	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	4	4	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	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	—	4	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
101	C₂×C₁₃×C₄⋊C₄	D₄	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×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×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	—	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	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	—	2	1	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	—	2	2	no	—
122	C₁₃×#107	—	2	2	no	—
123	C₁₃×#107	—	4	1	no	—
124	C₁₃×#107	—	4	1	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	2	2	no	—
128	C₁₃×#102	—	2	2	no	—
129	C₁₃×#102	—	2	2	no	—
130	C₁₃×#102	—	4	1	no	—
131	C₁₃×#102	—	4	1	no	—
132	C₁₃×#102	D₄	1	4	yes	complemented
133	C₁₃×C₂²⋊C₈	—	2	2	no	—
134	C₁₃×C₂²⋊C₈	—	2	2	no	—
135	C₁₃×C₂²⋊C₈	—	4	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	#24861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂⁴×C₁₃	—	4	2	no	—
144	C₂⁴×C₁₃	—	4	2	no	—
145	C₂⁴×C₁₃	—	4	2	no	—
146	C₂⁴×C₁₃	—	4	2	no	—
147	C₂⁴×C₁₃	—	4	2	no	—
148	C₂⁴×C₁₃	—	8	1	no	—
149	C₂⁴×C₁₃	—	8	1	no	—
150	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	8	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	—	2	1	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	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	—	4	2	no	—
172	C₂×D₄×C₁₃	—	4	2	no	—
173	C₂×D₄×C₁₃	—	4	2	no	—
174	C₂×D₄×C₁₃	—	4	2	no	—
175	C₂×D₄×C₁₃	—	8	1	no	—
176	C₂×D₄×C₁₃	—	8	1	no	—
177	C₂×D₄×C₁₃	D₈	1	4	yes	—
178	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	1	no	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	4	2	no	—
197	C₂²×C₄×C₁₃	—	4	2	no	—
198	C₂²×C₄×C₁₃	—	4	2	no	—
199	C₂²×C₄×C₁₃	—	4	2	no	—
200	C₂²×C₄×C₁₃	—	8	1	no	—
201	C₂²×C₄×C₁₃	—	8	1	no	—
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	#41	1	2	yes	—
207	C₂²×C₄×C₁₃	#41	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₈×C₁₃	—	2	1	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	—	4	4	no	—
221	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	—	4	2	no	—
236	C₁₃×C₄⋊C₄	—	4	2	no	—
237	C₁₃×C₄⋊C₄	—	8	1	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	—	2	2	no	—
241	C₁₃×C₂²⋊C₄	—	4	2	no	—
242	C₁₃×C₂²⋊C₄	—	4	2	no	—
243	C₁₃×C₂²⋊C₄	—	4	2	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	—	4	2	no	—
248	C₁₃×C₂²⋊C₄	—	8	1	no	—
249	C₁₃×C₂²⋊C₄	—	8	1	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	2	1	no	—
252	C₄²×C₁₃	—	4	2	no	—
253	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2408	C₂×C₁₃	1	1	yes	characteristic
256	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1874	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1869	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	1	no	—
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	4	8	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	—	4	1	no	—
293	C₂³×C₁₃	—	8	4	no	—
294	C₂³×C₁₃	—	8	4	no	—
295	C₂³×C₁₃	—	8	4	no	—
296	C₂³×C₁₃	—	8	4	no	—
297	C₂³×C₁₃	—	8	4	no	—
298	C₂³×C₁₃	—	8	4	no	—
299	C₂³×C₁₃	#123	1	2	yes	—
300	C₂³×C₁₃	C₂×D₈	1	2	yes	—
301	C₂³×C₁₃	C₂×D₈	1	2	yes	—
302	C₂³×C₁₃	#137	1	2	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	D₄×C₁₃	—	2	8	no	—
305	D₄×C₁₃	—	2	2	no	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	2	2	no	—
308	D₄×C₁₃	—	2	2	no	—
309	D₄×C₁₃	—	4	8	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	—	4	1	no	—
314	D₄×C₁₃	—	8	4	no	—
315	D₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	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	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	—	8	4	no	—
354	C₂×C₄×C₁₃	#123	1	2	yes	—
355	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₈×C₁₃	—	2	2	no	—
363	C₈×C₁₃	—	4	1	no	—
364	C₈×C₁₃	—	4	1	no	—
365	C₈×C₁₃	—	4	1	no	—
366	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#120	—	2	1	no	—
371	C₂×C₄×D₄	—	2	1	no	—
372	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
375	#480	—	2	4	no	—
376	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
377	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
378	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	C₂×#102	—	2	4	no	—
381	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#102	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×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	#394	—	2	1	no	—
393	#392	—	2	1	no	—
394	#390	C₂²×C₁₃	1	1	yes	characteristic
395	#390	C₂²×C₁₃	1	1	yes	characteristic
396	#389	—	2	1	no	—
397	#385	—	2	1	no	—
398	#385	—	2	1	no	—
399	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	#380	C₂²×C₁₃	1	1	yes	characteristic
401	#380	C₂²×C₁₃	1	1	yes	characteristic
402	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#379	—	2	1	no	—
404	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	4	1	no	—
421	C₂²×C₁₃	—	4	1	no	—
422	C₂²×C₁₃	—	4	1	no	—
423	C₂²×C₁₃	—	4	1	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	8	16	no	—
431	C₂²×C₁₃	—	8	1	no	—
432	C₂²×C₁₃	—	8	1	no	—
433	C₂²×C₁₃	—	8	1	no	—
434	C₂²×C₁₃	—	8	1	no	—
435	C₂²×C₁₃	—	8	1	no	—
436	C₂²×C₁₃	—	8	1	no	—
437	C₂²×C₁₃	—	8	1	no	—
438	C₂²×C₁₃	—	8	1	no	—
439	C₂²×C₁₃	#480	1	4	yes	complemented
440	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
441	C₂²×C₁₃	D₄²	1	1	yes	characteristic
442	C₂²×C₁₃	#546	1	1	yes	characteristic
443	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
444	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
445	C₂²×C₁₃	#576	1	1	yes	characteristic
446	C₂²×C₁₃	#577	1	1	yes	characteristic
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	4	1	no	—
450	C₄×C₁₃	—	4	1	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	8	1	no	—
453	C₄×C₁₃	—	8	1	no	—
454	C₄×C₁₃	—	8	1	no	—
455	C₄×C₁₃	—	8	1	no	—
456	C₄×C₁₃	—	8	1	no	—
457	C₄×C₁₃	#525	1	1	yes	characteristic
458	C₄×C₁₃	#538	1	1	yes	characteristic
459	C₄×C₁₃	#546	1	1	yes	characteristic
460	C₄×C₁₃	#551	1	1	yes	characteristic
461	C₂⁵	—	2	1	no	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	—	4	1	no	—
470	C₂²×D₄	—	4	1	no	—
471	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×C₈	—	2	2	no	—
479	C₂²×C₈	—	2	2	no	—
480	C₂²×C₈	—	4	1	no	—
481	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	4	1	no	—
488	#121	—	4	1	no	—
489	#120	—	4	4	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	4	4	no	—
493	C₂×C₄⋊C₄	—	2	2	no	—
494	C₂×C₄⋊C₄	—	2	2	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	4	1	no	—
500	C₂×C₄⋊C₄	—	4	1	no	—
501	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
521	#107	—	2	2	no	—
522	#107	—	2	2	no	—
523	#107	—	4	1	no	—
524	#107	—	4	1	no	—
525	#102	—	2	2	no	—
526	#102	—	2	2	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	#102	—	4	1	no	—
531	#102	—	4	1	no	—
532	#102	D₄×C₁₃	1	4	yes	complemented
533	C₂²⋊C₈	—	2	2	no	—
534	C₂²⋊C₈	—	2	2	no	—
535	C₂²⋊C₈	—	4	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	C₂×C₁₃	—	2	4	no	—
541	C₂×C₁₃	—	4	2	no	—
542	C₂×C₁₃	—	8	2	no	—
543	C₂×C₁₃	—	8	2	no	—
544	C₂×C₁₃	#2418	1	1	yes	characteristic
545	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
546	C₂×C₁₃	#3096	1	1	yes	characteristic
547	C₂×C₁₃	#3266	1	1	yes	characteristic
548	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
549	C₂×C₁₃	#3294	1	1	yes	characteristic
550	C₂×C₁₃	#3314	1	1	yes	characteristic
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	2	1	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	—	4	2	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	—	4	2	no	—
558	C₂⁴	—	8	1	no	—
559	C₂⁴	—	8	1	no	—
560	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	8	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	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	8	1	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	C₁₃×D₈	1	4	yes	—
588	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
589	C₂×D₄	C₁₃×#41	1	2	yes	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	8	1	no	—
611	C₂²×C₄	—	8	1	no	—
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₁₃×#41	1	2	yes	—
617	C₂²×C₄	C₁₃×#41	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	4	4	no	—
631	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	8	1	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₂²⋊C₄	—	8	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	4	2	no	—
663	C₁₃	#24861	1	1	yes	characteristic, direct product factor, Sylow
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	4	8	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	—	8	4	no	—
692	C₂³	—	8	4	no	—
693	C₂³	—	8	4	no	—
694	C₂³	—	8	4	no	—
695	C₂³	C₁₃×#123	1	2	yes	—
696	C₂³	C₂×C₁₃×D₈	1	2	yes	—
697	C₂³	C₂×C₁₃×D₈	1	2	yes	—
698	C₂³	C₁₃×#137	1	2	yes	—
699	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	D₄	—	2	8	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	1	no	—
707	D₄	—	4	1	no	—
708	D₄	—	4	1	no	—
709	D₄	—	4	1	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	C₁₃×#123	1	2	yes	—
751	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
754	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
755	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
756	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
757	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	8	16	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	—	8	1	no	—
786	C₂²	—	8	1	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	C₁₃×#480	1	4	yes	complemented
791	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
792	C₂²	D₄²×C₁₃	1	1	yes	characteristic
793	C₂²	C₁₃×#546	1	1	yes	characteristic
794	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
795	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
796	C₂²	C₁₃×#576	1	1	yes	characteristic
797	C₂²	C₁₃×#577	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	8	1	no	—
804	C₄	—	8	1	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	C₁₃×#525	1	1	yes	characteristic
809	C₄	C₁₃×#538	1	1	yes	characteristic
810	C₄	C₁₃×#546	1	1	yes	characteristic
811	C₄	C₁₃×#551	1	1	yes	characteristic
812	C₂	—	2	4	no	—
813	C₂	—	4	2	no	—
814	C₂	—	8	2	no	—
815	C₂	—	8	2	no	—
816	C₂	C₁₃×#2418	1	1	yes	characteristic
817	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
818	C₂	C₁₃×#3096	1	1	yes	characteristic
819	C₂	C₁₃×#3266	1	1	yes	characteristic
820	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
821	C₂	C₁₃×#3294	1	1	yes	characteristic
822	C₂	C₁₃×#3314	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2408	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×#480	C₂	semidirect
2. C₂²×C₁₃×#102	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2093	C₂	semidirect
6. C₁₃×#2071	C₂	semidirect
7. C₁₃×#2033	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1874	C₂	semidirect
12. C₁₃×#1869	C₂	semidirect
13. C₁₃×#1852	C₂	semidirect
14. C₁₃×#1808	C₂	semidirect
15. C₁₃×#1786	C₂	semidirect
24. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂×C₁₃×#107	C₂²	semidirect
27. C₂×C₁₃×#107	C₂²	semidirect
28. C₂×C₁₃×#107	C₂²	semidirect
29. C₂×C₁₃×#107	C₂²	semidirect
40. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
49. C₁₃×#384	C₂²	semidirect
52. C₁₃×#380	C₂²	semidirect
54. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
55. C₁₃×#340	C₂²	semidirect
56. C₁₃×#340	C₂²	semidirect
57. C₁₃×#340	C₂²	semidirect
58. C₁₃×#340	C₂²	semidirect
59. C₁₃×#336	C₂²	semidirect
60. C₁₃×#336	C₂²	semidirect
132. C₁₃×#102	D₄	semidirect
140. #24861	C₁₃	direct (N × H)
253. C₂×#480	C₂×C₁₃	semidirect
254. C₂²×#102	C₂×C₁₃	semidirect
256. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
257. #2093	C₂×C₁₃	semidirect
258. #2071	C₂×C₁₃	semidirect
259. #2033	C₂×C₁₃	semidirect
260. #2033	C₂×C₁₃	semidirect
261. #1925	C₂×C₁₃	semidirect
262. #1925	C₂×C₁₃	semidirect
263. #1874	C₂×C₁₃	semidirect
264. #1869	C₂×C₁₃	semidirect
265. #1852	C₂×C₁₃	semidirect
266. #1808	C₂×C₁₃	semidirect
267. #1786	C₂×C₁₃	semidirect
374. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
376. C₂×#107	C₂²×C₁₃	semidirect
377. C₂×#107	C₂²×C₁₃	semidirect
378. C₂×#107	C₂²×C₁₃	semidirect
379. C₂×#107	C₂²×C₁₃	semidirect
390. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
391. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
399. #384	C₂²×C₁₃	semidirect
402. #380	C₂²×C₁₃	semidirect
404. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
405. #340	C₂²×C₁₃	semidirect
406. #340	C₂²×C₁₃	semidirect
407. #340	C₂²×C₁₃	semidirect
408. #340	C₂²×C₁₃	semidirect
409. #336	C₂²×C₁₃	semidirect
410. #336	C₂²×C₁₃	semidirect
439. C₂²×C₁₃	#480	semidirect
532. #102	D₄×C₁₃	semidirect
663. C₁₃	#24861	direct (N × H)
790. C₂²	C₁₃×#480	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#480	2
C₂²×C₁₃×#102	2
C₁₃×#2408	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2093	2
C₁₃×#2071	2
C₁₃×#2033	2
C₁₃×#1925	2
C₁₃×#1874	2
C₁₃×#1869	2
C₁₃×#1852	2
C₁₃×#1808	2
C₁₃×#1786	2
#24861	13

Subgroups — C13×#24861 #15711200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24861 #15711200