Subgroups — C₁₃×#62040 #15748379

Order 3328.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
27	C₁₃×#560	—	2	2	no	—
28	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#555	C₂²	1	1	yes	characteristic
30	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#553	—	2	1	no	—
33	C₁₃×#553	C₂²	1	2	yes	complemented
34	C₁₃×#550	C₂²	1	2	yes	complemented
35	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	—	2	2	no	—
41	C₁₃×#546	C₂²	1	2	yes	complemented
42	D₄²×C₁₃	C₂²	1	1	yes	characteristic
43	D₄²×C₁₃	C₂²	1	2	yes	complemented
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#542	C₂²	1	2	yes	complemented
46	C₁₃×#540	C₂²	1	2	yes	complemented
47	C₁₃×#538	—	2	2	no	—
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	—	2	1	no	—
50	C₁₃×#535	—	2	1	no	—
51	C₁₃×#535	C₂²	1	2	yes	complemented
52	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#529	C₂²	1	1	yes	characteristic
56	C₁₃×#525	—	2	1	no	—
57	C₂×C₁₃×#121	—	2	1	no	—
58	C₁₃×#518	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#496	C₂²	1	2	yes	complemented
61	C₁₃×#493	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#490	C₂²	1	2	yes	complemented
65	C₁₃×#488	C₂²	1	2	yes	complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#480	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#480	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#478	C₂²	1	2	yes	complemented
74	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#469	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	complemented
81	C₁₃×#469	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#463	C₂²	1	2	yes	—
86	C₁₃×#463	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	2	yes	complemented
90	C₁₃×#463	C₂²	1	2	yes	complemented
91	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	C₂²	1	2	yes	complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic
95	C₁₃×#459	C₂²	1	1	yes	characteristic
96	C₁₃×#459	C₂²	1	2	yes	complemented
97	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#459	C₂²	1	2	yes	complemented
99	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
101	C₁₃×#459	C₂²	1	2	yes	complemented
102	C₁₃×#459	C₂²	1	2	yes	complemented
103	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#450	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	complemented
106	C₁₃×#449	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	2	yes	complemented
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#447	C₂²	1	1	yes	characteristic
110	C₁₃×#447	C₂²	1	2	yes	—
111	C₁₃×#447	C₂²	1	2	yes	complemented
112	C₁₃×#447	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#447	C₂²	1	2	yes	complemented
114	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#442	C₂²	1	2	yes	complemented
117	C₁₃×#440	C₂²	1	2	yes	complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
123	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#436	C₂²	1	2	yes	complemented
126	C₁₃×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#433	C₂²	1	2	yes	complemented
129	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#424	C₂²	1	2	yes	complemented
131	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
132	C₁₃×#418	C₂²	1	2	yes	complemented
133	C₁₃×#417	C₂²	1	2	yes	complemented
134	C₁₃×#416	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
140	C₂×C₁₃×#41	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	—	2	2	no	—
143	C₂²×D₄×C₁₃	—	2	1	no	—
144	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃	—	2	1	no	—
148	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
149	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×D₈	—	4	4	no	—
155	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×D₈	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×D₈	C₂³	1	2	yes	—
160	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×D₈	C₂³	1	2	yes	—
162	C₂×C₁₃×D₈	C₂³	1	2	yes	—
163	C₂×C₁₃×D₈	C₂³	1	2	yes	—
164	C₂×C₁₃×D₈	C₂³	1	2	yes	—
165	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
167	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
168	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₃×#127	—	2	2	no	—
172	C₁₃×#127	C₂³	1	1	yes	characteristic
173	C₁₃×#127	C₂³	1	1	yes	characteristic
174	C₁₃×#127	C₂³	1	2	yes	—
175	C₁₃×#127	C₂³	1	1	yes	characteristic
176	C₁₃×#127	C₂³	1	2	yes	—
177	C₁₃×#126	—	2	2	no	—
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#126	—	2	2	no	—
180	C₁₃×#126	D₄	1	2	yes	—
181	C₁₃×#125	D₄	1	1	yes	characteristic
182	C₁₃×#125	C₂³	1	2	yes	—
183	C₁₃×#124	—	2	2	no	—
184	C₁₃×#124	—	2	2	no	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#124	—	2	1	no	—
187	C₁₃×#124	D₄	1	1	yes	characteristic
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	D₄	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	—	2	1	no	—
198	C₁₃×C₂²⋊Q₈	—	2	1	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	1	no	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	D₄	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	1	yes	characteristic
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	1	yes	characteristic
230	C₁₃×#121	C₂³	1	2	yes	—
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₁₃×#120	—	2	2	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₁₃×#120	—	2	2	no	—
236	C₁₃×#120	—	2	2	no	—
237	C₁₃×#120	—	2	2	no	—
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	2	yes	—
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₃	C₂³	1	2	yes	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	C₂³	1	2	yes	—
265	C₁₃×#117	C₂³	1	2	yes	—
266	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	1	yes	characteristic
276	C₁₃×#107	C₂³	1	1	yes	characteristic
277	C₁₃×#107	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	1	yes	characteristic
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₃	C₂³	1	2	yes	—
315	#62040	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	1	no	—
317	C₂⁴×C₁₃	—	2	2	no	—
318	C₂⁴×C₁₃	—	2	2	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	4	2	no	—
322	C₁₃×#41	—	4	2	no	—
323	C₁₃×#41	—	8	2	no	—
324	C₁₃×#41	—	8	2	no	—
325	C₁₃×#41	—	8	2	no	—
326	C₁₃×#41	—	8	2	no	—
327	C₂×Q₈×C₁₃	—	2	1	no	—
328	C₂×Q₈×C₁₃	—	2	1	no	—
329	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₁₃	—	2	4	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	1	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	1	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	2	1	no	—
346	C₂×D₄×C₁₃	—	2	1	no	—
347	C₂×D₄×C₁₃	—	2	2	no	—
348	C₂×D₄×C₁₃	—	2	2	no	—
349	C₂×D₄×C₁₃	—	2	1	no	—
350	C₂×D₄×C₁₃	—	2	1	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	4	2	no	—
355	C₂×D₄×C₁₃	—	4	1	no	—
356	C₂×D₄×C₁₃	—	4	2	no	—
357	C₂×D₄×C₁₃	—	4	2	no	—
358	C₂×D₄×C₁₃	—	8	2	no	—
359	C₂×D₄×C₁₃	—	8	2	no	—
360	C₂×D₄×C₁₃	—	8	4	no	—
361	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
365	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	—	2	1	no	—
370	C₂²×C₄×C₁₃	—	2	1	no	—
371	C₂²×C₄×C₁₃	—	2	1	no	—
372	C₂²×C₄×C₁₃	—	2	1	no	—
373	C₂²×C₄×C₁₃	—	2	1	no	—
374	C₂²×C₄×C₁₃	—	2	1	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	2	2	no	—
380	C₂²×C₄×C₁₃	—	2	2	no	—
381	C₂²×C₄×C₁₃	—	2	1	no	—
382	C₂²×C₄×C₁₃	—	8	2	no	—
383	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
387	C₁₃×SD₁₆	—	2	4	no	—
388	C₁₃×SD₁₆	—	4	2	no	—
389	C₁₃×SD₁₆	—	4	2	no	—
390	C₁₃×SD₁₆	—	4	2	no	—
391	C₁₃×D₈	—	2	2	no	—
392	C₁₃×D₈	—	2	4	no	—
393	C₁₃×D₈	—	2	2	no	—
394	C₁₃×D₈	—	4	2	no	—
395	C₁₃×D₈	—	4	2	no	—
396	C₁₃×D₈	—	4	1	no	—
397	C₁₃×D₈	—	4	2	no	—
398	C₁₃×D₈	—	4	1	no	—
399	C₁₃×D₈	—	4	2	no	—
400	C₁₃×D₈	—	4	2	no	—
401	C₁₃×M₁₆	—	4	2	no	—
402	C₁₃×M₁₆	—	4	2	no	—
403	C₂×C₈×C₁₃	—	4	2	no	—
404	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
410	C₁₃×C₄⋊C₄	—	2	1	no	—
411	C₁₃×C₄⋊C₄	—	2	1	no	—
412	C₁₃×C₄⋊C₄	—	2	2	no	—
413	C₁₃×C₄⋊C₄	—	2	2	no	—
414	C₁₃×C₄⋊C₄	—	2	1	no	—
415	C₁₃×C₄⋊C₄	—	2	2	no	—
416	C₁₃×C₄⋊C₄	—	2	1	no	—
417	C₁₃×C₄⋊C₄	—	2	1	no	—
418	C₁₃×C₄⋊C₄	—	2	2	no	—
419	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
425	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
429	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	1	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	1	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	—	2	2	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	1	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	1	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	no	—
451	C₁₃×C₂²⋊C₄	—	2	1	no	—
452	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
455	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
456	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
457	C₄²×C₁₃	—	2	2	no	—
458	C₄²×C₁₃	—	2	2	no	—
459	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
462	C₄²×C₁₃	C₂⁴	1	2	yes	—
463	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
464	#3546	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3519	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3322	C₂×C₁₃	1	2	yes	complemented
472	#3309	C₂×C₁₃	1	2	yes	complemented
473	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
474	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3274	C₂×C₁₃	1	2	yes	complemented
476	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3264	C₂×C₁₃	1	2	yes	complemented
478	#3257	C₂×C₁₃	1	2	yes	complemented
479	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3220	C₂×C₁₃	1	2	yes	complemented
481	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3118	C₂×C₁₃	1	2	yes	complemented
483	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3041	C₂×C₁₃	1	2	yes	complemented
485	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#2993	C₂×C₁₃	1	1	yes	characteristic, complemented
487	C₂³×C₁₃	—	2	1	no	—
488	C₂³×C₁₃	—	2	1	no	—
489	C₂³×C₁₃	—	2	2	no	—
490	C₂³×C₁₃	—	2	1	no	—
491	C₂³×C₁₃	—	2	2	no	—
492	C₂³×C₁₃	—	2	1	no	—
493	C₂³×C₁₃	—	4	2	no	—
494	C₂³×C₁₃	—	4	4	no	—
495	C₂³×C₁₃	—	4	2	no	—
496	C₂³×C₁₃	—	8	1	no	—
497	C₂³×C₁₃	—	8	2	no	—
498	C₂³×C₁₃	—	8	2	no	—
499	C₂³×C₁₃	—	8	2	no	—
500	C₂³×C₁₃	—	8	2	no	—
501	C₂³×C₁₃	—	8	2	no	—
502	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
503	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
504	Q₈×C₁₃	—	2	2	no	—
505	Q₈×C₁₃	—	2	2	no	—
506	Q₈×C₁₃	—	2	2	no	—
507	Q₈×C₁₃	—	8	1	no	—
508	Q₈×C₁₃	—	8	1	no	—
509	D₄×C₁₃	—	2	2	no	—
510	D₄×C₁₃	—	2	1	no	—
511	D₄×C₁₃	—	2	2	no	—
512	D₄×C₁₃	—	2	1	no	—
513	D₄×C₁₃	—	2	2	no	—
514	D₄×C₁₃	—	2	1	no	—
515	D₄×C₁₃	—	2	1	no	—
516	D₄×C₁₃	—	2	1	no	—
517	D₄×C₁₃	—	2	2	no	—
518	D₄×C₁₃	—	2	1	no	—
519	D₄×C₁₃	—	2	2	no	—
520	D₄×C₁₃	—	2	1	no	—
521	D₄×C₁₃	—	4	2	no	—
522	D₄×C₁₃	—	4	2	no	—
523	D₄×C₁₃	—	4	4	no	—
524	D₄×C₁₃	—	4	4	no	—
525	D₄×C₁₃	—	4	2	no	—
526	D₄×C₁₃	—	4	2	no	—
527	D₄×C₁₃	—	8	1	no	—
528	D₄×C₁₃	—	8	1	no	—
529	D₄×C₁₃	—	8	2	no	—
530	D₄×C₁₃	—	8	2	no	—
531	D₄×C₁₃	—	8	2	no	—
532	D₄×C₁₃	—	8	1	no	—
533	D₄×C₁₃	—	8	1	no	—
534	D₄×C₁₃	—	8	2	no	—
535	D₄×C₁₃	—	8	2	no	—
536	D₄×C₁₃	—	8	2	no	—
537	D₄×C₁₃	—	8	2	no	—
538	D₄×C₁₃	—	8	2	no	—
539	D₄×C₁₃	—	8	2	no	—
540	D₄×C₁₃	—	8	2	no	—
541	D₄×C₁₃	—	8	1	no	—
542	D₄×C₁₃	—	8	1	no	—
543	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
544	C₂×C₄×C₁₃	—	2	2	no	—
545	C₂×C₄×C₁₃	—	2	2	no	—
546	C₂×C₄×C₁₃	—	2	1	no	—
547	C₂×C₄×C₁₃	—	2	2	no	—
548	C₂×C₄×C₁₃	—	2	1	no	—
549	C₂×C₄×C₁₃	—	2	1	no	—
550	C₂×C₄×C₁₃	—	2	1	no	—
551	C₂×C₄×C₁₃	—	2	2	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	1	no	—
554	C₂×C₄×C₁₃	—	2	1	no	—
555	C₂×C₄×C₁₃	—	4	1	no	—
556	C₂×C₄×C₁₃	—	4	2	no	—
557	C₂×C₄×C₁₃	—	4	2	no	—
558	C₂×C₄×C₁₃	—	4	2	no	—
559	C₂×C₄×C₁₃	—	4	2	no	—
560	C₂×C₄×C₁₃	—	8	1	no	—
561	C₂×C₄×C₁₃	—	8	1	no	—
562	C₂×C₄×C₁₃	—	8	2	no	—
563	C₂×C₄×C₁₃	—	8	2	no	—
564	C₂×C₄×C₁₃	—	8	2	no	—
565	C₂×C₄×C₁₃	—	8	2	no	—
566	C₂×C₄×C₁₃	—	8	2	no	—
567	C₂×C₄×C₁₃	—	8	2	no	—
568	C₂×C₄×C₁₃	—	8	1	no	—
569	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
576	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
578	C₈×C₁₃	—	2	1	no	—
579	C₈×C₁₃	—	2	2	no	—
580	C₈×C₁₃	—	2	1	no	—
581	C₈×C₁₃	—	2	2	no	—
582	C₈×C₁₃	—	2	1	no	—
583	C₈×C₁₃	—	2	1	no	—
584	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
585	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
586	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
587	#560	—	2	2	no	—
588	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#555	C₂²×C₁₃	1	1	yes	characteristic
590	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#553	—	2	1	no	—
592	#553	—	2	1	no	—
593	#553	C₂²×C₁₃	1	2	yes	complemented
594	#550	C₂²×C₁₃	1	2	yes	complemented
595	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
597	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#546	—	2	1	no	—
599	#546	—	2	1	no	—
600	#546	—	2	2	no	—
601	#546	C₂²×C₁₃	1	2	yes	complemented
602	D₄²	C₂²×C₁₃	1	1	yes	characteristic
603	D₄²	C₂²×C₁₃	1	2	yes	complemented
604	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#542	C₂²×C₁₃	1	2	yes	complemented
606	#540	C₂²×C₁₃	1	2	yes	complemented
607	#538	—	2	2	no	—
608	#538	—	2	2	no	—
609	#537	—	2	1	no	—
610	#535	—	2	1	no	—
611	#535	C₂²×C₁₃	1	2	yes	complemented
612	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#529	C₂²×C₁₃	1	1	yes	characteristic
616	#525	—	2	1	no	—
617	C₂×#121	—	2	1	no	—
618	#518	C₂²×C₁₃	1	2	yes	complemented
619	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#496	C₂²×C₁₃	1	2	yes	complemented
621	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#493	C₂²×C₁₃	1	2	yes	complemented
623	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#490	C₂²×C₁₃	1	2	yes	complemented
625	#488	C₂²×C₁₃	1	2	yes	complemented
626	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#485	C₂²×C₁₃	1	2	yes	complemented
629	#482	C₂²×C₁₃	1	2	yes	complemented
630	#480	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#480	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#479	C₂²×C₁₃	1	2	yes	complemented
633	#478	C₂²×C₁₃	1	2	yes	complemented
634	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#476	C₂²×C₁₃	1	2	yes	complemented
637	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#469	C₂²×C₁₃	1	2	yes	complemented
640	#469	C₂²×C₁₃	1	2	yes	complemented
641	#469	C₂²×C₁₃	1	2	yes	complemented
642	#468	C₂²×C₁₃	1	2	yes	complemented
643	#466	C₂²×C₁₃	1	2	yes	complemented
644	#465	C₂²×C₁₃	1	2	yes	complemented
645	#463	C₂²×C₁₃	1	2	yes	—
646	#463	C₂²×C₁₃	1	2	yes	complemented
647	#463	C₂²×C₁₃	1	2	yes	complemented
648	#463	C₂²×C₁₃	1	2	yes	complemented
649	#463	C₂²×C₁₃	1	2	yes	complemented
650	#463	C₂²×C₁₃	1	2	yes	complemented
651	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#460	C₂²×C₁₃	1	2	yes	complemented
654	#459	C₂²×C₁₃	1	1	yes	characteristic
655	#459	C₂²×C₁₃	1	1	yes	characteristic
656	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#459	C₂²×C₁₃	1	2	yes	complemented
658	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#459	C₂²×C₁₃	1	2	yes	complemented
660	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#459	C₂²×C₁₃	1	2	yes	complemented
662	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	#459	C₂²×C₁₃	1	2	yes	complemented
664	#450	C₂²×C₁₃	1	2	yes	complemented
665	#449	C₂²×C₁₃	1	2	yes	complemented
666	#449	C₂²×C₁₃	1	2	yes	complemented
667	#449	C₂²×C₁₃	1	2	yes	complemented
668	#449	C₂²×C₁₃	1	2	yes	complemented
669	#447	C₂²×C₁₃	1	1	yes	characteristic
670	#447	C₂²×C₁₃	1	2	yes	—
671	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#447	C₂²×C₁₃	1	2	yes	complemented
673	#447	C₂²×C₁₃	1	2	yes	complemented
674	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#442	C₂²×C₁₃	1	2	yes	complemented
677	#440	C₂²×C₁₃	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
679	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
683	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
684	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
685	#436	C₂²×C₁₃	1	2	yes	complemented
686	#435	C₂²×C₁₃	1	2	yes	complemented
687	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
688	#433	C₂²×C₁₃	1	2	yes	complemented
689	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	#424	C₂²×C₁₃	1	2	yes	complemented
691	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	#418	C₂²×C₁₃	1	2	yes	complemented
693	#417	C₂²×C₁₃	1	2	yes	complemented
694	#416	C₂²×C₁₃	1	2	yes	complemented
695	C₂²×C₁₃	—	2	1	no	—
696	C₂²×C₁₃	—	2	2	no	—
697	C₂²×C₁₃	—	2	1	no	—
698	C₂²×C₁₃	—	2	2	no	—
699	C₂²×C₁₃	—	2	2	no	—
700	C₂²×C₁₃	—	2	1	no	—
701	C₂²×C₁₃	—	2	2	no	—
702	C₂²×C₁₃	—	4	1	no	—
703	C₂²×C₁₃	—	4	1	no	—
704	C₂²×C₁₃	—	4	2	no	—
705	C₂²×C₁₃	—	4	1	no	—
706	C₂²×C₁₃	—	4	1	no	—
707	C₂²×C₁₃	—	4	2	no	—
708	C₂²×C₁₃	—	4	1	no	—
709	C₂²×C₁₃	—	4	1	no	—
710	C₂²×C₁₃	—	4	2	no	—
711	C₂²×C₁₃	—	4	1	no	—
712	C₂²×C₁₃	—	4	2	no	—
713	C₂²×C₁₃	—	4	1	no	—
714	C₂²×C₁₃	—	4	1	no	—
715	C₂²×C₁₃	—	4	1	no	—
716	C₂²×C₁₃	—	4	1	no	—
717	C₂²×C₁₃	—	4	2	no	—
718	C₂²×C₁₃	—	4	2	no	—
719	C₂²×C₁₃	—	8	4	no	—
720	C₂²×C₁₃	—	16	4	no	—
721	C₂²×C₁₃	—	16	4	no	—
722	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
723	C₄×C₁₃	—	2	1	no	—
724	C₄×C₁₃	—	2	1	no	—
725	C₄×C₁₃	—	2	2	no	—
726	C₄×C₁₃	—	2	1	no	—
727	C₄×C₁₃	—	2	2	no	—
728	C₄×C₁₃	—	2	1	no	—
729	C₄×C₁₃	—	2	2	no	—
730	C₄×C₁₃	—	4	2	no	—
731	C₄×C₁₃	—	4	2	no	—
732	C₄×C₁₃	—	4	1	no	—
733	C₄×C₁₃	—	4	1	no	—
734	C₄×C₁₃	—	4	1	no	—
735	C₄×C₁₃	—	4	1	no	—
736	C₄×C₁₃	#576	1	2	yes	—
737	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
738	C₄×C₁₃	#585	1	1	yes	characteristic
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	2	1	no	—
743	C₂×#41	C₂³×C₁₃	1	2	yes	—
744	C₂×#41	C₂³×C₁₃	1	2	yes	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	—	2	2	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
751	C₂³×C₄	—	2	1	no	—
752	AGL(1,ℤ/8)	—	4	4	no	—
753	AGL(1,ℤ/8)	—	4	4	no	—
754	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
758	C₂×D₈	—	4	4	no	—
759	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₁₃	1	2	yes	—
761	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₂×D₈	C₂³×C₁₃	1	2	yes	—
763	C₂×D₈	C₂³×C₁₃	1	2	yes	—
764	C₂×D₈	C₂³×C₁₃	1	2	yes	—
765	C₂×D₈	C₂³×C₁₃	1	2	yes	—
766	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×D₈	C₂³×C₁₃	1	2	yes	—
768	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
770	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
771	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
772	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
775	#127	—	2	2	no	—
776	#127	C₂³×C₁₃	1	1	yes	characteristic
777	#127	C₂³×C₁₃	1	1	yes	characteristic
778	#127	C₂³×C₁₃	1	1	yes	characteristic
779	#127	C₂³×C₁₃	1	2	yes	—
780	#127	C₂³×C₁₃	1	2	yes	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	—	2	2	no	—
784	#126	D₄×C₁₃	1	2	yes	—
785	#125	D₄×C₁₃	1	1	yes	characteristic
786	#125	C₂³×C₁₃	1	2	yes	—
787	#124	—	2	2	no	—
788	#124	—	2	2	no	—
789	#124	—	2	1	no	—
790	#124	—	2	1	no	—
791	#124	D₄×C₁₃	1	1	yes	characteristic
792	#124	C₂³×C₁₃	1	2	yes	—
793	#124	C₂³×C₁₃	1	2	yes	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	D₄×C₁₃	1	2	yes	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
807	#121	—	2	2	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	D₄×C₁₃	1	1	yes	characteristic
829	#121	C₂³×C₁₃	1	2	yes	—
830	#121	C₂³×C₁₃	1	1	yes	characteristic
831	#121	C₂³×C₁₃	1	1	yes	characteristic
832	#121	C₂³×C₁₃	1	2	yes	—
833	#121	C₂³×C₁₃	1	2	yes	—
834	#121	C₂³×C₁₃	1	2	yes	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	#120	—	2	2	no	—
839	#120	—	2	2	no	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
843	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₁₃	1	2	yes	—
859	C₄×D₄	C₂³×C₁₃	1	2	yes	—
860	C₄×D₄	C₂³×C₁₃	1	2	yes	—
861	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₁₃	1	2	yes	—
864	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₁₃	1	2	yes	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	C₂³×C₁₃	1	2	yes	—
869	#117	C₂³×C₁₃	1	2	yes	—
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
873	C₂×C₂²⋊C₄	—	2	1	no	—
874	C₂×C₂²⋊C₄	—	2	2	no	—
875	C₂×C₂²⋊C₄	—	2	2	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
878	#107	C₂³×C₁₃	1	1	yes	characteristic
879	#107	C₂³×C₁₃	1	1	yes	characteristic
880	#107	C₂³×C₁₃	1	1	yes	characteristic
881	#107	C₂³×C₁₃	1	1	yes	characteristic
882	#106	C₂³×C₁₃	1	2	yes	—
883	#106	C₂³×C₁₃	1	2	yes	—
884	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
885	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
887	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
890	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
891	#103	C₂³×C₁₃	1	2	yes	—
892	#103	C₂³×C₁₃	1	2	yes	—
893	#103	C₂³×C₁₃	1	2	yes	—
894	#103	C₂³×C₁₃	1	2	yes	—
895	#102	C₂³×C₁₃	1	1	yes	characteristic
896	#102	C₂³×C₁₃	1	2	yes	—
897	#102	C₂³×C₁₃	1	2	yes	—
898	#102	C₂³×C₁₃	1	2	yes	—
899	#102	C₂³×C₁₃	1	1	yes	characteristic
900	#102	C₂³×C₁₃	1	2	yes	—
901	#102	C₂³×C₁₃	1	2	yes	—
902	#102	C₂³×C₁₃	1	1	yes	characteristic
903	#102	C₂³×C₁₃	1	1	yes	characteristic
904	#102	C₂³×C₁₃	1	1	yes	characteristic
905	#102	C₂³×C₁₃	1	1	yes	characteristic
906	#102	C₂³×C₁₃	1	1	yes	characteristic
907	#102	C₂³×C₁₃	1	1	yes	characteristic
908	#102	C₂³×C₁₃	1	2	yes	—
909	#102	C₂³×C₁₃	1	2	yes	—
910	#102	C₂³×C₁₃	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
912	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
913	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
915	#97	C₂³×C₁₃	1	2	yes	—
916	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
917	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
918	C₄×C₈	C₂³×C₁₃	1	2	yes	—
919	C₂×C₁₃	—	4	1	no	—
920	C₂×C₁₃	—	4	2	no	—
921	C₂×C₁₃	—	4	2	no	—
922	C₂×C₁₃	—	8	1	no	—
923	C₂×C₁₃	—	8	1	no	—
924	C₂×C₁₃	—	8	2	no	—
925	C₂×C₁₃	—	8	2	no	—
926	C₂×C₁₃	—	8	1	no	—
927	C₂×C₁₃	#3488	1	1	yes	characteristic
928	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
929	C₂×C₁₃	#3585	1	1	yes	characteristic
930	C₂⁴	—	2	1	no	—
931	C₂⁴	—	2	2	no	—
932	C₂⁴	—	2	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	8	2	no	—
938	#41	—	8	2	no	—
939	#41	—	8	2	no	—
940	#41	—	8	2	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	2	1	no	—
943	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
944	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	1	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	8	2	no	—
973	C₂×D₄	—	8	2	no	—
974	C₂×D₄	—	8	4	no	—
975	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
976	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
977	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
978	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
979	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
980	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
981	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
982	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	8	2	no	—
997	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1001	SD₁₆	—	2	4	no	—
1002	SD₁₆	—	4	2	no	—
1003	SD₁₆	—	4	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	D₈	—	2	2	no	—
1006	D₈	—	2	4	no	—
1007	D₈	—	2	2	no	—
1008	D₈	—	4	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	—	4	2	no	—
1011	D₈	—	4	2	no	—
1012	D₈	—	4	1	no	—
1013	D₈	—	4	2	no	—
1014	D₈	—	4	1	no	—
1015	M₁₆	—	4	2	no	—
1016	M₁₆	—	4	2	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1022	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1036	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1037	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1038	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1039	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1040	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1042	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1043	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1067	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1068	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1069	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1070	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	2	no	—
1073	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1074	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1075	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1076	C₄²	C₂⁴×C₁₃	1	2	yes	—
1077	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1078	C₁₃	#62040	1	1	yes	characteristic, direct product factor, Sylow
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	4	2	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	—	8	1	no	—
1089	C₂³	—	8	2	no	—
1090	C₂³	—	8	2	no	—
1091	C₂³	—	8	2	no	—
1092	C₂³	—	8	2	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1095	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	8	1	no	—
1100	Q₈	—	8	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	4	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	1	no	—
1122	D₄	—	8	1	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	1	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	1	no	—
1134	D₄	—	8	1	no	—
1135	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	8	1	no	—
1153	C₂×C₄	—	8	1	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1169	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1170	C₈	—	2	1	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	8	4	no	—
1201	C₂²	—	16	4	no	—
1202	C₂²	—	16	4	no	—
1203	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	1	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	2	no	—
1217	C₄	C₁₃×#576	1	2	yes	—
1218	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1219	C₄	C₁₃×#585	1	1	yes	characteristic
1220	C₂	—	4	1	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	4	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	—	8	1	no	—
1225	C₂	—	8	2	no	—
1226	C₂	—	8	2	no	—
1227	C₂	—	8	1	no	—
1228	C₂	C₁₃×#3488	1	1	yes	characteristic
1229	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1230	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3546	C₂	semidirect
2. C₁₃×#3519	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3391	C₂	semidirect
5. C₁₃×#3366	C₂	semidirect
6. C₁₃×#3360	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3322	C₂	semidirect
9. C₁₃×#3309	C₂	semidirect
10. C₁₃×#3303	C₂	semidirect
11. D₄×C₁₃×D₈	C₂	semidirect
12. C₁₃×#3274	C₂	semidirect
13. C₁₃×#3272	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3257	C₂	semidirect
16. C₁₃×#3253	C₂	semidirect
17. C₁₃×#3220	C₂	semidirect
18. C₁₃×#3207	C₂	semidirect
19. C₁₃×#3118	C₂	semidirect
20. C₁₃×#3100	C₂	semidirect
21. C₁₃×#3041	C₂	semidirect
22. C₁₃×#3036	C₂	semidirect
23. C₁₃×#2993	C₂	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
30. C₁₃×#554	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
43. D₄²×C₁₃	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
45. C₁₃×#542	C₂²	semidirect
46. C₁₃×#540	C₂²	semidirect
51. C₁₃×#535	C₂²	semidirect
52. C₁₃×#532	C₂²	semidirect
53. C₁₃×#532	C₂²	semidirect
54. C₁₃×#532	C₂²	semidirect
58. C₁₃×#518	C₂²	semidirect
59. C₂×C₄×D₄×C₁₃	C₂²	semidirect
60. C₁₃×#496	C₂²	semidirect
61. C₁₃×#493	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#488	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
67. C₁₃×#486	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#480	C₂²	semidirect
71. C₁₃×#480	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#478	C₂²	semidirect
74. C₁₃×#476	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#469	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#463	C₂²	semidirect
91. C₁₃×#461	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
96. C₁₃×#459	C₂²	semidirect
97. C₁₃×#459	C₂²	semidirect
98. C₁₃×#459	C₂²	semidirect
99. C₁₃×#459	C₂²	semidirect
100. C₁₃×#459	C₂²	semidirect
101. C₁₃×#459	C₂²	semidirect
102. C₁₃×#459	C₂²	semidirect
103. C₁₃×#459	C₂²	semidirect
104. C₁₃×#450	C₂²	semidirect
105. C₁₃×#449	C₂²	semidirect
106. C₁₃×#449	C₂²	semidirect
107. C₁₃×#449	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
111. C₁₃×#447	C₂²	semidirect
112. C₁₃×#447	C₂²	semidirect
113. C₁₃×#447	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₁₃×#442	C₂²	semidirect
117. C₁₃×#440	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₄×C₁₃×D₈	C₂²	semidirect
122. C₄×C₁₃×D₈	C₂²	semidirect
123. C₄×C₁₃×D₈	C₂²	semidirect
124. C₁₃×#436	C₂²	semidirect
125. C₁₃×#436	C₂²	semidirect
126. C₁₃×#435	C₂²	semidirect
127. C₈×D₄×C₁₃	C₂²	semidirect
128. C₁₃×#433	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#424	C₂²	semidirect
131. C₁₃×#423	C₂²	semidirect
132. C₁₃×#418	C₂²	semidirect
133. C₁₃×#417	C₂²	semidirect
134. C₁₃×#416	C₂²	semidirect
315. #62040	C₁₃	direct (N × H)
464. #3546	C₂×C₁₃	semidirect
465. #3519	C₂×C₁₃	semidirect
466. #3397	C₂×C₁₃	semidirect
467. #3391	C₂×C₁₃	semidirect
468. #3366	C₂×C₁₃	semidirect
469. #3360	C₂×C₁₃	semidirect
470. #3325	C₂×C₁₃	semidirect
471. #3322	C₂×C₁₃	semidirect
472. #3309	C₂×C₁₃	semidirect
473. #3303	C₂×C₁₃	semidirect
474. D₄×D₈	C₂×C₁₃	semidirect
475. #3274	C₂×C₁₃	semidirect
476. #3272	C₂×C₁₃	semidirect
477. #3264	C₂×C₁₃	semidirect
478. #3257	C₂×C₁₃	semidirect
479. #3253	C₂×C₁₃	semidirect
480. #3220	C₂×C₁₃	semidirect
481. #3207	C₂×C₁₃	semidirect
482. #3118	C₂×C₁₃	semidirect
483. #3100	C₂×C₁₃	semidirect
484. #3041	C₂×C₁₃	semidirect
485. #3036	C₂×C₁₃	semidirect
486. #2993	C₂×C₁₃	semidirect
584. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
585. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
588. #556	C₂²×C₁₃	semidirect
590. #554	C₂²×C₁₃	semidirect
593. #553	C₂²×C₁₃	semidirect
594. #550	C₂²×C₁₃	semidirect
595. #550	C₂²×C₁₃	semidirect
596. #550	C₂²×C₁₃	semidirect
597. #547	C₂²×C₁₃	semidirect
601. #546	C₂²×C₁₃	semidirect
603. D₄²	C₂²×C₁₃	semidirect
604. D₄²	C₂²×C₁₃	semidirect
605. #542	C₂²×C₁₃	semidirect
606. #540	C₂²×C₁₃	semidirect
611. #535	C₂²×C₁₃	semidirect
612. #532	C₂²×C₁₃	semidirect
613. #532	C₂²×C₁₃	semidirect
614. #532	C₂²×C₁₃	semidirect
618. #518	C₂²×C₁₃	semidirect
619. C₂×C₄×D₄	C₂²×C₁₃	semidirect
620. #496	C₂²×C₁₃	semidirect
621. #493	C₂²×C₁₃	semidirect
622. #493	C₂²×C₁₃	semidirect
623. #492	C₂²×C₁₃	semidirect
624. #490	C₂²×C₁₃	semidirect
625. #488	C₂²×C₁₃	semidirect
626. #487	C₂²×C₁₃	semidirect
627. #486	C₂²×C₁₃	semidirect
628. #485	C₂²×C₁₃	semidirect
629. #482	C₂²×C₁₃	semidirect
630. #480	C₂²×C₁₃	semidirect
631. #480	C₂²×C₁₃	semidirect
632. #479	C₂²×C₁₃	semidirect
633. #478	C₂²×C₁₃	semidirect
634. #476	C₂²×C₁₃	semidirect
635. #476	C₂²×C₁₃	semidirect
636. #476	C₂²×C₁₃	semidirect
637. #474	C₂²×C₁₃	semidirect
638. #474	C₂²×C₁₃	semidirect
639. #469	C₂²×C₁₃	semidirect
640. #469	C₂²×C₁₃	semidirect
641. #469	C₂²×C₁₃	semidirect
642. #468	C₂²×C₁₃	semidirect
643. #466	C₂²×C₁₃	semidirect
644. #465	C₂²×C₁₃	semidirect
646. #463	C₂²×C₁₃	semidirect
647. #463	C₂²×C₁₃	semidirect
648. #463	C₂²×C₁₃	semidirect
649. #463	C₂²×C₁₃	semidirect
650. #463	C₂²×C₁₃	semidirect
651. #461	C₂²×C₁₃	semidirect
652. #461	C₂²×C₁₃	semidirect
653. #460	C₂²×C₁₃	semidirect
656. #459	C₂²×C₁₃	semidirect
657. #459	C₂²×C₁₃	semidirect
658. #459	C₂²×C₁₃	semidirect
659. #459	C₂²×C₁₃	semidirect
660. #459	C₂²×C₁₃	semidirect
661. #459	C₂²×C₁₃	semidirect
662. #459	C₂²×C₁₃	semidirect
663. #459	C₂²×C₁₃	semidirect
664. #450	C₂²×C₁₃	semidirect
665. #449	C₂²×C₁₃	semidirect
666. #449	C₂²×C₁₃	semidirect
667. #449	C₂²×C₁₃	semidirect
668. #449	C₂²×C₁₃	semidirect
671. #447	C₂²×C₁₃	semidirect
672. #447	C₂²×C₁₃	semidirect
673. #447	C₂²×C₁₃	semidirect
674. #446	C₂²×C₁₃	semidirect
675. C₈×Q₈	C₂²×C₁₃	semidirect
676. #442	C₂²×C₁₃	semidirect
677. #440	C₂²×C₁₃	semidirect
678. C₄×SD₁₆	C₂²×C₁₃	semidirect
680. C₄×D₈	C₂²×C₁₃	semidirect
681. C₄×D₈	C₂²×C₁₃	semidirect
682. C₄×D₈	C₂²×C₁₃	semidirect
683. C₄×D₈	C₂²×C₁₃	semidirect
684. #436	C₂²×C₁₃	semidirect
685. #436	C₂²×C₁₃	semidirect
686. #435	C₂²×C₁₃	semidirect
687. C₈×D₄	C₂²×C₁₃	semidirect
688. #433	C₂²×C₁₃	semidirect
689. #431	C₂²×C₁₃	semidirect
690. #424	C₂²×C₁₃	semidirect
691. #423	C₂²×C₁₃	semidirect
692. #418	C₂²×C₁₃	semidirect
693. #417	C₂²×C₁₃	semidirect
694. #416	C₂²×C₁₃	semidirect
1078. C₁₃	#62040	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3546	2
C₁₃×#3519	2
C₁₃×#3397	2
C₁₃×#3391	2
C₁₃×#3366	2
C₁₃×#3360	2
C₁₃×#3325	2
C₁₃×#3322	2
C₁₃×#3309	2
C₁₃×#3303	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3264	2
C₁₃×#3257	2
C₁₃×#3253	2
C₁₃×#3220	2
C₁₃×#3207	2
C₁₃×#3118	2
C₁₃×#3100	2
C₁₃×#3041	2
C₁₃×#3036	2
C₁₃×#2993	2
#62040	13

Subgroups — C13×#62040 #15748379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62040 #15748379