Subgroups — C₁₃×#61543 #15747882

Order 3328.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3326	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
13	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3179	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#556	—	2	2	no	—
28	C₁₃×#556	—	2	1	no	—
29	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#556	C₂²	1	2	yes	complemented
31	C₁₃×#555	—	2	1	no	—
32	C₁₃×#555	C₂²	1	1	yes	characteristic
33	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#554	C₂²	1	1	yes	characteristic
35	C₁₃×#553	—	2	1	no	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#548	C₂²	1	2	yes	complemented
40	C₁₃×#546	—	2	1	no	—
41	C₁₃×#546	—	2	2	no	—
42	D₄²×C₁₃	C₂²	1	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#542	—	2	2	no	—
45	C₁₃×#542	C₂²	1	2	yes	complemented
46	C₁₃×#540	C₂²	1	2	yes	—
47	C₁₃×#538	—	2	2	no	—
48	C₁₃×#533	—	2	1	no	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#532	C₂²	1	1	yes	characteristic
51	C₁₃×#529	—	2	1	no	—
52	C₁₃×#529	C₂²	1	1	yes	characteristic
53	C₁₃×#525	—	2	1	no	—
54	C₂×C₁₃×#121	—	2	1	no	—
55	C₁₃×#519	C₂²	1	2	yes	complemented
56	C₁₃×#518	C₂²	1	2	yes	—
57	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#496	C₂²	1	2	yes	complemented
62	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	complemented
64	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#486	C₂²	1	2	yes	complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#476	C₂²	1	1	yes	characteristic
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#476	C₂²	1	2	yes	complemented
80	C₁₃×#474	C₂²	1	2	yes	—
81	C₁₃×#469	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#468	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	2	yes	complemented
85	C₁₃×#466	C₂²	1	2	yes	complemented
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#461	C₂²	1	1	yes	characteristic
90	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	C₂²	1	2	yes	complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#450	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	2	yes	—
97	C₁₃×#449	C₂²	1	2	yes	complemented
98	C₁₃×#448	C₂²	1	2	yes	complemented
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	1	yes	characteristic
104	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	1	yes	characteristic
107	C₁₃×#440	C₂²	1	2	yes	complemented
108	C₁₃×#440	C₂²	1	2	yes	complemented
109	C₁₃×#440	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#440	C₂²	1	2	yes	complemented
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
121	C₁₃×#436	C₂²	1	2	yes	complemented
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#427	C₂²	1	2	yes	complemented
129	C₁₃×#419	C₂²	1	2	yes	complemented
130	C₁₃×#418	C₂²	1	1	yes	characteristic
131	C₁₃×#418	C₂²	1	2	yes	—
132	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, 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	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	2	no	—
141	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃	—	2	1	no	—
144	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
145	C₂×C₁₃×SD₁₆	—	2	8	no	—
146	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×D₈	C₂³	1	2	yes	—
156	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	—	2	1	no	—
161	C₁₃×C₄⋊Q₈	—	2	1	no	—
162	C₁₃×C₄⋊Q₈	—	2	2	no	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#127	C₂³	1	1	yes	characteristic
168	C₁₃×#127	C₂³	1	2	yes	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	D₄	1	2	yes	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	D₄	1	1	yes	characteristic
177	C₁₃×#125	C₂³	1	2	yes	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	2	no	—
180	C₁₃×#124	—	2	2	no	—
181	C₁₃×#124	—	2	2	no	—
182	C₁₃×#124	—	2	2	no	—
183	C₁₃×#124	—	2	1	no	—
184	C₁₃×#124	D₄	1	1	yes	characteristic
185	C₁₃×#124	C₂³	1	2	yes	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×#123	D₄	1	2	yes	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	2	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	D₄	1	1	yes	characteristic
213	C₁₃×#121	C₂³	1	2	yes	—
214	C₁₃×#121	C₂³	1	2	yes	—
215	C₁₃×#121	C₂³	1	2	yes	—
216	C₁₃×#121	C₂³	1	2	yes	—
217	C₁₃×#120	—	2	2	no	—
218	C₁₃×#120	—	2	2	no	—
219	C₁₃×#120	—	2	2	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	—	2	2	no	—
222	C₄×Q₈×C₁₃	—	2	2	no	—
223	C₄×Q₈×C₁₃	—	2	2	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	—	2	1	no	—
239	C₄×D₄×C₁₃	—	2	1	no	—
240	C₄×D₄×C₁₃	—	2	1	no	—
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
248	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	1	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	C₂³	1	2	yes	—
260	C₁₃×#117	C₂³	1	1	yes	characteristic
261	C₁₃×#117	C₂³	1	2	yes	—
262	C₁₃×#117	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²×C₁₃	—	2	1	no	—
269	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	1	yes	characteristic
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	2	yes	—
276	C₁₃×#106	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	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	1	yes	characteristic
308	C₁₃×#97	C₂³	1	1	yes	characteristic
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	2	yes	—
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61543	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	4	1	no	—
319	C₁₃×#41	—	8	2	no	—
320	C₁₃×#41	—	8	2	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	4	no	—
326	C₂×Q₈×C₁₃	—	4	2	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₁₃	—	2	4	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	2	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	1	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	4	2	no	—
344	C₂×D₄×C₁₃	—	4	1	no	—
345	C₂×D₄×C₁₃	—	8	2	no	—
346	C₂×D₄×C₁₃	—	8	4	no	—
347	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
352	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	1	no	—
358	C₂²×C₄×C₁₃	—	2	1	no	—
359	C₂²×C₄×C₁₃	—	2	1	no	—
360	C₂²×C₄×C₁₃	—	2	1	no	—
361	C₂²×C₄×C₁₃	—	2	2	no	—
362	C₂²×C₄×C₁₃	—	2	2	no	—
363	C₂²×C₄×C₁₃	—	2	2	no	—
364	C₂²×C₄×C₁₃	—	2	1	no	—
365	C₂²×C₄×C₁₃	—	8	2	no	—
366	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
370	C₁₃×SD₁₆	—	2	4	no	—
371	C₁₃×SD₁₆	—	2	2	no	—
372	C₁₃×SD₁₆	—	2	4	no	—
373	C₁₃×SD₁₆	—	2	4	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	#41	1	4	yes	complemented
377	C₁₃×D₈	—	2	2	no	—
378	C₁₃×D₈	—	2	2	no	—
379	C₁₃×D₈	—	4	2	no	—
380	C₁₃×M₁₆	—	2	2	no	—
381	C₁₃×M₁₆	—	4	2	no	—
382	C₁₃×M₁₆	—	4	1	no	—
383	C₂×C₈×C₁₃	—	2	4	no	—
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	1	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	1	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	2	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	—	2	2	no	—
449	C₄²×C₁₃	—	2	2	no	—
450	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₁₃	C₂⁴	1	2	yes	—
455	#3519	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3350	C₂×C₁₃	1	2	yes	complemented
462	#3341	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3329	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3326	C₂×C₁₃	1	2	yes	complemented
465	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3324	C₂×C₁₃	1	2	yes	complemented
467	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3265	C₂×C₁₃	1	2	yes	complemented
469	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3179	C₂×C₁₃	1	2	yes	complemented
471	#3126	C₂×C₁₃	1	2	yes	complemented
472	#3118	C₂×C₁₃	1	2	yes	complemented
473	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#2969	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#2949	C₂×C₁₃	1	2	yes	complemented
477	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
478	C₂³×C₁₃	—	2	1	no	—
479	C₂³×C₁₃	—	2	1	no	—
480	C₂³×C₁₃	—	2	2	no	—
481	C₂³×C₁₃	—	2	1	no	—
482	C₂³×C₁₃	—	4	2	no	—
483	C₂³×C₁₃	—	4	4	no	—
484	C₂³×C₁₃	—	4	2	no	—
485	C₂³×C₁₃	—	8	1	no	—
486	C₂³×C₁₃	—	8	2	no	—
487	C₂³×C₁₃	—	8	2	no	—
488	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₁₃	—	2	2	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	2	2	no	—
493	Q₈×C₁₃	—	2	2	no	—
494	Q₈×C₁₃	—	4	4	no	—
495	Q₈×C₁₃	—	8	1	no	—
496	Q₈×C₁₃	—	8	2	no	—
497	Q₈×C₁₃	—	8	1	no	—
498	Q₈×C₁₃	C₂×#41	1	2	yes	—
499	D₄×C₁₃	—	2	2	no	—
500	D₄×C₁₃	—	2	1	no	—
501	D₄×C₁₃	—	2	1	no	—
502	D₄×C₁₃	—	2	2	no	—
503	D₄×C₁₃	—	2	1	no	—
504	D₄×C₁₃	—	2	1	no	—
505	D₄×C₁₃	—	2	2	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	4	2	no	—
508	D₄×C₁₃	—	4	2	no	—
509	D₄×C₁₃	—	4	4	no	—
510	D₄×C₁₃	—	4	2	no	—
511	D₄×C₁₃	—	4	4	no	—
512	D₄×C₁₃	—	4	2	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	—	8	1	no	—
515	D₄×C₁₃	—	8	2	no	—
516	D₄×C₁₃	—	8	2	no	—
517	D₄×C₁₃	—	8	2	no	—
518	D₄×C₁₃	—	8	2	no	—
519	D₄×C₁₃	C₂×#41	1	2	yes	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	2	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	2	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	2	no	—
530	C₂×C₄×C₁₃	—	2	1	no	—
531	C₂×C₄×C₁₃	—	2	2	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	4	1	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	4	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	4	2	no	—
539	C₂×C₄×C₁₃	—	8	1	no	—
540	C₂×C₄×C₁₃	—	8	1	no	—
541	C₂×C₄×C₁₃	—	8	1	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	—	8	2	no	—
545	C₂×C₄×C₁₃	—	8	1	no	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
555	C₈×C₁₃	—	2	2	no	—
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	1	no	—
558	C₈×C₁₃	—	2	2	no	—
559	C₈×C₁₃	—	2	1	no	—
560	C₈×C₁₃	C₂×#41	1	2	yes	—
561	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
562	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
563	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	#556	—	2	2	no	—
565	#556	—	2	1	no	—
566	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
567	#556	C₂²×C₁₃	1	2	yes	complemented
568	#555	—	2	1	no	—
569	#555	C₂²×C₁₃	1	1	yes	characteristic
570	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
571	#554	C₂²×C₁₃	1	1	yes	characteristic
572	#553	—	2	1	no	—
573	#553	C₂²×C₁₃	1	2	yes	—
574	#550	C₂²×C₁₃	1	1	yes	characteristic
575	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#548	C₂²×C₁₃	1	2	yes	complemented
577	#546	—	2	1	no	—
578	#546	—	2	2	no	—
579	D₄²	C₂²×C₁₃	1	2	yes	—
580	D₄²	C₂²×C₁₃	1	1	yes	characteristic
581	#542	—	2	2	no	—
582	#542	C₂²×C₁₃	1	2	yes	complemented
583	#540	C₂²×C₁₃	1	2	yes	—
584	#538	—	2	2	no	—
585	#533	—	2	1	no	—
586	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	#532	C₂²×C₁₃	1	1	yes	characteristic
588	#529	—	2	1	no	—
589	#529	C₂²×C₁₃	1	1	yes	characteristic
590	#525	—	2	1	no	—
591	C₂×#121	—	2	1	no	—
592	#519	C₂²×C₁₃	1	2	yes	complemented
593	#518	C₂²×C₁₃	1	2	yes	—
594	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
595	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
596	#501	C₂²×C₁₃	1	2	yes	complemented
597	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#496	C₂²×C₁₃	1	2	yes	complemented
599	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	#488	C₂²×C₁₃	1	2	yes	complemented
601	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#486	C₂²×C₁₃	1	2	yes	complemented
603	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#485	C₂²×C₁₃	1	2	yes	complemented
605	#483	C₂²×C₁₃	1	2	yes	complemented
606	#482	C₂²×C₁₃	1	2	yes	complemented
607	#482	C₂²×C₁₃	1	2	yes	complemented
608	#482	C₂²×C₁₃	1	2	yes	complemented
609	#482	C₂²×C₁₃	1	2	yes	complemented
610	#479	C₂²×C₁₃	1	2	yes	complemented
611	#479	C₂²×C₁₃	1	2	yes	complemented
612	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#476	C₂²×C₁₃	1	1	yes	characteristic
614	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#476	C₂²×C₁₃	1	2	yes	complemented
617	#474	C₂²×C₁₃	1	2	yes	—
618	#469	C₂²×C₁₃	1	2	yes	complemented
619	#468	C₂²×C₁₃	1	2	yes	complemented
620	#468	C₂²×C₁₃	1	2	yes	complemented
621	#468	C₂²×C₁₃	1	2	yes	complemented
622	#466	C₂²×C₁₃	1	2	yes	complemented
623	#465	C₂²×C₁₃	1	2	yes	complemented
624	#463	C₂²×C₁₃	1	2	yes	—
625	#463	C₂²×C₁₃	1	2	yes	complemented
626	#461	C₂²×C₁₃	1	1	yes	characteristic
627	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#460	C₂²×C₁₃	1	2	yes	complemented
630	#460	C₂²×C₁₃	1	2	yes	complemented
631	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#450	C₂²×C₁₃	1	2	yes	—
633	#450	C₂²×C₁₃	1	2	yes	—
634	#449	C₂²×C₁₃	1	2	yes	complemented
635	#448	C₂²×C₁₃	1	2	yes	complemented
636	#448	C₂²×C₁₃	1	2	yes	complemented
637	#447	C₂²×C₁₃	1	2	yes	—
638	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#442	C₂²×C₁₃	1	1	yes	characteristic
641	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#440	C₂²×C₁₃	1	2	yes	—
643	#440	C₂²×C₁₃	1	1	yes	characteristic
644	#440	C₂²×C₁₃	1	2	yes	complemented
645	#440	C₂²×C₁₃	1	2	yes	complemented
646	#440	C₂²×C₁₃	1	1	yes	characteristic, complemented
647	#440	C₂²×C₁₃	1	2	yes	complemented
648	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
649	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
650	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
651	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
653	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
654	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
655	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
656	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
658	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#436	C₂²×C₁₃	1	2	yes	complemented
660	#435	C₂²×C₁₃	1	2	yes	complemented
661	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#433	C₂²×C₁₃	1	2	yes	complemented
663	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#427	C₂²×C₁₃	1	2	yes	complemented
666	#419	C₂²×C₁₃	1	2	yes	complemented
667	#418	C₂²×C₁₃	1	1	yes	characteristic
668	#418	C₂²×C₁₃	1	2	yes	—
669	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#405	C₂²×C₁₃	1	2	yes	complemented
671	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	C₂²×C₁₃	—	2	1	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	2	1	no	—
678	C₂²×C₁₃	—	2	2	no	—
679	C₂²×C₁₃	—	4	1	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	2	no	—
682	C₂²×C₁₃	—	4	1	no	—
683	C₂²×C₁₃	—	4	1	no	—
684	C₂²×C₁₃	—	4	1	no	—
685	C₂²×C₁₃	—	4	1	no	—
686	C₂²×C₁₃	—	4	2	no	—
687	C₂²×C₁₃	—	4	1	no	—
688	C₂²×C₁₃	—	4	1	no	—
689	C₂²×C₁₃	—	4	2	no	—
690	C₂²×C₁₃	—	8	4	no	—
691	C₂²×C₁₃	—	16	4	no	—
692	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
693	C₄×C₁₃	—	2	1	no	—
694	C₄×C₁₃	—	2	1	no	—
695	C₄×C₁₃	—	2	2	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	no	—
698	C₄×C₁₃	—	2	2	no	—
699	C₄×C₁₃	—	2	1	no	—
700	C₄×C₁₃	—	2	2	no	—
701	C₄×C₁₃	—	4	2	no	—
702	C₄×C₁₃	—	4	1	no	—
703	C₄×C₁₃	—	4	2	no	—
704	C₄×C₁₃	—	4	2	no	—
705	C₄×C₁₃	—	4	1	no	—
706	C₄×C₁₃	—	4	1	no	—
707	C₄×C₁₃	—	4	1	no	—
708	C₄×C₁₃	#577	1	2	yes	—
709	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
710	C₄×C₁₃	#585	1	1	yes	characteristic
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
714	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
715	C₂²×D₄	—	2	1	no	—
716	C₂²×D₄	—	2	2	no	—
717	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
718	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
719	C₂³×C₄	—	2	1	no	—
720	AGL(1,ℤ/8)	—	2	4	no	—
721	C₂×SD₁₆	—	2	8	no	—
722	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×D₈	C₂³×C₁₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
733	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
735	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	2	no	—
739	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
743	#127	C₂³×C₁₃	1	1	yes	characteristic
744	#127	C₂³×C₁₃	1	2	yes	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	D₄×C₁₃	1	2	yes	—
751	#125	—	2	1	no	—
752	#125	D₄×C₁₃	1	1	yes	characteristic
753	#125	C₂³×C₁₃	1	2	yes	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	D₄×C₁₃	1	1	yes	characteristic
761	#124	C₂³×C₁₃	1	2	yes	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₁₃	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	D₄×C₁₃	1	1	yes	characteristic
789	#121	C₂³×C₁₃	1	2	yes	—
790	#121	C₂³×C₁₃	1	2	yes	—
791	#121	C₂³×C₁₃	1	2	yes	—
792	#121	C₂³×C₁₃	1	2	yes	—
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	2	no	—
798	C₄×Q₈	—	2	2	no	—
799	C₄×Q₈	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
804	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
805	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
806	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₁₃	1	2	yes	—
824	C₄×D₄	C₂³×C₁₃	1	2	yes	—
825	C₄×D₄	C₂³×C₁₃	1	2	yes	—
826	C₄×D₄	C₂³×C₁₃	1	2	yes	—
827	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	—	2	1	no	—
835	#117	C₂³×C₁₃	1	1	yes	characteristic
836	#117	C₂³×C₁₃	1	2	yes	—
837	#117	C₂³×C₁₃	1	2	yes	—
838	#117	C₂³×C₁₃	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
846	#107	C₂³×C₁₃	1	1	yes	characteristic
847	#107	C₂³×C₁₃	1	2	yes	—
848	#107	C₂³×C₁₃	1	1	yes	characteristic
849	#107	C₂³×C₁₃	1	2	yes	—
850	#107	C₂³×C₁₃	1	2	yes	—
851	#106	C₂³×C₁₃	1	2	yes	—
852	#106	C₂³×C₁₃	1	2	yes	—
853	#106	C₂³×C₁₃	1	1	yes	characteristic
854	#106	C₂³×C₁₃	1	1	yes	characteristic
855	#106	C₂³×C₁₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	1	yes	characteristic
861	#103	C₂³×C₁₃	1	1	yes	characteristic
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	2	yes	—
864	#103	C₂³×C₁₃	1	2	yes	—
865	#103	C₂³×C₁₃	1	2	yes	—
866	#103	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	1	yes	characteristic
868	#102	C₂³×C₁₃	1	1	yes	characteristic
869	#102	C₂³×C₁₃	1	1	yes	characteristic
870	#102	C₂³×C₁₃	1	1	yes	characteristic
871	#102	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	1	yes	characteristic
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	2	yes	—
875	#102	C₂³×C₁₃	1	1	yes	characteristic
876	#102	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	2	yes	—
878	#102	C₂³×C₁₃	1	2	yes	—
879	#102	C₂³×C₁₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
883	#97	C₂³×C₁₃	1	1	yes	characteristic
884	#97	C₂³×C₁₃	1	1	yes	characteristic
885	#97	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	4	1	no	—
891	C₂×C₁₃	—	4	2	no	—
892	C₂×C₁₃	—	4	2	no	—
893	C₂×C₁₃	—	8	1	no	—
894	C₂×C₁₃	—	8	1	no	—
895	C₂×C₁₃	—	8	2	no	—
896	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
897	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
898	C₂×C₁₃	#3585	1	1	yes	characteristic
899	C₂⁴	—	2	1	no	—
900	C₂⁴	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	4	1	no	—
903	#41	—	8	2	no	—
904	#41	—	8	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	4	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
914	C₂×D₄	—	2	4	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	1	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	—	8	4	no	—
931	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
933	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
936	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	8	2	no	—
950	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
951	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	C₁₃×#41	1	4	yes	complemented
961	D₈	—	2	2	no	—
962	D₈	—	2	2	no	—
963	D₈	—	4	2	no	—
964	M₁₆	—	2	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	1	no	—
967	C₂×C₈	—	2	4	no	—
968	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
970	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
973	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₁₃	1	2	yes	—
1039	C₁₃	#61543	1	1	yes	characteristic, direct product factor, Sylow
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	8	1	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1051	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	4	4	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	C₂×C₁₃×#41	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	C₂×C₁₃×#41	1	2	yes	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	C₂×C₁₃×#41	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	2	no	—
1159	C₄	C₁₃×#577	1	2	yes	—
1160	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1161	C₄	C₁₃×#585	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	2	no	—
1167	C₂	—	8	1	no	—
1168	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1169	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1170	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×#3519	C₂	semidirect
2. C₁₃×#3518	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3362	C₂	semidirect
6. C₁₃×#3360	C₂	semidirect
7. C₁₃×#3350	C₂	semidirect
8. C₁₃×#3341	C₂	semidirect
9. C₁₃×#3329	C₂	semidirect
10. C₁₃×#3326	C₂	semidirect
11. C₁₃×#3325	C₂	semidirect
12. C₁₃×#3324	C₂	semidirect
13. D₄×C₁₃×SD₁₆	C₂	semidirect
14. C₁₃×#3265	C₂	semidirect
15. C₁₃×#3182	C₂	semidirect
16. C₁₃×#3179	C₂	semidirect
17. C₁₃×#3126	C₂	semidirect
18. C₁₃×#3118	C₂	semidirect
19. C₁₃×#3106	C₂	semidirect
20. C₁₃×#3101	C₂	semidirect
21. C₁₃×#2969	C₂	semidirect
22. C₁₃×#2949	C₂	semidirect
23. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
26. Q₈²×C₁₃	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
33. C₁₃×#555	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#548	C₂²	semidirect
45. C₁₃×#542	C₂²	semidirect
49. C₁₃×#533	C₂²	semidirect
55. C₁₃×#519	C₂²	semidirect
57. C₄×C₁₃×#41	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#500	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#492	C₂²	semidirect
63. C₁₃×#488	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#476	C₂²	semidirect
79. C₁₃×#476	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#468	C₂²	semidirect
84. C₁₃×#468	C₂²	semidirect
85. C₁₃×#466	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
97. C₁₃×#449	C₂²	semidirect
98. C₁₃×#448	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
107. C₁₃×#440	C₂²	semidirect
108. C₁₃×#440	C₂²	semidirect
109. C₁₃×#440	C₂²	semidirect
110. C₁₃×#440	C₂²	semidirect
114. C₄×C₁₃×SD₁₆	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₁₃×#427	C₂²	semidirect
129. C₁₃×#419	C₂²	semidirect
132. C₁₃×#417	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₄×C₁₃×M₁₆	C₂²	semidirect
314. #61543	C₁₃	direct (N × H)
376. C₁₃×SD₁₆	#41	semidirect
455. #3519	C₂×C₁₃	semidirect
456. #3518	C₂×C₁₃	semidirect
457. #3397	C₂×C₁₃	semidirect
458. #3385	C₂×C₁₃	semidirect
459. #3362	C₂×C₁₃	semidirect
460. #3360	C₂×C₁₃	semidirect
461. #3350	C₂×C₁₃	semidirect
462. #3341	C₂×C₁₃	semidirect
463. #3329	C₂×C₁₃	semidirect
464. #3326	C₂×C₁₃	semidirect
465. #3325	C₂×C₁₃	semidirect
466. #3324	C₂×C₁₃	semidirect
467. D₄×SD₁₆	C₂×C₁₃	semidirect
468. #3265	C₂×C₁₃	semidirect
469. #3182	C₂×C₁₃	semidirect
470. #3179	C₂×C₁₃	semidirect
471. #3126	C₂×C₁₃	semidirect
472. #3118	C₂×C₁₃	semidirect
473. #3106	C₂×C₁₃	semidirect
474. #3101	C₂×C₁₃	semidirect
475. #2969	C₂×C₁₃	semidirect
476. #2949	C₂×C₁₃	semidirect
477. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
563. Q₈²	C₂²×C₁₃	semidirect
566. #556	C₂²×C₁₃	semidirect
567. #556	C₂²×C₁₃	semidirect
570. #555	C₂²×C₁₃	semidirect
575. D₄×Q₈	C₂²×C₁₃	semidirect
576. #548	C₂²×C₁₃	semidirect
582. #542	C₂²×C₁₃	semidirect
586. #533	C₂²×C₁₃	semidirect
592. #519	C₂²×C₁₃	semidirect
594. C₄×#41	C₂²×C₁₃	semidirect
596. #501	C₂²×C₁₃	semidirect
597. #500	C₂²×C₁₃	semidirect
598. #496	C₂²×C₁₃	semidirect
599. #492	C₂²×C₁₃	semidirect
600. #488	C₂²×C₁₃	semidirect
601. #487	C₂²×C₁₃	semidirect
602. #486	C₂²×C₁₃	semidirect
603. #486	C₂²×C₁₃	semidirect
604. #485	C₂²×C₁₃	semidirect
605. #483	C₂²×C₁₃	semidirect
606. #482	C₂²×C₁₃	semidirect
607. #482	C₂²×C₁₃	semidirect
608. #482	C₂²×C₁₃	semidirect
609. #482	C₂²×C₁₃	semidirect
610. #479	C₂²×C₁₃	semidirect
611. #479	C₂²×C₁₃	semidirect
612. #477	C₂²×C₁₃	semidirect
614. #476	C₂²×C₁₃	semidirect
615. #476	C₂²×C₁₃	semidirect
616. #476	C₂²×C₁₃	semidirect
618. #469	C₂²×C₁₃	semidirect
619. #468	C₂²×C₁₃	semidirect
620. #468	C₂²×C₁₃	semidirect
621. #468	C₂²×C₁₃	semidirect
622. #466	C₂²×C₁₃	semidirect
623. #465	C₂²×C₁₃	semidirect
625. #463	C₂²×C₁₃	semidirect
627. #461	C₂²×C₁₃	semidirect
628. #460	C₂²×C₁₃	semidirect
629. #460	C₂²×C₁₃	semidirect
630. #460	C₂²×C₁₃	semidirect
631. #459	C₂²×C₁₃	semidirect
634. #449	C₂²×C₁₃	semidirect
635. #448	C₂²×C₁₃	semidirect
636. #448	C₂²×C₁₃	semidirect
638. #446	C₂²×C₁₃	semidirect
639. C₈×Q₈	C₂²×C₁₃	semidirect
641. #442	C₂²×C₁₃	semidirect
644. #440	C₂²×C₁₃	semidirect
645. #440	C₂²×C₁₃	semidirect
646. #440	C₂²×C₁₃	semidirect
647. #440	C₂²×C₁₃	semidirect
651. C₄×SD₁₆	C₂²×C₁₃	semidirect
652. C₄×SD₁₆	C₂²×C₁₃	semidirect
653. C₄×SD₁₆	C₂²×C₁₃	semidirect
654. C₄×SD₁₆	C₂²×C₁₃	semidirect
656. C₄×D₈	C₂²×C₁₃	semidirect
657. C₄×D₈	C₂²×C₁₃	semidirect
658. #436	C₂²×C₁₃	semidirect
659. #436	C₂²×C₁₃	semidirect
660. #435	C₂²×C₁₃	semidirect
661. C₈×D₄	C₂²×C₁₃	semidirect
662. #433	C₂²×C₁₃	semidirect
663. #431	C₂²×C₁₃	semidirect
664. #428	C₂²×C₁₃	semidirect
665. #427	C₂²×C₁₃	semidirect
666. #419	C₂²×C₁₃	semidirect
669. #417	C₂²×C₁₃	semidirect
670. #405	C₂²×C₁₃	semidirect
671. C₄×M₁₆	C₂²×C₁₃	semidirect
960. SD₁₆	C₁₃×#41	semidirect
1039. C₁₃	#61543	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×#3519	2
C₁₃×#3518	2
C₁₃×#3397	2
C₁₃×#3385	2
C₁₃×#3362	2
C₁₃×#3360	2
C₁₃×#3350	2
C₁₃×#3341	2
C₁₃×#3329	2
C₁₃×#3326	2
C₁₃×#3325	2
C₁₃×#3324	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3265	2
C₁₃×#3182	2
C₁₃×#3179	2
C₁₃×#3126	2
C₁₃×#3118	2
C₁₃×#3106	2
C₁₃×#3101	2
C₁₃×#2969	2
C₁₃×#2949	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61543	13

Subgroups — C13×#61543 #15747882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61543 #15747882