Subgroups — C₁₃×#61688 #15748027

Order 3328.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1282 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×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3318	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3268	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3199	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
29	C₁₃×#560	—	2	2	no	—
30	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#553	C₂²	1	2	yes	complemented
32	C₁₃×#550	—	2	1	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic
34	C₁₃×#550	C₂²	1	2	yes	complemented
35	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	C₂²	1	2	yes	complemented
40	D₄²×C₁₃	—	2	1	no	—
41	D₄²×C₁₃	—	2	2	no	—
42	D₄²×C₁₃	—	2	1	no	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	D₄²×C₁₃	C₂²	1	2	yes	complemented
45	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#542	—	2	1	no	—
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	C₂²	1	2	yes	complemented
50	C₁₃×#535	—	2	1	no	—
51	C₁₃×#535	—	2	2	no	—
52	C₁₃×#535	C₂²	1	2	yes	complemented
53	C₁₃×#535	C₂²	1	2	yes	complemented
54	C₁₃×#532	—	2	1	no	—
55	C₁₃×#532	C₂²	1	1	yes	characteristic
56	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#127	—	2	1	no	—
58	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#496	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#490	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#482	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#469	C₂²	1	2	yes	complemented
79	C₁₃×#469	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#466	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	complemented
84	C₁₃×#466	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#459	C₂²	1	2	yes	complemented
92	C₁₃×#459	C₂²	1	2	yes	complemented
93	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#452	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#452	C₂²	1	2	yes	complemented
98	C₁₃×#450	C₂²	1	2	yes	complemented
99	C₁₃×#450	C₂²	1	2	yes	complemented
100	C₁₃×#449	C₂²	1	1	yes	characteristic
101	C₁₃×#449	C₂²	1	2	yes	complemented
102	C₁₃×#449	C₂²	1	2	yes	complemented
103	C₁₃×#449	C₂²	1	2	yes	complemented
104	C₁₃×#449	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	complemented
106	C₁₃×#449	C₂²	1	2	yes	complemented
107	C₁₃×#447	C₂²	1	2	yes	complemented
108	C₁₃×#447	C₂²	1	2	yes	complemented
109	C₁₃×#447	C₂²	1	2	yes	complemented
110	C₁₃×#447	C₂²	1	2	yes	complemented
111	C₁₃×#447	C₂²	1	2	yes	complemented
112	C₁₃×#447	C₂²	1	2	yes	complemented
113	C₁₃×#447	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₁₃×#442	C₂²	1	2	yes	complemented
116	C₁₃×#440	C₂²	1	2	yes	complemented
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₁₃×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#418	C₂²	1	2	yes	complemented
130	C₁₃×#417	C₂²	1	2	yes	complemented
131	C₁₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₁₃×#408	C₂²	1	2	yes	complemented
134	C₁₃×#408	C₂²	1	2	yes	complemented
135	C₁₃×H(5,𝔽₂)	—	4	4	no	—
136	C₁₃×H(5,𝔽₂)	—	4	4	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	2	yes	—
143	C₂×C₁₃×#41	C₂³	1	2	yes	—
144	C₂×C₁₃×#41	C₂³	1	2	yes	—
145	C₂²×D₄×C₁₃	—	2	2	no	—
146	C₂²×D₄×C₁₃	—	2	2	no	—
147	C₂²×D₄×C₁₃	—	2	2	no	—
148	C₂²×D₄×C₁₃	—	2	1	no	—
149	C₂²×D₄×C₁₃	—	2	1	no	—
150	C₂²×D₄×C₁₃	—	2	2	no	—
151	C₂²×D₄×C₁₃	—	2	1	no	—
152	C₂²×D₄×C₁₃	—	2	1	no	—
153	C₂²×D₄×C₁₃	—	2	1	no	—
154	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
155	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
157	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
158	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
159	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
160	C₁₃×#135	—	4	4	no	—
161	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×D₈	—	4	4	no	—
168	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×D₈	C₂³	1	2	yes	—
170	C₂×C₁₃×D₈	C₂³	1	2	yes	—
171	C₂×C₁₃×D₈	C₂³	1	2	yes	—
172	C₂×C₁₃×D₈	C₂³	1	2	yes	—
173	C₂×C₁₃×D₈	C₂³	1	2	yes	—
174	C₂×C₁₃×D₈	C₂³	1	2	yes	—
175	C₂×C₁₃×D₈	C₂³	1	2	yes	—
176	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
177	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
178	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
179	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
180	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
181	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
182	C₁₃×#127	—	2	2	no	—
183	C₁₃×#127	—	2	1	no	—
184	C₁₃×#127	—	2	1	no	—
185	C₁₃×#127	—	2	2	no	—
186	C₁₃×#127	—	2	1	no	—
187	C₁₃×#127	—	2	2	no	—
188	C₁₃×#127	—	2	1	no	—
189	C₁₃×#127	—	2	1	no	—
190	C₁₃×#127	D₄	1	1	yes	characteristic
191	C₁₃×#127	C₂³	1	2	yes	—
192	C₁₃×#127	C₂³	1	1	yes	characteristic
193	C₁₃×#127	C₂³	1	1	yes	characteristic
194	C₁₃×#127	C₂³	1	1	yes	characteristic
195	C₁₃×#126	—	2	2	no	—
196	C₁₃×#126	—	2	2	no	—
197	C₁₃×#126	—	2	1	no	—
198	C₁₃×#125	C₂³	1	1	yes	characteristic
199	C₁₃×#124	—	2	2	no	—
200	C₁₃×#124	—	2	2	no	—
201	C₁₃×#124	—	2	1	no	—
202	C₁₃×#124	—	2	1	no	—
203	C₁₃×#124	D₄	1	2	yes	—
204	C₁₃×#124	C₂³	1	1	yes	characteristic
205	C₁₃×#123	—	2	1	no	—
206	C₁₃×#123	—	2	2	no	—
207	C₁₃×#123	—	2	2	no	—
208	C₁₃×#123	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	1	no	—
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	D₄	1	1	yes	characteristic
229	C₁₃×#121	D₄	1	1	yes	characteristic
230	C₁₃×#121	D₄	1	2	yes	—
231	C₁₃×#121	C₂³	1	1	yes	characteristic
232	C₁₃×#121	C₂³	1	2	yes	—
233	C₁₃×#121	C₂³	1	2	yes	—
234	C₁₃×#121	C₂³	1	2	yes	—
235	C₁₃×#121	C₂³	1	2	yes	—
236	C₁₃×#121	C₂³	1	2	yes	—
237	C₁₃×#121	C₂³	1	2	yes	—
238	C₁₃×#121	C₂³	1	2	yes	—
239	C₁₃×#121	C₂³	1	2	yes	—
240	C₁₃×#120	—	2	2	no	—
241	C₁₃×#120	—	2	2	no	—
242	C₁₃×#120	—	2	2	no	—
243	C₁₃×#120	—	2	2	no	—
244	C₁₃×#120	—	2	2	no	—
245	C₁₃×#120	—	2	2	no	—
246	C₁₃×#120	—	2	2	no	—
247	C₁₃×#120	—	2	2	no	—
248	C₁₃×#120	—	2	2	no	—
249	C₁₃×#120	—	2	2	no	—
250	C₄×Q₈×C₁₃	—	2	1	no	—
251	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
258	C₄×D₄×C₁₃	—	2	1	no	—
259	C₄×D₄×C₁₃	—	2	2	no	—
260	C₄×D₄×C₁₃	—	2	1	no	—
261	C₄×D₄×C₁₃	—	2	2	no	—
262	C₄×D₄×C₁₃	—	2	1	no	—
263	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₁₃	C₂³	1	2	yes	—
266	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
267	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₁₃	C₂³	1	2	yes	—
270	C₁₃×#117	—	2	1	no	—
271	C₁₃×#117	—	2	1	no	—
272	C₁₃×#117	C₂³	1	2	yes	—
273	C₁₃×#117	C₂³	1	1	yes	characteristic
274	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²×C₁₃	—	2	1	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	1	yes	characteristic
280	C₁₃×#107	C₂³	1	2	yes	—
281	C₁₃×#106	C₂³	1	1	yes	characteristic
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	2	yes	—
284	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	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	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	C₂³	1	2	yes	—
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₁₃×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
318	#61688	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂⁴×C₁₃	—	2	2	no	—
320	C₂⁴×C₁₃	—	2	2	no	—
321	C₂⁴×C₁₃	—	2	2	no	—
322	C₂⁴×C₁₃	—	2	2	no	—
323	C₁₃×#41	—	2	2	no	—
324	C₁₃×#41	—	2	2	no	—
325	C₁₃×#41	—	2	4	no	—
326	C₁₃×#41	—	2	4	no	—
327	C₁₃×#41	—	4	2	no	—
328	C₁₃×#41	—	4	2	no	—
329	C₁₃×#41	—	4	2	no	—
330	C₁₃×#41	—	4	2	no	—
331	C₁₃×#41	—	4	8	no	—
332	C₁₃×#41	—	4	2	no	—
333	C₁₃×#41	—	4	2	no	—
334	C₁₃×#41	—	8	2	no	—
335	C₁₃×#41	—	8	2	no	—
336	C₂×Q₈×C₁₃	—	2	1	no	—
337	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
338	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	4	no	—
342	C₂×D₄×C₁₃	—	2	4	no	—
343	C₂×D₄×C₁₃	—	2	2	no	—
344	C₂×D₄×C₁₃	—	2	2	no	—
345	C₂×D₄×C₁₃	—	2	1	no	—
346	C₂×D₄×C₁₃	—	2	2	no	—
347	C₂×D₄×C₁₃	—	2	2	no	—
348	C₂×D₄×C₁₃	—	2	2	no	—
349	C₂×D₄×C₁₃	—	2	2	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	1	no	—
356	C₂×D₄×C₁₃	—	2	2	no	—
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	1	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	2	no	—
362	C₂×D₄×C₁₃	—	2	1	no	—
363	C₂×D₄×C₁₃	—	2	1	no	—
364	C₂×D₄×C₁₃	—	2	1	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	—	2	2	no	—
367	C₂×D₄×C₁₃	—	4	2	no	—
368	C₂×D₄×C₁₃	—	4	2	no	—
369	C₂×D₄×C₁₃	—	4	2	no	—
370	C₂×D₄×C₁₃	—	4	2	no	—
371	C₂×D₄×C₁₃	—	4	2	no	—
372	C₂×D₄×C₁₃	—	4	2	no	—
373	C₂×D₄×C₁₃	—	4	8	no	—
374	C₂×D₄×C₁₃	—	4	8	no	—
375	C₂×D₄×C₁₃	—	4	8	no	—
376	C₂×D₄×C₁₃	—	8	2	no	—
377	C₂×D₄×C₁₃	—	8	2	no	—
378	C₂×D₄×C₁₃	—	8	2	no	—
379	C₂×D₄×C₁₃	—	8	2	no	—
380	C₂×D₄×C₁₃	—	8	2	no	—
381	C₂×D₄×C₁₃	—	8	4	no	—
382	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
385	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
386	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
387	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
388	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
389	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
390	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
392	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₁₃	—	2	1	no	—
394	C₂²×C₄×C₁₃	—	2	2	no	—
395	C₂²×C₄×C₁₃	—	2	1	no	—
396	C₂²×C₄×C₁₃	—	2	1	no	—
397	C₂²×C₄×C₁₃	—	2	1	no	—
398	C₂²×C₄×C₁₃	—	2	2	no	—
399	C₂²×C₄×C₁₃	—	2	2	no	—
400	C₂²×C₄×C₁₃	—	2	2	no	—
401	C₂²×C₄×C₁₃	—	2	2	no	—
402	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
407	C₁₃×Q₁₆	—	2	2	no	—
408	C₁₃×SD₁₆	—	2	4	no	—
409	C₁₃×SD₁₆	—	2	2	no	—
410	C₁₃×SD₁₆	—	2	2	no	—
411	C₁₃×SD₁₆	—	4	2	no	—
412	C₁₃×SD₁₆	—	4	2	no	—
413	C₁₃×D₈	—	2	2	no	—
414	C₁₃×D₈	—	2	4	no	—
415	C₁₃×D₈	—	4	2	no	—
416	C₁₃×D₈	—	4	2	no	—
417	C₁₃×D₈	—	4	2	no	—
418	C₁₃×D₈	—	4	2	no	—
419	C₁₃×D₈	—	4	2	no	—
420	C₁₃×D₈	—	4	2	no	—
421	C₁₃×M₁₆	—	4	2	no	—
422	C₁₃×M₁₆	—	4	2	no	—
423	C₂×C₈×C₁₃	—	4	2	no	—
424	C₂×C₈×C₁₃	—	4	2	no	—
425	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
430	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	—	2	1	no	—
434	C₁₃×C₄⋊C₄	—	2	1	no	—
435	C₁₃×C₄⋊C₄	—	2	1	no	—
436	C₁₃×C₄⋊C₄	—	2	1	no	—
437	C₁₃×C₄⋊C₄	—	2	1	no	—
438	C₁₃×C₄⋊C₄	—	2	2	no	—
439	C₁₃×C₄⋊C₄	—	2	1	no	—
440	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
441	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
443	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
445	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	1	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	no	—
451	C₁₃×C₂²⋊C₄	—	2	1	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	2	no	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	1	no	—
457	C₁₃×C₂²⋊C₄	—	2	1	no	—
458	C₁₃×C₂²⋊C₄	—	2	2	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	2	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	2	no	—
465	C₁₃×C₂²⋊C₄	—	2	1	no	—
466	C₁₃×C₂²⋊C₄	—	2	2	no	—
467	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₄²×C₁₃	—	2	1	no	—
472	C₄²×C₁₃	—	2	1	no	—
473	C₄²×C₁₃	—	2	1	no	—
474	C₄²×C₁₃	—	2	1	no	—
475	C₄²×C₁₃	—	2	2	no	—
476	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
479	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
480	#3546	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3332	C₂×C₁₃	1	1	yes	characteristic, complemented
483	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3318	C₂×C₁₃	1	2	yes	complemented
485	#3309	C₂×C₁₃	1	2	yes	complemented
486	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
488	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
489	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
490	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3268	C₂×C₁₃	1	2	yes	complemented
493	#3264	C₂×C₁₃	1	2	yes	complemented
494	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3199	C₂×C₁₃	1	2	yes	complemented
497	#3198	C₂×C₁₃	1	2	yes	complemented
498	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#3012	C₂×C₁₃	1	2	yes	complemented
501	#3008	C₂×C₁₃	1	2	yes	complemented
502	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
503	C₂³×C₁₃	—	2	1	no	—
504	C₂³×C₁₃	—	2	1	no	—
505	C₂³×C₁₃	—	2	2	no	—
506	C₂³×C₁₃	—	2	2	no	—
507	C₂³×C₁₃	—	2	2	no	—
508	C₂³×C₁₃	—	4	4	no	—
509	C₂³×C₁₃	—	4	4	no	—
510	C₂³×C₁₃	—	4	4	no	—
511	C₂³×C₁₃	—	8	2	no	—
512	C₂³×C₁₃	—	8	2	no	—
513	C₂³×C₁₃	—	8	2	no	—
514	C₂³×C₁₃	—	8	2	no	—
515	C₂³×C₁₃	—	8	2	no	—
516	C₂³×C₁₃	—	8	2	no	—
517	C₂³×C₁₃	—	8	2	no	—
518	C₂³×C₁₃	—	8	2	no	—
519	C₂³×C₁₃	—	8	2	no	—
520	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
521	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
522	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
523	Q₈×C₁₃	—	2	1	no	—
524	Q₈×C₁₃	—	2	1	no	—
525	Q₈×C₁₃	—	2	1	no	—
526	Q₈×C₁₃	—	4	2	no	—
527	Q₈×C₁₃	—	4	2	no	—
528	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
529	D₄×C₁₃	—	2	4	no	—
530	D₄×C₁₃	—	2	2	no	—
531	D₄×C₁₃	—	2	2	no	—
532	D₄×C₁₃	—	2	1	no	—
533	D₄×C₁₃	—	2	1	no	—
534	D₄×C₁₃	—	2	2	no	—
535	D₄×C₁₃	—	2	1	no	—
536	D₄×C₁₃	—	2	2	no	—
537	D₄×C₁₃	—	2	2	no	—
538	D₄×C₁₃	—	2	2	no	—
539	D₄×C₁₃	—	2	2	no	—
540	D₄×C₁₃	—	2	2	no	—
541	D₄×C₁₃	—	4	2	no	—
542	D₄×C₁₃	—	4	2	no	—
543	D₄×C₁₃	—	4	2	no	—
544	D₄×C₁₃	—	4	2	no	—
545	D₄×C₁₃	—	4	4	no	—
546	D₄×C₁₃	—	4	4	no	—
547	D₄×C₁₃	—	4	4	no	—
548	D₄×C₁₃	—	4	4	no	—
549	D₄×C₁₃	—	4	4	no	—
550	D₄×C₁₃	—	4	4	no	—
551	D₄×C₁₃	—	4	2	no	—
552	D₄×C₁₃	—	4	2	no	—
553	D₄×C₁₃	—	4	2	no	—
554	D₄×C₁₃	—	8	1	no	—
555	D₄×C₁₃	—	8	2	no	—
556	D₄×C₁₃	—	8	1	no	—
557	D₄×C₁₃	—	8	1	no	—
558	D₄×C₁₃	—	8	2	no	—
559	D₄×C₁₃	—	8	1	no	—
560	D₄×C₁₃	—	8	2	no	—
561	D₄×C₁₃	—	8	2	no	—
562	D₄×C₁₃	—	8	2	no	—
563	D₄×C₁₃	—	8	2	no	—
564	D₄×C₁₃	—	8	2	no	—
565	D₄×C₁₃	—	8	2	no	—
566	D₄×C₁₃	—	8	2	no	—
567	D₄×C₁₃	—	8	2	no	—
568	D₄×C₁₃	—	8	2	no	—
569	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄×C₁₃	—	2	4	no	—
571	C₂×C₄×C₁₃	—	2	1	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	2	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	2	2	no	—
577	C₂×C₄×C₁₃	—	2	1	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	1	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	2	1	no	—
582	C₂×C₄×C₁₃	—	2	1	no	—
583	C₂×C₄×C₁₃	—	2	2	no	—
584	C₂×C₄×C₁₃	—	2	1	no	—
585	C₂×C₄×C₁₃	—	4	1	no	—
586	C₂×C₄×C₁₃	—	4	4	no	—
587	C₂×C₄×C₁₃	—	4	4	no	—
588	C₂×C₄×C₁₃	—	4	2	no	—
589	C₂×C₄×C₁₃	—	4	2	no	—
590	C₂×C₄×C₁₃	—	4	2	no	—
591	C₂×C₄×C₁₃	—	8	2	no	—
592	C₂×C₄×C₁₃	—	8	2	no	—
593	C₂×C₄×C₁₃	—	8	2	no	—
594	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
597	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
600	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
602	C₈×C₁₃	—	2	1	no	—
603	C₈×C₁₃	—	2	1	no	—
604	C₈×C₁₃	—	2	2	no	—
605	C₈×C₁₃	—	2	2	no	—
606	C₈×C₁₃	—	2	1	no	—
607	C₈×C₁₃	—	2	1	no	—
608	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
609	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
610	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
611	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
612	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
613	#560	—	2	2	no	—
614	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#553	C₂²×C₁₃	1	2	yes	complemented
616	#550	—	2	1	no	—
617	#550	C₂²×C₁₃	1	1	yes	characteristic
618	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	#550	C₂²×C₁₃	1	2	yes	complemented
620	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#546	—	2	1	no	—
623	#546	C₂²×C₁₃	1	2	yes	complemented
624	D₄²	—	2	1	no	—
625	D₄²	—	2	2	no	—
626	D₄²	—	2	1	no	—
627	D₄²	C₂²×C₁₃	1	1	yes	characteristic
628	D₄²	C₂²×C₁₃	1	2	yes	complemented
629	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#542	—	2	1	no	—
632	#538	—	2	2	no	—
633	#537	C₂²×C₁₃	1	2	yes	complemented
634	#535	—	2	1	no	—
635	#535	—	2	2	no	—
636	#535	C₂²×C₁₃	1	2	yes	complemented
637	#535	C₂²×C₁₃	1	2	yes	complemented
638	#532	—	2	1	no	—
639	#532	C₂²×C₁₃	1	1	yes	characteristic
640	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	C₂×#127	—	2	1	no	—
642	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#496	C₂²×C₁₃	1	2	yes	complemented
646	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
647	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#490	C₂²×C₁₃	1	2	yes	complemented
649	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#482	C₂²×C₁₃	1	2	yes	complemented
654	#482	C₂²×C₁₃	1	2	yes	complemented
655	#482	C₂²×C₁₃	1	2	yes	complemented
656	#481	C₂²×C₁₃	1	2	yes	complemented
657	#480	C₂²×C₁₃	1	2	yes	complemented
658	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#469	C₂²×C₁₃	1	2	yes	complemented
663	#469	C₂²×C₁₃	1	2	yes	complemented
664	#469	C₂²×C₁₃	1	2	yes	complemented
665	#468	C₂²×C₁₃	1	2	yes	complemented
666	#466	C₂²×C₁₃	1	2	yes	complemented
667	#466	C₂²×C₁₃	1	2	yes	complemented
668	#466	C₂²×C₁₃	1	2	yes	complemented
669	#465	C₂²×C₁₃	1	2	yes	complemented
670	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
673	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
677	#459	C₂²×C₁₃	1	2	yes	complemented
678	#459	C₂²×C₁₃	1	2	yes	complemented
679	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
680	#452	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	#452	C₂²×C₁₃	1	2	yes	complemented
682	#450	C₂²×C₁₃	1	2	yes	complemented
683	#450	C₂²×C₁₃	1	2	yes	complemented
684	#449	C₂²×C₁₃	1	1	yes	characteristic
685	#449	C₂²×C₁₃	1	2	yes	complemented
686	#449	C₂²×C₁₃	1	2	yes	complemented
687	#449	C₂²×C₁₃	1	2	yes	complemented
688	#449	C₂²×C₁₃	1	2	yes	complemented
689	#449	C₂²×C₁₃	1	2	yes	complemented
690	#449	C₂²×C₁₃	1	2	yes	complemented
691	#447	C₂²×C₁₃	1	2	yes	complemented
692	#447	C₂²×C₁₃	1	2	yes	complemented
693	#447	C₂²×C₁₃	1	2	yes	complemented
694	#447	C₂²×C₁₃	1	2	yes	complemented
695	#447	C₂²×C₁₃	1	2	yes	complemented
696	#447	C₂²×C₁₃	1	2	yes	complemented
697	#447	C₂²×C₁₃	1	2	yes	complemented
698	#447	C₂²×C₁₃	1	2	yes	complemented
699	#442	C₂²×C₁₃	1	2	yes	complemented
700	#440	C₂²×C₁₃	1	2	yes	complemented
701	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
704	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
705	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
706	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
707	#435	C₂²×C₁₃	1	2	yes	complemented
708	#435	C₂²×C₁₃	1	2	yes	complemented
709	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
710	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
711	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	#418	C₂²×C₁₃	1	2	yes	complemented
714	#417	C₂²×C₁₃	1	2	yes	complemented
715	#416	C₂²×C₁₃	1	2	yes	complemented
716	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
717	#408	C₂²×C₁₃	1	2	yes	complemented
718	#408	C₂²×C₁₃	1	2	yes	complemented
719	C₂²×C₁₃	—	2	1	no	—
720	C₂²×C₁₃	—	2	2	no	—
721	C₂²×C₁₃	—	2	2	no	—
722	C₂²×C₁₃	—	2	1	no	—
723	C₂²×C₁₃	—	2	2	no	—
724	C₂²×C₁₃	—	2	2	no	—
725	C₂²×C₁₃	—	2	2	no	—
726	C₂²×C₁₃	—	2	1	no	—
727	C₂²×C₁₃	—	2	2	no	—
728	C₂²×C₁₃	—	2	2	no	—
729	C₂²×C₁₃	—	4	1	no	—
730	C₂²×C₁₃	—	4	1	no	—
731	C₂²×C₁₃	—	4	2	no	—
732	C₂²×C₁₃	—	4	2	no	—
733	C₂²×C₁₃	—	4	2	no	—
734	C₂²×C₁₃	—	4	1	no	—
735	C₂²×C₁₃	—	4	2	no	—
736	C₂²×C₁₃	—	4	2	no	—
737	C₂²×C₁₃	—	4	2	no	—
738	C₂²×C₁₃	—	4	1	no	—
739	C₂²×C₁₃	—	4	1	no	—
740	C₂²×C₁₃	—	4	2	no	—
741	C₂²×C₁₃	—	4	2	no	—
742	C₂²×C₁₃	—	4	2	no	—
743	C₂²×C₁₃	—	16	4	no	—
744	C₂²×C₁₃	—	16	4	no	—
745	C₂²×C₁₃	—	16	4	no	—
746	C₂²×C₁₃	—	16	4	no	—
747	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
748	C₄×C₁₃	—	2	1	no	—
749	C₄×C₁₃	—	2	1	no	—
750	C₄×C₁₃	—	2	1	no	—
751	C₄×C₁₃	—	2	2	no	—
752	C₄×C₁₃	—	2	2	no	—
753	C₄×C₁₃	—	2	2	no	—
754	C₄×C₁₃	—	2	1	no	—
755	C₄×C₁₃	—	4	1	no	—
756	C₄×C₁₃	—	4	1	no	—
757	C₄×C₁₃	—	4	1	no	—
758	C₄×C₁₃	—	4	1	no	—
759	C₄×C₁₃	—	4	1	no	—
760	C₄×C₁₃	—	4	2	no	—
761	C₄×C₁₃	#576	1	2	yes	—
762	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
763	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
764	H(5,𝔽₂)	—	4	4	no	—
765	H(5,𝔽₂)	—	4	4	no	—
766	C₂×#41	—	2	2	no	—
767	C₂×#41	—	2	1	no	—
768	C₂×#41	—	2	1	no	—
769	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×#41	C₂³×C₁₃	1	2	yes	—
771	C₂×#41	C₂³×C₁₃	1	2	yes	—
772	C₂×#41	C₂³×C₁₃	1	2	yes	—
773	C₂×#41	C₂³×C₁₃	1	2	yes	—
774	C₂²×D₄	—	2	2	no	—
775	C₂²×D₄	—	2	2	no	—
776	C₂²×D₄	—	2	2	no	—
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	—	2	1	no	—
779	C₂²×D₄	—	2	2	no	—
780	C₂²×D₄	—	2	1	no	—
781	C₂²×D₄	—	2	1	no	—
782	C₂²×D₄	—	2	1	no	—
783	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
784	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
785	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
786	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
787	AGL(1,ℤ/8)	—	4	4	no	—
788	AGL(1,ℤ/8)	—	4	4	no	—
789	#135	—	4	4	no	—
790	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
791	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
793	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
795	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
796	C₂×D₈	—	4	4	no	—
797	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
798	C₂×D₈	C₂³×C₁₃	1	2	yes	—
799	C₂×D₈	C₂³×C₁₃	1	2	yes	—
800	C₂×D₈	C₂³×C₁₃	1	2	yes	—
801	C₂×D₈	C₂³×C₁₃	1	2	yes	—
802	C₂×D₈	C₂³×C₁₃	1	2	yes	—
803	C₂×D₈	C₂³×C₁₃	1	2	yes	—
804	C₂×D₈	C₂³×C₁₃	1	2	yes	—
805	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
806	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
807	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
808	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
809	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
810	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
811	#127	—	2	2	no	—
812	#127	—	2	1	no	—
813	#127	—	2	1	no	—
814	#127	—	2	2	no	—
815	#127	—	2	1	no	—
816	#127	—	2	2	no	—
817	#127	—	2	1	no	—
818	#127	—	2	1	no	—
819	#127	D₄×C₁₃	1	1	yes	characteristic
820	#127	C₂³×C₁₃	1	1	yes	characteristic
821	#127	C₂³×C₁₃	1	1	yes	characteristic
822	#127	C₂³×C₁₃	1	2	yes	—
823	#127	C₂³×C₁₃	1	1	yes	characteristic
824	#126	—	2	2	no	—
825	#126	—	2	2	no	—
826	#126	—	2	1	no	—
827	#125	C₂³×C₁₃	1	1	yes	characteristic
828	#124	—	2	2	no	—
829	#124	—	2	2	no	—
830	#124	—	2	1	no	—
831	#124	—	2	1	no	—
832	#124	D₄×C₁₃	1	2	yes	—
833	#124	C₂³×C₁₃	1	1	yes	characteristic
834	#123	—	2	1	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	—	2	2	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
841	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	2	no	—
850	#121	—	2	1	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	2	no	—
856	#121	—	2	2	no	—
857	#121	D₄×C₁₃	1	1	yes	characteristic
858	#121	D₄×C₁₃	1	1	yes	characteristic
859	#121	D₄×C₁₃	1	2	yes	—
860	#121	C₂³×C₁₃	1	1	yes	characteristic
861	#121	C₂³×C₁₃	1	2	yes	—
862	#121	C₂³×C₁₃	1	2	yes	—
863	#121	C₂³×C₁₃	1	2	yes	—
864	#121	C₂³×C₁₃	1	2	yes	—
865	#121	C₂³×C₁₃	1	2	yes	—
866	#121	C₂³×C₁₃	1	2	yes	—
867	#121	C₂³×C₁₃	1	2	yes	—
868	#121	C₂³×C₁₃	1	2	yes	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	#120	—	2	2	no	—
873	#120	—	2	2	no	—
874	#120	—	2	2	no	—
875	#120	—	2	2	no	—
876	#120	—	2	2	no	—
877	#120	—	2	2	no	—
878	#120	—	2	2	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
882	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	—	2	1	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	2	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
893	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
894	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
895	C₄×D₄	C₂³×C₁₃	1	2	yes	—
896	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
897	C₄×D₄	C₂³×C₁₃	1	2	yes	—
898	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
899	#117	—	2	1	no	—
900	#117	—	2	1	no	—
901	#117	C₂³×C₁₃	1	1	yes	characteristic
902	#117	C₂³×C₁₃	1	2	yes	—
903	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
904	C₂×C₂²⋊C₄	—	2	2	no	—
905	C₂×C₄²	—	2	1	no	—
906	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
907	#107	C₂³×C₁₃	1	1	yes	characteristic
908	#107	C₂³×C₁₃	1	1	yes	characteristic
909	#107	C₂³×C₁₃	1	2	yes	—
910	#106	C₂³×C₁₃	1	1	yes	characteristic
911	#106	C₂³×C₁₃	1	1	yes	characteristic
912	#106	C₂³×C₁₃	1	2	yes	—
913	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
914	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
915	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
916	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
917	#103	C₂³×C₁₃	1	1	yes	characteristic
918	#103	C₂³×C₁₃	1	2	yes	—
919	#103	C₂³×C₁₃	1	1	yes	characteristic
920	#103	C₂³×C₁₃	1	1	yes	characteristic
921	#103	C₂³×C₁₃	1	1	yes	characteristic
922	#102	C₂³×C₁₃	1	1	yes	characteristic
923	#102	C₂³×C₁₃	1	2	yes	—
924	#102	C₂³×C₁₃	1	2	yes	—
925	#102	C₂³×C₁₃	1	2	yes	—
926	#102	C₂³×C₁₃	1	2	yes	—
927	#102	C₂³×C₁₃	1	2	yes	—
928	#102	C₂³×C₁₃	1	2	yes	—
929	#102	C₂³×C₁₃	1	2	yes	—
930	#102	C₂³×C₁₃	1	1	yes	characteristic
931	#102	C₂³×C₁₃	1	2	yes	—
932	#102	C₂³×C₁₃	1	2	yes	—
933	#102	C₂³×C₁₃	1	1	yes	characteristic
934	#102	C₂³×C₁₃	1	1	yes	characteristic
935	#102	C₂³×C₁₃	1	2	yes	—
936	#102	C₂³×C₁₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
938	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
939	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
944	#97	C₂³×C₁₃	1	2	yes	—
945	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
946	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
947	C₂×C₁₃	—	4	2	no	—
948	C₂×C₁₃	—	4	1	no	—
949	C₂×C₁₃	—	4	2	no	—
950	C₂×C₁₃	—	4	2	no	—
951	C₂×C₁₃	—	8	2	no	—
952	C₂×C₁₃	—	8	2	no	—
953	C₂×C₁₃	—	8	2	no	—
954	C₂×C₁₃	—	8	1	no	—
955	C₂×C₁₃	#3484	1	1	yes	characteristic
956	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
957	C₂×C₁₃	#3585	1	1	yes	characteristic
958	C₂⁴	—	2	2	no	—
959	C₂⁴	—	2	2	no	—
960	C₂⁴	—	2	2	no	—
961	C₂⁴	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	4	no	—
965	#41	—	2	4	no	—
966	#41	—	4	2	no	—
967	#41	—	4	2	no	—
968	#41	—	4	2	no	—
969	#41	—	4	2	no	—
970	#41	—	4	8	no	—
971	#41	—	4	2	no	—
972	#41	—	4	2	no	—
973	#41	—	8	2	no	—
974	#41	—	8	2	no	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
977	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
978	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	4	no	—
981	C₂×D₄	—	2	4	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	2	no	—
1008	C₂×D₄	—	4	2	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	2	no	—
1012	C₂×D₄	—	4	8	no	—
1013	C₂×D₄	—	4	8	no	—
1014	C₂×D₄	—	4	8	no	—
1015	C₂×D₄	—	8	2	no	—
1016	C₂×D₄	—	8	2	no	—
1017	C₂×D₄	—	8	2	no	—
1018	C₂×D₄	—	8	2	no	—
1019	C₂×D₄	—	8	2	no	—
1020	C₂×D₄	—	8	4	no	—
1021	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1022	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1023	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1026	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1027	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1028	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1029	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1030	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1031	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1045	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1046	Q₁₆	—	2	2	no	—
1047	SD₁₆	—	2	4	no	—
1048	SD₁₆	—	2	2	no	—
1049	SD₁₆	—	2	2	no	—
1050	SD₁₆	—	4	2	no	—
1051	SD₁₆	—	4	2	no	—
1052	D₈	—	2	2	no	—
1053	D₈	—	2	4	no	—
1054	D₈	—	4	2	no	—
1055	D₈	—	4	2	no	—
1056	D₈	—	4	2	no	—
1057	D₈	—	4	2	no	—
1058	D₈	—	4	2	no	—
1059	D₈	—	4	2	no	—
1060	M₁₆	—	4	2	no	—
1061	M₁₆	—	4	2	no	—
1062	C₂×C₈	—	4	2	no	—
1063	C₂×C₈	—	4	2	no	—
1064	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1065	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1066	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1067	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1068	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1069	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1107	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1108	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1109	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	2	no	—
1115	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1116	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1117	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1118	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1119	C₁₃	#61688	1	1	yes	characteristic, direct product factor, Sylow
1120	C₂³	—	2	1	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	2	no	—
1123	C₂³	—	2	2	no	—
1124	C₂³	—	2	2	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	4	no	—
1127	C₂³	—	4	4	no	—
1128	C₂³	—	8	2	no	—
1129	C₂³	—	8	2	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	2	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	—	8	2	no	—
1134	C₂³	—	8	2	no	—
1135	C₂³	—	8	2	no	—
1136	C₂³	—	8	2	no	—
1137	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1138	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1139	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	2	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	2	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	4	no	—
1163	D₄	—	4	4	no	—
1164	D₄	—	4	4	no	—
1165	D₄	—	4	4	no	—
1166	D₄	—	4	4	no	—
1167	D₄	—	4	4	no	—
1168	D₄	—	4	2	no	—
1169	D₄	—	4	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	8	2	no	—
1172	D₄	—	8	2	no	—
1173	D₄	—	8	1	no	—
1174	D₄	—	8	1	no	—
1175	D₄	—	8	1	no	—
1176	D₄	—	8	2	no	—
1177	D₄	—	8	2	no	—
1178	D₄	—	8	2	no	—
1179	D₄	—	8	2	no	—
1180	D₄	—	8	2	no	—
1181	D₄	—	8	1	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1187	C₂×C₄	—	2	4	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	4	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	2	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	8	2	no	—
1209	C₂×C₄	—	8	2	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1212	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1213	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1214	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1215	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1217	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1218	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1219	C₈	—	2	1	no	—
1220	C₈	—	2	1	no	—
1221	C₈	—	2	2	no	—
1222	C₈	—	2	2	no	—
1223	C₈	—	2	1	no	—
1224	C₈	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	2	no	—
1228	C₂²	—	2	1	no	—
1229	C₂²	—	2	2	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	2	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	1	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	2	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	2	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	2	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	16	4	no	—
1250	C₂²	—	16	4	no	—
1251	C₂²	—	16	4	no	—
1252	C₂²	—	16	4	no	—
1253	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	C₁₃×#576	1	2	yes	—
1268	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1269	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1270	C₂	—	4	1	no	—
1271	C₂	—	4	2	no	—
1272	C₂	—	4	2	no	—
1273	C₂	—	4	2	no	—
1274	C₂	—	8	1	no	—
1275	C₂	—	8	2	no	—
1276	C₂	—	8	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	C₁₃×#3484	1	1	yes	characteristic
1279	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1280	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3546	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3324	C₂	semidirect
5. C₁₃×#3318	C₂	semidirect
6. C₁₃×#3309	C₂	semidirect
7. C₁₃×#3304	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. C₁₃×#3287	C₂	semidirect
10. D₄×C₁₃×D₈	C₂	semidirect
11. C₁₃×#3274	C₂	semidirect
12. C₁₃×#3274	C₂	semidirect
13. C₁₃×#3268	C₂	semidirect
14. C₁₃×#3264	C₂	semidirect
15. C₁₃×#3217	C₂	semidirect
16. C₁₃×#3205	C₂	semidirect
17. C₁₃×#3199	C₂	semidirect
18. C₁₃×#3198	C₂	semidirect
19. C₁₃×#3115	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3012	C₂	semidirect
22. C₁₃×#3008	C₂	semidirect
23. C₁₃×#2981	C₂	semidirect
24. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
39. C₁₃×#546	C₂²	semidirect
44. D₄²×C₁₃	C₂²	semidirect
45. D₄²×C₁₃	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
49. C₁₃×#537	C₂²	semidirect
52. C₁₃×#535	C₂²	semidirect
53. C₁₃×#535	C₂²	semidirect
56. C₁₃×#532	C₂²	semidirect
58. C₂×C₁₃×#127	C₂²	semidirect
59. C₁₃×#529	C₂²	semidirect
60. C₄×C₁₃×#41	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#493	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#482	C₂²	semidirect
69. C₁₃×#482	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#481	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#469	C₂²	semidirect
79. C₁₃×#469	C₂²	semidirect
80. C₁₃×#469	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#466	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#460	C₂²	semidirect
89. C₁₃×#460	C₂²	semidirect
90. C₁₃×#460	C₂²	semidirect
91. C₁₃×#459	C₂²	semidirect
92. C₁₃×#459	C₂²	semidirect
93. C₁₃×#459	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
97. C₁₃×#452	C₂²	semidirect
98. C₁₃×#450	C₂²	semidirect
99. C₁₃×#450	C₂²	semidirect
101. C₁₃×#449	C₂²	semidirect
102. C₁₃×#449	C₂²	semidirect
103. C₁₃×#449	C₂²	semidirect
104. C₁₃×#449	C₂²	semidirect
105. C₁₃×#449	C₂²	semidirect
106. C₁₃×#449	C₂²	semidirect
107. C₁₃×#447	C₂²	semidirect
108. C₁₃×#447	C₂²	semidirect
109. C₁₃×#447	C₂²	semidirect
110. C₁₃×#447	C₂²	semidirect
111. C₁₃×#447	C₂²	semidirect
112. C₁₃×#447	C₂²	semidirect
113. C₁₃×#447	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₁₃×#442	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₄×C₁₃×Q₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₁₃×#435	C₂²	semidirect
125. C₈×D₄×C₁₃	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₁₃×#432	C₂²	semidirect
128. C₁₃×#431	C₂²	semidirect
129. C₁₃×#418	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₁₃×#416	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#408	C₂²	semidirect
134. C₁₃×#408	C₂²	semidirect
318. #61688	C₁₃	direct (N × H)
480. #3546	C₂×C₁₃	semidirect
481. #3498	C₂×C₁₃	semidirect
482. #3332	C₂×C₁₃	semidirect
483. #3324	C₂×C₁₃	semidirect
484. #3318	C₂×C₁₃	semidirect
485. #3309	C₂×C₁₃	semidirect
486. #3304	C₂×C₁₃	semidirect
487. #3294	C₂×C₁₃	semidirect
488. #3287	C₂×C₁₃	semidirect
489. D₄×D₈	C₂×C₁₃	semidirect
490. #3274	C₂×C₁₃	semidirect
491. #3274	C₂×C₁₃	semidirect
492. #3268	C₂×C₁₃	semidirect
493. #3264	C₂×C₁₃	semidirect
494. #3217	C₂×C₁₃	semidirect
495. #3205	C₂×C₁₃	semidirect
496. #3199	C₂×C₁₃	semidirect
497. #3198	C₂×C₁₃	semidirect
498. #3115	C₂×C₁₃	semidirect
499. #3102	C₂×C₁₃	semidirect
500. #3012	C₂×C₁₃	semidirect
501. #3008	C₂×C₁₃	semidirect
502. #2981	C₂×C₁₃	semidirect
608. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
609. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
610. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
611. C₂×#135	C₂²×C₁₃	semidirect
612. C₂²×D₈	C₂²×C₁₃	semidirect
614. #556	C₂²×C₁₃	semidirect
615. #553	C₂²×C₁₃	semidirect
618. #550	C₂²×C₁₃	semidirect
619. #550	C₂²×C₁₃	semidirect
620. #550	C₂²×C₁₃	semidirect
621. #547	C₂²×C₁₃	semidirect
623. #546	C₂²×C₁₃	semidirect
628. D₄²	C₂²×C₁₃	semidirect
629. D₄²	C₂²×C₁₃	semidirect
630. D₄²	C₂²×C₁₃	semidirect
633. #537	C₂²×C₁₃	semidirect
636. #535	C₂²×C₁₃	semidirect
637. #535	C₂²×C₁₃	semidirect
640. #532	C₂²×C₁₃	semidirect
642. C₂×#127	C₂²×C₁₃	semidirect
643. #529	C₂²×C₁₃	semidirect
644. C₄×#41	C₂²×C₁₃	semidirect
645. #496	C₂²×C₁₃	semidirect
646. #493	C₂²×C₁₃	semidirect
647. #493	C₂²×C₁₃	semidirect
648. #490	C₂²×C₁₃	semidirect
649. #486	C₂²×C₁₃	semidirect
650. #486	C₂²×C₁₃	semidirect
651. #485	C₂²×C₁₃	semidirect
652. #482	C₂²×C₁₃	semidirect
653. #482	C₂²×C₁₃	semidirect
654. #482	C₂²×C₁₃	semidirect
655. #482	C₂²×C₁₃	semidirect
656. #481	C₂²×C₁₃	semidirect
657. #480	C₂²×C₁₃	semidirect
658. #479	C₂²×C₁₃	semidirect
659. #478	C₂²×C₁₃	semidirect
660. #475	C₂²×C₁₃	semidirect
661. #474	C₂²×C₁₃	semidirect
662. #469	C₂²×C₁₃	semidirect
663. #469	C₂²×C₁₃	semidirect
664. #469	C₂²×C₁₃	semidirect
665. #468	C₂²×C₁₃	semidirect
666. #466	C₂²×C₁₃	semidirect
667. #466	C₂²×C₁₃	semidirect
668. #466	C₂²×C₁₃	semidirect
669. #465	C₂²×C₁₃	semidirect
670. #464	C₂²×C₁₃	semidirect
671. #463	C₂²×C₁₃	semidirect
672. #460	C₂²×C₁₃	semidirect
673. #460	C₂²×C₁₃	semidirect
674. #460	C₂²×C₁₃	semidirect
675. #459	C₂²×C₁₃	semidirect
676. #459	C₂²×C₁₃	semidirect
677. #459	C₂²×C₁₃	semidirect
678. #459	C₂²×C₁₃	semidirect
679. #459	C₂²×C₁₃	semidirect
680. #452	C₂²×C₁₃	semidirect
681. #452	C₂²×C₁₃	semidirect
682. #450	C₂²×C₁₃	semidirect
683. #450	C₂²×C₁₃	semidirect
685. #449	C₂²×C₁₃	semidirect
686. #449	C₂²×C₁₃	semidirect
687. #449	C₂²×C₁₃	semidirect
688. #449	C₂²×C₁₃	semidirect
689. #449	C₂²×C₁₃	semidirect
690. #449	C₂²×C₁₃	semidirect
691. #447	C₂²×C₁₃	semidirect
692. #447	C₂²×C₁₃	semidirect
693. #447	C₂²×C₁₃	semidirect
694. #447	C₂²×C₁₃	semidirect
695. #447	C₂²×C₁₃	semidirect
696. #447	C₂²×C₁₃	semidirect
697. #447	C₂²×C₁₃	semidirect
698. #447	C₂²×C₁₃	semidirect
699. #442	C₂²×C₁₃	semidirect
700. #440	C₂²×C₁₃	semidirect
701. C₄×Q₁₆	C₂²×C₁₃	semidirect
702. C₄×SD₁₆	C₂²×C₁₃	semidirect
703. C₄×SD₁₆	C₂²×C₁₃	semidirect
704. C₄×D₈	C₂²×C₁₃	semidirect
705. #436	C₂²×C₁₃	semidirect
706. #436	C₂²×C₁₃	semidirect
707. #435	C₂²×C₁₃	semidirect
708. #435	C₂²×C₁₃	semidirect
709. C₈×D₄	C₂²×C₁₃	semidirect
710. C₈×D₄	C₂²×C₁₃	semidirect
711. #432	C₂²×C₁₃	semidirect
712. #431	C₂²×C₁₃	semidirect
713. #418	C₂²×C₁₃	semidirect
714. #417	C₂²×C₁₃	semidirect
715. #416	C₂²×C₁₃	semidirect
716. C₂×#102	C₂²×C₁₃	semidirect
717. #408	C₂²×C₁₃	semidirect
718. #408	C₂²×C₁₃	semidirect
1119. C₁₃	#61688	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×#3498	2
C₁₃×#3332	2
C₁₃×#3324	2
C₁₃×#3318	2
C₁₃×#3309	2
C₁₃×#3304	2
C₁₃×#3294	2
C₁₃×#3287	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3268	2
C₁₃×#3264	2
C₁₃×#3217	2
C₁₃×#3205	2
C₁₃×#3199	2
C₁₃×#3198	2
C₁₃×#3115	2
C₁₃×#3102	2
C₁₃×#3012	2
C₁₃×#3008	2
C₁₃×#2981	2
#61688	13

Subgroups — C13×#61688 #15748027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61688 #15748027