Subgroups — C₁₃×#62031 #15748370

Order 3328.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3038	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	complemented
27	C₁₃×#560	—	2	2	no	—
28	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#555	C₂²	1	2	yes	complemented
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic
34	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#548	—	2	1	no	—
37	C₁₃×#546	—	2	1	no	—
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	C₂²	1	2	yes	complemented
40	C₁₃×#546	C₂²	1	2	yes	complemented
41	D₄²×C₁₃	—	2	1	no	—
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	—	2	1	no	—
47	C₁₃×#540	C₂²	1	2	yes	complemented
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#535	—	2	1	no	—
50	C₁₃×#535	C₂²	1	2	yes	complemented
51	C₁₃×#534	—	2	2	no	—
52	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#529	—	2	1	no	—
55	C₁₃×#529	C₂²	1	1	yes	characteristic
56	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#124	—	2	1	no	—
58	C₁₃×#518	C₂²	1	2	yes	complemented
59	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#496	C₂²	1	2	yes	complemented
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic
63	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#486	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#476	C₂²	1	2	yes	complemented
76	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#474	C₂²	1	2	yes	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×#468	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×#464	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
90	C₁₃×#463	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#460	C₂²	1	2	yes	complemented
96	C₁₃×#459	C₂²	1	1	yes	characteristic
97	C₁₃×#459	C₂²	1	2	yes	complemented
98	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#459	C₂²	1	2	yes	complemented
101	C₁₃×#459	C₂²	1	2	yes	complemented
102	C₁₃×#459	C₂²	1	2	yes	complemented
103	C₁₃×#459	C₂²	1	2	yes	complemented
104	C₁₃×#452	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#450	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	1	yes	characteristic
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#447	C₂²	1	2	yes	complemented
110	C₁₃×#447	C₂²	1	2	yes	complemented
111	C₁₃×#447	C₂²	1	2	yes	complemented
112	C₁₃×#447	C₂²	1	2	yes	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×#442	C₂²	1	2	yes	complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
122	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
124	C₁₃×#436	C₂²	1	2	yes	complemented
125	C₁₃×#436	C₂²	1	1	yes	characteristic, 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×#418	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	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	—	2	2	no	—
142	C₂²×D₄×C₁₃	—	2	1	no	—
143	C₂²×D₄×C₁₃	—	2	1	no	—
144	C₂²×D₄×C₁₃	—	2	1	no	—
145	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
148	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
149	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
150	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×D₈	—	4	4	no	—
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	2	yes	—
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	2	yes	—
170	C₁₃×#127	—	2	1	no	—
171	C₁₃×#127	—	2	1	no	—
172	C₁₃×#127	—	2	1	no	—
173	C₁₃×#127	C₂³	1	1	yes	characteristic
174	C₁₃×#127	C₂³	1	2	yes	—
175	C₁₃×#127	C₂³	1	2	yes	—
176	C₁₃×#127	C₂³	1	1	yes	characteristic
177	C₁₃×#127	C₂³	1	1	yes	characteristic
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#126	—	2	2	no	—
180	C₁₃×#126	—	2	1	no	—
181	C₁₃×#126	D₄	1	2	yes	—
182	C₁₃×#125	D₄	1	1	yes	characteristic
183	C₁₃×#125	C₂³	1	1	yes	characteristic
184	C₁₃×#124	—	2	1	no	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#124	—	2	1	no	—
187	C₁₃×#124	—	2	2	no	—
188	C₁₃×#124	—	2	2	no	—
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	1	no	—
191	C₁₃×#124	D₄	1	1	yes	characteristic
192	C₁₃×#124	C₂³	1	1	yes	characteristic
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#123	—	2	1	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	D₄	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₃×#121	—	2	2	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	2	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	1	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	2	yes	—
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	1	yes	characteristic
230	C₁₃×#120	—	2	2	no	—
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	—	2	1	no	—
239	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	2	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
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	2	yes	—
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	2	no	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	C₂³	1	2	yes	—
266	C₁₃×#117	C₂³	1	1	yes	characteristic
267	C₁₃×#117	C₂³	1	2	yes	—
268	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²×C₁₃	—	2	1	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	2	yes	—
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	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	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	1	yes	characteristic
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	#62031	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₂⁴×C₁₃	—	2	2	no	—
318	C₂⁴×C₁₃	—	2	2	no	—
319	C₁₃×#41	—	2	2	no	—
320	C₁₃×#41	—	4	1	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	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	—	8	2	no	—
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	4	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	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	1	no	—
342	C₂×D₄×C₁₃	—	2	1	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	2	no	—
345	C₂×D₄×C₁₃	—	2	2	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	2	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	1	no	—
352	C₂×D₄×C₁₃	—	4	2	no	—
353	C₂×D₄×C₁₃	—	4	2	no	—
354	C₂×D₄×C₁₃	—	4	2	no	—
355	C₂×D₄×C₁₃	—	4	2	no	—
356	C₂×D₄×C₁₃	—	4	2	no	—
357	C₂×D₄×C₁₃	—	8	2	no	—
358	C₂×D₄×C₁₃	—	8	2	no	—
359	C₂×D₄×C₁₃	—	8	2	no	—
360	C₂×D₄×C₁₃	—	8	2	no	—
361	C₂×D₄×C₁₃	—	8	4	no	—
362	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
374	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
383	C₁₃×Q₁₆	—	4	1	no	—
384	C₁₃×SD₁₆	—	2	2	no	—
385	C₁₃×SD₁₆	—	4	1	no	—
386	C₁₃×SD₁₆	—	4	2	no	—
387	C₁₃×SD₁₆	—	4	2	no	—
388	C₁₃×SD₁₆	—	4	2	no	—
389	C₁₃×D₈	—	2	2	no	—
390	C₁₃×D₈	—	2	4	no	—
391	C₁₃×D₈	—	2	4	no	—
392	C₁₃×D₈	—	4	2	no	—
393	C₁₃×D₈	—	4	2	no	—
394	C₁₃×D₈	—	4	2	no	—
395	C₁₃×D₈	—	4	2	no	—
396	C₁₃×D₈	—	4	2	no	—
397	C₁₃×M₁₆	—	4	2	no	—
398	C₁₃×M₁₆	—	4	2	no	—
399	C₂×C₈×C₁₃	—	4	2	no	—
400	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
403	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	1	no	—
408	C₁₃×C₄⋊C₄	—	2	1	no	—
409	C₁₃×C₄⋊C₄	—	2	1	no	—
410	C₁₃×C₄⋊C₄	—	2	2	no	—
411	C₁₃×C₄⋊C₄	—	2	1	no	—
412	C₁₃×C₄⋊C₄	—	2	1	no	—
413	C₁₃×C₄⋊C₄	—	2	2	no	—
414	C₁₃×C₄⋊C₄	—	2	1	no	—
415	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
423	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	1	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	1	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	1	no	—
441	C₁₃×C₂²⋊C₄	—	2	2	no	—
442	C₁₃×C₂²⋊C₄	—	2	1	no	—
443	C₁₃×C₂²⋊C₄	—	2	2	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	1	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
451	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
452	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₄²×C₁₃	—	2	1	no	—
455	C₄²×C₁₃	—	2	1	no	—
456	C₄²×C₁₃	—	2	1	no	—
457	C₄²×C₁₃	—	2	2	no	—
458	C₄²×C₁₃	—	2	1	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	#3543	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3399	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3325	C₂×C₁₃	1	2	yes	complemented
471	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3319	C₂×C₁₃	1	2	yes	complemented
473	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
474	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#3273	C₂×C₁₃	1	2	yes	complemented
477	#3264	C₂×C₁₃	1	2	yes	complemented
478	#3257	C₂×C₁₃	1	2	yes	complemented
479	#3251	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3224	C₂×C₁₃	1	2	yes	complemented
481	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3122	C₂×C₁₃	1	2	yes	complemented
483	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3041	C₂×C₁₃	1	2	yes	complemented
485	#3038	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	2	no	—
489	C₂³×C₁₃	—	2	2	no	—
490	C₂³×C₁₃	—	2	1	no	—
491	C₂³×C₁₃	—	2	2	no	—
492	C₂³×C₁₃	—	4	4	no	—
493	C₂³×C₁₃	—	4	4	no	—
494	C₂³×C₁₃	—	8	2	no	—
495	C₂³×C₁₃	—	8	2	no	—
496	C₂³×C₁₃	—	8	2	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	C₂²×D₄	1	2	yes	—
502	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
503	Q₈×C₁₃	—	2	2	no	—
504	Q₈×C₁₃	—	2	1	no	—
505	Q₈×C₁₃	—	2	1	no	—
506	Q₈×C₁₃	—	2	1	no	—
507	Q₈×C₁₃	—	2	1	no	—
508	Q₈×C₁₃	—	4	2	no	—
509	Q₈×C₁₃	—	8	2	no	—
510	D₄×C₁₃	—	2	2	no	—
511	D₄×C₁₃	—	2	1	no	—
512	D₄×C₁₃	—	2	2	no	—
513	D₄×C₁₃	—	2	2	no	—
514	D₄×C₁₃	—	2	2	no	—
515	D₄×C₁₃	—	2	1	no	—
516	D₄×C₁₃	—	2	2	no	—
517	D₄×C₁₃	—	2	2	no	—
518	D₄×C₁₃	—	2	2	no	—
519	D₄×C₁₃	—	2	1	no	—
520	D₄×C₁₃	—	4	2	no	—
521	D₄×C₁₃	—	4	4	no	—
522	D₄×C₁₃	—	4	2	no	—
523	D₄×C₁₃	—	4	2	no	—
524	D₄×C₁₃	—	4	2	no	—
525	D₄×C₁₃	—	4	2	no	—
526	D₄×C₁₃	—	4	2	no	—
527	D₄×C₁₃	—	8	1	no	—
528	D₄×C₁₃	—	8	2	no	—
529	D₄×C₁₃	—	8	2	no	—
530	D₄×C₁₃	—	8	2	no	—
531	D₄×C₁₃	—	8	1	no	—
532	D₄×C₁₃	—	8	1	no	—
533	D₄×C₁₃	—	8	2	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	H(5,𝔽₂)	1	2	yes	—
542	C₂×C₄×C₁₃	—	2	2	no	—
543	C₂×C₄×C₁₃	—	2	2	no	—
544	C₂×C₄×C₁₃	—	2	1	no	—
545	C₂×C₄×C₁₃	—	2	1	no	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	1	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	1	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	1	no	—
554	C₂×C₄×C₁₃	—	4	1	no	—
555	C₂×C₄×C₁₃	—	4	2	no	—
556	C₂×C₄×C₁₃	—	4	2	no	—
557	C₂×C₄×C₁₃	—	4	2	no	—
558	C₂×C₄×C₁₃	—	8	1	no	—
559	C₂×C₄×C₁₃	—	8	2	no	—
560	C₂×C₄×C₁₃	—	8	2	no	—
561	C₂×C₄×C₁₃	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
572	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
574	C₈×C₁₃	—	2	1	no	—
575	C₈×C₁₃	—	2	2	no	—
576	C₈×C₁₃	—	2	2	no	—
577	C₈×C₁₃	—	2	1	no	—
578	C₈×C₁₃	—	2	1	no	—
579	C₈×C₁₃	—	2	1	no	—
580	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
581	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
582	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
583	#560	—	2	2	no	—
584	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
586	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	#555	C₂²×C₁₃	1	2	yes	complemented
588	#551	—	2	2	no	—
589	#550	C₂²×C₁₃	1	1	yes	characteristic
590	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	#548	—	2	1	no	—
593	#546	—	2	1	no	—
594	#546	—	2	1	no	—
595	#546	C₂²×C₁₃	1	2	yes	complemented
596	#546	C₂²×C₁₃	1	2	yes	complemented
597	D₄²	—	2	1	no	—
598	D₄²	C₂²×C₁₃	1	1	yes	characteristic
599	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	D₄²	C₂²×C₁₃	1	2	yes	complemented
601	#542	C₂²×C₁₃	1	2	yes	complemented
602	#540	—	2	1	no	—
603	#540	C₂²×C₁₃	1	2	yes	complemented
604	#538	—	2	2	no	—
605	#535	—	2	1	no	—
606	#535	C₂²×C₁₃	1	2	yes	complemented
607	#534	—	2	2	no	—
608	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#529	—	2	1	no	—
611	#529	C₂²×C₁₃	1	1	yes	characteristic
612	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₂×#124	—	2	1	no	—
614	#518	C₂²×C₁₃	1	2	yes	complemented
615	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#496	C₂²×C₁₃	1	2	yes	complemented
617	#495	C₂²×C₁₃	1	2	yes	complemented
618	#493	C₂²×C₁₃	1	1	yes	characteristic
619	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#489	C₂²×C₁₃	1	2	yes	complemented
621	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#486	C₂²×C₁₃	1	2	yes	complemented
623	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#482	C₂²×C₁₃	1	2	yes	complemented
627	#482	C₂²×C₁₃	1	2	yes	complemented
628	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#478	C₂²×C₁₃	1	2	yes	complemented
631	#476	C₂²×C₁₃	1	2	yes	complemented
632	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#474	C₂²×C₁₃	1	2	yes	complemented
635	#469	C₂²×C₁₃	1	2	yes	complemented
636	#469	C₂²×C₁₃	1	2	yes	complemented
637	#468	C₂²×C₁₃	1	2	yes	complemented
638	#468	C₂²×C₁₃	1	2	yes	complemented
639	#466	C₂²×C₁₃	1	2	yes	complemented
640	#465	C₂²×C₁₃	1	2	yes	complemented
641	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#463	C₂²×C₁₃	1	2	yes	complemented
644	#463	C₂²×C₁₃	1	2	yes	complemented
645	#463	C₂²×C₁₃	1	2	yes	complemented
646	#463	C₂²×C₁₃	1	2	yes	complemented
647	#463	C₂²×C₁₃	1	2	yes	complemented
648	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#460	C₂²×C₁₃	1	2	yes	complemented
652	#459	C₂²×C₁₃	1	1	yes	characteristic
653	#459	C₂²×C₁₃	1	2	yes	complemented
654	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#459	C₂²×C₁₃	1	2	yes	complemented
656	#459	C₂²×C₁₃	1	2	yes	complemented
657	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	#459	C₂²×C₁₃	1	2	yes	complemented
659	#459	C₂²×C₁₃	1	2	yes	complemented
660	#452	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#452	C₂²×C₁₃	1	2	yes	complemented
662	#450	C₂²×C₁₃	1	2	yes	complemented
663	#449	C₂²×C₁₃	1	1	yes	characteristic
664	#449	C₂²×C₁₃	1	2	yes	complemented
665	#447	C₂²×C₁₃	1	2	yes	complemented
666	#447	C₂²×C₁₃	1	2	yes	complemented
667	#447	C₂²×C₁₃	1	2	yes	complemented
668	#447	C₂²×C₁₃	1	2	yes	complemented
669	#447	C₂²×C₁₃	1	2	yes	complemented
670	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#442	C₂²×C₁₃	1	2	yes	complemented
673	#442	C₂²×C₁₃	1	2	yes	complemented
674	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
677	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
678	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
679	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
680	#436	C₂²×C₁₃	1	2	yes	complemented
681	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	#435	C₂²×C₁₃	1	2	yes	complemented
683	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	#433	C₂²×C₁₃	1	2	yes	complemented
685	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
686	#424	C₂²×C₁₃	1	2	yes	complemented
687	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
688	#418	C₂²×C₁₃	1	2	yes	complemented
689	#418	C₂²×C₁₃	1	2	yes	complemented
690	#416	C₂²×C₁₃	1	2	yes	complemented
691	C₂²×C₁₃	—	2	1	no	—
692	C₂²×C₁₃	—	2	2	no	—
693	C₂²×C₁₃	—	2	1	no	—
694	C₂²×C₁₃	—	2	2	no	—
695	C₂²×C₁₃	—	2	2	no	—
696	C₂²×C₁₃	—	2	1	no	—
697	C₂²×C₁₃	—	2	2	no	—
698	C₂²×C₁₃	—	4	1	no	—
699	C₂²×C₁₃	—	4	1	no	—
700	C₂²×C₁₃	—	4	2	no	—
701	C₂²×C₁₃	—	4	2	no	—
702	C₂²×C₁₃	—	4	1	no	—
703	C₂²×C₁₃	—	4	2	no	—
704	C₂²×C₁₃	—	4	2	no	—
705	C₂²×C₁₃	—	4	2	no	—
706	C₂²×C₁₃	—	4	1	no	—
707	C₂²×C₁₃	—	4	2	no	—
708	C₂²×C₁₃	—	4	1	no	—
709	C₂²×C₁₃	—	4	2	no	—
710	C₂²×C₁₃	—	4	2	no	—
711	C₂²×C₁₃	—	4	2	no	—
712	C₂²×C₁₃	—	16	4	no	—
713	C₂²×C₁₃	—	16	4	no	—
714	C₂²×C₁₃	—	16	4	no	—
715	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
716	C₄×C₁₃	—	2	1	no	—
717	C₄×C₁₃	—	2	1	no	—
718	C₄×C₁₃	—	2	2	no	—
719	C₄×C₁₃	—	2	1	no	—
720	C₄×C₁₃	—	2	2	no	—
721	C₄×C₁₃	—	2	1	no	—
722	C₄×C₁₃	—	2	2	no	—
723	C₄×C₁₃	—	4	1	no	—
724	C₄×C₁₃	—	4	1	no	—
725	C₄×C₁₃	—	4	1	no	—
726	C₄×C₁₃	—	4	1	no	—
727	C₄×C₁₃	—	4	1	no	—
728	C₄×C₁₃	—	4	1	no	—
729	C₄×C₁₃	—	4	2	no	—
730	C₄×C₁₃	#576	1	2	yes	—
731	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
732	C₄×C₁₃	#585	1	1	yes	characteristic
733	C₂×#41	—	2	1	no	—
734	C₂×#41	—	2	1	no	—
735	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×#41	C₂³×C₁₃	1	2	yes	—
737	C₂²×Q₈	—	2	1	no	—
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	—	2	2	no	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
744	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
745	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
746	AGL(1,ℤ/8)	—	4	4	no	—
747	AGL(1,ℤ/8)	—	4	4	no	—
748	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
754	C₂×D₈	—	4	4	no	—
755	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₂×D₈	C₂³×C₁₃	1	2	yes	—
757	C₂×D₈	C₂³×C₁₃	1	2	yes	—
758	C₂×D₈	C₂³×C₁₃	1	2	yes	—
759	C₂×D₈	C₂³×C₁₃	1	2	yes	—
760	C₂×D₈	C₂³×C₁₃	1	2	yes	—
761	C₂×D₈	C₂³×C₁₃	1	2	yes	—
762	C₂×D₈	C₂³×C₁₃	1	2	yes	—
763	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
764	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
765	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
766	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
767	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
768	#127	—	2	1	no	—
769	#127	—	2	1	no	—
770	#127	—	2	1	no	—
771	#127	C₂³×C₁₃	1	2	yes	—
772	#127	C₂³×C₁₃	1	1	yes	characteristic
773	#127	C₂³×C₁₃	1	1	yes	characteristic
774	#127	C₂³×C₁₃	1	1	yes	characteristic
775	#127	C₂³×C₁₃	1	2	yes	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	1	no	—
779	#126	D₄×C₁₃	1	2	yes	—
780	#125	D₄×C₁₃	1	1	yes	characteristic
781	#125	C₂³×C₁₃	1	1	yes	characteristic
782	#124	—	2	1	no	—
783	#124	—	2	1	no	—
784	#124	—	2	1	no	—
785	#124	—	2	2	no	—
786	#124	—	2	2	no	—
787	#124	—	2	2	no	—
788	#124	—	2	1	no	—
789	#124	D₄×C₁₃	1	1	yes	characteristic
790	#124	C₂³×C₁₃	1	1	yes	characteristic
791	#124	C₂³×C₁₃	1	2	yes	—
792	#124	C₂³×C₁₃	1	2	yes	—
793	#123	—	2	1	no	—
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	—	2	2	no	—
801	#123	D₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
808	#121	—	2	2	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	D₄×C₁₃	1	1	yes	characteristic
823	#121	C₂³×C₁₃	1	1	yes	characteristic
824	#121	C₂³×C₁₃	1	2	yes	—
825	#121	C₂³×C₁₃	1	2	yes	—
826	#121	C₂³×C₁₃	1	2	yes	—
827	#121	C₂³×C₁₃	1	2	yes	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	—	2	2	no	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	C₄×Q₈	—	2	1	no	—
837	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
838	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₁₃	1	2	yes	—
853	C₄×D₄	C₂³×C₁₃	1	2	yes	—
854	C₄×D₄	C₂³×C₁₃	1	2	yes	—
855	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₁₃	1	2	yes	—
857	C₄×D₄	C₂³×C₁₃	1	2	yes	—
858	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₁₃	1	2	yes	—
860	#117	—	2	2	no	—
861	#117	—	2	1	no	—
862	#117	—	2	1	no	—
863	#117	C₂³×C₁₃	1	1	yes	characteristic
864	#117	C₂³×C₁₃	1	2	yes	—
865	#117	C₂³×C₁₃	1	2	yes	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₂²⋊C₄	—	2	2	no	—
870	C₂×C₄²	—	2	1	no	—
871	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
872	#107	C₂³×C₁₃	1	1	yes	characteristic
873	#107	C₂³×C₁₃	1	1	yes	characteristic
874	#107	C₂³×C₁₃	1	2	yes	—
875	#106	C₂³×C₁₃	1	1	yes	characteristic
876	#106	C₂³×C₁₃	1	1	yes	characteristic
877	#106	C₂³×C₁₃	1	2	yes	—
878	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
879	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
883	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
884	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
885	#103	C₂³×C₁₃	1	1	yes	characteristic
886	#103	C₂³×C₁₃	1	2	yes	—
887	#103	C₂³×C₁₃	1	1	yes	characteristic
888	#103	C₂³×C₁₃	1	1	yes	characteristic
889	#103	C₂³×C₁₃	1	1	yes	characteristic
890	#102	C₂³×C₁₃	1	2	yes	—
891	#102	C₂³×C₁₃	1	2	yes	—
892	#102	C₂³×C₁₃	1	2	yes	—
893	#102	C₂³×C₁₃	1	1	yes	characteristic
894	#102	C₂³×C₁₃	1	2	yes	—
895	#102	C₂³×C₁₃	1	2	yes	—
896	#102	C₂³×C₁₃	1	2	yes	—
897	#102	C₂³×C₁₃	1	2	yes	—
898	#102	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
904	#102	C₂³×C₁₃	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
906	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
907	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
909	#97	C₂³×C₁₃	1	2	yes	—
910	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₁₃	1	2	yes	—
913	C₂×C₁₃	—	4	1	no	—
914	C₂×C₁₃	—	4	2	no	—
915	C₂×C₁₃	—	4	2	no	—
916	C₂×C₁₃	—	8	2	no	—
917	C₂×C₁₃	—	8	2	no	—
918	C₂×C₁₃	—	8	2	no	—
919	C₂×C₁₃	—	8	1	no	—
920	C₂×C₁₃	#3488	1	1	yes	characteristic
921	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
922	C₂×C₁₃	#3585	1	1	yes	characteristic
923	C₂⁴	—	2	2	no	—
924	C₂⁴	—	2	2	no	—
925	C₂⁴	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	4	1	no	—
928	#41	—	4	2	no	—
929	#41	—	4	2	no	—
930	#41	—	8	2	no	—
931	#41	—	8	2	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	8	2	no	—
935	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
936	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
937	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	4	2	no	—
960	C₂×D₄	—	4	2	no	—
961	C₂×D₄	—	4	2	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	8	2	no	—
965	C₂×D₄	—	8	2	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	2	no	—
968	C₂×D₄	—	8	4	no	—
969	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
970	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
971	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
973	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
974	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
988	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
990	Q₁₆	—	4	1	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	4	2	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	1	no	—
996	D₈	—	2	2	no	—
997	D₈	—	2	4	no	—
998	D₈	—	2	4	no	—
999	D₈	—	4	2	no	—
1000	D₈	—	4	2	no	—
1001	D₈	—	4	2	no	—
1002	D₈	—	4	2	no	—
1003	D₈	—	4	2	no	—
1004	M₁₆	—	4	2	no	—
1005	M₁₆	—	4	2	no	—
1006	C₂×C₈	—	4	2	no	—
1007	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1010	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1011	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1026	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1030	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	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	2	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	C₂×D₄×C₁₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1067	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₁₃	1	2	yes	—
1070	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1071	C₁₃	#62031	1	1	yes	characteristic, direct product factor, Sylow
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	4	4	no	—
1078	C₂³	—	4	4	no	—
1079	C₂³	—	8	2	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	2	no	—
1083	C₂³	—	8	2	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	—	8	2	no	—
1086	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1087	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	2	no	—
1094	Q₈	—	8	2	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	D₄	—	4	2	no	—
1111	D₄	—	4	2	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	2	no	—
1114	D₄	—	8	2	no	—
1115	D₄	—	8	2	no	—
1116	D₄	—	8	1	no	—
1117	D₄	—	8	1	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	1	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1153	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1154	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1155	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1156	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1157	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1158	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₈	—	2	1	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	1	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	1	no	—
1170	C₂²	—	2	2	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	2	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	16	4	no	—
1187	C₂²	—	16	4	no	—
1188	C₂²	—	16	4	no	—
1189	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1190	C₄	—	2	1	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	1	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	2	2	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	C₁₃×#576	1	2	yes	—
1205	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1206	C₄	C₁₃×#585	1	1	yes	characteristic
1207	C₂	—	4	1	no	—
1208	C₂	—	4	2	no	—
1209	C₂	—	4	2	no	—
1210	C₂	—	8	1	no	—
1211	C₂	—	8	2	no	—
1212	C₂	—	8	2	no	—
1213	C₂	—	8	2	no	—
1214	C₂	C₁₃×#3488	1	1	yes	characteristic
1215	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1216	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×#3543	C₂	semidirect
2. C₁₃×#3514	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3396	C₂	semidirect
5. C₁₃×#3373	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3324	C₂	semidirect
9. C₁₃×#3319	C₂	semidirect
10. C₁₃×#3304	C₂	semidirect
11. D₄×C₁₃×D₈	C₂	semidirect
12. C₁₃×#3274	C₂	semidirect
13. C₁₃×#3273	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3257	C₂	semidirect
16. C₁₃×#3251	C₂	semidirect
17. C₁₃×#3224	C₂	semidirect
18. C₁₃×#3205	C₂	semidirect
19. C₁₃×#3122	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3041	C₂	semidirect
22. C₁₃×#3038	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
26. C₂²×C₁₃×D₈	C₂²	semidirect
28. C₁₃×#559	C₂²	semidirect
29. C₁₃×#559	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. D₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#546	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
43. D₄²×C₁₃	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
45. C₁₃×#542	C₂²	semidirect
47. C₁₃×#540	C₂²	semidirect
50. C₁₃×#535	C₂²	semidirect
52. C₁₃×#532	C₂²	semidirect
53. C₂×C₁₃×#127	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
58. C₁₃×#518	C₂²	semidirect
59. C₄×C₁₃×#41	C₂²	semidirect
60. C₁₃×#496	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
63. C₁₃×#493	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#486	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#478	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#469	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#464	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×#463	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#460	C₂²	semidirect
95. C₁₃×#460	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×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#450	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
109. C₁₃×#447	C₂²	semidirect
110. C₁₃×#447	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×#442	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×SD₁₆	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×#418	C₂²	semidirect
134. C₁₃×#416	C₂²	semidirect
315. #62031	C₁₃	direct (N × H)
464. #3543	C₂×C₁₃	semidirect
465. #3514	C₂×C₁₃	semidirect
466. #3399	C₂×C₁₃	semidirect
467. #3396	C₂×C₁₃	semidirect
468. #3373	C₂×C₁₃	semidirect
469. #3358	C₂×C₁₃	semidirect
470. #3325	C₂×C₁₃	semidirect
471. #3324	C₂×C₁₃	semidirect
472. #3319	C₂×C₁₃	semidirect
473. #3304	C₂×C₁₃	semidirect
474. D₄×D₈	C₂×C₁₃	semidirect
475. #3274	C₂×C₁₃	semidirect
476. #3273	C₂×C₁₃	semidirect
477. #3264	C₂×C₁₃	semidirect
478. #3257	C₂×C₁₃	semidirect
479. #3251	C₂×C₁₃	semidirect
480. #3224	C₂×C₁₃	semidirect
481. #3205	C₂×C₁₃	semidirect
482. #3122	C₂×C₁₃	semidirect
483. #3102	C₂×C₁₃	semidirect
484. #3041	C₂×C₁₃	semidirect
485. #3038	C₂×C₁₃	semidirect
486. #2993	C₂×C₁₃	semidirect
580. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
581. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
582. C₂²×D₈	C₂²×C₁₃	semidirect
584. #559	C₂²×C₁₃	semidirect
585. #559	C₂²×C₁₃	semidirect
586. #556	C₂²×C₁₃	semidirect
587. #555	C₂²×C₁₃	semidirect
590. #550	C₂²×C₁₃	semidirect
591. D₄×Q₈	C₂²×C₁₃	semidirect
595. #546	C₂²×C₁₃	semidirect
596. #546	C₂²×C₁₃	semidirect
599. D₄²	C₂²×C₁₃	semidirect
600. D₄²	C₂²×C₁₃	semidirect
601. #542	C₂²×C₁₃	semidirect
603. #540	C₂²×C₁₃	semidirect
606. #535	C₂²×C₁₃	semidirect
608. #532	C₂²×C₁₃	semidirect
609. C₂×#127	C₂²×C₁₃	semidirect
612. #529	C₂²×C₁₃	semidirect
614. #518	C₂²×C₁₃	semidirect
615. C₄×#41	C₂²×C₁₃	semidirect
616. #496	C₂²×C₁₃	semidirect
617. #495	C₂²×C₁₃	semidirect
619. #493	C₂²×C₁₃	semidirect
620. #489	C₂²×C₁₃	semidirect
621. #486	C₂²×C₁₃	semidirect
622. #486	C₂²×C₁₃	semidirect
623. #486	C₂²×C₁₃	semidirect
624. #485	C₂²×C₁₃	semidirect
625. #482	C₂²×C₁₃	semidirect
626. #482	C₂²×C₁₃	semidirect
627. #482	C₂²×C₁₃	semidirect
628. #479	C₂²×C₁₃	semidirect
629. #478	C₂²×C₁₃	semidirect
630. #478	C₂²×C₁₃	semidirect
631. #476	C₂²×C₁₃	semidirect
632. #475	C₂²×C₁₃	semidirect
633. #474	C₂²×C₁₃	semidirect
634. #474	C₂²×C₁₃	semidirect
635. #469	C₂²×C₁₃	semidirect
636. #469	C₂²×C₁₃	semidirect
637. #468	C₂²×C₁₃	semidirect
638. #468	C₂²×C₁₃	semidirect
639. #466	C₂²×C₁₃	semidirect
640. #465	C₂²×C₁₃	semidirect
641. #464	C₂²×C₁₃	semidirect
642. #463	C₂²×C₁₃	semidirect
643. #463	C₂²×C₁₃	semidirect
644. #463	C₂²×C₁₃	semidirect
645. #463	C₂²×C₁₃	semidirect
646. #463	C₂²×C₁₃	semidirect
647. #463	C₂²×C₁₃	semidirect
648. #460	C₂²×C₁₃	semidirect
649. #460	C₂²×C₁₃	semidirect
650. #460	C₂²×C₁₃	semidirect
651. #460	C₂²×C₁₃	semidirect
653. #459	C₂²×C₁₃	semidirect
654. #459	C₂²×C₁₃	semidirect
655. #459	C₂²×C₁₃	semidirect
656. #459	C₂²×C₁₃	semidirect
657. #459	C₂²×C₁₃	semidirect
658. #459	C₂²×C₁₃	semidirect
659. #459	C₂²×C₁₃	semidirect
660. #452	C₂²×C₁₃	semidirect
661. #452	C₂²×C₁₃	semidirect
662. #450	C₂²×C₁₃	semidirect
664. #449	C₂²×C₁₃	semidirect
665. #447	C₂²×C₁₃	semidirect
666. #447	C₂²×C₁₃	semidirect
667. #447	C₂²×C₁₃	semidirect
668. #447	C₂²×C₁₃	semidirect
669. #447	C₂²×C₁₃	semidirect
670. #446	C₂²×C₁₃	semidirect
671. C₈×Q₈	C₂²×C₁₃	semidirect
672. #442	C₂²×C₁₃	semidirect
673. #442	C₂²×C₁₃	semidirect
674. C₄×Q₁₆	C₂²×C₁₃	semidirect
675. C₄×SD₁₆	C₂²×C₁₃	semidirect
676. C₄×SD₁₆	C₂²×C₁₃	semidirect
677. C₄×D₈	C₂²×C₁₃	semidirect
678. C₄×D₈	C₂²×C₁₃	semidirect
679. C₄×D₈	C₂²×C₁₃	semidirect
680. #436	C₂²×C₁₃	semidirect
681. #436	C₂²×C₁₃	semidirect
682. #435	C₂²×C₁₃	semidirect
683. C₈×D₄	C₂²×C₁₃	semidirect
684. #433	C₂²×C₁₃	semidirect
685. #431	C₂²×C₁₃	semidirect
686. #424	C₂²×C₁₃	semidirect
687. #423	C₂²×C₁₃	semidirect
688. #418	C₂²×C₁₃	semidirect
689. #418	C₂²×C₁₃	semidirect
690. #416	C₂²×C₁₃	semidirect
1071. C₁₃	#62031	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×#3543	2
C₁₃×#3514	2
C₁₃×#3399	2
C₁₃×#3396	2
C₁₃×#3373	2
C₁₃×#3358	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3319	2
C₁₃×#3304	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3273	2
C₁₃×#3264	2
C₁₃×#3257	2
C₁₃×#3251	2
C₁₃×#3224	2
C₁₃×#3205	2
C₁₃×#3122	2
C₁₃×#3102	2
C₁₃×#3041	2
C₁₃×#3038	2
C₁₃×#2993	2
#62031	13

Subgroups — C13×#62031 #15748370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62031 #15748370