Subgroups — C₁₃×#61657 #15747996

Order 3328.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1272 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×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3273	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3203	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3100	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×#2979	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, complemented
34	C₁₃×#547	—	2	1	no	—
35	C₁₃×#547	C₂²	1	1	yes	characteristic
36	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#546	—	2	2	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	C₂²	1	2	yes	complemented
41	C₁₃×#546	C₂²	1	2	yes	complemented
42	C₁₃×#546	C₂²	1	2	yes	complemented
43	D₄²×C₁₃	—	2	1	no	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
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×#537	C₂²	1	2	yes	complemented
51	C₁₃×#535	—	2	1	no	—
52	C₁₃×#535	C₂²	1	2	yes	complemented
53	C₁₃×#534	—	2	2	no	—
54	C₁₃×#532	C₂²	1	1	yes	characteristic
55	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#121	—	2	1	no	—
59	C₂×C₁₃×#121	—	2	1	no	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#484	C₂²	1	2	yes	complemented
69	C₁₃×#484	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#481	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#480	C₂²	1	2	yes	complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#474	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×#468	C₂²	1	2	yes	complemented
80	C₁₃×#468	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#467	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×#463	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#463	C₂²	1	2	yes	complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
97	C₁₃×#452	C₂²	1	2	yes	complemented
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#450	C₂²	1	2	yes	complemented
101	C₁₃×#450	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×#449	C₂²	1	2	yes	complemented
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#447	C₂²	1	1	yes	characteristic
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	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#436	C₂²	1	2	yes	complemented
123	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
126	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#431	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	2	yes	—
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	1	no	—
151	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
155	C₂³×C₄×C₁₃	—	2	1	no	—
156	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
157	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
158	C₁₃×#135	—	4	4	no	—
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×D₈	—	4	4	no	—
167	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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×M₁₆	C₂³	1	2	yes	—
175	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
176	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
178	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
181	C₁₃×#127	—	2	1	no	—
182	C₁₃×#127	—	2	2	no	—
183	C₁₃×#127	D₄	1	1	yes	characteristic
184	C₁₃×#127	C₂³	1	1	yes	characteristic
185	C₁₃×#127	C₂³	1	1	yes	characteristic
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#126	—	2	2	no	—
188	C₁₃×#126	—	2	1	no	—
189	C₁₃×#125	C₂³	1	1	yes	characteristic
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	—	2	1	no	—
192	C₁₃×#124	—	2	1	no	—
193	C₁₃×#124	D₄	1	2	yes	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#124	C₂³	1	1	yes	characteristic
196	C₁₃×#123	—	2	1	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	1	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	1	no	—
223	C₁₃×#121	—	2	1	no	—
224	C₁₃×#121	—	2	1	no	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	—	2	2	no	—
229	C₁₃×#121	—	2	2	no	—
230	C₁₃×#121	D₄	1	1	yes	characteristic
231	C₁₃×#121	D₄	1	1	yes	characteristic
232	C₁₃×#121	D₄	1	2	yes	—
233	C₁₃×#121	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₁₃	—	2	1	no	—
249	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
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	—	2	1	no	—
258	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₁₃	C₂³	1	2	yes	—
267	C₁₃×#117	—	2	1	no	—
268	C₁₃×#117	C₂³	1	2	yes	—
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	2	yes	—
280	C₁₃×#107	C₂³	1	2	yes	—
281	C₁₃×#107	C₂³	1	1	yes	characteristic
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	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	1	yes	characteristic
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	C₄×C₈×C₁₃	C₂³	1	2	yes	—
316	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
318	#61657	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂⁴×C₁₃	—	2	1	no	—
320	C₂⁴×C₁₃	—	2	2	no	—
321	C₂⁴×C₁₃	—	2	2	no	—
322	C₂⁴×C₁₃	—	2	2	no	—
323	C₁₃×#41	—	2	4	no	—
324	C₁₃×#41	—	2	4	no	—
325	C₁₃×#41	—	4	2	no	—
326	C₁₃×#41	—	4	2	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	2	no	—
332	C₁₃×#41	—	4	2	no	—
333	C₁₃×#41	—	4	8	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	2	yes	—
339	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	2	4	no	—
343	C₂×D₄×C₁₃	—	2	4	no	—
344	C₂×D₄×C₁₃	—	2	2	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	2	no	—
347	C₂×D₄×C₁₃	—	2	1	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	1	no	—
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	2	no	—
360	C₂×D₄×C₁₃	—	2	1	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	4	2	no	—
364	C₂×D₄×C₁₃	—	4	2	no	—
365	C₂×D₄×C₁₃	—	4	2	no	—
366	C₂×D₄×C₁₃	—	4	2	no	—
367	C₂×D₄×C₁₃	—	4	8	no	—
368	C₂×D₄×C₁₃	—	4	8	no	—
369	C₂×D₄×C₁₃	—	4	8	no	—
370	C₂×D₄×C₁₃	—	8	2	no	—
371	C₂×D₄×C₁₃	—	8	2	no	—
372	C₂×D₄×C₁₃	—	8	2	no	—
373	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
378	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
380	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
382	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	2	no	—
386	C₂²×C₄×C₁₃	—	2	2	no	—
387	C₂²×C₄×C₁₃	—	2	2	no	—
388	C₂²×C₄×C₁₃	—	2	1	no	—
389	C₂²×C₄×C₁₃	—	2	1	no	—
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	2	1	no	—
393	C₂²×C₄×C₁₃	—	2	1	no	—
394	C₂²×C₄×C₁₃	—	2	2	no	—
395	C₂²×C₄×C₁₃	—	2	2	no	—
396	C₂²×C₄×C₁₃	—	8	2	no	—
397	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
401	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
402	C₁₃×Q₁₆	—	4	2	no	—
403	C₁₃×SD₁₆	—	2	2	no	—
404	C₁₃×SD₁₆	—	2	2	no	—
405	C₁₃×SD₁₆	—	4	2	no	—
406	C₁₃×SD₁₆	—	4	2	no	—
407	C₁₃×SD₁₆	—	4	2	no	—
408	C₁₃×SD₁₆	—	4	2	no	—
409	C₁₃×D₈	—	2	2	no	—
410	C₁₃×D₈	—	2	4	no	—
411	C₁₃×D₈	—	2	4	no	—
412	C₁₃×D₈	—	2	2	no	—
413	C₁₃×D₈	—	4	2	no	—
414	C₁₃×D₈	—	4	2	no	—
415	C₁₃×D₈	—	4	2	no	—
416	C₁₃×M₁₆	—	4	2	no	—
417	C₁₃×M₁₆	—	4	2	no	—
418	C₂×C₈×C₁₃	—	4	2	no	—
419	C₂×C₈×C₁₃	—	4	2	no	—
420	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
422	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
423	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
426	C₁₃×C₄⋊C₄	—	2	1	no	—
427	C₁₃×C₄⋊C₄	—	2	2	no	—
428	C₁₃×C₄⋊C₄	—	2	2	no	—
429	C₁₃×C₄⋊C₄	—	2	1	no	—
430	C₁₃×C₄⋊C₄	—	2	2	no	—
431	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
437	C₁₃×C₄⋊C₄	—	2	1	no	—
438	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
441	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
444	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	1	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	2	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	1	no	—
461	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
466	C₁₃×C₂²⋊C₄	—	2	1	no	—
467	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
472	C₄²×C₁₃	—	2	1	no	—
473	C₄²×C₁₃	—	2	2	no	—
474	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
477	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
478	#3546	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3322	C₂×C₁₃	1	2	yes	complemented
483	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3297	C₂×C₁₃	1	2	yes	complemented
485	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3280	C₂×C₁₃	1	2	yes	complemented
488	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
490	#3273	C₂×C₁₃	1	2	yes	complemented
491	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3203	C₂×C₁₃	1	2	yes	complemented
495	#3198	C₂×C₁₃	1	2	yes	complemented
496	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3012	C₂×C₁₃	1	2	yes	complemented
499	#3008	C₂×C₁₃	1	2	yes	complemented
500	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
501	C₂³×C₁₃	—	2	4	no	—
502	C₂³×C₁₃	—	2	1	no	—
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	—	4	4	no	—
508	C₂³×C₁₃	—	4	4	no	—
509	C₂³×C₁₃	—	8	1	no	—
510	C₂³×C₁₃	—	8	1	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	C₂²×D₄	1	2	yes	—
519	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
520	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
521	Q₈×C₁₃	—	2	1	no	—
522	Q₈×C₁₃	—	2	1	no	—
523	Q₈×C₁₃	—	2	2	no	—
524	Q₈×C₁₃	—	2	2	no	—
525	Q₈×C₁₃	—	4	2	no	—
526	Q₈×C₁₃	—	4	2	no	—
527	D₄×C₁₃	—	2	4	no	—
528	D₄×C₁₃	—	2	2	no	—
529	D₄×C₁₃	—	2	2	no	—
530	D₄×C₁₃	—	2	1	no	—
531	D₄×C₁₃	—	2	1	no	—
532	D₄×C₁₃	—	2	1	no	—
533	D₄×C₁₃	—	2	2	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	—	4	2	no	—
539	D₄×C₁₃	—	4	2	no	—
540	D₄×C₁₃	—	4	2	no	—
541	D₄×C₁₃	—	4	2	no	—
542	D₄×C₁₃	—	4	4	no	—
543	D₄×C₁₃	—	4	4	no	—
544	D₄×C₁₃	—	4	4	no	—
545	D₄×C₁₃	—	4	4	no	—
546	D₄×C₁₃	—	4	4	no	—
547	D₄×C₁₃	—	4	2	no	—
548	D₄×C₁₃	—	4	2	no	—
549	D₄×C₁₃	—	8	1	no	—
550	D₄×C₁₃	—	8	1	no	—
551	D₄×C₁₃	—	8	2	no	—
552	D₄×C₁₃	—	8	1	no	—
553	D₄×C₁₃	—	8	2	no	—
554	D₄×C₁₃	—	8	2	no	—
555	D₄×C₁₃	—	8	2	no	—
556	D₄×C₁₃	—	8	2	no	—
557	D₄×C₁₃	—	8	2	no	—
558	D₄×C₁₃	—	8	2	no	—
559	D₄×C₁₃	—	8	2	no	—
560	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
561	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	2	no	—
564	C₂×C₄×C₁₃	—	2	2	no	—
565	C₂×C₄×C₁₃	—	2	2	no	—
566	C₂×C₄×C₁₃	—	2	2	no	—
567	C₂×C₄×C₁₃	—	2	1	no	—
568	C₂×C₄×C₁₃	—	2	1	no	—
569	C₂×C₄×C₁₃	—	2	1	no	—
570	C₂×C₄×C₁₃	—	2	1	no	—
571	C₂×C₄×C₁₃	—	2	2	no	—
572	C₂×C₄×C₁₃	—	2	1	no	—
573	C₂×C₄×C₁₃	—	2	1	no	—
574	C₂×C₄×C₁₃	—	2	1	no	—
575	C₂×C₄×C₁₃	—	2	2	no	—
576	C₂×C₄×C₁₃	—	4	1	no	—
577	C₂×C₄×C₁₃	—	4	4	no	—
578	C₂×C₄×C₁₃	—	4	4	no	—
579	C₂×C₄×C₁₃	—	4	4	no	—
580	C₂×C₄×C₁₃	—	4	2	no	—
581	C₂×C₄×C₁₃	—	4	2	no	—
582	C₂×C₄×C₁₃	—	4	2	no	—
583	C₂×C₄×C₁₃	—	8	1	no	—
584	C₂×C₄×C₁₃	—	8	1	no	—
585	C₂×C₄×C₁₃	—	8	2	no	—
586	C₂×C₄×C₁₃	—	8	2	no	—
587	C₂×C₄×C₁₃	—	8	1	no	—
588	C₂×C₄×C₁₃	—	8	2	no	—
589	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
590	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
592	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
593	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
595	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
597	C₈×C₁₃	—	2	1	no	—
598	C₈×C₁₃	—	2	2	no	—
599	C₈×C₁₃	—	2	1	no	—
600	C₈×C₁₃	—	2	2	no	—
601	C₈×C₁₃	—	2	1	no	—
602	C₈×C₁₃	—	2	1	no	—
603	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
604	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
605	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
606	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
607	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
608	#560	—	2	2	no	—
609	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#553	C₂²×C₁₃	1	2	yes	complemented
611	#550	—	2	1	no	—
612	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#547	—	2	1	no	—
614	#547	C₂²×C₁₃	1	1	yes	characteristic
615	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	#546	—	2	2	no	—
618	#546	—	2	1	no	—
619	#546	C₂²×C₁₃	1	2	yes	complemented
620	#546	C₂²×C₁₃	1	2	yes	complemented
621	#546	C₂²×C₁₃	1	2	yes	complemented
622	D₄²	—	2	1	no	—
623	D₄²	C₂²×C₁₃	1	1	yes	characteristic
624	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	D₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#542	—	2	1	no	—
627	#538	—	2	2	no	—
628	#537	C₂²×C₁₃	1	2	yes	complemented
629	#537	C₂²×C₁₃	1	2	yes	complemented
630	#535	—	2	1	no	—
631	#535	C₂²×C₁₃	1	2	yes	complemented
632	#534	—	2	2	no	—
633	#532	C₂²×C₁₃	1	1	yes	characteristic
634	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	C₂×#121	—	2	1	no	—
638	C₂×#121	—	2	1	no	—
639	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#495	C₂²×C₁₃	1	2	yes	complemented
641	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#488	C₂²×C₁₃	1	2	yes	complemented
644	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	#485	C₂²×C₁₃	1	2	yes	complemented
647	#484	C₂²×C₁₃	1	2	yes	complemented
648	#484	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#482	C₂²×C₁₃	1	2	yes	complemented
650	#481	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#480	C₂²×C₁₃	1	2	yes	complemented
652	#480	C₂²×C₁₃	1	2	yes	complemented
653	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#469	C₂²×C₁₃	1	2	yes	complemented
658	#468	C₂²×C₁₃	1	2	yes	complemented
659	#468	C₂²×C₁₃	1	2	yes	complemented
660	#468	C₂²×C₁₃	1	2	yes	complemented
661	#467	C₂²×C₁₃	1	2	yes	complemented
662	#466	C₂²×C₁₃	1	2	yes	complemented
663	#466	C₂²×C₁₃	1	2	yes	complemented
664	#465	C₂²×C₁₃	1	2	yes	complemented
665	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
666	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#463	C₂²×C₁₃	1	2	yes	complemented
668	#463	C₂²×C₁₃	1	2	yes	complemented
669	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
671	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
673	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
675	#452	C₂²×C₁₃	1	2	yes	complemented
676	#452	C₂²×C₁₃	1	2	yes	complemented
677	#452	C₂²×C₁₃	1	2	yes	complemented
678	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	#450	C₂²×C₁₃	1	2	yes	complemented
680	#450	C₂²×C₁₃	1	2	yes	complemented
681	#449	C₂²×C₁₃	1	2	yes	complemented
682	#449	C₂²×C₁₃	1	2	yes	complemented
683	#449	C₂²×C₁₃	1	2	yes	complemented
684	#449	C₂²×C₁₃	1	2	yes	complemented
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	#447	C₂²×C₁₃	1	1	yes	characteristic
689	#447	C₂²×C₁₃	1	2	yes	complemented
690	#447	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	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
695	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
696	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
697	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
698	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
699	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#436	C₂²×C₁₃	1	2	yes	complemented
703	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
704	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
705	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
706	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
707	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
708	#418	C₂²×C₁₃	1	2	yes	complemented
709	#417	C₂²×C₁₃	1	2	yes	complemented
710	#416	C₂²×C₁₃	1	2	yes	complemented
711	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
712	#408	C₂²×C₁₃	1	2	yes	complemented
713	#408	C₂²×C₁₃	1	2	yes	complemented
714	C₂²×C₁₃	—	2	1	no	—
715	C₂²×C₁₃	—	2	2	no	—
716	C₂²×C₁₃	—	2	2	no	—
717	C₂²×C₁₃	—	2	1	no	—
718	C₂²×C₁₃	—	2	2	no	—
719	C₂²×C₁₃	—	2	2	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	—	4	1	no	—
726	C₂²×C₁₃	—	4	1	no	—
727	C₂²×C₁₃	—	4	1	no	—
728	C₂²×C₁₃	—	4	1	no	—
729	C₂²×C₁₃	—	4	2	no	—
730	C₂²×C₁₃	—	4	2	no	—
731	C₂²×C₁₃	—	4	1	no	—
732	C₂²×C₁₃	—	4	2	no	—
733	C₂²×C₁₃	—	4	2	no	—
734	C₂²×C₁₃	—	4	1	no	—
735	C₂²×C₁₃	—	4	1	no	—
736	C₂²×C₁₃	—	4	2	no	—
737	C₂²×C₁₃	—	4	2	no	—
738	C₂²×C₁₃	—	8	4	no	—
739	C₂²×C₁₃	—	16	4	no	—
740	C₂²×C₁₃	—	16	4	no	—
741	C₂²×C₁₃	—	16	4	no	—
742	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
743	C₄×C₁₃	—	2	1	no	—
744	C₄×C₁₃	—	2	1	no	—
745	C₄×C₁₃	—	2	1	no	—
746	C₄×C₁₃	—	2	2	no	—
747	C₄×C₁₃	—	2	2	no	—
748	C₄×C₁₃	—	2	1	no	—
749	C₄×C₁₃	—	4	1	no	—
750	C₄×C₁₃	—	4	2	no	—
751	C₄×C₁₃	—	4	1	no	—
752	C₄×C₁₃	—	4	1	no	—
753	C₄×C₁₃	—	4	1	no	—
754	C₄×C₁₃	—	4	1	no	—
755	C₄×C₁₃	—	4	2	no	—
756	C₄×C₁₃	#576	1	2	yes	—
757	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
758	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
759	H(5,𝔽₂)	—	4	4	no	—
760	H(5,𝔽₂)	—	4	4	no	—
761	C₂×#41	—	2	2	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	C₂³×C₁₃	1	2	yes	—
765	C₂×#41	C₂³×C₁₃	1	2	yes	—
766	C₂×#41	C₂³×C₁₃	1	2	yes	—
767	C₂×#41	C₂³×C₁₃	1	2	yes	—
768	C₂×#41	C₂³×C₁₃	1	2	yes	—
769	C₂²×D₄	—	2	2	no	—
770	C₂²×D₄	—	2	2	no	—
771	C₂²×D₄	—	2	2	no	—
772	C₂²×D₄	—	2	1	no	—
773	C₂²×D₄	—	2	1	no	—
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
776	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
777	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
778	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
779	C₂³×C₄	—	2	1	no	—
780	AGL(1,ℤ/8)	—	4	4	no	—
781	AGL(1,ℤ/8)	—	4	4	no	—
782	#135	—	4	4	no	—
783	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
785	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
787	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
788	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
789	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
790	C₂×D₈	—	4	4	no	—
791	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
792	C₂×D₈	C₂³×C₁₃	1	2	yes	—
793	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×D₈	C₂³×C₁₃	1	2	yes	—
795	C₂×D₈	C₂³×C₁₃	1	2	yes	—
796	C₂×D₈	C₂³×C₁₃	1	2	yes	—
797	C₂×D₈	C₂³×C₁₃	1	2	yes	—
798	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
799	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
800	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
801	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
802	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
803	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
805	#127	—	2	1	no	—
806	#127	—	2	2	no	—
807	#127	D₄×C₁₃	1	1	yes	characteristic
808	#127	C₂³×C₁₃	1	1	yes	characteristic
809	#127	C₂³×C₁₃	1	1	yes	characteristic
810	#126	—	2	2	no	—
811	#126	—	2	2	no	—
812	#126	—	2	1	no	—
813	#125	C₂³×C₁₃	1	1	yes	characteristic
814	#124	—	2	2	no	—
815	#124	—	2	1	no	—
816	#124	—	2	1	no	—
817	#124	D₄×C₁₃	1	2	yes	—
818	#124	C₂³×C₁₃	1	1	yes	characteristic
819	#124	C₂³×C₁₃	1	2	yes	—
820	#123	—	2	1	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
832	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
834	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	1	no	—
845	#121	—	2	1	no	—
846	#121	—	2	1	no	—
847	#121	—	2	1	no	—
848	#121	—	2	1	no	—
849	#121	—	2	1	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	D₄×C₁₃	1	1	yes	characteristic
855	#121	D₄×C₁₃	1	1	yes	characteristic
856	#121	D₄×C₁₃	1	2	yes	—
857	#121	C₂³×C₁₃	1	1	yes	characteristic
858	#121	C₂³×C₁₃	1	2	yes	—
859	#121	C₂³×C₁₃	1	2	yes	—
860	#121	C₂³×C₁₃	1	2	yes	—
861	#121	C₂³×C₁₃	1	2	yes	—
862	#121	C₂³×C₁₃	1	2	yes	—
863	#121	C₂³×C₁₃	1	2	yes	—
864	#120	—	2	2	no	—
865	#120	—	2	2	no	—
866	#120	—	2	2	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	C₄×Q₈	—	2	1	no	—
873	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	2	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
884	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
885	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
886	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
887	C₄×D₄	C₂³×C₁₃	1	2	yes	—
888	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
889	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₁₃	1	2	yes	—
891	#117	—	2	1	no	—
892	#117	C₂³×C₁₃	1	2	yes	—
893	C₂×C₄⋊C₄	—	2	1	no	—
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
897	C₂×C₂²⋊C₄	—	2	1	no	—
898	C₂×C₂²⋊C₄	—	2	2	no	—
899	C₂×C₂²⋊C₄	—	2	2	no	—
900	C₂×C₂²⋊C₄	—	2	2	no	—
901	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
902	#107	C₂³×C₁₃	1	1	yes	characteristic
903	#107	C₂³×C₁₃	1	2	yes	—
904	#107	C₂³×C₁₃	1	2	yes	—
905	#107	C₂³×C₁₃	1	1	yes	characteristic
906	#106	C₂³×C₁₃	1	1	yes	characteristic
907	#106	C₂³×C₁₃	1	1	yes	characteristic
908	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
909	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
910	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
912	#103	C₂³×C₁₃	1	2	yes	—
913	#103	C₂³×C₁₃	1	2	yes	—
914	#103	C₂³×C₁₃	1	2	yes	—
915	#103	C₂³×C₁₃	1	2	yes	—
916	#103	C₂³×C₁₃	1	1	yes	characteristic
917	#103	C₂³×C₁₃	1	1	yes	characteristic
918	#102	C₂³×C₁₃	1	1	yes	characteristic
919	#102	C₂³×C₁₃	1	2	yes	—
920	#102	C₂³×C₁₃	1	2	yes	—
921	#102	C₂³×C₁₃	1	2	yes	—
922	#102	C₂³×C₁₃	1	1	yes	characteristic
923	#102	C₂³×C₁₃	1	1	yes	characteristic
924	#102	C₂³×C₁₃	1	2	yes	—
925	#102	C₂³×C₁₃	1	1	yes	characteristic
926	#102	C₂³×C₁₃	1	2	yes	—
927	#102	C₂³×C₁₃	1	2	yes	—
928	#102	C₂³×C₁₃	1	1	yes	characteristic
929	#102	C₂³×C₁₃	1	2	yes	—
930	#102	C₂³×C₁₃	1	2	yes	—
931	#102	C₂³×C₁₃	1	1	yes	characteristic
932	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
933	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
935	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
939	C₄×C₈	C₂³×C₁₃	1	2	yes	—
940	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
941	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
942	C₂×C₁₃	—	4	1	no	—
943	C₂×C₁₃	—	4	2	no	—
944	C₂×C₁₃	—	4	2	no	—
945	C₂×C₁₃	—	4	2	no	—
946	C₂×C₁₃	—	4	2	no	—
947	C₂×C₁₃	—	8	2	no	—
948	C₂×C₁₃	—	8	2	no	—
949	C₂×C₁₃	—	8	1	no	—
950	C₂×C₁₃	#3484	1	1	yes	characteristic
951	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
952	C₂×C₁₃	#3584	1	1	yes	characteristic
953	C₂⁴	—	2	1	no	—
954	C₂⁴	—	2	2	no	—
955	C₂⁴	—	2	2	no	—
956	C₂⁴	—	2	2	no	—
957	#41	—	2	4	no	—
958	#41	—	2	4	no	—
959	#41	—	4	2	no	—
960	#41	—	4	2	no	—
961	#41	—	4	2	no	—
962	#41	—	4	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	4	2	no	—
967	#41	—	4	8	no	—
968	#41	—	8	2	no	—
969	#41	—	8	2	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
972	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
973	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	4	no	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	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	1	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	4	2	no	—
998	C₂×D₄	—	4	2	no	—
999	C₂×D₄	—	4	2	no	—
1000	C₂×D₄	—	4	2	no	—
1001	C₂×D₄	—	4	8	no	—
1002	C₂×D₄	—	4	8	no	—
1003	C₂×D₄	—	4	8	no	—
1004	C₂×D₄	—	8	2	no	—
1005	C₂×D₄	—	8	2	no	—
1006	C₂×D₄	—	8	2	no	—
1007	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1008	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1010	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1011	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1012	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1013	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1015	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1016	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	8	2	no	—
1031	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1032	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1035	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1036	Q₁₆	—	4	2	no	—
1037	SD₁₆	—	2	2	no	—
1038	SD₁₆	—	2	2	no	—
1039	SD₁₆	—	4	2	no	—
1040	SD₁₆	—	4	2	no	—
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	D₈	—	2	2	no	—
1044	D₈	—	2	4	no	—
1045	D₈	—	2	4	no	—
1046	D₈	—	2	2	no	—
1047	D₈	—	4	2	no	—
1048	D₈	—	4	2	no	—
1049	D₈	—	4	2	no	—
1050	M₁₆	—	4	2	no	—
1051	M₁₆	—	4	2	no	—
1052	C₂×C₈	—	4	2	no	—
1053	C₂×C₈	—	4	2	no	—
1054	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1055	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1057	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1058	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1059	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1075	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1078	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1103	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1104	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	2	no	—
1108	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1109	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1110	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1111	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1112	C₁₃	#61657	1	1	yes	characteristic, direct product factor, Sylow
1113	C₂³	—	2	4	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	2	1	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	4	4	no	—
1120	C₂³	—	4	4	no	—
1121	C₂³	—	8	1	no	—
1122	C₂³	—	8	1	no	—
1123	C₂³	—	8	2	no	—
1124	C₂³	—	8	2	no	—
1125	C₂³	—	8	2	no	—
1126	C₂³	—	8	2	no	—
1127	C₂³	—	8	2	no	—
1128	C₂³	—	8	2	no	—
1129	C₂³	—	8	2	no	—
1130	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1131	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1132	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	4	2	no	—
1138	Q₈	—	4	2	no	—
1139	D₄	—	2	4	no	—
1140	D₄	—	2	2	no	—
1141	D₄	—	2	2	no	—
1142	D₄	—	2	1	no	—
1143	D₄	—	2	1	no	—
1144	D₄	—	2	1	no	—
1145	D₄	—	2	2	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	1	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	4	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	4	4	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	4	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	8	2	no	—
1162	D₄	—	8	1	no	—
1163	D₄	—	8	1	no	—
1164	D₄	—	8	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	1	no	—
1168	D₄	—	8	2	no	—
1169	D₄	—	8	2	no	—
1170	D₄	—	8	2	no	—
1171	D₄	—	8	2	no	—
1172	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1173	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	4	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	2	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	—	8	2	no	—
1201	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1207	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1208	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1209	C₈	—	2	1	no	—
1210	C₈	—	2	2	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	2	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	1	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	8	4	no	—
1240	C₂²	—	16	4	no	—
1241	C₂²	—	16	4	no	—
1242	C₂²	—	16	4	no	—
1243	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1244	C₄	—	2	1	no	—
1245	C₄	—	2	1	no	—
1246	C₄	—	2	1	no	—
1247	C₄	—	2	1	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	2	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	C₁₃×#576	1	2	yes	—
1258	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1259	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1260	C₂	—	4	1	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	4	2	no	—
1265	C₂	—	8	1	no	—
1266	C₂	—	8	2	no	—
1267	C₂	—	8	2	no	—
1268	C₂	C₁₃×#3484	1	1	yes	characteristic
1269	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1270	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×#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×#3496	C₂	semidirect
3. C₁₃×#3330	C₂	semidirect
4. C₁₃×#3324	C₂	semidirect
5. C₁₃×#3322	C₂	semidirect
6. C₁₃×#3302	C₂	semidirect
7. C₁₃×#3297	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. C₁₃×#3284	C₂	semidirect
10. C₁₃×#3280	C₂	semidirect
11. D₄×C₁₃×D₈	C₂	semidirect
12. C₁₃×#3274	C₂	semidirect
13. C₁₃×#3273	C₂	semidirect
14. C₁₃×#3272	C₂	semidirect
15. C₁₃×#3212	C₂	semidirect
16. C₁₃×#3207	C₂	semidirect
17. C₁₃×#3203	C₂	semidirect
18. C₁₃×#3198	C₂	semidirect
19. C₁₃×#3105	C₂	semidirect
20. C₁₃×#3100	C₂	semidirect
21. C₁₃×#3012	C₂	semidirect
22. C₁₃×#3008	C₂	semidirect
23. C₁₃×#2979	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
33. C₁₃×#550	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
45. D₄²×C₁₃	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
49. C₁₃×#537	C₂²	semidirect
50. C₁₃×#537	C₂²	semidirect
52. C₁₃×#535	C₂²	semidirect
55. C₁₃×#532	C₂²	semidirect
56. C₁₃×#532	C₂²	semidirect
57. C₁₃×#529	C₂²	semidirect
60. C₂×C₄×D₄×C₁₃	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
62. C₁₃×#493	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#484	C₂²	semidirect
69. C₁₃×#484	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#481	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#474	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#469	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#468	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#467	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#466	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#461	C₂²	semidirect
92. C₁₃×#460	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×#452	C₂²	semidirect
99. C₁₃×#450	C₂²	semidirect
100. C₁₃×#450	C₂²	semidirect
101. C₁₃×#450	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×#449	C₂²	semidirect
108. C₁₃×#449	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. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×D₈	C₂²	semidirect
118. C₄×C₁₃×D₈	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#436	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₈×D₄×C₁₃	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₁₃×#431	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. #61657	C₁₃	direct (N × H)
478. #3546	C₂×C₁₃	semidirect
479. #3496	C₂×C₁₃	semidirect
480. #3330	C₂×C₁₃	semidirect
481. #3324	C₂×C₁₃	semidirect
482. #3322	C₂×C₁₃	semidirect
483. #3302	C₂×C₁₃	semidirect
484. #3297	C₂×C₁₃	semidirect
485. #3294	C₂×C₁₃	semidirect
486. #3284	C₂×C₁₃	semidirect
487. #3280	C₂×C₁₃	semidirect
488. D₄×D₈	C₂×C₁₃	semidirect
489. #3274	C₂×C₁₃	semidirect
490. #3273	C₂×C₁₃	semidirect
491. #3272	C₂×C₁₃	semidirect
492. #3212	C₂×C₁₃	semidirect
493. #3207	C₂×C₁₃	semidirect
494. #3203	C₂×C₁₃	semidirect
495. #3198	C₂×C₁₃	semidirect
496. #3105	C₂×C₁₃	semidirect
497. #3100	C₂×C₁₃	semidirect
498. #3012	C₂×C₁₃	semidirect
499. #3008	C₂×C₁₃	semidirect
500. #2979	C₂×C₁₃	semidirect
603. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
604. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
605. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
606. C₂×#135	C₂²×C₁₃	semidirect
607. C₂²×D₈	C₂²×C₁₃	semidirect
609. #556	C₂²×C₁₃	semidirect
610. #553	C₂²×C₁₃	semidirect
612. #550	C₂²×C₁₃	semidirect
615. #547	C₂²×C₁₃	semidirect
616. #547	C₂²×C₁₃	semidirect
619. #546	C₂²×C₁₃	semidirect
620. #546	C₂²×C₁₃	semidirect
621. #546	C₂²×C₁₃	semidirect
624. D₄²	C₂²×C₁₃	semidirect
625. D₄²	C₂²×C₁₃	semidirect
628. #537	C₂²×C₁₃	semidirect
629. #537	C₂²×C₁₃	semidirect
631. #535	C₂²×C₁₃	semidirect
634. #532	C₂²×C₁₃	semidirect
635. #532	C₂²×C₁₃	semidirect
636. #529	C₂²×C₁₃	semidirect
639. C₂×C₄×D₄	C₂²×C₁₃	semidirect
640. #495	C₂²×C₁₃	semidirect
641. #493	C₂²×C₁₃	semidirect
642. #492	C₂²×C₁₃	semidirect
643. #488	C₂²×C₁₃	semidirect
644. #487	C₂²×C₁₃	semidirect
645. #486	C₂²×C₁₃	semidirect
646. #485	C₂²×C₁₃	semidirect
647. #484	C₂²×C₁₃	semidirect
648. #484	C₂²×C₁₃	semidirect
649. #482	C₂²×C₁₃	semidirect
650. #481	C₂²×C₁₃	semidirect
651. #480	C₂²×C₁₃	semidirect
652. #480	C₂²×C₁₃	semidirect
653. #478	C₂²×C₁₃	semidirect
654. #478	C₂²×C₁₃	semidirect
655. #474	C₂²×C₁₃	semidirect
656. #474	C₂²×C₁₃	semidirect
657. #469	C₂²×C₁₃	semidirect
658. #468	C₂²×C₁₃	semidirect
659. #468	C₂²×C₁₃	semidirect
660. #468	C₂²×C₁₃	semidirect
661. #467	C₂²×C₁₃	semidirect
662. #466	C₂²×C₁₃	semidirect
663. #466	C₂²×C₁₃	semidirect
664. #465	C₂²×C₁₃	semidirect
665. #463	C₂²×C₁₃	semidirect
666. #463	C₂²×C₁₃	semidirect
667. #463	C₂²×C₁₃	semidirect
668. #463	C₂²×C₁₃	semidirect
669. #462	C₂²×C₁₃	semidirect
670. #461	C₂²×C₁₃	semidirect
671. #460	C₂²×C₁₃	semidirect
672. #459	C₂²×C₁₃	semidirect
673. #459	C₂²×C₁₃	semidirect
674. #459	C₂²×C₁₃	semidirect
675. #452	C₂²×C₁₃	semidirect
676. #452	C₂²×C₁₃	semidirect
677. #452	C₂²×C₁₃	semidirect
678. #450	C₂²×C₁₃	semidirect
679. #450	C₂²×C₁₃	semidirect
680. #450	C₂²×C₁₃	semidirect
681. #449	C₂²×C₁₃	semidirect
682. #449	C₂²×C₁₃	semidirect
683. #449	C₂²×C₁₃	semidirect
684. #449	C₂²×C₁₃	semidirect
685. #449	C₂²×C₁₃	semidirect
686. #449	C₂²×C₁₃	semidirect
687. #449	C₂²×C₁₃	semidirect
689. #447	C₂²×C₁₃	semidirect
690. #447	C₂²×C₁₃	semidirect
691. #447	C₂²×C₁₃	semidirect
692. #447	C₂²×C₁₃	semidirect
693. #447	C₂²×C₁₃	semidirect
694. C₄×SD₁₆	C₂²×C₁₃	semidirect
695. C₄×SD₁₆	C₂²×C₁₃	semidirect
696. C₄×D₈	C₂²×C₁₃	semidirect
697. C₄×D₈	C₂²×C₁₃	semidirect
698. C₄×D₈	C₂²×C₁₃	semidirect
699. C₄×D₈	C₂²×C₁₃	semidirect
700. #436	C₂²×C₁₃	semidirect
701. #436	C₂²×C₁₃	semidirect
702. #436	C₂²×C₁₃	semidirect
703. C₈×D₄	C₂²×C₁₃	semidirect
704. C₈×D₄	C₂²×C₁₃	semidirect
705. C₈×D₄	C₂²×C₁₃	semidirect
706. #431	C₂²×C₁₃	semidirect
707. #431	C₂²×C₁₃	semidirect
708. #418	C₂²×C₁₃	semidirect
709. #417	C₂²×C₁₃	semidirect
710. #416	C₂²×C₁₃	semidirect
711. C₂×#102	C₂²×C₁₃	semidirect
712. #408	C₂²×C₁₃	semidirect
713. #408	C₂²×C₁₃	semidirect
1112. C₁₃	#61657	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×#3496	2
C₁₃×#3330	2
C₁₃×#3324	2
C₁₃×#3322	2
C₁₃×#3302	2
C₁₃×#3297	2
C₁₃×#3294	2
C₁₃×#3284	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3273	2
C₁₃×#3272	2
C₁₃×#3212	2
C₁₃×#3207	2
C₁₃×#3203	2
C₁₃×#3198	2
C₁₃×#3105	2
C₁₃×#3100	2
C₁₃×#3012	2
C₁₃×#3008	2
C₁₃×#2979	2
#61657	13

Subgroups — C13×#61657 #15747996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61657 #15747996