Subgroups — C₁₃×#25136 #15711475

Order 3328.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2408	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#120	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₁₃×#468	—	2	4	no	—
29	C₁₃×#450	—	2	4	no	—
30	C₁₃×#436	—	2	4	no	—
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#418	—	2	4	no	—
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#397	—	2	1	no	—
47	C₁₃×#394	—	2	1	no	—
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#392	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#389	—	2	1	no	—
54	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#388	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#379	—	2	1	no	—
59	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#340	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	2	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	—	4	1	no	—
73	C₂²×D₄×C₁₃	—	4	1	no	—
74	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	4	1	no	—
84	C₂×C₁₃×SD₁₆	—	4	1	no	—
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	—	2	2	no	—
88	C₂×C₁₃×M₁₆	—	2	2	no	—
89	C₂×C₁₃×M₁₆	—	4	1	no	—
90	C₂×C₁₃×M₁₆	—	4	1	no	—
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×C₂²⋊Q₈	—	2	2	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	4	1	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	4	1	no	—
102	C₁₃×#121	—	4	1	no	—
103	C₁₃×#120	—	4	4	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	4	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	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	—	4	1	no	—
134	C₁₃×C₄⋊C₈	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	4	1	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	D₄	1	4	yes	complemented
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₁₃×C₂²⋊C₈	D₄	1	4	yes	complemented
145	C₄×C₈×C₁₃	—	2	2	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	—	2	1	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	#25136	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	4	2	no	—
155	C₂⁴×C₁₃	—	4	2	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	—	4	2	no	—
158	C₂⁴×C₁₃	—	4	2	no	—
159	C₂⁴×C₁₃	—	8	1	no	—
160	C₂⁴×C₁₃	—	8	1	no	—
161	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	2	no	—
171	C₂×D₄×C₁₃	—	2	2	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	4	4	no	—
183	C₂×D₄×C₁₃	—	4	4	no	—
184	C₂×D₄×C₁₃	—	4	1	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	2	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	8	1	no	—
194	C₂×D₄×C₁₃	—	8	1	no	—
195	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₃	#41	1	2	yes	—
197	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	#41	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₁₃×SD₁₆	—	4	4	no	—
221	C₁₃×SD₁₆	—	4	4	no	—
222	C₁₃×M₁₆	—	4	4	no	—
223	C₁₃×M₁₆	—	4	4	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	—	4	2	no	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	4	2	no	—
254	C₁₃×C₂²⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	4	2	no	—
256	C₁₃×C₂²⋊C₄	—	4	2	no	—
257	C₁₃×C₂²⋊C₄	—	4	2	no	—
258	C₁₃×C₂²⋊C₄	—	4	2	no	—
259	C₁₃×C₂²⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	4	2	no	—
261	C₁₃×C₂²⋊C₄	—	8	1	no	—
262	C₁₃×C₂²⋊C₄	—	8	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	4	2	no	—
266	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
267	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2415	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2408	C₂×C₁₃	1	1	yes	characteristic
272	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1934	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1895	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₁₃	—	2	1	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	—	2	1	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	4	8	no	—
297	C₂³×C₁₃	—	4	1	no	—
298	C₂³×C₁₃	—	4	1	no	—
299	C₂³×C₁₃	—	4	1	no	—
300	C₂³×C₁₃	—	4	1	no	—
301	C₂³×C₁₃	—	4	1	no	—
302	C₂³×C₁₃	—	4	1	no	—
303	C₂³×C₁₃	—	4	1	no	—
304	C₂³×C₁₃	—	4	1	no	—
305	C₂³×C₁₃	—	4	1	no	—
306	C₂³×C₁₃	—	4	1	no	—
307	C₂³×C₁₃	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	8	4	no	—
310	C₂³×C₁₃	—	8	4	no	—
311	C₂³×C₁₃	—	8	4	no	—
312	C₂³×C₁₃	—	8	4	no	—
313	C₂³×C₁₃	—	8	4	no	—
314	C₂³×C₁₃	—	8	4	no	—
315	C₂³×C₁₃	#121	1	2	yes	—
316	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₁₃	—	4	1	no	—
318	Q₈×C₁₃	—	4	1	no	—
319	Q₈×C₁₃	—	4	1	no	—
320	Q₈×C₁₃	—	4	1	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	4	no	—
326	D₄×C₁₃	—	4	8	no	—
327	D₄×C₁₃	—	4	1	no	—
328	D₄×C₁₃	—	4	1	no	—
329	D₄×C₁₃	—	4	1	no	—
330	D₄×C₁₃	—	4	1	no	—
331	D₄×C₁₃	—	8	4	no	—
332	D₄×C₁₃	—	8	4	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	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	—	4	1	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	#121	1	2	yes	—
370	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
377	C₈×C₁₃	—	2	2	no	—
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	4	1	no	—
381	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#120	—	2	1	no	—
391	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
393	#468	—	2	4	no	—
394	#450	—	2	4	no	—
395	#436	—	2	4	no	—
396	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
399	#418	—	2	4	no	—
400	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
402	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#397	—	2	1	no	—
412	#394	—	2	1	no	—
413	#394	—	2	1	no	—
414	#392	—	2	1	no	—
415	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#390	C₂²×C₁₃	1	1	yes	characteristic
417	#390	C₂²×C₁₃	1	1	yes	characteristic
418	#389	—	2	1	no	—
419	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#388	—	2	1	no	—
421	#380	C₂²×C₁₃	1	1	yes	characteristic
422	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#379	—	2	1	no	—
424	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	C₂²×C₁₃	—	2	2	no	—
429	C₂²×C₁₃	—	2	2	no	—
430	C₂²×C₁₃	—	2	2	no	—
431	C₂²×C₁₃	—	4	1	no	—
432	C₂²×C₁₃	—	4	1	no	—
433	C₂²×C₁₃	—	4	1	no	—
434	C₂²×C₁₃	—	4	1	no	—
435	C₂²×C₁₃	—	4	1	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	1	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	1	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	1	no	—
443	C₂²×C₁₃	—	4	1	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	1	no	—
447	C₂²×C₁₃	—	4	2	no	—
448	C₂²×C₁₃	—	8	16	no	—
449	C₂²×C₁₃	—	8	1	no	—
450	C₂²×C₁₃	—	8	1	no	—
451	C₂²×C₁₃	—	8	1	no	—
452	C₂²×C₁₃	—	8	1	no	—
453	C₂²×C₁₃	—	8	1	no	—
454	C₂²×C₁₃	—	8	1	no	—
455	C₂²×C₁₃	—	8	1	no	—
456	C₂²×C₁₃	—	8	1	no	—
457	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
458	C₂²×C₁₃	D₄²	1	1	yes	characteristic
459	C₂²×C₁₃	#546	1	1	yes	characteristic
460	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂²×C₁₃	#575	1	1	yes	characteristic
462	C₂²×C₁₃	#577	1	1	yes	characteristic
463	C₂²×C₁₃	#577	1	1	yes	characteristic
464	C₄×C₁₃	—	2	2	no	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	8	1	no	—
470	C₄×C₁₃	—	8	1	no	—
471	C₄×C₁₃	—	8	1	no	—
472	C₄×C₁₃	—	8	1	no	—
473	C₄×C₁₃	—	8	1	no	—
474	C₄×C₁₃	#525	1	1	yes	characteristic
475	C₄×C₁₃	#538	1	1	yes	characteristic
476	C₄×C₁₃	D₄²	1	1	yes	characteristic
477	C₄×C₁₃	#546	1	1	yes	characteristic
478	C₂⁵	—	2	1	no	—
479	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	2	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	2	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	—	4	1	no	—
488	C₂²×D₄	—	4	1	no	—
489	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
490	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	4	1	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×M₁₆	—	2	2	no	—
501	C₂×M₁₆	—	2	2	no	—
502	C₂×M₁₆	—	2	2	no	—
503	C₂×M₁₆	—	2	2	no	—
504	C₂×M₁₆	—	4	1	no	—
505	C₂×M₁₆	—	4	1	no	—
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	—	4	1	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	4	1	no	—
517	#121	—	4	1	no	—
518	#120	—	4	4	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	—	4	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
547	#107	—	2	2	no	—
548	#106	—	4	1	no	—
549	C₄⋊C₈	—	2	2	no	—
550	#103	—	2	2	no	—
551	#103	—	4	1	no	—
552	#102	—	2	2	no	—
553	#102	—	2	2	no	—
554	#102	—	2	2	no	—
555	#102	—	2	2	no	—
556	#102	—	2	2	no	—
557	#102	D₄×C₁₃	1	4	yes	complemented
558	C₂²⋊C₈	—	2	2	no	—
559	C₂²⋊C₈	D₄×C₁₃	1	4	yes	complemented
560	C₄×C₈	—	2	2	no	—
561	#95	—	2	1	no	—
562	#95	—	2	1	no	—
563	#95	—	2	1	no	—
564	#95	—	2	1	no	—
565	#95	—	2	1	no	—
566	C₂×C₁₃	—	4	2	no	—
567	C₂×C₁₃	—	8	1	no	—
568	C₂×C₁₃	—	8	2	no	—
569	C₂×C₁₃	—	8	2	no	—
570	C₂×C₁₃	#2424	1	1	yes	characteristic
571	C₂×C₁₃	#3055	1	1	yes	characteristic
572	C₂×C₁₃	#3057	1	1	yes	characteristic
573	C₂×C₁₃	#3272	1	1	yes	characteristic
574	C₂×C₁₃	#3275	1	1	yes	characteristic
575	C₂×C₁₃	#3323	1	1	yes	characteristic
576	C₂×C₁₃	#3324	1	1	yes	characteristic
577	C₂⁴	—	2	1	no	—
578	C₂⁴	—	2	1	no	—
579	C₂⁴	—	4	2	no	—
580	C₂⁴	—	4	2	no	—
581	C₂⁴	—	4	2	no	—
582	C₂⁴	—	4	2	no	—
583	C₂⁴	—	4	2	no	—
584	C₂⁴	—	8	1	no	—
585	C₂⁴	—	8	1	no	—
586	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	1	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	4	2	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	8	1	no	—
619	C₂×D₄	—	8	1	no	—
620	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
621	C₂×D₄	C₁₃×#41	1	2	yes	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₁₃×#41	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
645	SD₁₆	—	4	4	no	—
646	SD₁₆	—	4	4	no	—
647	M₁₆	—	4	4	no	—
648	M₁₆	—	4	4	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
659	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
660	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	—	8	1	no	—
687	C₂²⋊C₄	—	8	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	4	2	no	—
691	C₁₃	#25136	1	1	yes	characteristic, direct product factor, Sylow
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	4	no	—
723	C₂³	—	8	4	no	—
724	C₂³	—	8	4	no	—
725	C₂³	—	8	4	no	—
726	C₂³	C₁₃×#121	1	2	yes	—
727	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	Q₈	—	4	1	no	—
729	Q₈	—	4	1	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	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	C₁₃×#121	1	2	yes	—
781	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
784	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
785	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
786	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
787	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	4	1	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	8	16	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	—	8	1	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	8	1	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	1	no	—
821	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
822	C₂²	D₄²×C₁₃	1	1	yes	characteristic
823	C₂²	C₁₃×#546	1	1	yes	characteristic
824	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
825	C₂²	C₁₃×#575	1	1	yes	characteristic
826	C₂²	C₁₃×#577	1	1	yes	characteristic
827	C₂²	C₁₃×#577	1	1	yes	characteristic
828	C₄	—	2	2	no	—
829	C₄	—	2	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	8	1	no	—
834	C₄	—	8	1	no	—
835	C₄	—	8	1	no	—
836	C₄	—	8	1	no	—
837	C₄	—	8	1	no	—
838	C₄	C₁₃×#525	1	1	yes	characteristic
839	C₄	C₁₃×#538	1	1	yes	characteristic
840	C₄	D₄²×C₁₃	1	1	yes	characteristic
841	C₄	C₁₃×#546	1	1	yes	characteristic
842	C₂	—	4	2	no	—
843	C₂	—	8	1	no	—
844	C₂	—	8	2	no	—
845	C₂	—	8	2	no	—
846	C₂	C₁₃×#2424	1	1	yes	characteristic
847	C₂	C₁₃×#3055	1	1	yes	characteristic
848	C₂	C₁₃×#3057	1	1	yes	characteristic
849	C₂	C₁₃×#3272	1	1	yes	characteristic
850	C₂	C₁₃×#3275	1	1	yes	characteristic
851	C₂	C₁₃×#3323	1	1	yes	characteristic
852	C₂	C₁₃×#3324	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×#468	C₂	semidirect
2. C₂×C₁₃×#450	C₂	semidirect
3. C₂×C₁₃×#436	C₂	semidirect
4. C₂×C₁₃×#418	C₂	semidirect
5. C₁₃×#2415	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2034	C₂	semidirect
10. C₁₃×#2000	C₂	semidirect
11. C₁₃×#1968	C₂	semidirect
12. C₁₃×#1934	C₂	semidirect
13. C₁₃×#1895	C₂	semidirect
14. C₁₃×#1894	C₂	semidirect
15. C₁₃×#1854	C₂	semidirect
20. C₂²×C₁₃×M₁₆	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×#107	C₂²	semidirect
32. C₂×C₁₃×#106	C₂²	semidirect
33. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
45. C₂×C₄×C₈×C₁₃	C₂²	semidirect
50. C₁₃×#391	C₂²	semidirect
54. C₁₃×#389	C₂²	semidirect
57. C₁₃×#380	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
142. C₁₃×#102	D₄	semidirect
144. C₁₃×C₂²⋊C₈	D₄	semidirect
151. #25136	C₁₃	direct (N × H)
266. C₂×#468	C₂×C₁₃	semidirect
267. C₂×#450	C₂×C₁₃	semidirect
268. C₂×#436	C₂×C₁₃	semidirect
269. C₂×#418	C₂×C₁₃	semidirect
270. #2415	C₂×C₁₃	semidirect
272. #2067	C₂×C₁₃	semidirect
273. #2055	C₂×C₁₃	semidirect
274. #2034	C₂×C₁₃	semidirect
275. #2000	C₂×C₁₃	semidirect
276. #1968	C₂×C₁₃	semidirect
277. #1934	C₂×C₁₃	semidirect
278. #1895	C₂×C₁₃	semidirect
279. #1894	C₂×C₁₃	semidirect
280. #1854	C₂×C₁₃	semidirect
385. C₂²×M₁₆	C₂²×C₁₃	semidirect
387. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
396. C₂×#107	C₂²×C₁₃	semidirect
397. C₂×#106	C₂²×C₁₃	semidirect
398. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
400. C₂×#103	C₂²×C₁₃	semidirect
401. C₂×#103	C₂²×C₁₃	semidirect
409. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
410. C₂×C₄×C₈	C₂²×C₁₃	semidirect
415. #391	C₂²×C₁₃	semidirect
419. #389	C₂²×C₁₃	semidirect
422. #380	C₂²×C₁₃	semidirect
424. #340	C₂²×C₁₃	semidirect
425. #340	C₂²×C₁₃	semidirect
426. #340	C₂²×C₁₃	semidirect
427. #340	C₂²×C₁₃	semidirect
557. #102	D₄×C₁₃	semidirect
559. C₂²⋊C₈	D₄×C₁₃	semidirect
691. C₁₃	#25136	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×#468	2
C₂×C₁₃×#450	2
C₂×C₁₃×#436	2
C₂×C₁₃×#418	2
C₁₃×#2415	2
C₁₃×#2408	2
C₁₃×#2067	2
C₁₃×#2055	2
C₁₃×#2034	2
C₁₃×#2000	2
C₁₃×#1968	2
C₁₃×#1934	2
C₁₃×#1895	2
C₁₃×#1894	2
C₁₃×#1854	2
#25136	13

Subgroups — C13×#25136 #15711475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25136 #15711475