Subgroups — C₁₃×#24909 #15711248

Order 3328.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	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	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	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×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
24	C₁₃×#447	—	2	4	no	—
25	C₁₃×#442	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
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, complemented
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#397	—	2	1	no	—
41	C₁₃×#394	—	2	1	no	—
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#386	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#386	—	2	1	no	—
49	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#381	—	2	1	no	—
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₁₃×#379	—	2	1	no	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	4	1	no	—
69	C₂²×D₄×C₁₃	—	4	1	no	—
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×D₈	—	2	2	no	—
78	C₂×C₁₃×D₈	—	2	2	no	—
79	C₂×C₁₃×D₈	—	2	2	no	—
80	C₂×C₁₃×D₈	—	2	2	no	—
81	C₂×C₁₃×D₈	—	4	1	no	—
82	C₂×C₁₃×D₈	D₄	1	4	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	4	1	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	4	1	no	—
93	C₄×D₄×C₁₃	—	4	1	no	—
94	C₄×D₄×C₁₃	—	4	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	—	4	1	no	—
119	C₁₃×#106	—	2	2	no	—
120	C₁₃×C₄⋊C₈	—	4	1	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	4	1	no	—
128	C₁₃×#102	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×C₂²⋊C₈	—	4	1	no	—
131	C₁₃×#97	—	2	2	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	D₄	1	1	yes	characteristic
138	C₁₃×#95	D₄	1	1	yes	characteristic
139	#24909	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	1	no	—
141	C₂⁴×C₁₃	—	2	4	no	—
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂⁴×C₁₃	—	2	1	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	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	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	—	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	2	no	—
166	C₂×D₄×C₁₃	—	4	2	no	—
167	C₂×D₄×C₁₃	—	4	4	no	—
168	C₂×D₄×C₁₃	—	4	4	no	—
169	C₂×D₄×C₁₃	—	4	4	no	—
170	C₂×D₄×C₁₃	—	4	4	no	—
171	C₂×D₄×C₁₃	—	4	2	no	—
172	C₂×D₄×C₁₃	—	4	2	no	—
173	C₂×D₄×C₁₃	—	8	1	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₁₃	#41	1	2	yes	—
177	C₂×D₄×C₁₃	#41	1	2	yes	—
178	C₂×D₄×C₁₃	#41	1	2	yes	—
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	—	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	—	4	2	no	—
191	C₂²×C₄×C₁₃	—	4	2	no	—
192	C₂²×C₄×C₁₃	—	4	2	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	4	2	no	—
195	C₂²×C₄×C₁₃	—	4	2	no	—
196	C₂²×C₄×C₁₃	—	8	1	no	—
197	C₂²×C₄×C₁₃	—	8	1	no	—
198	C₂²×C₄×C₁₃	—	8	1	no	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₁₃×D₈	—	2	8	no	—
206	C₁₃×D₈	—	4	4	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	1	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	—	8	1	no	—
230	C₁₃×C₂²⋊C₄	—	2	2	no	—
231	C₁₃×C₂²⋊C₄	—	4	1	no	—
232	C₁₃×C₂²⋊C₄	—	4	2	no	—
233	C₁₃×C₂²⋊C₄	—	4	2	no	—
234	C₁₃×C₂²⋊C₄	—	4	2	no	—
235	C₁₃×C₂²⋊C₄	—	4	2	no	—
236	C₁₃×C₂²⋊C₄	—	4	2	no	—
237	C₁₃×C₂²⋊C₄	—	4	2	no	—
238	C₁₃×C₂²⋊C₄	—	4	2	no	—
239	C₁₃×C₂²⋊C₄	—	8	1	no	—
240	C₁₃×C₂²⋊C₄	—	8	1	no	—
241	C₁₃×C₂²⋊C₄	—	8	1	no	—
242	C₁₃×C₂²⋊C₄	—	8	1	no	—
243	C₁₃×C₂²⋊C₄	—	8	1	no	—
244	C₄²×C₁₃	—	2	1	no	—
245	C₄²×C₁₃	—	2	1	no	—
246	C₄²×C₁₃	—	2	1	no	—
247	C₄²×C₁₃	—	2	1	no	—
248	C₂×#447	C₂×C₁₃	1	1	yes	characteristic
249	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2420	C₂×C₁₃	1	1	yes	characteristic, complemented
251	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1924	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	2	no	—
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	2	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	4	8	no	—
275	C₂³×C₁₃	—	4	8	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	—	4	1	no	—
279	C₂³×C₁₃	—	4	1	no	—
280	C₂³×C₁₃	—	4	1	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	—	8	4	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	AGL(1,ℤ/8)	1	2	yes	—
298	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	D₄×C₁₃	—	2	2	no	—
300	D₄×C₁₃	—	2	2	no	—
301	D₄×C₁₃	—	2	2	no	—
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	8	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	8	4	no	—
312	D₄×C₁₃	#123	1	4	yes	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	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	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	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	—	8	4	no	—
348	C₂×C₄×C₁₃	—	8	4	no	—
349	C₂×C₄×C₁₃	—	8	4	no	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
356	C₈×C₁₃	—	2	2	no	—
357	C₈×C₁₃	—	4	1	no	—
358	C₈×C₁₃	—	4	1	no	—
359	C₈×C₁₃	—	4	1	no	—
360	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	C₂²×C₂²⋊C₄	—	2	1	no	—
368	#447	—	2	4	no	—
369	#442	—	2	4	no	—
370	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
372	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	#397	—	2	1	no	—
385	#394	—	2	1	no	—
386	#390	C₂²×C₁₃	1	1	yes	characteristic
387	#390	C₂²×C₁₃	1	1	yes	characteristic
388	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	#386	—	2	1	no	—
391	#386	—	2	1	no	—
392	#386	—	2	1	no	—
393	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	#381	—	2	1	no	—
395	#380	C₂²×C₁₃	1	1	yes	characteristic
396	#380	C₂²×C₁₃	1	1	yes	characteristic
397	#379	—	2	1	no	—
398	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
399	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
400	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
402	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	C₂²×C₁₃	—	2	2	no	—
406	C₂²×C₁₃	—	2	4	no	—
407	C₂²×C₁₃	—	2	2	no	—
408	C₂²×C₁₃	—	2	2	no	—
409	C₂²×C₁₃	—	4	2	no	—
410	C₂²×C₁₃	—	4	1	no	—
411	C₂²×C₁₃	—	4	2	no	—
412	C₂²×C₁₃	—	4	1	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	1	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	8	16	no	—
426	C₂²×C₁₃	—	8	1	no	—
427	C₂²×C₁₃	—	8	1	no	—
428	C₂²×C₁₃	—	8	1	no	—
429	C₂²×C₁₃	—	8	1	no	—
430	C₂²×C₁₃	—	8	1	no	—
431	C₂²×C₁₃	—	8	1	no	—
432	C₂²×C₁₃	—	8	1	no	—
433	C₂²×C₁₃	—	8	1	no	—
434	C₂²×C₁₃	#525	1	1	yes	characteristic
435	C₂²×C₁₃	D₄²	1	1	yes	characteristic
436	C₂²×C₁₃	#546	1	1	yes	characteristic
437	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
438	C₂²×C₁₃	#575	1	1	yes	characteristic
439	C₂²×C₁₃	#576	1	1	yes	characteristic
440	C₂²×C₁₃	#576	1	1	yes	characteristic
441	C₄×C₁₃	—	4	1	no	—
442	C₄×C₁₃	—	4	1	no	—
443	C₄×C₁₃	—	4	1	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	4	1	no	—
446	C₄×C₁₃	—	8	1	no	—
447	C₄×C₁₃	—	8	1	no	—
448	C₄×C₁₃	—	8	1	no	—
449	C₄×C₁₃	—	8	1	no	—
450	C₄×C₁₃	—	8	1	no	—
451	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
452	C₄×C₁₃	#538	1	1	yes	characteristic
453	C₄×C₁₃	#546	1	1	yes	characteristic
454	C₄×C₁₃	#551	1	1	yes	characteristic
455	C₂⁵	—	2	1	no	—
456	C₂²×D₄	—	2	2	no	—
457	C₂²×D₄	—	2	2	no	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	—	2	2	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	4	1	no	—
463	C₂²×D₄	—	4	1	no	—
464	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	—	2	1	no	—
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×D₈	—	2	2	no	—
472	C₂×D₈	—	2	2	no	—
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	4	1	no	—
476	C₂×D₈	D₄×C₁₃	1	4	yes	—
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	#121	—	2	2	no	—
482	#121	—	4	1	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	4	1	no	—
487	C₄×D₄	—	4	1	no	—
488	C₄×D₄	—	4	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	4	4	no	—
508	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
512	#107	—	4	1	no	—
513	#106	—	2	2	no	—
514	C₄⋊C₈	—	4	1	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	2	2	no	—
518	#102	—	2	2	no	—
519	#102	—	2	2	no	—
520	#102	—	2	2	no	—
521	#102	—	4	1	no	—
522	#102	—	4	1	no	—
523	C₂²⋊C₈	—	2	2	no	—
524	C₂²⋊C₈	—	4	1	no	—
525	#97	—	2	2	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	D₄×C₁₃	1	1	yes	characteristic
532	#95	D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₁₃	—	4	2	no	—
534	C₂×C₁₃	—	4	4	no	—
535	C₂×C₁₃	—	8	2	no	—
536	C₂×C₁₃	—	8	2	no	—
537	C₂×C₁₃	#2418	1	1	yes	characteristic
538	C₂×C₁₃	#3114	1	1	yes	characteristic
539	C₂×C₁₃	#3122	1	1	yes	characteristic
540	C₂×C₁₃	#3264	1	1	yes	characteristic
541	C₂×C₁₃	#3273	1	1	yes	characteristic
542	C₂×C₁₃	#3318	1	1	yes	characteristic
543	C₂×C₁₃	#3319	1	1	yes	characteristic
544	C₂⁴	—	2	1	no	—
545	C₂⁴	—	2	4	no	—
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	4	2	no	—
549	C₂⁴	—	4	2	no	—
550	C₂⁴	—	4	2	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	8	1	no	—
553	C₂⁴	—	8	1	no	—
554	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	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	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	8	1	no	—
578	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₂×D₄	C₁₃×#41	1	2	yes	—
581	C₂×D₄	C₁₃×#41	1	2	yes	—
582	C₂×D₄	C₁₃×#41	1	2	yes	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	8	1	no	—
601	C₂²×C₄	—	8	1	no	—
602	C₂²×C₄	—	8	1	no	—
603	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
609	D₈	—	2	8	no	—
610	D₈	—	4	4	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	8	1	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	8	1	no	—
644	C₂²⋊C₄	—	8	1	no	—
645	C₂²⋊C₄	—	8	1	no	—
646	C₂²⋊C₄	—	8	1	no	—
647	C₂²⋊C₄	—	8	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₁₃	#24909	1	1	yes	characteristic, direct product factor, Sylow
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	8	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	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	—	8	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
688	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	8	4	no	—
702	D₄	C₁₃×#123	1	4	yes	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	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	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	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	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
741	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
742	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
743	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
744	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
745	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₈	—	4	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	8	16	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	C₁₃×#525	1	1	yes	characteristic
780	C₂²	D₄²×C₁₃	1	1	yes	characteristic
781	C₂²	C₁₃×#546	1	1	yes	characteristic
782	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
783	C₂²	C₁₃×#575	1	1	yes	characteristic
784	C₂²	C₁₃×#576	1	1	yes	characteristic
785	C₂²	C₁₃×#576	1	1	yes	characteristic
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	8	1	no	—
792	C₄	—	8	1	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
797	C₄	C₁₃×#538	1	1	yes	characteristic
798	C₄	C₁₃×#546	1	1	yes	characteristic
799	C₄	C₁₃×#551	1	1	yes	characteristic
800	C₂	—	4	2	no	—
801	C₂	—	4	4	no	—
802	C₂	—	8	2	no	—
803	C₂	—	8	2	no	—
804	C₂	C₁₃×#2418	1	1	yes	characteristic
805	C₂	C₁₃×#3114	1	1	yes	characteristic
806	C₂	C₁₃×#3122	1	1	yes	characteristic
807	C₂	C₁₃×#3264	1	1	yes	characteristic
808	C₂	C₁₃×#3273	1	1	yes	characteristic
809	C₂	C₁₃×#3318	1	1	yes	characteristic
810	C₂	C₁₃×#3319	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#442	C₂	semidirect
3. C₁₃×#2420	C₂	semidirect
4. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
5. C₁₃×#2092	C₂	semidirect
6. C₁₃×#2077	C₂	semidirect
7. C₁₃×#2054	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1936	C₂	semidirect
10. C₁₃×#1924	C₂	semidirect
11. C₁₃×#1879	C₂	semidirect
12. C₁₃×#1879	C₂	semidirect
13. C₁₃×#1862	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₁₃×#1786	C₂	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₂×C₁₃×#107	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
28. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₃×#102	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
39. C₂×C₁₃×#97	C₂²	semidirect
44. C₁₃×#390	C₂²	semidirect
45. C₁₃×#389	C₂²	semidirect
49. C₁₃×#382	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
139. #24909	C₁₃	direct (N × H)
249. C₂×#442	C₂×C₁₃	semidirect
250. #2420	C₂×C₁₃	semidirect
251. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
252. #2092	C₂×C₁₃	semidirect
253. #2077	C₂×C₁₃	semidirect
254. #2054	C₂×C₁₃	semidirect
255. #2033	C₂×C₁₃	semidirect
256. #1936	C₂×C₁₃	semidirect
257. #1924	C₂×C₁₃	semidirect
258. #1879	C₂×C₁₃	semidirect
259. #1879	C₂×C₁₃	semidirect
260. #1862	C₂×C₁₃	semidirect
261. #1804	C₂×C₁₃	semidirect
262. #1786	C₂×C₁₃	semidirect
366. C₂×C₄×D₄	C₂²×C₁₃	semidirect
370. C₂×#107	C₂²×C₁₃	semidirect
371. C₂×#106	C₂²×C₁₃	semidirect
372. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
379. C₂×#102	C₂²×C₁₃	semidirect
380. C₂×#102	C₂²×C₁₃	semidirect
383. C₂×#97	C₂²×C₁₃	semidirect
388. #390	C₂²×C₁₃	semidirect
389. #389	C₂²×C₁₃	semidirect
393. #382	C₂²×C₁₃	semidirect
399. #340	C₂²×C₁₃	semidirect
400. #340	C₂²×C₁₃	semidirect
401. #340	C₂²×C₁₃	semidirect
402. #340	C₂²×C₁₃	semidirect
403. #336	C₂²×C₁₃	semidirect
404. #336	C₂²×C₁₃	semidirect
652. C₁₃	#24909	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×#447	2
C₂×C₁₃×#442	2
C₁₃×#2420	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2092	2
C₁₃×#2077	2
C₁₃×#2054	2
C₁₃×#2033	2
C₁₃×#1936	2
C₁₃×#1924	2
C₁₃×#1879	2
C₁₃×#1862	2
C₁₃×#1804	2
C₁₃×#1786	2
#24909	13

Subgroups — C13×#24909 #15711248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24909 #15711248