Subgroups — C₁₃×#62071 #15748410

Order 3328.

1844 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×#3546	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×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
12	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3263	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3035	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	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
27	C₁₃×#560	—	2	2	no	—
28	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	—	2	2	no	—
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic
32	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#556	C₂²	1	2	yes	complemented
34	C₁₃×#555	—	2	1	no	—
35	C₁₃×#555	C₂²	1	1	yes	characteristic
36	C₁₃×#553	—	2	1	no	—
37	C₁₃×#550	C₂²	1	2	yes	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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×#542	—	2	2	no	—
46	C₁₃×#542	C₂²	1	2	yes	—
47	C₁₃×#542	C₂²	1	2	yes	complemented
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	—	2	1	no	—
50	C₁₃×#535	—	2	1	no	—
51	C₁₃×#535	C₂²	1	2	yes	—
52	C₁₃×#533	—	2	1	no	—
53	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#532	C₂²	1	1	yes	characteristic
55	C₁₃×#532	C₂²	1	1	yes	characteristic
56	C₁₃×#529	—	2	1	no	—
57	C₁₃×#529	C₂²	1	1	yes	characteristic
58	C₁₃×#519	C₂²	1	2	yes	complemented
59	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#496	C₂²	1	2	yes	complemented
61	C₁₃×#495	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#489	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#486	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	1	yes	characteristic
71	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#476	C₂²	1	1	yes	characteristic
74	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#476	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#475	C₂²	1	2	yes	complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	—
81	C₁₃×#465	C₂²	1	2	yes	—
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	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#464	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#463	C₂²	1	2	yes	complemented
93	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#461	C₂²	1	1	yes	characteristic
95	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#460	C₂²	1	1	yes	characteristic
98	C₁₃×#460	C₂²	1	1	yes	characteristic
99	C₁₃×#460	C₂²	1	2	yes	—
100	C₁₃×#460	C₂²	1	2	yes	complemented
101	C₁₃×#460	C₂²	1	2	yes	complemented
102	C₁₃×#459	C₂²	1	1	yes	characteristic
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#452	C₂²	1	2	yes	complemented
107	C₁₃×#451	C₂²	1	2	yes	complemented
108	C₁₃×#450	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	1	yes	characteristic
110	C₁₃×#449	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#449	C₂²	1	2	yes	complemented
112	C₁₃×#448	C₂²	1	2	yes	—
113	C₁₃×#447	C₂²	1	2	yes	—
114	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#441	C₂²	1	2	yes	complemented
117	C₁₃×#440	C₂²	1	2	yes	complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
123	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#436	C₂²	1	1	yes	characteristic
125	C₁₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₁₃	C₂²	1	2	yes	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	—
133	C₁₃×#416	C₂²	1	2	yes	complemented
134	C₁₃×#416	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂×C₁₃×#41	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×#135	—	4	4	no	—
145	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
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	1	yes	characteristic
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
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	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	—	2	1	no	—
164	C₁₃×C₄⋊Q₈	—	2	1	no	—
165	C₁₃×C₄⋊Q₈	—	2	2	no	—
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₁₃×#127	—	2	2	no	—
172	C₁₃×#127	C₂³	1	1	yes	characteristic
173	C₁₃×#127	C₂³	1	1	yes	characteristic
174	C₁₃×#127	C₂³	1	2	yes	—
175	C₁₃×#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	2	no	—
180	C₁₃×#126	—	2	2	no	—
181	C₁₃×#126	D₄	1	2	yes	—
182	C₁₃×#125	—	2	1	no	—
183	C₁₃×#125	D₄	1	1	yes	characteristic
184	C₁₃×#124	—	2	2	no	—
185	C₁₃×#124	—	2	2	no	—
186	C₁₃×#124	—	2	2	no	—
187	C₁₃×#124	—	2	2	no	—
188	C₁₃×#124	—	2	2	no	—
189	C₁₃×#124	—	2	1	no	—
190	C₁₃×#124	D₄	1	1	yes	characteristic
191	C₁₃×#124	C₂³	1	2	yes	—
192	C₁₃×#124	C₂³	1	2	yes	—
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	D₄	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	1	no	—
201	C₁₃×C₂²⋊Q₈	—	2	1	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	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	D₄	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	1	yes	characteristic
228	C₁₃×#121	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	2	no	—
235	C₄×Q₈×C₁₃	—	2	2	no	—
236	C₄×Q₈×C₁₃	—	2	2	no	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	2	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	—	2	2	no	—
265	C₁₃×#117	—	2	2	no	—
266	C₁₃×#117	—	2	1	no	—
267	C₁₃×#117	C₂³	1	1	yes	characteristic
268	C₁₃×#117	C₂³	1	2	yes	—
269	C₁₃×#117	C₂³	1	2	yes	—
270	C₂×C₁₃×C₄⋊C₄	—	2	1	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×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	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	1	yes	characteristic
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
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	#62071	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	—	4	2	no	—
322	C₁₃×#41	—	4	2	no	—
323	C₁₃×#41	—	8	2	no	—
324	C₁₃×#41	—	8	2	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	2	1	no	—
327	C₂×Q₈×C₁₃	—	2	2	no	—
328	C₂×Q₈×C₁₃	—	2	1	no	—
329	C₂×Q₈×C₁₃	—	2	4	no	—
330	C₂×Q₈×C₁₃	—	4	2	no	—
331	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	2	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	1	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	1	no	—
347	C₂×D₄×C₁₃	—	2	2	no	—
348	C₂×D₄×C₁₃	—	2	2	no	—
349	C₂×D₄×C₁₃	—	4	2	no	—
350	C₂×D₄×C₁₃	—	4	2	no	—
351	C₂×D₄×C₁₃	—	8	2	no	—
352	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
356	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	1	no	—
360	C₂²×C₄×C₁₃	—	2	1	no	—
361	C₂²×C₄×C₁₃	—	2	1	no	—
362	C₂²×C₄×C₁₃	—	2	1	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	4	no	—
372	C₁₃×Q₁₆	—	4	2	no	—
373	C₁₃×Q₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	2	2	no	—
375	C₁₃×SD₁₆	—	2	4	no	—
376	C₁₃×SD₁₆	—	2	2	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	2	no	—
382	C₁₃×D₈	—	4	1	no	—
383	C₁₃×D₈	—	4	1	no	—
384	C₁₃×D₈	—	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	2	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	1	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	2	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	2	yes	—
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	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	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	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	1	no	—
439	C₁₃×C₂²⋊C₄	—	2	2	no	—
440	C₁₃×C₂²⋊C₄	—	2	1	no	—
441	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²×C₁₃	—	2	1	no	—
447	C₄²×C₁₃	—	2	1	no	—
448	C₄²×C₁₃	—	2	1	no	—
449	C₄²×C₁₃	—	2	2	no	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	2	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	#3546	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3311	C₂×C₁₃	1	2	yes	complemented
467	#3304	C₂×C₁₃	1	2	yes	complemented
468	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3282	C₂×C₁₃	1	2	yes	complemented
470	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3271	C₂×C₁₃	1	2	yes	complemented
473	#3263	C₂×C₁₃	1	2	yes	complemented
474	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3224	C₂×C₁₃	1	2	yes	complemented
476	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3121	C₂×C₁₃	1	2	yes	complemented
478	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3043	C₂×C₁₃	1	2	yes	complemented
480	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#2994	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	—	2	1	no	—
486	C₂³×C₁₃	—	8	2	no	—
487	C₂³×C₁₃	—	8	2	no	—
488	C₂³×C₁₃	—	8	2	no	—
489	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
490	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
491	Q₈×C₁₃	—	2	2	no	—
492	Q₈×C₁₃	—	2	1	no	—
493	Q₈×C₁₃	—	2	2	no	—
494	Q₈×C₁₃	—	2	2	no	—
495	Q₈×C₁₃	—	2	2	no	—
496	Q₈×C₁₃	—	2	2	no	—
497	Q₈×C₁₃	—	4	4	no	—
498	Q₈×C₁₃	—	8	1	no	—
499	Q₈×C₁₃	—	8	2	no	—
500	Q₈×C₁₃	—	8	1	no	—
501	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
502	D₄×C₁₃	—	2	2	no	—
503	D₄×C₁₃	—	2	1	no	—
504	D₄×C₁₃	—	2	2	no	—
505	D₄×C₁₃	—	2	1	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	2	1	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	2	2	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	1	no	—
516	D₄×C₁₃	—	8	2	no	—
517	D₄×C₁₃	—	8	2	no	—
518	D₄×C₁₃	—	8	1	no	—
519	D₄×C₁₃	—	8	2	no	—
520	D₄×C₁₃	—	8	2	no	—
521	D₄×C₁₃	—	8	2	no	—
522	D₄×C₁₃	—	8	2	no	—
523	D₄×C₁₃	—	8	2	no	—
524	D₄×C₁₃	—	8	1	no	—
525	D₄×C₁₃	—	8	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	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	2	2	no	—
534	C₂×C₄×C₁₃	—	2	2	no	—
535	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
540	C₂×C₄×C₁₃	—	4	2	no	—
541	C₂×C₄×C₁₃	—	4	4	no	—
542	C₂×C₄×C₁₃	—	4	2	no	—
543	C₂×C₄×C₁₃	—	4	2	no	—
544	C₂×C₄×C₁₃	—	4	2	no	—
545	C₂×C₄×C₁₃	—	8	1	no	—
546	C₂×C₄×C₁₃	—	8	2	no	—
547	C₂×C₄×C₁₃	—	8	2	no	—
548	C₂×C₄×C₁₃	—	8	2	no	—
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	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	1	yes	characteristic
556	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
558	C₈×C₁₃	—	2	1	no	—
559	C₈×C₁₃	—	2	2	no	—
560	C₈×C₁₃	—	2	2	no	—
561	C₈×C₁₃	—	2	1	no	—
562	C₈×C₁₃	—	2	1	no	—
563	C₈×C₁₃	—	2	1	no	—
564	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
565	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
566	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
567	#560	—	2	2	no	—
568	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
569	#556	—	2	2	no	—
570	#556	—	2	1	no	—
571	#556	C₂²×C₁₃	1	1	yes	characteristic
572	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	#556	C₂²×C₁₃	1	2	yes	complemented
574	#555	—	2	1	no	—
575	#555	C₂²×C₁₃	1	1	yes	characteristic
576	#553	—	2	1	no	—
577	#550	C₂²×C₁₃	1	2	yes	—
578	#550	C₂²×C₁₃	1	1	yes	characteristic
579	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
580	#548	C₂²×C₁₃	1	2	yes	complemented
581	#547	C₂²×C₁₃	1	1	yes	characteristic
582	#546	—	2	1	no	—
583	#546	C₂²×C₁₃	1	2	yes	—
584	D₄²	C₂²×C₁₃	1	1	yes	characteristic
585	#542	—	2	2	no	—
586	#542	C₂²×C₁₃	1	2	yes	—
587	#542	C₂²×C₁₃	1	2	yes	complemented
588	#538	—	2	2	no	—
589	#537	—	2	1	no	—
590	#535	—	2	1	no	—
591	#535	C₂²×C₁₃	1	2	yes	—
592	#533	—	2	1	no	—
593	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#532	C₂²×C₁₃	1	1	yes	characteristic
595	#532	C₂²×C₁₃	1	1	yes	characteristic
596	#529	—	2	1	no	—
597	#529	C₂²×C₁₃	1	1	yes	characteristic
598	#519	C₂²×C₁₃	1	2	yes	complemented
599	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	#496	C₂²×C₁₃	1	2	yes	complemented
601	#495	C₂²×C₁₃	1	2	yes	—
602	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
603	#492	C₂²×C₁₃	1	1	yes	characteristic
604	#489	C₂²×C₁₃	1	2	yes	—
605	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#486	C₂²×C₁₃	1	1	yes	characteristic
607	#486	C₂²×C₁₃	1	2	yes	complemented
608	#485	C₂²×C₁₃	1	2	yes	complemented
609	#482	C₂²×C₁₃	1	1	yes	characteristic
610	#482	C₂²×C₁₃	1	2	yes	—
611	#482	C₂²×C₁₃	1	1	yes	characteristic, 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	#475	C₂²×C₁₃	1	2	yes	complemented
618	#475	C₂²×C₁₃	1	2	yes	complemented
619	#470	C₂²×C₁₃	1	2	yes	complemented
620	#469	C₂²×C₁₃	1	2	yes	—
621	#465	C₂²×C₁₃	1	2	yes	—
622	#465	C₂²×C₁₃	1	2	yes	—
623	#465	C₂²×C₁₃	1	2	yes	complemented
624	#465	C₂²×C₁₃	1	2	yes	complemented
625	#464	C₂²×C₁₃	1	2	yes	—
626	#464	C₂²×C₁₃	1	2	yes	—
627	#464	C₂²×C₁₃	1	2	yes	complemented
628	#464	C₂²×C₁₃	1	2	yes	complemented
629	#464	C₂²×C₁₃	1	2	yes	complemented
630	#464	C₂²×C₁₃	1	2	yes	complemented
631	#463	C₂²×C₁₃	1	2	yes	complemented
632	#463	C₂²×C₁₃	1	2	yes	complemented
633	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#461	C₂²×C₁₃	1	1	yes	characteristic
635	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#460	C₂²×C₁₃	1	1	yes	characteristic
638	#460	C₂²×C₁₃	1	1	yes	characteristic
639	#460	C₂²×C₁₃	1	2	yes	—
640	#460	C₂²×C₁₃	1	2	yes	complemented
641	#460	C₂²×C₁₃	1	2	yes	complemented
642	#459	C₂²×C₁₃	1	1	yes	characteristic
643	#459	C₂²×C₁₃	1	1	yes	characteristic
644	#452	C₂²×C₁₃	1	2	yes	complemented
645	#452	C₂²×C₁₃	1	2	yes	complemented
646	#452	C₂²×C₁₃	1	2	yes	complemented
647	#451	C₂²×C₁₃	1	2	yes	complemented
648	#450	C₂²×C₁₃	1	2	yes	—
649	#449	C₂²×C₁₃	1	1	yes	characteristic
650	#449	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#449	C₂²×C₁₃	1	2	yes	complemented
652	#448	C₂²×C₁₃	1	2	yes	—
653	#447	C₂²×C₁₃	1	2	yes	—
654	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#441	C₂²×C₁₃	1	2	yes	complemented
657	#440	C₂²×C₁₃	1	2	yes	complemented
658	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
659	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
660	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
662	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
663	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	#436	C₂²×C₁₃	1	1	yes	characteristic
665	#435	C₂²×C₁₃	1	2	yes	complemented
666	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
667	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
668	#433	C₂²×C₁₃	1	2	yes	complemented
669	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#424	C₂²×C₁₃	1	2	yes	complemented
671	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#418	C₂²×C₁₃	1	2	yes	—
673	#416	C₂²×C₁₃	1	2	yes	complemented
674	#416	C₂²×C₁₃	1	2	yes	complemented
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	2	2	no	—
678	C₂²×C₁₃	—	2	1	no	—
679	C₂²×C₁₃	—	2	1	no	—
680	C₂²×C₁₃	—	2	2	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	1	no	—
683	C₂²×C₁₃	—	4	2	no	—
684	C₂²×C₁₃	—	4	1	no	—
685	C₂²×C₁₃	—	4	1	no	—
686	C₂²×C₁₃	—	4	1	no	—
687	C₂²×C₁₃	—	4	2	no	—
688	C₂²×C₁₃	—	4	1	no	—
689	C₂²×C₁₃	—	4	1	no	—
690	C₂²×C₁₃	—	4	1	no	—
691	C₂²×C₁₃	—	4	1	no	—
692	C₂²×C₁₃	—	4	2	no	—
693	C₂²×C₁₃	—	16	4	no	—
694	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
695	C₄×C₁₃	—	2	1	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	no	—
698	C₄×C₁₃	—	2	1	no	—
699	C₄×C₁₃	—	2	2	no	—
700	C₄×C₁₃	—	2	2	no	—
701	C₄×C₁₃	—	2	1	no	—
702	C₄×C₁₃	—	2	2	no	—
703	C₄×C₁₃	—	4	1	no	—
704	C₄×C₁₃	—	4	2	no	—
705	C₄×C₁₃	—	4	2	no	—
706	C₄×C₁₃	—	4	2	no	—
707	C₄×C₁₃	—	4	1	no	—
708	C₄×C₁₃	—	4	1	no	—
709	C₄×C₁₃	—	4	1	no	—
710	C₄×C₁₃	#577	1	2	yes	—
711	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
712	C₄×C₁₃	#585	1	1	yes	characteristic
713	C₂×#41	—	2	1	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×#41	C₂³×C₁₃	1	2	yes	—
717	C₂×#41	C₂³×C₁₃	1	2	yes	—
718	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
721	#137	—	4	4	no	—
722	#135	—	4	4	no	—
723	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
724	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂×SD₁₆	—	4	4	no	—
727	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
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×D₈	C₂³×C₁₃	1	2	yes	—
736	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
739	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
740	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	2	no	—
744	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
749	#127	—	2	2	no	—
750	#127	C₂³×C₁₃	1	1	yes	characteristic
751	#127	C₂³×C₁₃	1	1	yes	characteristic
752	#127	C₂³×C₁₃	1	2	yes	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	D₄×C₁₃	1	2	yes	—
760	#125	—	2	1	no	—
761	#125	D₄×C₁₃	1	1	yes	characteristic
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	1	no	—
768	#124	D₄×C₁₃	1	1	yes	characteristic
769	#124	C₂³×C₁₃	1	2	yes	—
770	#124	C₂³×C₁₃	1	2	yes	—
771	#124	C₂³×C₁₃	1	2	yes	—
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	1	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	D₄×C₁₃	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	D₄×C₁₃	1	1	yes	characteristic
803	#121	C₂³×C₁₃	1	1	yes	characteristic
804	#121	C₂³×C₁₃	1	1	yes	characteristic
805	#121	C₂³×C₁₃	1	2	yes	—
806	#121	C₂³×C₁₃	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	2	no	—
813	C₄×Q₈	—	2	2	no	—
814	C₄×Q₈	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
819	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
820	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
821	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
822	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₁₃	1	2	yes	—
836	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₁₃	1	2	yes	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	—	2	2	no	—
844	#117	—	2	1	no	—
845	#117	C₂³×C₁₃	1	1	yes	characteristic
846	#117	C₂³×C₁₃	1	2	yes	—
847	#117	C₂³×C₁₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
852	#107	C₂³×C₁₃	1	1	yes	characteristic
853	#107	C₂³×C₁₃	1	1	yes	characteristic
854	#106	C₂³×C₁₃	1	1	yes	characteristic
855	#106	C₂³×C₁₃	1	2	yes	—
856	#106	C₂³×C₁₃	1	1	yes	characteristic
857	#106	C₂³×C₁₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
864	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
865	#103	C₂³×C₁₃	1	2	yes	—
866	#103	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
872	#103	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	1	yes	characteristic
874	#102	C₂³×C₁₃	1	2	yes	—
875	#102	C₂³×C₁₃	1	2	yes	—
876	#102	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
882	#102	C₂³×C₁₃	1	1	yes	characteristic
883	#102	C₂³×C₁₃	1	2	yes	—
884	#102	C₂³×C₁₃	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
889	#97	C₂³×C₁₃	1	2	yes	—
890	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₁₃	1	2	yes	—
893	C₂×C₁₃	—	4	1	no	—
894	C₂×C₁₃	—	4	2	no	—
895	C₂×C₁₃	—	8	1	no	—
896	C₂×C₁₃	—	8	1	no	—
897	C₂×C₁₃	—	8	2	no	—
898	C₂×C₁₃	—	8	1	no	—
899	C₂×C₁₃	#3488	1	1	yes	characteristic
900	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
901	C₂×C₁₃	#3584	1	1	yes	characteristic
902	C₂⁴	—	2	2	no	—
903	#41	—	2	2	no	—
904	#41	—	4	1	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	2	4	no	—
916	C₂×Q₈	—	4	2	no	—
917	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
919	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
920	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	4	2	no	—
936	C₂×D₄	—	4	2	no	—
937	C₂×D₄	—	8	2	no	—
938	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
942	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
943	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	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	4	no	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	SD₁₆	—	2	2	no	—
961	SD₁₆	—	2	4	no	—
962	SD₁₆	—	2	2	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	D₈	—	4	2	no	—
969	D₈	—	4	1	no	—
970	D₈	—	4	1	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	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	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	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1041	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₁₃	1	2	yes	—
1044	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1045	C₁₃	#62071	1	1	yes	characteristic, direct product factor, Sylow
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1054	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	4	4	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	—	8	1	no	—
1064	Q₈	—	8	2	no	—
1065	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	1	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	1	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	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	16	4	no	—
1147	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	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	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	C₁₃×#577	1	2	yes	—
1164	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₁₃×#585	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₁₃×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1174	C₂	C₁₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3546	C₂	semidirect
2. C₁₃×#3518	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3393	C₂	semidirect
5. C₁₃×#3369	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3311	C₂	semidirect
9. C₁₃×#3304	C₂	semidirect
10. C₁₃×#3303	C₂	semidirect
11. C₁₃×#3282	C₂	semidirect
12. D₄×C₁₃×SD₁₆	C₂	semidirect
13. C₁₃×#3276	C₂	semidirect
14. C₁₃×#3271	C₂	semidirect
15. C₁₃×#3263	C₂	semidirect
16. C₁₃×#3246	C₂	semidirect
17. C₁₃×#3224	C₂	semidirect
18. C₁₃×#3210	C₂	semidirect
19. C₁₃×#3121	C₂	semidirect
20. C₁₃×#3106	C₂	semidirect
21. C₁₃×#3043	C₂	semidirect
22. C₁₃×#3035	C₂	semidirect
23. C₁₃×#2994	C₂	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
28. Q₈²×C₁₃	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
47. C₁₃×#542	C₂²	semidirect
53. C₁₃×#533	C₂²	semidirect
58. C₁₃×#519	C₂²	semidirect
59. C₄×C₁₃×#41	C₂²	semidirect
60. C₁₃×#496	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
67. C₁₃×#486	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#477	C₂²	semidirect
74. C₁₃×#476	C₂²	semidirect
75. C₁₃×#476	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#464	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#463	C₂²	semidirect
93. C₁₃×#462	C₂²	semidirect
95. C₁₃×#461	C₂²	semidirect
96. C₁₃×#461	C₂²	semidirect
100. C₁₃×#460	C₂²	semidirect
101. C₁₃×#460	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#452	C₂²	semidirect
107. C₁₃×#451	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#449	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₁₃×#441	C₂²	semidirect
117. C₁₃×#440	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
120. C₄×C₁₃×SD₁₆	C₂²	semidirect
121. C₄×C₁₃×SD₁₆	C₂²	semidirect
123. C₄×C₁₃×D₈	C₂²	semidirect
125. C₁₃×#435	C₂²	semidirect
127. C₈×D₄×C₁₃	C₂²	semidirect
128. C₁₃×#433	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#424	C₂²	semidirect
131. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
133. C₁₃×#416	C₂²	semidirect
134. C₁₃×#416	C₂²	semidirect
315. #62071	C₁₃	direct (N × H)
459. #3546	C₂×C₁₃	semidirect
460. #3518	C₂×C₁₃	semidirect
461. #3397	C₂×C₁₃	semidirect
462. #3393	C₂×C₁₃	semidirect
463. #3369	C₂×C₁₃	semidirect
464. #3362	C₂×C₁₃	semidirect
465. #3325	C₂×C₁₃	semidirect
466. #3311	C₂×C₁₃	semidirect
467. #3304	C₂×C₁₃	semidirect
468. #3303	C₂×C₁₃	semidirect
469. #3282	C₂×C₁₃	semidirect
470. D₄×SD₁₆	C₂×C₁₃	semidirect
471. #3276	C₂×C₁₃	semidirect
472. #3271	C₂×C₁₃	semidirect
473. #3263	C₂×C₁₃	semidirect
474. #3246	C₂×C₁₃	semidirect
475. #3224	C₂×C₁₃	semidirect
476. #3210	C₂×C₁₃	semidirect
477. #3121	C₂×C₁₃	semidirect
478. #3106	C₂×C₁₃	semidirect
479. #3043	C₂×C₁₃	semidirect
480. #3035	C₂×C₁₃	semidirect
481. #2994	C₂×C₁₃	semidirect
564. C₂×#137	C₂²×C₁₃	semidirect
565. C₂×#135	C₂²×C₁₃	semidirect
568. Q₈²	C₂²×C₁₃	semidirect
572. #556	C₂²×C₁₃	semidirect
573. #556	C₂²×C₁₃	semidirect
580. #548	C₂²×C₁₃	semidirect
587. #542	C₂²×C₁₃	semidirect
593. #533	C₂²×C₁₃	semidirect
598. #519	C₂²×C₁₃	semidirect
599. C₄×#41	C₂²×C₁₃	semidirect
600. #496	C₂²×C₁₃	semidirect
602. #494	C₂²×C₁₃	semidirect
605. #487	C₂²×C₁₃	semidirect
607. #486	C₂²×C₁₃	semidirect
608. #485	C₂²×C₁₃	semidirect
611. #482	C₂²×C₁₃	semidirect
612. #477	C₂²×C₁₃	semidirect
614. #476	C₂²×C₁₃	semidirect
615. #476	C₂²×C₁₃	semidirect
616. #476	C₂²×C₁₃	semidirect
617. #475	C₂²×C₁₃	semidirect
618. #475	C₂²×C₁₃	semidirect
619. #470	C₂²×C₁₃	semidirect
623. #465	C₂²×C₁₃	semidirect
624. #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. #463	C₂²×C₁₃	semidirect
632. #463	C₂²×C₁₃	semidirect
633. #462	C₂²×C₁₃	semidirect
635. #461	C₂²×C₁₃	semidirect
636. #461	C₂²×C₁₃	semidirect
640. #460	C₂²×C₁₃	semidirect
641. #460	C₂²×C₁₃	semidirect
644. #452	C₂²×C₁₃	semidirect
645. #452	C₂²×C₁₃	semidirect
646. #452	C₂²×C₁₃	semidirect
647. #451	C₂²×C₁₃	semidirect
650. #449	C₂²×C₁₃	semidirect
651. #449	C₂²×C₁₃	semidirect
654. #446	C₂²×C₁₃	semidirect
655. C₈×Q₈	C₂²×C₁₃	semidirect
656. #441	C₂²×C₁₃	semidirect
657. #440	C₂²×C₁₃	semidirect
658. C₄×Q₁₆	C₂²×C₁₃	semidirect
660. C₄×SD₁₆	C₂²×C₁₃	semidirect
661. C₄×SD₁₆	C₂²×C₁₃	semidirect
663. C₄×D₈	C₂²×C₁₃	semidirect
665. #435	C₂²×C₁₃	semidirect
667. C₈×D₄	C₂²×C₁₃	semidirect
668. #433	C₂²×C₁₃	semidirect
669. #431	C₂²×C₁₃	semidirect
670. #424	C₂²×C₁₃	semidirect
671. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
673. #416	C₂²×C₁₃	semidirect
674. #416	C₂²×C₁₃	semidirect
1045. C₁₃	#62071	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3546	2
C₁₃×#3518	2
C₁₃×#3397	2
C₁₃×#3393	2
C₁₃×#3369	2
C₁₃×#3362	2
C₁₃×#3325	2
C₁₃×#3311	2
C₁₃×#3304	2
C₁₃×#3303	2
C₁₃×#3282	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3276	2
C₁₃×#3271	2
C₁₃×#3263	2
C₁₃×#3246	2
C₁₃×#3224	2
C₁₃×#3210	2
C₁₃×#3121	2
C₁₃×#3106	2
C₁₃×#3043	2
C₁₃×#3035	2
C₁₃×#2994	2
#62071	13

Subgroups — C13×#62071 #15748410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62071 #15748410