Subgroups — C₁₃×#62055 #15748394

Order 3328.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1176 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
2	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
12	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3260	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
25	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
27	C₁₃×#560	—	2	2	no	—
28	C₁₃×#559	C₂²	1	1	yes	characteristic
29	C₁₃×#557	—	2	1	no	—
30	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#556	—	2	1	no	—
33	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#552	—	2	2	no	—
35	C₁₃×#552	C₂²	1	2	yes	complemented
36	C₁₃×#550	C₂²	1	1	yes	characteristic
37	C₁₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#546	—	2	1	no	—
41	C₁₃×#546	C₂²	1	2	yes	—
42	D₄²×C₁₃	—	2	1	no	—
43	D₄²×C₁₃	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#541	—	2	2	no	—
46	C₁₃×#541	C₂²	1	2	yes	complemented
47	C₁₃×#540	—	2	1	no	—
48	C₁₃×#540	C₂²	1	2	yes	—
49	C₁₃×#535	—	2	1	no	—
50	C₁₃×#535	C₂²	1	2	yes	—
51	C₁₃×#534	—	2	2	no	—
52	C₁₃×#533	—	2	1	no	—
53	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
55	C₁₃×#529	—	2	1	no	—
56	C₁₃×#529	C₂²	1	1	yes	characteristic
57	C₁₃×#529	C₂²	1	1	yes	characteristic
58	C₁₃×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#497	C₂²	1	2	yes	complemented
61	C₁₃×#492	C₂²	1	1	yes	characteristic
62	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	2	yes	complemented
64	C₁₃×#490	C₂²	1	2	yes	complemented
65	C₁₃×#488	C₂²	1	2	yes	complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#480	C₂²	1	1	yes	characteristic
72	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#478	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×#468	C₂²	1	2	yes	complemented
80	C₁₃×#468	C₂²	1	2	yes	complemented
81	C₁₃×#467	C₂²	1	2	yes	complemented
82	C₁₃×#465	C₂²	1	2	yes	—
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
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×#464	C₂²	1	2	yes	complemented
89	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#461	C₂²	1	2	yes	complemented
92	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#461	C₂²	1	2	yes	complemented
94	C₁₃×#460	C₂²	1	1	yes	characteristic
95	C₁₃×#460	C₂²	1	1	yes	characteristic
96	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#460	C₂²	1	2	yes	complemented
98	C₁₃×#460	C₂²	1	2	yes	complemented
99	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#460	C₂²	1	2	yes	complemented
101	C₁₃×#460	C₂²	1	2	yes	complemented
102	C₁₃×#460	C₂²	1	2	yes	complemented
103	C₁₃×#460	C₂²	1	2	yes	complemented
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#450	C₂²	1	2	yes	complemented
108	C₁₃×#450	C₂²	1	2	yes	complemented
109	C₁₃×#450	C₂²	1	2	yes	complemented
110	C₁₃×#450	C₂²	1	2	yes	complemented
111	C₁₃×#448	C₂²	1	1	yes	characteristic
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	complemented
117	C₁₃×#440	C₂²	1	2	yes	complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₁₃	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	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₁₃×#418	C₂²	1	2	yes	complemented
133	C₁₃×#416	C₂²	1	2	yes	complemented
134	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	—	2	2	no	—
140	C₂²×D₄×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	—	2	1	no	—
143	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
145	C₁₃×#137	—	4	4	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	—	4	4	no	—
150	C₂×C₁₃×SD₁₆	—	4	4	no	—
151	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
163	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
165	C₁₃×C₄⋊Q₈	—	2	1	no	—
166	C₁₃×C₄⋊Q₈	—	2	1	no	—
167	C₁₃×C₄⋊Q₈	—	2	2	no	—
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×#127	—	2	1	no	—
172	C₁₃×#127	—	2	1	no	—
173	C₁₃×#127	—	2	1	no	—
174	C₁₃×#127	C₂³	1	1	yes	characteristic
175	C₁₃×#127	C₂³	1	2	yes	—
176	C₁₃×#127	C₂³	1	1	yes	characteristic
177	C₁₃×#127	C₂³	1	2	yes	—
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#126	—	2	2	no	—
180	C₁₃×#126	—	2	2	no	—
181	C₁₃×#126	—	2	2	no	—
182	C₁₃×#126	—	2	1	no	—
183	C₁₃×#126	D₄	1	2	yes	—
184	C₁₃×#125	—	2	1	no	—
185	C₁₃×#125	—	2	2	no	—
186	C₁₃×#125	—	2	2	no	—
187	C₁₃×#125	—	2	2	no	—
188	C₁₃×#125	—	2	2	no	—
189	C₁₃×#125	—	2	2	no	—
190	C₁₃×#125	—	2	1	no	—
191	C₁₃×#125	D₄	1	1	yes	characteristic
192	C₁₃×#125	C₂³	1	2	yes	—
193	C₁₃×#125	C₂³	1	1	yes	characteristic
194	C₁₃×#124	—	2	1	no	—
195	C₁₃×#124	—	2	1	no	—
196	C₁₃×#124	D₄	1	1	yes	characteristic
197	C₁₃×#124	C₂³	1	1	yes	characteristic
198	C₁₃×#124	C₂³	1	2	yes	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	1	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	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	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	—	2	2	no	—
225	C₁₃×#121	D₄	1	1	yes	characteristic
226	C₁₃×#121	C₂³	1	1	yes	characteristic
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#120	—	2	2	no	—
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	C₄×Q₈×C₁₃	—	2	1	no	—
236	C₄×Q₈×C₁₃	—	2	2	no	—
237	C₄×Q₈×C₁₃	—	2	2	no	—
238	C₄×Q₈×C₁₃	—	2	1	no	—
239	C₄×Q₈×C₁₃	—	2	1	no	—
240	C₄×Q₈×C₁₃	—	2	1	no	—
241	C₄×Q₈×C₁₃	—	2	1	no	—
242	C₄×Q₈×C₁₃	—	2	1	no	—
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
251	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	—	2	2	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	1	no	—
255	C₄×D₄×C₁₃	—	2	1	no	—
256	C₄×D₄×C₁₃	—	2	1	no	—
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	2	yes	—
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	2	yes	—
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	2	no	—
264	C₁₃×#117	—	2	2	no	—
265	C₁₃×#117	—	2	2	no	—
266	C₁₃×#117	—	2	1	no	—
267	C₁₃×#117	C₂³	1	2	yes	—
268	C₁₃×#117	C₂³	1	2	yes	—
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
305	C₁₃×#102	C₂³	1	1	yes	characteristic
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	#62055	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₂⁴×C₁₃	—	2	2	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	8	2	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	4	no	—
326	C₂×Q₈×C₁₃	—	4	1	no	—
327	C₂×Q₈×C₁₃	—	4	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×Q₈×C₁₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	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	1	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	2	2	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	—	4	2	no	—
348	C₂×D₄×C₁₃	—	4	2	no	—
349	C₂×D₄×C₁₃	—	4	2	no	—
350	C₂×D₄×C₁₃	—	4	2	no	—
351	C₂×D₄×C₁₃	—	8	2	no	—
352	C₂×D₄×C₁₃	—	8	2	no	—
353	C₂×D₄×C₁₃	—	8	2	no	—
354	C₂×D₄×C₁₃	—	8	4	no	—
355	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
356	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
358	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₁₃	—	2	1	no	—
361	C₂²×C₄×C₁₃	—	2	1	no	—
362	C₂²×C₄×C₁₃	—	2	2	no	—
363	C₂²×C₄×C₁₃	—	2	1	no	—
364	C₂²×C₄×C₁₃	—	2	2	no	—
365	C₂²×C₄×C₁₃	—	2	2	no	—
366	C₂²×C₄×C₁₃	—	2	2	no	—
367	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
371	C₁₃×Q₁₆	—	2	2	no	—
372	C₁₃×Q₁₆	—	4	1	no	—
373	C₁₃×Q₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	2	2	no	—
375	C₁₃×SD₁₆	—	2	4	no	—
376	C₁₃×SD₁₆	—	2	4	no	—
377	C₁₃×SD₁₆	—	4	2	no	—
378	C₁₃×SD₁₆	—	4	2	no	—
379	C₁₃×SD₁₆	—	4	2	no	—
380	C₁₃×SD₁₆	—	4	2	no	—
381	C₁₃×SD₁₆	—	4	1	no	—
382	C₁₃×SD₁₆	—	4	2	no	—
383	C₁₃×SD₁₆	—	4	2	no	—
384	C₁₃×SD₁₆	—	4	2	no	—
385	C₁₃×M₁₆	—	4	2	no	—
386	C₂×C₈×C₁₃	—	4	2	no	—
387	C₂×C₈×C₁₃	—	4	2	no	—
388	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
398	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
404	C₁₃×C₄⋊C₄	—	2	1	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
412	C₁₃×C₄⋊C₄	—	2	2	no	—
413	C₁₃×C₄⋊C₄	—	2	2	no	—
414	C₁₃×C₄⋊C₄	—	2	2	no	—
415	C₁₃×C₄⋊C₄	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
422	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	1	no	—
435	C₁₃×C₂²⋊C₄	—	2	1	no	—
436	C₁₃×C₂²⋊C₄	—	2	1	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	—	2	2	no	—
442	C₁₃×C₂²⋊C₄	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	1	no	—
451	C₄²×C₁₃	—	2	2	no	—
452	C₄²×C₁₃	—	2	2	no	—
453	C₄²×C₁₃	—	2	2	no	—
454	C₄²×C₁₃	—	2	1	no	—
455	C₄²×C₁₃	—	2	2	no	—
456	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
459	C₄²×C₁₃	C₂⁴	1	2	yes	—
460	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
461	#3543	C₂×C₁₃	1	1	yes	characteristic
462	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3310	C₂×C₁₃	1	2	yes	complemented
469	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3296	C₂×C₁₃	1	2	yes	complemented
471	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
472	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3266	C₂×C₁₃	1	2	yes	complemented
475	#3260	C₂×C₁₃	1	2	yes	complemented
476	#3248	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3222	C₂×C₁₃	1	2	yes	complemented
478	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3126	C₂×C₁₃	1	2	yes	complemented
480	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3043	C₂×C₁₃	1	2	yes	complemented
482	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#2994	C₂×C₁₃	1	1	yes	characteristic, complemented
484	C₂³×C₁₃	—	2	1	no	—
485	C₂³×C₁₃	—	2	2	no	—
486	C₂³×C₁₃	—	2	2	no	—
487	C₂³×C₁₃	—	4	4	no	—
488	C₂³×C₁₃	—	8	2	no	—
489	C₂³×C₁₃	—	8	2	no	—
490	C₂³×C₁₃	—	8	2	no	—
491	C₂³×C₁₃	—	8	2	no	—
492	C₂³×C₁₃	—	8	2	no	—
493	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
494	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
495	Q₈×C₁₃	—	2	2	no	—
496	Q₈×C₁₃	—	2	1	no	—
497	Q₈×C₁₃	—	2	1	no	—
498	Q₈×C₁₃	—	2	2	no	—
499	Q₈×C₁₃	—	2	1	no	—
500	Q₈×C₁₃	—	2	2	no	—
501	Q₈×C₁₃	—	2	1	no	—
502	Q₈×C₁₃	—	2	1	no	—
503	Q₈×C₁₃	—	4	4	no	—
504	Q₈×C₁₃	—	4	2	no	—
505	Q₈×C₁₃	—	4	2	no	—
506	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
507	D₄×C₁₃	—	2	4	no	—
508	D₄×C₁₃	—	2	2	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	2	2	no	—
511	D₄×C₁₃	—	2	2	no	—
512	D₄×C₁₃	—	2	1	no	—
513	D₄×C₁₃	—	2	2	no	—
514	D₄×C₁₃	—	2	2	no	—
515	D₄×C₁₃	—	4	2	no	—
516	D₄×C₁₃	—	4	2	no	—
517	D₄×C₁₃	—	4	2	no	—
518	D₄×C₁₃	—	8	2	no	—
519	D₄×C₁₃	—	8	2	no	—
520	D₄×C₁₃	—	8	2	no	—
521	D₄×C₁₃	—	8	1	no	—
522	D₄×C₁₃	—	8	2	no	—
523	D₄×C₁₃	—	8	1	no	—
524	D₄×C₁₃	—	8	2	no	—
525	D₄×C₁₃	—	8	2	no	—
526	D₄×C₁₃	—	8	2	no	—
527	D₄×C₁₃	—	8	2	no	—
528	D₄×C₁₃	—	8	2	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	—	2	2	no	—
534	C₂×C₄×C₁₃	—	2	1	no	—
535	C₂×C₄×C₁₃	—	2	2	no	—
536	C₂×C₄×C₁₃	—	2	1	no	—
537	C₂×C₄×C₁₃	—	2	2	no	—
538	C₂×C₄×C₁₃	—	2	1	no	—
539	C₂×C₄×C₁₃	—	2	1	no	—
540	C₂×C₄×C₁₃	—	2	2	no	—
541	C₂×C₄×C₁₃	—	2	1	no	—
542	C₂×C₄×C₁₃	—	2	1	no	—
543	C₂×C₄×C₁₃	—	2	1	no	—
544	C₂×C₄×C₁₃	—	4	2	no	—
545	C₂×C₄×C₁₃	—	4	4	no	—
546	C₂×C₄×C₁₃	—	4	2	no	—
547	C₂×C₄×C₁₃	—	4	2	no	—
548	C₂×C₄×C₁₃	—	8	2	no	—
549	C₂×C₄×C₁₃	—	8	2	no	—
550	C₂×C₄×C₁₃	—	8	2	no	—
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
560	C₈×C₁₃	—	2	1	no	—
561	C₈×C₁₃	—	2	2	no	—
562	C₈×C₁₃	—	2	2	no	—
563	C₈×C₁₃	—	2	1	no	—
564	C₈×C₁₃	—	2	1	no	—
565	C₈×C₁₃	—	2	1	no	—
566	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
567	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
568	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
569	#560	—	2	2	no	—
570	#559	C₂²×C₁₃	1	1	yes	characteristic
571	#557	—	2	1	no	—
572	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
574	#556	—	2	1	no	—
575	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#552	—	2	2	no	—
577	#552	C₂²×C₁₃	1	2	yes	complemented
578	#550	C₂²×C₁₃	1	1	yes	characteristic
579	#550	C₂²×C₁₃	1	1	yes	characteristic
580	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
581	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	#546	—	2	1	no	—
583	#546	C₂²×C₁₃	1	2	yes	—
584	D₄²	—	2	1	no	—
585	D₄²	C₂²×C₁₃	1	2	yes	—
586	D₄²	C₂²×C₁₃	1	1	yes	characteristic
587	#541	—	2	2	no	—
588	#541	C₂²×C₁₃	1	2	yes	complemented
589	#540	—	2	1	no	—
590	#540	C₂²×C₁₃	1	2	yes	—
591	#535	—	2	1	no	—
592	#535	C₂²×C₁₃	1	2	yes	—
593	#534	—	2	2	no	—
594	#533	—	2	1	no	—
595	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
597	#529	—	2	1	no	—
598	#529	C₂²×C₁₃	1	1	yes	characteristic
599	#529	C₂²×C₁₃	1	1	yes	characteristic
600	#519	C₂²×C₁₃	1	2	yes	complemented
601	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#497	C₂²×C₁₃	1	2	yes	complemented
603	#492	C₂²×C₁₃	1	1	yes	characteristic
604	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#492	C₂²×C₁₃	1	2	yes	complemented
606	#490	C₂²×C₁₃	1	2	yes	complemented
607	#488	C₂²×C₁₃	1	2	yes	complemented
608	#486	C₂²×C₁₃	1	1	yes	characteristic
609	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	#482	C₂²×C₁₃	1	2	yes	complemented
612	#482	C₂²×C₁₃	1	2	yes	complemented
613	#480	C₂²×C₁₃	1	1	yes	characteristic
614	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#479	C₂²×C₁₃	1	2	yes	complemented
617	#478	C₂²×C₁₃	1	2	yes	complemented
618	#478	C₂²×C₁₃	1	2	yes	complemented
619	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#468	C₂²×C₁₃	1	2	yes	complemented
622	#468	C₂²×C₁₃	1	2	yes	complemented
623	#467	C₂²×C₁₃	1	2	yes	complemented
624	#465	C₂²×C₁₃	1	2	yes	—
625	#465	C₂²×C₁₃	1	2	yes	complemented
626	#465	C₂²×C₁₃	1	2	yes	complemented
627	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#464	C₂²×C₁₃	1	2	yes	complemented
630	#464	C₂²×C₁₃	1	2	yes	complemented
631	#464	C₂²×C₁₃	1	2	yes	complemented
632	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#461	C₂²×C₁₃	1	2	yes	complemented
635	#461	C₂²×C₁₃	1	2	yes	complemented
636	#460	C₂²×C₁₃	1	1	yes	characteristic
637	#460	C₂²×C₁₃	1	1	yes	characteristic
638	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#460	C₂²×C₁₃	1	2	yes	complemented
640	#460	C₂²×C₁₃	1	2	yes	complemented
641	#460	C₂²×C₁₃	1	2	yes	complemented
642	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#460	C₂²×C₁₃	1	2	yes	complemented
644	#460	C₂²×C₁₃	1	2	yes	complemented
645	#460	C₂²×C₁₃	1	2	yes	complemented
646	#452	C₂²×C₁₃	1	2	yes	complemented
647	#452	C₂²×C₁₃	1	2	yes	complemented
648	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#450	C₂²×C₁₃	1	2	yes	complemented
650	#450	C₂²×C₁₃	1	2	yes	complemented
651	#450	C₂²×C₁₃	1	2	yes	complemented
652	#450	C₂²×C₁₃	1	2	yes	complemented
653	#448	C₂²×C₁₃	1	1	yes	characteristic
654	#448	C₂²×C₁₃	1	2	yes	complemented
655	#448	C₂²×C₁₃	1	2	yes	complemented
656	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	#440	C₂²×C₁₃	1	2	yes	complemented
659	#440	C₂²×C₁₃	1	2	yes	complemented
660	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
665	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
666	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#435	C₂²×C₁₃	1	2	yes	complemented
668	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
669	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#433	C₂²×C₁₃	1	2	yes	complemented
671	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#424	C₂²×C₁₃	1	2	yes	complemented
673	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#418	C₂²×C₁₃	1	2	yes	complemented
675	#416	C₂²×C₁₃	1	2	yes	complemented
676	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
677	C₂²×C₁₃	—	2	1	no	—
678	C₂²×C₁₃	—	2	1	no	—
679	C₂²×C₁₃	—	2	2	no	—
680	C₂²×C₁₃	—	2	2	no	—
681	C₂²×C₁₃	—	2	2	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	4	1	no	—
684	C₂²×C₁₃	—	4	2	no	—
685	C₂²×C₁₃	—	4	1	no	—
686	C₂²×C₁₃	—	4	2	no	—
687	C₂²×C₁₃	—	4	2	no	—
688	C₂²×C₁₃	—	4	1	no	—
689	C₂²×C₁₃	—	4	2	no	—
690	C₂²×C₁₃	—	4	2	no	—
691	C₂²×C₁₃	—	16	4	no	—
692	C₂²×C₁₃	—	16	4	no	—
693	C₂²×C₁₃	#577	1	2	yes	—
694	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
695	C₄×C₁₃	—	2	2	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	no	—
698	C₄×C₁₃	—	2	1	no	—
699	C₄×C₁₃	—	2	1	no	—
700	C₄×C₁₃	—	2	1	no	—
701	C₄×C₁₃	—	2	2	no	—
702	C₄×C₁₃	—	2	2	no	—
703	C₄×C₁₃	—	4	1	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	—	4	1	no	—
709	C₄×C₁₃	—	4	1	no	—
710	C₄×C₁₃	—	4	2	no	—
711	C₄×C₁₃	#577	1	2	yes	—
712	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
713	C₄×C₁₃	#585	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₁₃	1	2	yes	—
716	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
717	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
718	C₂²×D₄	—	2	2	no	—
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	—	2	1	no	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
723	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
724	#137	—	4	4	no	—
725	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×SD₁₆	—	4	4	no	—
729	C₂×SD₁₆	—	4	4	no	—
730	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
741	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
742	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
743	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	2	no	—
747	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
749	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
750	#127	—	2	1	no	—
751	#127	—	2	1	no	—
752	#127	—	2	1	no	—
753	#127	C₂³×C₁₃	1	2	yes	—
754	#127	C₂³×C₁₃	1	1	yes	characteristic
755	#127	C₂³×C₁₃	1	1	yes	characteristic
756	#127	C₂³×C₁₃	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	1	no	—
762	#126	D₄×C₁₃	1	2	yes	—
763	#125	—	2	1	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	2	no	—
769	#125	—	2	1	no	—
770	#125	D₄×C₁₃	1	1	yes	characteristic
771	#125	C₂³×C₁₃	1	1	yes	characteristic
772	#125	C₂³×C₁₃	1	2	yes	—
773	#124	—	2	1	no	—
774	#124	—	2	1	no	—
775	#124	D₄×C₁₃	1	1	yes	characteristic
776	#124	C₂³×C₁₃	1	1	yes	characteristic
777	#124	C₂³×C₁₃	1	2	yes	—
778	#123	—	2	2	no	—
779	#123	—	2	1	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	D₄×C₁₃	1	2	yes	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	D₄×C₁₃	1	1	yes	characteristic
805	#121	C₂³×C₁₃	1	1	yes	characteristic
806	#121	C₂³×C₁₃	1	2	yes	—
807	#121	C₂³×C₁₃	1	2	yes	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	2	no	—
816	C₄×Q₈	—	2	2	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
827	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
829	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₁₃	1	2	yes	—
838	C₄×D₄	C₂³×C₁₃	1	2	yes	—
839	C₄×D₄	C₂³×C₁₃	1	2	yes	—
840	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	—	2	1	no	—
846	#117	C₂³×C₁₃	1	2	yes	—
847	#117	C₂³×C₁₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
853	#107	C₂³×C₁₃	1	1	yes	characteristic
854	#107	C₂³×C₁₃	1	1	yes	characteristic
855	#107	C₂³×C₁₃	1	2	yes	—
856	#106	C₂³×C₁₃	1	1	yes	characteristic
857	#106	C₂³×C₁₃	1	2	yes	—
858	#106	C₂³×C₁₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
864	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
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	#103	C₂³×C₁₃	1	1	yes	characteristic
872	#103	C₂³×C₁₃	1	1	yes	characteristic
873	#103	C₂³×C₁₃	1	1	yes	characteristic
874	#103	C₂³×C₁₃	1	2	yes	—
875	#102	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	1	yes	characteristic
881	#102	C₂³×C₁₃	1	2	yes	—
882	#102	C₂³×C₁₃	1	2	yes	—
883	#102	C₂³×C₁₃	1	2	yes	—
884	#102	C₂³×C₁₃	1	1	yes	characteristic
885	#102	C₂³×C₁₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
890	#97	C₂³×C₁₃	1	2	yes	—
891	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₁₃	1	2	yes	—
894	C₂×C₁₃	—	2	2	no	—
895	C₂×C₁₃	—	4	2	no	—
896	C₂×C₁₃	—	8	2	no	—
897	C₂×C₁₃	—	8	1	no	—
898	C₂×C₁₃	—	8	2	no	—
899	C₂×C₁₃	#3488	1	1	yes	characteristic
900	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
901	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
902	C₂⁴	—	2	2	no	—
903	C₂⁴	—	2	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	8	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	2	4	no	—
912	C₂×Q₈	—	4	1	no	—
913	C₂×Q₈	—	4	2	no	—
914	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	4	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	4	2	no	—
937	C₂×D₄	—	8	2	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	—	8	2	no	—
940	C₂×D₄	—	8	4	no	—
941	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
944	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
957	Q₁₆	—	2	2	no	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	1	no	—
960	SD₁₆	—	2	2	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	1	no	—
969	SD₁₆	—	4	2	no	—
970	SD₁₆	—	4	2	no	—
971	M₁₆	—	4	2	no	—
972	C₂×C₈	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
979	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1003	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1007	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	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	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1043	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₁₃	1	2	yes	—
1046	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1047	C₁₃	#62055	1	1	yes	characteristic, direct product factor, Sylow
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	—	8	2	no	—
1056	C₂³	—	8	2	no	—
1057	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1058	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	4	4	no	—
1068	Q₈	—	4	2	no	—
1069	Q₈	—	4	2	no	—
1070	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1071	D₄	—	2	4	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	4	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1123	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	—	16	4	no	—
1146	C₂²	C₁₃×#577	1	2	yes	—
1147	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	C₁₃×#577	1	2	yes	—
1165	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₁₃×#585	1	1	yes	characteristic
1167	C₂	—	2	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	2	no	—
1172	C₂	C₁₃×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1174	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3543	C₂
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
2. C₁₃×#3523	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3392	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3365	C₂	semidirect
7. C₁₃×#3324	C₂	semidirect
8. C₁₃×#3310	C₂	semidirect
9. C₁₃×#3304	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. D₄×C₁₃×SD₁₆	C₂	semidirect
12. D₄×C₁₃×SD₁₆	C₂	semidirect
13. C₁₃×#3278	C₂	semidirect
14. C₁₃×#3266	C₂	semidirect
15. C₁₃×#3260	C₂	semidirect
16. C₁₃×#3248	C₂	semidirect
17. C₁₃×#3222	C₂	semidirect
18. C₁₃×#3208	C₂	semidirect
19. C₁₃×#3126	C₂	semidirect
20. C₁₃×#3108	C₂	semidirect
21. C₁₃×#3043	C₂	semidirect
22. C₂×C₁₃×#460	C₂	semidirect
23. C₁₃×#2994	C₂	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
25. C₂²×C₁₃×SD₁₆	C₂²	semidirect
26. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₁₃×#557	C₂²	semidirect
31. C₁₃×#557	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
46. C₁₃×#541	C₂²	semidirect
53. C₁₃×#533	C₂²	semidirect
58. C₁₃×#519	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
60. C₁₃×#497	C₂²	semidirect
62. C₁₃×#492	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#488	C₂²	semidirect
67. C₁₃×#486	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#478	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#468	C₂²	semidirect
81. C₁₃×#467	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#464	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#464	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#461	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
96. C₁₃×#460	C₂²	semidirect
97. C₁₃×#460	C₂²	semidirect
98. C₁₃×#460	C₂²	semidirect
99. C₁₃×#460	C₂²	semidirect
100. C₁₃×#460	C₂²	semidirect
101. C₁₃×#460	C₂²	semidirect
102. C₁₃×#460	C₂²	semidirect
103. C₁₃×#460	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#451	C₂²	semidirect
107. C₁₃×#450	C₂²	semidirect
108. C₁₃×#450	C₂²	semidirect
109. C₁₃×#450	C₂²	semidirect
110. C₁₃×#450	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#448	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₁₃×#440	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
119. C₄×C₁₃×Q₁₆	C₂²	semidirect
120. C₄×C₁₃×SD₁₆	C₂²	semidirect
121. C₄×C₁₃×SD₁₆	C₂²	semidirect
122. C₄×C₁₃×SD₁₆	C₂²	semidirect
123. C₄×C₁₃×SD₁₆	C₂²	semidirect
124. C₁₃×#436	C₂²	semidirect
125. C₁₃×#435	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₈×D₄×C₁₃	C₂²	semidirect
128. C₁₃×#433	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#424	C₂²	semidirect
131. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
132. C₁₃×#418	C₂²	semidirect
133. C₁₃×#416	C₂²	semidirect
134. C₂×C₁₃×#102	C₂²	semidirect
315. #62055	C₁₃	direct (N × H)
462. #3523	C₂×C₁₃	semidirect
463. #3400	C₂×C₁₃	semidirect
464. #3392	C₂×C₁₃	semidirect
465. #3368	C₂×C₁₃	semidirect
466. #3365	C₂×C₁₃	semidirect
467. #3324	C₂×C₁₃	semidirect
468. #3310	C₂×C₁₃	semidirect
469. #3304	C₂×C₁₃	semidirect
470. #3296	C₂×C₁₃	semidirect
471. D₄×SD₁₆	C₂×C₁₃	semidirect
472. D₄×SD₁₆	C₂×C₁₃	semidirect
473. #3278	C₂×C₁₃	semidirect
474. #3266	C₂×C₁₃	semidirect
475. #3260	C₂×C₁₃	semidirect
476. #3248	C₂×C₁₃	semidirect
477. #3222	C₂×C₁₃	semidirect
478. #3208	C₂×C₁₃	semidirect
479. #3126	C₂×C₁₃	semidirect
480. #3108	C₂×C₁₃	semidirect
481. #3043	C₂×C₁₃	semidirect
482. C₂×#460	C₂×C₁₃	semidirect
483. #2994	C₂×C₁₃	semidirect
566. C₂×#137	C₂²×C₁₃	semidirect
567. C₂²×SD₁₆	C₂²×C₁₃	semidirect
568. C₂²×SD₁₆	C₂²×C₁₃	semidirect
572. #557	C₂²×C₁₃	semidirect
573. #557	C₂²×C₁₃	semidirect
575. #556	C₂²×C₁₃	semidirect
577. #552	C₂²×C₁₃	semidirect
580. D₄×Q₈	C₂²×C₁₃	semidirect
581. D₄×Q₈	C₂²×C₁₃	semidirect
588. #541	C₂²×C₁₃	semidirect
595. #533	C₂²×C₁₃	semidirect
600. #519	C₂²×C₁₃	semidirect
601. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
602. #497	C₂²×C₁₃	semidirect
604. #492	C₂²×C₁₃	semidirect
605. #492	C₂²×C₁₃	semidirect
606. #490	C₂²×C₁₃	semidirect
607. #488	C₂²×C₁₃	semidirect
609. #486	C₂²×C₁₃	semidirect
610. #483	C₂²×C₁₃	semidirect
611. #482	C₂²×C₁₃	semidirect
612. #482	C₂²×C₁₃	semidirect
614. #479	C₂²×C₁₃	semidirect
615. #479	C₂²×C₁₃	semidirect
616. #479	C₂²×C₁₃	semidirect
617. #478	C₂²×C₁₃	semidirect
618. #478	C₂²×C₁₃	semidirect
619. #475	C₂²×C₁₃	semidirect
620. #474	C₂²×C₁₃	semidirect
621. #468	C₂²×C₁₃	semidirect
622. #468	C₂²×C₁₃	semidirect
623. #467	C₂²×C₁₃	semidirect
625. #465	C₂²×C₁₃	semidirect
626. #465	C₂²×C₁₃	semidirect
627. #464	C₂²×C₁₃	semidirect
628. #464	C₂²×C₁₃	semidirect
629. #464	C₂²×C₁₃	semidirect
630. #464	C₂²×C₁₃	semidirect
631. #464	C₂²×C₁₃	semidirect
632. #462	C₂²×C₁₃	semidirect
633. #461	C₂²×C₁₃	semidirect
634. #461	C₂²×C₁₃	semidirect
635. #461	C₂²×C₁₃	semidirect
638. #460	C₂²×C₁₃	semidirect
639. #460	C₂²×C₁₃	semidirect
640. #460	C₂²×C₁₃	semidirect
641. #460	C₂²×C₁₃	semidirect
642. #460	C₂²×C₁₃	semidirect
643. #460	C₂²×C₁₃	semidirect
644. #460	C₂²×C₁₃	semidirect
645. #460	C₂²×C₁₃	semidirect
646. #452	C₂²×C₁₃	semidirect
647. #452	C₂²×C₁₃	semidirect
648. #451	C₂²×C₁₃	semidirect
649. #450	C₂²×C₁₃	semidirect
650. #450	C₂²×C₁₃	semidirect
651. #450	C₂²×C₁₃	semidirect
652. #450	C₂²×C₁₃	semidirect
654. #448	C₂²×C₁₃	semidirect
655. #448	C₂²×C₁₃	semidirect
656. #446	C₂²×C₁₃	semidirect
657. C₈×Q₈	C₂²×C₁₃	semidirect
658. #440	C₂²×C₁₃	semidirect
659. #440	C₂²×C₁₃	semidirect
660. C₄×Q₁₆	C₂²×C₁₃	semidirect
661. C₄×Q₁₆	C₂²×C₁₃	semidirect
662. C₄×SD₁₆	C₂²×C₁₃	semidirect
663. C₄×SD₁₆	C₂²×C₁₃	semidirect
664. C₄×SD₁₆	C₂²×C₁₃	semidirect
665. C₄×SD₁₆	C₂²×C₁₃	semidirect
666. #436	C₂²×C₁₃	semidirect
667. #435	C₂²×C₁₃	semidirect
668. C₈×D₄	C₂²×C₁₃	semidirect
669. C₈×D₄	C₂²×C₁₃	semidirect
670. #433	C₂²×C₁₃	semidirect
671. #431	C₂²×C₁₃	semidirect
672. #424	C₂²×C₁₃	semidirect
673. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
674. #418	C₂²×C₁₃	semidirect
675. #416	C₂²×C₁₃	semidirect
676. C₂×#102	C₂²×C₁₃	semidirect
1047. C₁₃	#62055	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×#3523	2
C₁₃×#3400	2
C₁₃×#3392	2
C₁₃×#3368	2
C₁₃×#3365	2
C₁₃×#3324	2
C₁₃×#3310	2
C₁₃×#3304	2
C₁₃×#3296	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3278	2
C₁₃×#3266	2
C₁₃×#3260	2
C₁₃×#3248	2
C₁₃×#3222	2
C₁₃×#3208	2
C₁₃×#3126	2
C₁₃×#3108	2
C₁₃×#3043	2
C₂×C₁₃×#460	2
C₁₃×#2994	2
#62055	13

Subgroups — C13×#62055 #15748394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62055 #15748394