Subgroups — C₁₃×#24136 #15710475

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₁₃×#553	—	2	4	no	—
18	C₁₃×#553	—	2	4	no	—
19	C₂×C₁₃×#126	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#123	—	2	1	no	—
22	C₂×C₁₃×#121	—	2	1	no	—
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#478	—	2	4	no	—
35	C₁₃×#442	—	2	4	no	—
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
51	C₁₃×#394	—	2	1	no	—
52	C₁₃×#394	—	2	1	no	—
53	C₁₃×#384	C₂²	1	1	yes	characteristic
54	C₁₃×#380	—	2	1	no	—
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	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×D₄×C₁₃	—	2	1	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	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
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	C₂×C₁₃×D₈	—	2	2	no	—
76	C₂×C₁₃×D₈	—	2	2	no	—
77	C₂×C₁₃×D₈	—	2	2	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×#126	—	2	8	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	D₄	1	4	yes	complemented
85	C₁₃×#123	—	2	8	no	—
86	C₁₃×#121	—	2	8	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	2	2	no	—
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	4	1	no	—
94	C₁₃×#121	—	4	1	no	—
95	C₁₃×#121	—	4	4	no	—
96	C₄×D₄×C₁₃	—	2	8	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	2	no	—
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#107	—	2	2	no	—
133	C₁₃×#106	—	2	2	no	—
134	C₁₃×#106	—	2	2	no	—
135	C₁₃×C₄⋊C₈	—	2	2	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	4	1	no	—
141	C₁₃×#102	—	4	1	no	—
142	C₁₃×C₂²⋊C₈	—	2	2	no	—
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₁₃×C₂²⋊C₈	—	4	1	no	—
145	C₁₃×C₂²⋊C₈	—	4	1	no	—
146	C₁₃×#97	—	2	2	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	—	2	1	no	—
149	#24136	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	—	2	1	no	—
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	4	1	no	—
169	C₂×D₄×C₁₃	—	4	2	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	—	8	1	no	—
178	C₂×D₄×C₁₃	—	8	1	no	—
179	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
180	C₂×D₄×C₁₃	#41	1	2	yes	—
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	4	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	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	2	no	—
204	C₂²×C₄×C₁₃	—	8	1	no	—
205	C₂²×C₄×C₁₃	—	8	1	no	—
206	C₂²×C₄×C₁₃	—	8	1	no	—
207	C₂²×C₄×C₁₃	—	8	1	no	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×D₈	—	2	8	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	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	#41	1	2	yes	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	4	2	no	—
240	C₁₃×C₄⋊C₄	—	8	1	no	—
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	4	2	no	—
251	C₁₃×C₂²⋊C₄	—	4	2	no	—
252	C₁₃×C₂²⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	4	2	no	—
254	C₁₃×C₂²⋊C₄	—	4	2	no	—
255	C₄²×C₁₃	—	2	4	no	—
256	C₄²×C₁₃	C₂×D₄	1	2	yes	—
257	C₄²×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2537	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1999	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1999	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1992	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1955	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1874	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
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	1	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	—	2	1	no	—
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	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	—	4	1	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	—	4	1	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	—	4	1	no	—
298	C₂³×C₁₃	—	4	1	no	—
299	C₂³×C₁₃	—	4	1	no	—
300	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
301	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	D₄×C₁₃	—	2	2	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	2	2	no	—
305	D₄×C₁₃	—	2	2	no	—
306	D₄×C₁₃	—	4	4	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	8	4	no	—
313	D₄×C₁₃	—	8	4	no	—
314	D₄×C₁₃	—	8	4	no	—
315	C₂×C₄×C₁₃	—	2	1	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	1	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	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	—	8	4	no	—
354	C₂×C₄×C₁₃	#120	1	2	yes	—
355	C₂×C₄×C₁₃	#120	1	2	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	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	2₋¹⁺⁴	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	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
367	#553	—	2	4	no	—
368	#553	—	2	4	no	—
369	C₂×#126	—	2	1	no	—
370	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#123	—	2	1	no	—
372	C₂×#121	—	2	1	no	—
373	C₂×#121	—	2	1	no	—
374	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×D₄	—	2	1	no	—
379	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
384	#478	—	2	4	no	—
385	#442	—	2	4	no	—
386	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
401	#394	—	2	1	no	—
402	#394	—	2	1	no	—
403	#384	C₂²×C₁₃	1	1	yes	characteristic
404	#380	—	2	1	no	—
405	#380	C₂²×C₁₃	1	1	yes	characteristic
406	#380	C₂²×C₁₃	1	1	yes	characteristic
407	#340	C₂²×C₁₃	1	1	yes	characteristic
408	#340	C₂²×C₁₃	1	1	yes	characteristic
409	#340	C₂²×C₁₃	1	1	yes	characteristic
410	#340	C₂²×C₁₃	1	1	yes	characteristic
411	#340	C₂²×C₁₃	1	1	yes	characteristic
412	#340	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₁₃	—	2	2	no	—
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	4	1	no	—
417	C₂²×C₁₃	—	4	1	no	—
418	C₂²×C₁₃	—	4	1	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	—	4	1	no	—
421	C₂²×C₁₃	—	4	1	no	—
422	C₂²×C₁₃	—	4	1	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	1	no	—
429	C₂²×C₁₃	—	4	1	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	1	no	—
432	C₂²×C₁₃	—	4	2	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	—	8	1	no	—
440	C₂²×C₁₃	—	8	1	no	—
441	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
442	C₂²×C₁₃	#546	1	1	yes	characteristic
443	C₂²×C₁₃	#547	1	1	yes	characteristic
444	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂²×C₁₃	#575	1	1	yes	characteristic
446	C₂²×C₁₃	#576	1	1	yes	characteristic
447	C₂²×C₁₃	#577	1	1	yes	characteristic
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	4	1	no	—
451	C₄×C₁₃	—	4	1	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	8	1	no	—
456	C₄×C₁₃	—	8	1	no	—
457	C₄×C₁₃	—	8	1	no	—
458	C₄×C₁₃	#525	1	1	yes	characteristic
459	C₄×C₁₃	#537	1	1	yes	characteristic
460	C₄×C₁₃	#548	1	1	yes	characteristic
461	C₄×C₁₃	#550	1	1	yes	characteristic
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	2	2	no	—
476	C₂×D₈	—	2	2	no	—
477	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	#126	—	2	8	no	—
482	#125	—	2	2	no	—
483	#125	D₄×C₁₃	1	4	yes	complemented
484	#123	—	2	8	no	—
485	#121	—	2	8	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	4	1	no	—
493	#121	—	4	1	no	—
494	#121	—	4	4	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
502	#117	—	2	2	no	—
503	#117	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	#107	—	2	2	no	—
532	#106	—	2	2	no	—
533	#106	—	2	2	no	—
534	C₄⋊C₈	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	4	1	no	—
540	#102	—	4	1	no	—
541	C₂²⋊C₈	—	2	2	no	—
542	C₂²⋊C₈	—	2	2	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	C₂²⋊C₈	—	4	1	no	—
545	#97	—	2	2	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	C₂×C₁₃	—	4	2	no	—
549	C₂×C₁₃	—	8	1	no	—
550	C₂×C₁₃	—	8	2	no	—
551	C₂×C₁₃	—	8	2	no	—
552	C₂×C₁₃	#2407	1	1	yes	characteristic
553	C₂×C₁₃	#3006	1	1	yes	characteristic
554	C₂×C₁₃	#3012	1	1	yes	characteristic
555	C₂×C₁₃	#3307	1	1	yes	characteristic
556	C₂×C₁₃	#3318	1	1	yes	characteristic
557	C₂×C₁₃	#3345	1	1	yes	characteristic
558	C₂×C₁₃	#3347	1	1	yes	characteristic
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	2	1	no	—
561	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	2	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	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	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	—	8	1	no	—
585	C₂×D₄	—	8	1	no	—
586	C₂×D₄	—	8	1	no	—
587	C₂×D₄	—	8	1	no	—
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	4	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	—	2	4	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	8	1	no	—
614	C₂²×C₄	—	8	1	no	—
615	C₂²×C₄	—	8	1	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
622	D₈	—	2	8	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	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	C₁₃×#41	1	2	yes	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	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	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	8	1	no	—
650	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₄²	—	2	4	no	—
665	C₄²	C₂×D₄×C₁₃	1	2	yes	—
666	C₄²	C₂×D₄×C₁₃	1	2	yes	—
667	C₁₃	#24136	1	1	yes	characteristic, direct product factor, Sylow
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	1	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	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	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
696	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	—	8	4	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	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	—	8	4	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	C₁₃×#120	1	2	yes	—
750	C₂×C₄	C₁₃×#120	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
756	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	4	1	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	8	1	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	C₂×C₁₃×#120	1	1	yes	characteristic
790	C₂²	C₁₃×#546	1	1	yes	characteristic
791	C₂²	C₁₃×#547	1	1	yes	characteristic
792	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
793	C₂²	C₁₃×#575	1	1	yes	characteristic
794	C₂²	C₁₃×#576	1	1	yes	characteristic
795	C₂²	C₁₃×#577	1	1	yes	characteristic
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	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	C₁₃×#525	1	1	yes	characteristic
807	C₄	C₁₃×#537	1	1	yes	characteristic
808	C₄	C₁₃×#548	1	1	yes	characteristic
809	C₄	C₁₃×#550	1	1	yes	characteristic
810	C₂	—	4	2	no	—
811	C₂	—	8	1	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	2	no	—
814	C₂	C₁₃×#2407	1	1	yes	characteristic
815	C₂	C₁₃×#3006	1	1	yes	characteristic
816	C₂	C₁₃×#3012	1	1	yes	characteristic
817	C₂	C₁₃×#3307	1	1	yes	characteristic
818	C₂	C₁₃×#3318	1	1	yes	characteristic
819	C₂	C₁₃×#3345	1	1	yes	characteristic
820	C₂	C₁₃×#3347	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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×#553	C₂	semidirect
2. C₂×C₁₃×#478	C₂	semidirect
3. C₂×C₁₃×#442	C₂	semidirect
4. C₁₃×#2537	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#2033	C₂	semidirect
7. C₁₃×#1999	C₂	semidirect
8. C₁₃×#1999	C₂	semidirect
9. C₁₃×#1992	C₂	semidirect
10. C₁₃×#1955	C₂	semidirect
11. C₁₃×#1875	C₂	semidirect
12. C₁₃×#1874	C₂	semidirect
13. C₁₃×#1854	C₂	semidirect
14. C₁₃×#1853	C₂	semidirect
15. C₁₃×#1802	C₂	semidirect
84. C₁₃×#125	D₄	semidirect
102. C₄×D₄×C₁₃	D₄	semidirect
149. #24136	C₁₃	direct (N × H)
258. C₂×#553	C₂×C₁₃	semidirect
259. C₂×#478	C₂×C₁₃	semidirect
260. C₂×#442	C₂×C₁₃	semidirect
261. #2537	C₂×C₁₃	semidirect
262. #2034	C₂×C₁₃	semidirect
263. #2033	C₂×C₁₃	semidirect
264. #1999	C₂×C₁₃	semidirect
265. #1999	C₂×C₁₃	semidirect
266. #1992	C₂×C₁₃	semidirect
267. #1955	C₂×C₁₃	semidirect
268. #1875	C₂×C₁₃	semidirect
269. #1874	C₂×C₁₃	semidirect
270. #1854	C₂×C₁₃	semidirect
271. #1853	C₂×C₁₃	semidirect
272. #1802	C₂×C₁₃	semidirect
483. #125	D₄×C₁₃	semidirect
501. C₄×D₄	D₄×C₁₃	semidirect
667. C₁₃	#24136	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×#553	2
C₂×C₁₃×#478	2
C₂×C₁₃×#442	2
C₁₃×#2537	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1999	2
C₁₃×#1992	2
C₁₃×#1955	2
C₁₃×#1875	2
C₁₃×#1874	2
C₁₃×#1854	2
C₁₃×#1853	2
C₁₃×#1802	2
#24136	13

Subgroups — C13×#24136 #15710475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24136 #15710475