Subgroups — C₁₃×#62032 #15748371

Order 3328.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3275	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3123	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	—
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
27	C₁₃×#563	—	2	2	no	—
28	C₁₃×#559	C₂²	1	1	yes	characteristic
29	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#556	C₂²	1	1	yes	characteristic
31	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#555	C₂²	1	2	yes	—
33	C₁₃×#554	—	2	1	no	—
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#551	—	2	2	no	—
36	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
39	C₁₃×#548	—	2	1	no	—
40	C₁₃×#548	C₂²	1	2	yes	complemented
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#546	—	2	1	no	—
43	C₁₃×#546	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#544	—	2	1	no	—
46	C₁₃×#542	—	2	1	no	—
47	C₁₃×#542	C₂²	1	2	yes	—
48	C₁₃×#541	C₂²	1	2	yes	complemented
49	C₁₃×#539	—	2	2	no	—
50	C₁₃×#538	—	2	2	no	—
51	C₁₃×#536	C₂²	1	2	yes	complemented
52	C₁₃×#532	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊Q₈	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	—
59	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
60	C₁₃×#497	C₂²	1	2	yes	complemented
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#492	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#487	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#485	C₂²	1	1	yes	characteristic, 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
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#475	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	—
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#467	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	1	yes	characteristic
90	C₁₃×#463	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#462	C₂²	1	2	yes	complemented
95	C₁₃×#461	C₂²	1	2	yes	—
96	C₁₃×#461	C₂²	1	1	yes	characteristic
97	C₁₃×#461	C₂²	1	1	yes	characteristic
98	C₁₃×#461	C₂²	1	2	yes	—
99	C₁₃×#461	C₂²	1	2	yes	complemented
100	C₁₃×#461	C₂²	1	2	yes	complemented
101	C₁₃×#461	C₂²	1	2	yes	complemented
102	C₁₃×#460	C₂²	1	1	yes	characteristic
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	1	yes	characteristic
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#451	C₂²	1	2	yes	complemented
107	C₁₃×#450	C₂²	1	2	yes	—
108	C₁₃×#450	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	2	yes	—
110	C₁₃×#449	C₂²	1	1	yes	characteristic
111	C₁₃×#448	C₂²	1	2	yes	—
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#448	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×#440	C₂²	1	2	yes	—
117	C₁₃×#440	C₂²	1	2	yes	complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
124	C₁₃×#436	C₂²	1	1	yes	characteristic
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
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×#419	C₂²	1	2	yes	complemented
133	C₁₃×#419	C₂²	1	2	yes	complemented
134	C₁₃×#416	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	—	2	1	no	—
139	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₁₃×#137	—	4	4	no	—
144	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
145	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	—	4	4	no	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×D₈	C₂³	1	2	yes	—
160	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	—	2	1	no	—
164	C₁₃×C₄⋊Q₈	—	2	2	no	—
165	C₁₃×C₄⋊Q₈	—	2	1	no	—
166	C₁₃×C₄⋊Q₈	—	2	1	no	—
167	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×#127	C₂³	1	1	yes	characteristic
174	C₁₃×#126	—	2	2	no	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#126	—	2	2	no	—
177	C₁₃×#126	—	2	2	no	—
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#126	—	2	1	no	—
180	C₁₃×#126	D₄	1	2	yes	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	2	no	—
183	C₁₃×#125	—	2	2	no	—
184	C₁₃×#125	—	2	1	no	—
185	C₁₃×#125	D₄	1	1	yes	characteristic
186	C₁₃×#125	C₂³	1	1	yes	characteristic
187	C₁₃×#124	—	2	1	no	—
188	C₁₃×#124	—	2	1	no	—
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	—	2	2	no	—
193	C₁₃×#124	—	2	1	no	—
194	C₁₃×#124	D₄	1	1	yes	characteristic
195	C₁₃×#124	C₂³	1	1	yes	characteristic
196	C₁₃×#124	C₂³	1	2	yes	—
197	C₁₃×#124	C₂³	1	2	yes	—
198	C₁₃×#123	—	2	1	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	—	2	2	no	—
204	C₁₃×#123	—	2	2	no	—
205	C₁₃×#123	D₄	1	2	yes	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	1	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	—	2	2	no	—
216	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	1	no	—
224	C₁₃×#121	—	2	1	no	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	D₄	1	1	yes	characteristic
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#121	C₂³	1	2	yes	—
230	C₁₃×#121	C₂³	1	1	yes	characteristic
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	1	no	—
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
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	2	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	2	yes	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	C₂³	1	2	yes	—
264	C₁₃×#117	C₂³	1	1	yes	characteristic
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	—	2	1	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	2	yes	—
279	C₁₃×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	1	yes	characteristic
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	1	yes	characteristic
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	#62032	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	4	1	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	8	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	4	2	no	—
327	C₂×Q₈×C₁₃	—	4	2	no	—
328	C₂×Q₈×C₁₃	—	4	2	no	—
329	C₂×Q₈×C₁₃	—	4	2	no	—
330	C₂×Q₈×C₁₃	—	8	2	no	—
331	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₁₃	—	2	4	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	4	2	no	—
346	C₂×D₄×C₁₃	—	8	2	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	2	yes	—
351	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₁₃	—	2	2	no	—
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	2	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	—	2	2	no	—
361	C₂²×C₄×C₁₃	—	2	2	no	—
362	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
366	C₁₃×Q₁₆	—	4	1	no	—
367	C₁₃×Q₁₆	—	4	2	no	—
368	C₁₃×Q₁₆	—	4	2	no	—
369	C₁₃×SD₁₆	—	2	2	no	—
370	C₁₃×SD₁₆	—	2	4	no	—
371	C₁₃×SD₁₆	—	2	4	no	—
372	C₁₃×SD₁₆	—	4	2	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×SD₁₆	—	4	1	no	—
376	C₁₃×SD₁₆	—	4	2	no	—
377	C₁₃×SD₁₆	—	4	2	no	—
378	C₁₃×D₈	—	2	2	no	—
379	C₁₃×D₈	—	4	2	no	—
380	C₁₃×M₁₆	—	4	2	no	—
381	C₁₃×M₁₆	—	4	2	no	—
382	C₂×C₈×C₁₃	—	4	2	no	—
383	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
387	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	1	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	1	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	2	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	1	no	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
420	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	1	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	1	no	—
442	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²×C₁₃	—	2	1	no	—
448	C₄²×C₁₃	—	2	1	no	—
449	C₄²×C₁₃	—	2	1	no	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	1	no	—
452	C₄²×C₁₃	—	2	2	no	—
453	C₄²×C₁₃	—	2	2	no	—
454	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₃	C₂⁴	1	2	yes	—
458	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
459	#3552	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3329	C₂×C₁₃	1	2	yes	complemented
466	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3321	C₂×C₁₃	1	2	yes	complemented
468	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
469	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3275	C₂×C₁₃	1	2	yes	complemented
471	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3266	C₂×C₁₃	1	2	yes	complemented
473	#3258	C₂×C₁₃	1	2	yes	complemented
474	#3251	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3225	C₂×C₁₃	1	2	yes	complemented
476	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3123	C₂×C₁₃	1	2	yes	complemented
478	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3042	C₂×C₁₃	1	2	yes	complemented
480	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#2993	C₂×C₁₃	1	1	yes	characteristic, complemented
482	C₂³×C₁₃	—	2	1	no	—
483	C₂³×C₁₃	—	2	1	no	—
484	C₂³×C₁₃	—	2	2	no	—
485	C₂³×C₁₃	—	4	4	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	—	2	1	no	—
495	Q₈×C₁₃	—	2	1	no	—
496	Q₈×C₁₃	—	2	2	no	—
497	Q₈×C₁₃	—	2	2	no	—
498	Q₈×C₁₃	—	2	1	no	—
499	Q₈×C₁₃	—	4	2	no	—
500	Q₈×C₁₃	—	8	2	no	—
501	Q₈×C₁₃	—	8	2	no	—
502	Q₈×C₁₃	—	8	2	no	—
503	D₄×C₁₃	—	2	2	no	—
504	D₄×C₁₃	—	2	1	no	—
505	D₄×C₁₃	—	2	2	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	2	2	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	4	2	no	—
510	D₄×C₁₃	—	4	4	no	—
511	D₄×C₁₃	—	4	2	no	—
512	D₄×C₁₃	—	4	2	no	—
513	D₄×C₁₃	—	4	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	H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄×C₁₃	—	2	2	no	—
520	C₂×C₄×C₁₃	—	2	2	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	1	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	2	no	—
533	C₂×C₄×C₁₃	—	4	1	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	8	1	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₃	—	2	1	no	—
554	C₈×C₁₃	—	2	2	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	2	no	—
557	C₈×C₁₃	—	2	1	no	—
558	C₈×C₁₃	—	2	1	no	—
559	C₂×#137	C₂²×C₁₃	1	2	yes	—
560	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
561	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
562	#563	—	2	2	no	—
563	#559	C₂²×C₁₃	1	1	yes	characteristic
564	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#556	C₂²×C₁₃	1	1	yes	characteristic
566	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
567	#555	C₂²×C₁₃	1	2	yes	—
568	#554	—	2	1	no	—
569	#553	—	2	1	no	—
570	#551	—	2	2	no	—
571	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
572	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
573	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
574	#548	—	2	1	no	—
575	#548	C₂²×C₁₃	1	2	yes	complemented
576	#547	C₂²×C₁₃	1	1	yes	characteristic
577	#546	—	2	1	no	—
578	#546	C₂²×C₁₃	1	2	yes	—
579	D₄²	C₂²×C₁₃	1	1	yes	characteristic
580	#544	—	2	1	no	—
581	#542	—	2	1	no	—
582	#542	C₂²×C₁₃	1	2	yes	—
583	#541	C₂²×C₁₃	1	2	yes	complemented
584	#539	—	2	2	no	—
585	#538	—	2	2	no	—
586	#536	C₂²×C₁₃	1	2	yes	complemented
587	#532	C₂²×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#529	—	2	1	no	—
590	#529	C₂²×C₁₃	1	1	yes	characteristic
591	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	C₂×#124	—	2	1	no	—
593	#518	C₂²×C₁₃	1	2	yes	—
594	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
595	#497	C₂²×C₁₃	1	2	yes	complemented
596	#495	C₂²×C₁₃	1	2	yes	complemented
597	#492	C₂²×C₁₃	1	1	yes	characteristic
598	#492	C₂²×C₁₃	1	1	yes	characteristic
599	#489	C₂²×C₁₃	1	2	yes	complemented
600	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#487	C₂²×C₁₃	1	2	yes	complemented
602	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#485	C₂²×C₁₃	1	2	yes	complemented
604	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#485	C₂²×C₁₃	1	2	yes	complemented
606	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#478	C₂²×C₁₃	1	1	yes	characteristic
609	#478	C₂²×C₁₃	1	2	yes	complemented
610	#477	C₂²×C₁₃	1	2	yes	complemented
611	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#475	C₂²×C₁₃	1	2	yes	complemented
613	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#470	C₂²×C₁₃	1	2	yes	complemented
615	#469	C₂²×C₁₃	1	2	yes	complemented
616	#468	C₂²×C₁₃	1	2	yes	—
617	#468	C₂²×C₁₃	1	2	yes	complemented
618	#467	C₂²×C₁₃	1	2	yes	complemented
619	#465	C₂²×C₁₃	1	2	yes	—
620	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#464	C₂²×C₁₃	1	2	yes	complemented
622	#464	C₂²×C₁₃	1	2	yes	complemented
623	#463	C₂²×C₁₃	1	1	yes	characteristic
624	#463	C₂²×C₁₃	1	2	yes	—
625	#463	C₂²×C₁₃	1	2	yes	complemented
626	#463	C₂²×C₁₃	1	2	yes	complemented
627	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#462	C₂²×C₁₃	1	2	yes	complemented
630	#461	C₂²×C₁₃	1	2	yes	—
631	#461	C₂²×C₁₃	1	1	yes	characteristic
632	#461	C₂²×C₁₃	1	1	yes	characteristic
633	#461	C₂²×C₁₃	1	2	yes	—
634	#461	C₂²×C₁₃	1	2	yes	complemented
635	#461	C₂²×C₁₃	1	2	yes	complemented
636	#461	C₂²×C₁₃	1	2	yes	complemented
637	#460	C₂²×C₁₃	1	1	yes	characteristic
638	#459	C₂²×C₁₃	1	1	yes	characteristic
639	#452	C₂²×C₁₃	1	1	yes	characteristic
640	#452	C₂²×C₁₃	1	2	yes	complemented
641	#451	C₂²×C₁₃	1	2	yes	complemented
642	#450	C₂²×C₁₃	1	2	yes	—
643	#450	C₂²×C₁₃	1	2	yes	—
644	#449	C₂²×C₁₃	1	1	yes	characteristic
645	#449	C₂²×C₁₃	1	2	yes	—
646	#448	C₂²×C₁₃	1	2	yes	—
647	#448	C₂²×C₁₃	1	2	yes	complemented
648	#448	C₂²×C₁₃	1	2	yes	complemented
649	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#440	C₂²×C₁₃	1	2	yes	—
652	#440	C₂²×C₁₃	1	2	yes	complemented
653	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
655	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
656	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
657	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
659	#436	C₂²×C₁₃	1	1	yes	characteristic
660	#436	C₂²×C₁₃	1	2	yes	complemented
661	#435	C₂²×C₁₃	1	2	yes	complemented
662	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
663	#433	C₂²×C₁₃	1	2	yes	complemented
664	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#424	C₂²×C₁₃	1	2	yes	complemented
666	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#419	C₂²×C₁₃	1	2	yes	complemented
668	#419	C₂²×C₁₃	1	2	yes	complemented
669	#416	C₂²×C₁₃	1	2	yes	complemented
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
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	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	4	1	no	—
684	C₂²×C₁₃	—	4	2	no	—
685	C₂²×C₁₃	—	16	4	no	—
686	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	1	no	—
689	C₄×C₁₃	—	2	2	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	2	no	—
692	C₄×C₁₃	—	2	1	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	1	no	—
697	C₄×C₁₃	—	4	2	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	2	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	1	no	—
702	C₄×C₁₃	—	4	2	no	—
703	C₄×C₁₃	#577	1	2	yes	—
704	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₄×C₁₃	#585	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×#41	C₂³×C₁₃	1	2	yes	—
709	C₂²×Q₈	—	2	1	no	—
710	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
711	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
714	#137	—	4	4	no	—
715	AGL(1,ℤ/8)	—	4	4	no	—
716	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×SD₁₆	—	4	4	no	—
720	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
729	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₁₃	1	2	yes	—
731	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
733	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	2	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
739	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
742	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
744	#127	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
751	#126	D₄×C₁₃	1	2	yes	—
752	#125	—	2	2	no	—
753	#125	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	D₄×C₁₃	1	1	yes	characteristic
757	#125	C₂³×C₁₃	1	1	yes	characteristic
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	1	no	—
765	#124	D₄×C₁₃	1	1	yes	characteristic
766	#124	C₂³×C₁₃	1	1	yes	characteristic
767	#124	C₂³×C₁₃	1	2	yes	—
768	#124	C₂³×C₁₃	1	2	yes	—
769	#123	—	2	1	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	D₄×C₁₃	1	2	yes	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
790	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	D₄×C₁₃	1	1	yes	characteristic
799	#121	C₂³×C₁₃	1	1	yes	characteristic
800	#121	C₂³×C₁₃	1	2	yes	—
801	#121	C₂³×C₁₃	1	2	yes	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
810	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
811	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₁₃	1	2	yes	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	C₂³×C₁₃	1	1	yes	characteristic
835	#117	C₂³×C₁₃	1	2	yes	—
836	#117	C₂³×C₁₃	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
845	#107	C₂³×C₁₃	1	1	yes	characteristic
846	#107	C₂³×C₁₃	1	1	yes	characteristic
847	#107	C₂³×C₁₃	1	2	yes	—
848	#106	C₂³×C₁₃	1	1	yes	characteristic
849	#106	C₂³×C₁₃	1	2	yes	—
850	#106	C₂³×C₁₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
867	#103	C₂³×C₁₃	1	2	yes	—
868	#103	C₂³×C₁₃	1	1	yes	characteristic
869	#103	C₂³×C₁₃	1	1	yes	characteristic
870	#103	C₂³×C₁₃	1	2	yes	—
871	#102	C₂³×C₁₃	1	1	yes	characteristic
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	1	yes	characteristic
874	#102	C₂³×C₁₃	1	1	yes	characteristic
875	#102	C₂³×C₁₃	1	1	yes	characteristic
876	#102	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
882	#97	C₂³×C₁₃	1	2	yes	—
883	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₁₃	1	2	yes	—
886	C₂×C₁₃	—	4	1	no	—
887	C₂×C₁₃	—	4	2	no	—
888	C₂×C₁₃	—	4	2	no	—
889	C₂×C₁₃	—	8	1	no	—
890	C₂×C₁₃	—	8	2	no	—
891	C₂×C₁₃	#3488	1	1	yes	characteristic
892	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
893	C₂×C₁₃	#3586	1	1	yes	characteristic
894	C₂⁴	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
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	1	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	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	8	2	no	—
925	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
927	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
929	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	1	no	—
947	SD₁₆	—	2	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	D₈	—	2	2	no	—
957	D₈	—	4	2	no	—
958	M₁₆	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
965	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₂⁴×C₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₁₃	1	2	yes	—
1036	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₁₃	#62032	1	1	yes	characteristic, direct product factor, Sylow
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1045	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	Q₈	—	8	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₁₃×#577	1	2	yes	—
1149	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1150	C₄	C₁₃×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₁₃×#3488	1	1	yes	characteristic
1157	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1158	C₂	C₁₃×#3586	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×#3552	C₂	semidirect
2. C₁₃×#3514	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3367	C₂	semidirect
6. C₁₃×#3359	C₂	semidirect
7. C₁₃×#3329	C₂	semidirect
8. C₁₃×#3328	C₂	semidirect
9. C₁₃×#3321	C₂	semidirect
10. C₁₃×#3302	C₂	semidirect
11. D₄×C₁₃×SD₁₆	C₂	semidirect
12. C₁₃×#3275	C₂	semidirect
13. C₁₃×#3272	C₂	semidirect
14. C₁₃×#3266	C₂	semidirect
15. C₁₃×#3258	C₂	semidirect
16. C₁₃×#3251	C₂	semidirect
17. C₁₃×#3225	C₂	semidirect
18. C₁₃×#3206	C₂	semidirect
19. C₁₃×#3123	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3042	C₂	semidirect
22. C₁₃×#3039	C₂	semidirect
23. C₁₃×#2993	C₂	semidirect
29. C₁₃×#557	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
48. C₁₃×#541	C₂²	semidirect
51. C₁₃×#536	C₂²	semidirect
53. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
60. C₁₃×#497	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
67. C₁₃×#487	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#485	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#467	C₂²	semidirect
85. C₁₃×#464	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
90. C₁₃×#463	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#462	C₂²	semidirect
94. C₁₃×#462	C₂²	semidirect
99. C₁₃×#461	C₂²	semidirect
100. C₁₃×#461	C₂²	semidirect
101. C₁₃×#461	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#451	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#448	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
117. C₁₃×#440	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
121. C₄×C₁₃×SD₁₆	C₂²	semidirect
122. C₄×C₁₃×SD₁₆	C₂²	semidirect
125. C₁₃×#436	C₂²	semidirect
126. C₁₃×#435	C₂²	semidirect
128. C₁₃×#433	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#424	C₂²	semidirect
131. C₁₃×#423	C₂²	semidirect
132. C₁₃×#419	C₂²	semidirect
133. C₁₃×#419	C₂²	semidirect
134. C₁₃×#416	C₂²	semidirect
315. #62032	C₁₃	direct (N × H)
459. #3552	C₂×C₁₃	semidirect
460. #3514	C₂×C₁₃	semidirect
461. #3400	C₂×C₁₃	semidirect
462. #3394	C₂×C₁₃	semidirect
463. #3367	C₂×C₁₃	semidirect
464. #3359	C₂×C₁₃	semidirect
465. #3329	C₂×C₁₃	semidirect
466. #3328	C₂×C₁₃	semidirect
467. #3321	C₂×C₁₃	semidirect
468. #3302	C₂×C₁₃	semidirect
469. D₄×SD₁₆	C₂×C₁₃	semidirect
470. #3275	C₂×C₁₃	semidirect
471. #3272	C₂×C₁₃	semidirect
472. #3266	C₂×C₁₃	semidirect
473. #3258	C₂×C₁₃	semidirect
474. #3251	C₂×C₁₃	semidirect
475. #3225	C₂×C₁₃	semidirect
476. #3206	C₂×C₁₃	semidirect
477. #3123	C₂×C₁₃	semidirect
478. #3102	C₂×C₁₃	semidirect
479. #3042	C₂×C₁₃	semidirect
480. #3039	C₂×C₁₃	semidirect
481. #2993	C₂×C₁₃	semidirect
564. #557	C₂²×C₁₃	semidirect
566. #556	C₂²×C₁₃	semidirect
573. D₄×Q₈	C₂²×C₁₃	semidirect
575. #548	C₂²×C₁₃	semidirect
583. #541	C₂²×C₁₃	semidirect
586. #536	C₂²×C₁₃	semidirect
588. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
591. #529	C₂²×C₁₃	semidirect
595. #497	C₂²×C₁₃	semidirect
596. #495	C₂²×C₁₃	semidirect
599. #489	C₂²×C₁₃	semidirect
600. #487	C₂²×C₁₃	semidirect
601. #487	C₂²×C₁₃	semidirect
602. #487	C₂²×C₁₃	semidirect
603. #485	C₂²×C₁₃	semidirect
604. #485	C₂²×C₁₃	semidirect
605. #485	C₂²×C₁₃	semidirect
606. #482	C₂²×C₁₃	semidirect
607. #479	C₂²×C₁₃	semidirect
609. #478	C₂²×C₁₃	semidirect
610. #477	C₂²×C₁₃	semidirect
611. #475	C₂²×C₁₃	semidirect
612. #475	C₂²×C₁₃	semidirect
613. #474	C₂²×C₁₃	semidirect
614. #470	C₂²×C₁₃	semidirect
615. #469	C₂²×C₁₃	semidirect
617. #468	C₂²×C₁₃	semidirect
618. #467	C₂²×C₁₃	semidirect
620. #464	C₂²×C₁₃	semidirect
621. #464	C₂²×C₁₃	semidirect
622. #464	C₂²×C₁₃	semidirect
625. #463	C₂²×C₁₃	semidirect
626. #463	C₂²×C₁₃	semidirect
627. #462	C₂²×C₁₃	semidirect
628. #462	C₂²×C₁₃	semidirect
629. #462	C₂²×C₁₃	semidirect
634. #461	C₂²×C₁₃	semidirect
635. #461	C₂²×C₁₃	semidirect
636. #461	C₂²×C₁₃	semidirect
640. #452	C₂²×C₁₃	semidirect
641. #451	C₂²×C₁₃	semidirect
647. #448	C₂²×C₁₃	semidirect
648. #448	C₂²×C₁₃	semidirect
649. #446	C₂²×C₁₃	semidirect
650. C₈×Q₈	C₂²×C₁₃	semidirect
652. #440	C₂²×C₁₃	semidirect
653. C₄×Q₁₆	C₂²×C₁₃	semidirect
656. C₄×SD₁₆	C₂²×C₁₃	semidirect
657. C₄×SD₁₆	C₂²×C₁₃	semidirect
660. #436	C₂²×C₁₃	semidirect
661. #435	C₂²×C₁₃	semidirect
663. #433	C₂²×C₁₃	semidirect
664. #431	C₂²×C₁₃	semidirect
665. #424	C₂²×C₁₃	semidirect
666. #423	C₂²×C₁₃	semidirect
667. #419	C₂²×C₁₃	semidirect
668. #419	C₂²×C₁₃	semidirect
669. #416	C₂²×C₁₃	semidirect
1037. C₁₃	#62032	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×#3552	2
C₁₃×#3514	2
C₁₃×#3400	2
C₁₃×#3394	2
C₁₃×#3367	2
C₁₃×#3359	2
C₁₃×#3329	2
C₁₃×#3328	2
C₁₃×#3321	2
C₁₃×#3302	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3275	2
C₁₃×#3272	2
C₁₃×#3266	2
C₁₃×#3258	2
C₁₃×#3251	2
C₁₃×#3225	2
C₁₃×#3206	2
C₁₃×#3123	2
C₁₃×#3102	2
C₁₃×#3042	2
C₁₃×#3039	2
C₁₃×#2993	2
#62032	13

Subgroups — C13×#62032 #15748371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62032 #15748371