Subgroups — C₁₃×#25890 #15712229

Order 3328.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#546	—	2	4	no	—
19	C₁₃×#546	—	2	4	no	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	—	2	1	no	—
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#120	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
30	C₁₃×#488	—	2	4	no	—
31	C₁₃×#478	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#102	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×#102	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, complemented
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#400	—	2	1	no	—
53	C₁₃×#394	—	2	1	no	—
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#388	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	—	2	1	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂×C₁₃×#41	—	4	1	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	—	2	2	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	2	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	4	1	no	—
79	C₂²×D₄×C₁₃	—	4	1	no	—
80	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#125	—	2	2	no	—
92	C₁₃×#125	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	D₄	1	4	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×#121	—	2	8	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#120	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	D₄	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	8	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
126	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#107	—	2	2	no	—
130	C₁₃×#106	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	4	1	no	—
135	C₁₃×#103	—	4	1	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	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	4	1	no	—
143	C₁₃×#102	—	4	1	no	—
144	C₁₃×C₂²⋊C₈	—	4	1	no	—
145	C₁₃×C₂²⋊C₈	—	4	1	no	—
146	C₁₃×C₂²⋊C₈	—	4	1	no	—
147	C₁₃×C₂²⋊C₈	—	4	1	no	—
148	C₄×C₈×C₁₃	—	2	2	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	#25890	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₂⁴×C₁₃	—	2	4	no	—
157	C₂⁴×C₁₃	—	2	1	no	—
158	C₂⁴×C₁₃	—	4	2	no	—
159	C₂⁴×C₁₃	—	4	2	no	—
160	C₂⁴×C₁₃	—	4	2	no	—
161	C₂⁴×C₁₃	—	4	2	no	—
162	C₂⁴×C₁₃	—	8	1	no	—
163	C₂⁴×C₁₃	—	8	1	no	—
164	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₁₃×#41	—	4	4	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	2	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	4	1	no	—
190	C₂×D₄×C₁₃	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	4	no	—
198	C₂×D₄×C₁₃	—	8	1	no	—
199	C₂×D₄×C₁₃	—	8	1	no	—
200	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₁₃	#41	1	2	yes	—
203	C₂×D₄×C₁₃	#41	1	2	yes	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	8	1	no	—
227	C₂²×C₄×C₁₃	—	8	1	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	8	1	no	—
269	C₁₃×C₂²⋊C₄	—	8	1	no	—
270	C₄²×C₁₃	—	8	1	no	—
271	C₄²×C₁₃	C₂×D₄	1	2	yes	—
272	C₄²×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
274	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2562	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1983	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	1	no	—
301	C₂³×C₁₃	—	2	1	no	—
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	2	1	no	—
304	C₂³×C₁₃	—	2	1	no	—
305	C₂³×C₁₃	—	4	8	no	—
306	C₂³×C₁₃	—	4	8	no	—
307	C₂³×C₁₃	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	4	1	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	8	4	no	—
318	C₂³×C₁₃	—	8	4	no	—
319	C₂³×C₁₃	—	8	4	no	—
320	C₂³×C₁₃	—	8	4	no	—
321	C₂³×C₁₃	—	8	4	no	—
322	C₂³×C₁₃	#135	1	2	yes	—
323	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₃	—	2	2	no	—
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	4	1	no	—
327	Q₈×C₁₃	—	4	1	no	—
328	D₄×C₁₃	—	2	2	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	2	no	—
331	D₄×C₁₃	—	2	2	no	—
332	D₄×C₁₃	—	2	2	no	—
333	D₄×C₁₃	—	4	4	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	1	no	—
337	D₄×C₁₃	—	4	1	no	—
338	D₄×C₁₃	—	8	4	no	—
339	D₄×C₁₃	#124	1	4	yes	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	4	8	no	—
353	C₂×C₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	#120	1	2	yes	—
379	C₂×C₄×C₁₃	#120	1	2	yes	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
386	C₈×C₁₃	—	4	1	no	—
387	C₈×C₁₃	—	4	1	no	—
388	C₈×C₁₃	—	4	1	no	—
389	C₈×C₁₃	—	4	1	no	—
390	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
391	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
392	#546	—	2	4	no	—
393	#546	—	2	4	no	—
394	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#123	—	2	1	no	—
397	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#121	—	2	1	no	—
399	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#120	—	2	1	no	—
401	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	—	2	1	no	—
404	#488	—	2	4	no	—
405	#478	—	2	4	no	—
406	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#400	—	2	1	no	—
427	#394	—	2	1	no	—
428	#388	—	2	1	no	—
429	#388	—	2	1	no	—
430	#380	C₂²×C₁₃	1	1	yes	characteristic
431	#380	C₂²×C₁₃	1	1	yes	characteristic
432	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	C₂²×C₁₃	—	2	4	no	—
438	C₂²×C₁₃	—	2	2	no	—
439	C₂²×C₁₃	—	2	2	no	—
440	C₂²×C₁₃	—	2	2	no	—
441	C₂²×C₁₃	—	4	1	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	1	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	1	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	8	16	no	—
462	C₂²×C₁₃	—	8	1	no	—
463	C₂²×C₁₃	—	8	1	no	—
464	C₂²×C₁₃	—	8	1	no	—
465	C₂²×C₁₃	—	8	1	no	—
466	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
467	C₂²×C₁₃	#546	1	1	yes	characteristic
468	C₂²×C₁₃	#546	1	1	yes	characteristic
469	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
470	C₂²×C₁₃	#575	1	1	yes	characteristic
471	C₂²×C₁₃	#576	1	1	yes	characteristic
472	C₂²×C₁₃	#577	1	1	yes	characteristic
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	2	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	8	1	no	—
480	C₄×C₁₃	—	8	1	no	—
481	C₄×C₁₃	—	8	1	no	—
482	C₄×C₁₃	—	8	1	no	—
483	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
484	C₄×C₁₃	#535	1	1	yes	characteristic
485	C₄×C₁₃	#546	1	1	yes	characteristic
486	C₄×C₁₃	#546	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	4	1	no	—
493	C₂×#41	—	4	1	no	—
494	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	4	1	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	#125	—	2	2	no	—
516	#125	—	2	2	no	—
517	#124	—	2	2	no	—
518	#124	D₄×C₁₃	1	4	yes	—
519	#123	—	2	8	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	#121	—	2	8	no	—
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#120	—	2	8	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	D₄×C₁₃	1	4	yes	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	2	8	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	#107	—	2	2	no	—
554	#106	—	2	2	no	—
555	C₄⋊C₈	—	2	2	no	—
556	#103	—	2	2	no	—
557	#103	—	2	2	no	—
558	#103	—	4	1	no	—
559	#103	—	4	1	no	—
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	2	2	no	—
563	#102	—	2	2	no	—
564	#102	—	2	2	no	—
565	#102	—	2	2	no	—
566	#102	—	4	1	no	—
567	#102	—	4	1	no	—
568	C₂²⋊C₈	—	4	1	no	—
569	C₂²⋊C₈	—	4	1	no	—
570	C₂²⋊C₈	—	4	1	no	—
571	C₂²⋊C₈	—	4	1	no	—
572	C₄×C₈	—	2	2	no	—
573	#95	—	2	1	no	—
574	#95	—	2	1	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	—	2	1	no	—
578	C₂×C₁₃	—	4	2	no	—
579	C₂×C₁₃	—	4	4	no	—
580	C₂×C₁₃	—	8	1	no	—
581	C₂×C₁₃	—	8	2	no	—
582	C₂×C₁₃	#2435	1	1	yes	characteristic
583	C₂×C₁₃	#3002	1	1	yes	characteristic
584	C₂×C₁₃	#3012	1	1	yes	characteristic
585	C₂×C₁₃	#3296	1	1	yes	characteristic
586	C₂×C₁₃	#3297	1	1	yes	characteristic
587	C₂×C₁₃	#3322	1	1	yes	characteristic
588	C₂×C₁₃	#3323	1	1	yes	characteristic
589	C₂⁴	—	2	1	no	—
590	C₂⁴	—	2	4	no	—
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	4	2	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	8	1	no	—
597	C₂⁴	—	8	1	no	—
598	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
600	#41	—	4	4	no	—
601	#41	—	4	4	no	—
602	#41	—	4	4	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	8	1	no	—
633	C₂×D₄	—	8	1	no	—
634	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₂×D₄	C₁₃×#41	1	2	yes	—
637	C₂×D₄	C₁₃×#41	1	2	yes	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	8	1	no	—
661	C₂²×C₄	—	8	1	no	—
662	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	8	1	no	—
703	C₂²⋊C₄	—	8	1	no	—
704	C₄²	—	8	1	no	—
705	C₄²	C₂×D₄×C₁₃	1	2	yes	—
706	C₄²	C₂×D₄×C₁₃	1	2	yes	—
707	C₁₃	#25890	1	1	yes	characteristic, direct product factor, Sylow
708	C₂³	—	2	1	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	8	4	no	—
738	C₂³	—	8	4	no	—
739	C₂³	—	8	4	no	—
740	C₂³	—	8	4	no	—
741	C₂³	—	8	4	no	—
742	C₂³	C₁₃×#135	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	2	2	no	—
746	Q₈	—	4	1	no	—
747	Q₈	—	4	1	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	2	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	8	no	—
755	D₄	—	4	8	no	—
756	D₄	—	4	1	no	—
757	D₄	—	4	1	no	—
758	D₄	—	8	4	no	—
759	D₄	C₁₃×#124	1	4	yes	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	C₁₃×#120	1	2	yes	—
799	C₂×C₄	C₁₃×#120	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
803	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
804	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
806	C₈	—	4	1	no	—
807	C₈	—	4	1	no	—
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	8	16	no	—
835	C₂²	—	8	1	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
840	C₂²	C₁₃×#546	1	1	yes	characteristic
841	C₂²	C₁₃×#546	1	1	yes	characteristic
842	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
843	C₂²	C₁₃×#575	1	1	yes	characteristic
844	C₂²	C₁₃×#576	1	1	yes	characteristic
845	C₂²	C₁₃×#577	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	8	1	no	—
853	C₄	—	8	1	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
857	C₄	C₁₃×#535	1	1	yes	characteristic
858	C₄	C₁₃×#546	1	1	yes	characteristic
859	C₄	C₁₃×#546	1	1	yes	characteristic
860	C₂	—	4	2	no	—
861	C₂	—	4	4	no	—
862	C₂	—	8	1	no	—
863	C₂	—	8	2	no	—
864	C₂	C₁₃×#2435	1	1	yes	characteristic
865	C₂	C₁₃×#3002	1	1	yes	characteristic
866	C₂	C₁₃×#3012	1	1	yes	characteristic
867	C₂	C₁₃×#3296	1	1	yes	characteristic
868	C₂	C₁₃×#3297	1	1	yes	characteristic
869	C₂	C₁₃×#3322	1	1	yes	characteristic
870	C₂	C₁₃×#3323	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#546	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
2. C₂×C₁₃×#488	C₂	semidirect
3. C₂×C₁₃×#478	C₂	semidirect
4. C₁₃×#2562	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#2035	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1983	C₂	semidirect
10. C₁₃×#1954	C₂	semidirect
11. C₁₃×#1788	C₂	semidirect
12. C₁₃×#1788	C₂	semidirect
13. C₁₃×#1786	C₂	semidirect
14. C₁₃×#1786	C₂	semidirect
15. C₄×C₁₃×#102	C₂	semidirect
20. C₂×C₁₃×#125	C₂²	semidirect
32. C₂×C₁₃×#107	C₂²	semidirect
33. C₂×C₁₃×#106	C₂²	semidirect
34. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
37. C₂×C₁₃×#103	C₂²	semidirect
38. C₂×C₁₃×#103	C₂²	semidirect
49. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
50. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
51. C₂×C₄×C₈×C₁₃	C₂²	semidirect
58. C₁₃×#380	C₂²	semidirect
59. C₁₃×#380	C₂²	semidirect
60. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
154. #25890	C₁₃	direct (N × H)
274. C₂×#488	C₂×C₁₃	semidirect
275. C₂×#478	C₂×C₁₃	semidirect
276. #2562	C₂×C₁₃	semidirect
277. #2036	C₂×C₁₃	semidirect
278. #2035	C₂×C₁₃	semidirect
279. #2034	C₂×C₁₃	semidirect
280. #2033	C₂×C₁₃	semidirect
281. #1983	C₂×C₁₃	semidirect
282. #1954	C₂×C₁₃	semidirect
283. #1788	C₂×C₁₃	semidirect
284. #1788	C₂×C₁₃	semidirect
285. #1786	C₂×C₁₃	semidirect
286. #1786	C₂×C₁₃	semidirect
287. C₄×#102	C₂×C₁₃	semidirect
394. C₂×#125	C₂²×C₁₃	semidirect
406. C₂×#107	C₂²×C₁₃	semidirect
407. C₂×#106	C₂²×C₁₃	semidirect
408. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
409. C₂×#103	C₂²×C₁₃	semidirect
410. C₂×#103	C₂²×C₁₃	semidirect
411. C₂×#103	C₂²×C₁₃	semidirect
412. C₂×#103	C₂²×C₁₃	semidirect
423. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
424. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
425. C₂×C₄×C₈	C₂²×C₁₃	semidirect
432. #380	C₂²×C₁₃	semidirect
433. #380	C₂²×C₁₃	semidirect
434. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
435. #340	C₂²×C₁₃	semidirect
436. #340	C₂²×C₁₃	semidirect
707. C₁₃	#25890	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×#546	2
C₂×C₁₃×#488	2
C₂×C₁₃×#478	2
C₁₃×#2562	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1983	2
C₁₃×#1954	2
C₁₃×#1788	2
C₁₃×#1786	2
C₄×C₁₃×#102	2
#25890	13

Subgroups — C13×#25890 #15712229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25890 #15712229