Subgroups — C₁₃×#61689 #15748028

Order 3328.

2150 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3116	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×#3009	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	—
25	C₂×C₁₃×#137	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×SD₁₆	C₂²	1	2	yes	complemented
29	C₁₃×#562	—	2	2	no	—
30	C₁₃×#555	—	2	1	no	—
31	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#552	C₂²	1	2	yes	complemented
35	C₁₃×#550	C₂²	1	2	yes	—
36	C₁₃×#550	C₂²	1	1	yes	characteristic
37	C₁₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#548	C₂²	1	2	yes	complemented
40	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
41	D₄²×C₁₃	—	2	1	no	—
42	D₄²×C₁₃	—	2	1	no	—
43	D₄²×C₁₃	—	2	2	no	—
44	D₄²×C₁₃	C₂²	1	2	yes	—
45	D₄²×C₁₃	C₂²	1	1	yes	characteristic
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#544	—	2	1	no	—
48	C₁₃×#542	—	2	2	no	—
49	C₁₃×#540	—	2	1	no	—
50	C₁₃×#537	C₂²	1	2	yes	complemented
51	C₁₃×#536	C₂²	1	2	yes	complemented
52	C₁₃×#535	—	2	2	no	—
53	C₁₃×#535	C₂²	1	2	yes	—
54	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#532	—	2	1	no	—
56	C₁₃×#532	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#127	—	2	1	no	—
58	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
59	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
61	C₁₃×#496	C₂²	1	2	yes	complemented
62	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	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×#485	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	1	yes	characteristic, 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×#477	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#476	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×#466	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	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×#462	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#460	C₂²	1	2	yes	complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#460	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
97	C₁₃×#452	C₂²	1	2	yes	—
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#452	C₂²	1	2	yes	complemented
100	C₁₃×#452	C₂²	1	2	yes	complemented
101	C₁₃×#450	C₂²	1	2	yes	complemented
102	C₁₃×#450	C₂²	1	2	yes	complemented
103	C₁₃×#450	C₂²	1	2	yes	complemented
104	C₁₃×#450	C₂²	1	2	yes	complemented
105	C₁₃×#450	C₂²	1	2	yes	complemented
106	C₁₃×#450	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	1	yes	characteristic
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#449	C₂²	1	2	yes	complemented
110	C₁₃×#449	C₂²	1	2	yes	complemented
111	C₁₃×#448	C₂²	1	2	yes	complemented
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#447	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₁₃×#441	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	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
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	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₁₃	—	2	2	no	—
145	C₂²×D₄×C₁₃	—	2	2	no	—
146	C₂²×D₄×C₁₃	—	2	2	no	—
147	C₂²×D₄×C₁₃	—	2	1	no	—
148	C₂²×D₄×C₁₃	—	2	1	no	—
149	C₂²×D₄×C₁₃	—	2	2	no	—
150	C₂²×D₄×C₁₃	—	2	1	no	—
151	C₂²×D₄×C₁₃	—	2	1	no	—
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	C₁₃×#137	—	4	4	no	—
156	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
157	C₁₃×#135	—	4	4	no	—
158	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	—	4	4	no	—
161	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
170	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×D₈	C₂³	1	2	yes	—
172	C₂×C₁₃×D₈	C₂³	1	2	yes	—
173	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
174	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
177	C₁₃×C₄⋊Q₈	—	2	2	no	—
178	C₁₃×C₄⋊Q₈	—	2	1	no	—
179	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
180	C₁₃×C₄⋊Q₈	C₂³	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	1	no	—
188	C₁₃×#127	D₄	1	1	yes	characteristic
189	C₁₃×#127	C₂³	1	1	yes	characteristic
190	C₁₃×#127	C₂³	1	1	yes	characteristic
191	C₁₃×#127	C₂³	1	2	yes	—
192	C₁₃×#126	—	2	2	no	—
193	C₁₃×#126	—	2	1	no	—
194	C₁₃×#125	—	2	2	no	—
195	C₁₃×#125	—	2	1	no	—
196	C₁₃×#125	—	2	1	no	—
197	C₁₃×#125	C₂³	1	1	yes	characteristic
198	C₁₃×#124	—	2	2	no	—
199	C₁₃×#124	—	2	2	no	—
200	C₁₃×#124	—	2	2	no	—
201	C₁₃×#124	—	2	2	no	—
202	C₁₃×#124	D₄	1	2	yes	—
203	C₁₃×#124	C₂³	1	1	yes	characteristic
204	C₁₃×#123	—	2	2	no	—
205	C₁₃×#123	—	2	2	no	—
206	C₁₃×#123	—	2	2	no	—
207	C₁₃×#123	—	2	1	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	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	1	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	1	no	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	1	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	—	2	2	no	—
229	C₁₃×#121	—	2	2	no	—
230	C₁₃×#121	—	2	2	no	—
231	C₁₃×#121	—	2	2	no	—
232	C₁₃×#121	D₄	1	1	yes	characteristic
233	C₁₃×#121	D₄	1	1	yes	characteristic
234	C₁₃×#121	D₄	1	2	yes	—
235	C₁₃×#121	C₂³	1	1	yes	characteristic
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×#121	C₂³	1	2	yes	—
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	C₄×Q₈×C₁₃	—	2	1	no	—
248	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
251	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	—	2	1	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	—	2	1	no	—
259	C₄×D₄×C₁₃	—	2	2	no	—
260	C₄×D₄×C₁₃	—	2	2	no	—
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	—	2	1	no	—
269	C₁₃×#117	—	2	2	no	—
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	—	2	1	no	—
275	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
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	#61689	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	C₁₃×#41	—	2	2	no	—
323	C₁₃×#41	—	2	2	no	—
324	C₁₃×#41	—	2	4	no	—
325	C₁₃×#41	—	2	4	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	8	no	—
331	C₁₃×#41	—	4	2	no	—
332	C₁₃×#41	—	4	2	no	—
333	C₂×Q₈×C₁₃	—	2	1	no	—
334	C₂×Q₈×C₁₃	—	2	2	no	—
335	C₂×Q₈×C₁₃	—	4	2	no	—
336	C₂×Q₈×C₁₃	—	4	2	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	2	yes	—
340	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₁₃	—	2	1	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	1	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	1	no	—
355	C₂×D₄×C₁₃	—	2	1	no	—
356	C₂×D₄×C₁₃	—	2	2	no	—
357	C₂×D₄×C₁₃	—	2	2	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	—	4	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	8	no	—
367	C₂×D₄×C₁₃	—	4	8	no	—
368	C₂×D₄×C₁₃	—	4	8	no	—
369	C₂×D₄×C₁₃	—	8	2	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	—	8	4	no	—
374	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
380	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
388	C₂²×C₄×C₁₃	—	2	1	no	—
389	C₂²×C₄×C₁₃	—	2	1	no	—
390	C₂²×C₄×C₁₃	—	2	2	no	—
391	C₂²×C₄×C₁₃	—	2	2	no	—
392	C₂²×C₄×C₁₃	—	2	2	no	—
393	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
398	C₁₃×Q₁₆	—	2	4	no	—
399	C₁₃×Q₁₆	—	2	2	no	—
400	C₁₃×SD₁₆	—	2	2	no	—
401	C₁₃×SD₁₆	—	2	2	no	—
402	C₁₃×SD₁₆	—	2	4	no	—
403	C₁₃×SD₁₆	—	4	2	no	—
404	C₁₃×SD₁₆	—	4	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	—	4	2	no	—
411	C₁₃×D₈	—	4	2	no	—
412	C₁₃×M₁₆	—	4	2	no	—
413	C₁₃×M₁₆	—	4	2	no	—
414	C₂×C₈×C₁₃	—	4	2	no	—
415	C₂×C₈×C₁₃	—	4	2	no	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
421	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	2	no	—
424	C₁₃×C₄⋊C₄	—	2	2	no	—
425	C₁₃×C₄⋊C₄	—	2	1	no	—
426	C₁₃×C₄⋊C₄	—	2	1	no	—
427	C₁₃×C₄⋊C₄	—	2	1	no	—
428	C₁₃×C₄⋊C₄	—	2	1	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	1	no	—
431	C₁₃×C₄⋊C₄	—	2	1	no	—
432	C₁₃×C₄⋊C₄	—	2	2	no	—
433	C₁₃×C₄⋊C₄	—	2	2	no	—
434	C₁₃×C₄⋊C₄	—	2	1	no	—
435	C₁₃×C₄⋊C₄	—	2	2	no	—
436	C₁₃×C₄⋊C₄	—	2	1	no	—
437	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
442	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	1	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
463	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₄²×C₁₃	—	2	1	no	—
468	C₄²×C₁₃	—	2	1	no	—
469	C₄²×C₁₃	—	2	1	no	—
470	C₄²×C₁₃	—	2	2	no	—
471	C₄²×C₁₃	—	2	2	no	—
472	C₄²×C₁₃	—	2	1	no	—
473	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
476	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
477	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
480	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3317	C₂×C₁₃	1	2	yes	complemented
482	#3310	C₂×C₁₃	1	2	yes	complemented
483	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
485	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
486	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
488	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3271	C₂×C₁₃	1	2	yes	complemented
490	#3265	C₂×C₁₃	1	2	yes	complemented
491	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3200	C₂×C₁₃	1	2	yes	complemented
494	#3198	C₂×C₁₃	1	2	yes	complemented
495	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3012	C₂×C₁₃	1	2	yes	complemented
498	#3009	C₂×C₁₃	1	2	yes	complemented
499	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
500	C₂³×C₁₃	—	2	1	no	—
501	C₂³×C₁₃	—	2	1	no	—
502	C₂³×C₁₃	—	2	2	no	—
503	C₂³×C₁₃	—	2	2	no	—
504	C₂³×C₁₃	—	4	4	no	—
505	C₂³×C₁₃	—	4	4	no	—
506	C₂³×C₁₃	—	4	4	no	—
507	C₂³×C₁₃	—	8	2	no	—
508	C₂³×C₁₃	—	8	2	no	—
509	C₂³×C₁₃	—	8	2	no	—
510	C₂³×C₁₃	—	8	2	no	—
511	C₂³×C₁₃	—	8	2	no	—
512	C₂³×C₁₃	—	8	2	no	—
513	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
515	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
516	Q₈×C₁₃	—	2	1	no	—
517	Q₈×C₁₃	—	2	1	no	—
518	Q₈×C₁₃	—	2	2	no	—
519	Q₈×C₁₃	—	2	1	no	—
520	Q₈×C₁₃	—	2	2	no	—
521	Q₈×C₁₃	—	4	2	no	—
522	Q₈×C₁₃	—	8	1	no	—
523	Q₈×C₁₃	—	8	2	no	—
524	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
525	D₄×C₁₃	—	2	4	no	—
526	D₄×C₁₃	—	2	2	no	—
527	D₄×C₁₃	—	2	2	no	—
528	D₄×C₁₃	—	2	1	no	—
529	D₄×C₁₃	—	2	1	no	—
530	D₄×C₁₃	—	2	1	no	—
531	D₄×C₁₃	—	2	2	no	—
532	D₄×C₁₃	—	2	2	no	—
533	D₄×C₁₃	—	2	2	no	—
534	D₄×C₁₃	—	2	2	no	—
535	D₄×C₁₃	—	4	2	no	—
536	D₄×C₁₃	—	4	2	no	—
537	D₄×C₁₃	—	4	2	no	—
538	D₄×C₁₃	—	4	2	no	—
539	D₄×C₁₃	—	4	4	no	—
540	D₄×C₁₃	—	4	4	no	—
541	D₄×C₁₃	—	4	4	no	—
542	D₄×C₁₃	—	4	4	no	—
543	D₄×C₁₃	—	4	4	no	—
544	D₄×C₁₃	—	4	4	no	—
545	D₄×C₁₃	—	4	2	no	—
546	D₄×C₁₃	—	4	2	no	—
547	D₄×C₁₃	—	8	1	no	—
548	D₄×C₁₃	—	8	1	no	—
549	D₄×C₁₃	—	8	2	no	—
550	D₄×C₁₃	—	8	1	no	—
551	D₄×C₁₃	—	8	2	no	—
552	D₄×C₁₃	—	8	2	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	H(5,𝔽₂)	1	2	yes	—
558	C₂×C₄×C₁₃	—	2	4	no	—
559	C₂×C₄×C₁₃	—	2	1	no	—
560	C₂×C₄×C₁₃	—	2	2	no	—
561	C₂×C₄×C₁₃	—	2	2	no	—
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	1	no	—
566	C₂×C₄×C₁₃	—	2	1	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	2	no	—
571	C₂×C₄×C₁₃	—	2	1	no	—
572	C₂×C₄×C₁₃	—	2	1	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	4	1	no	—
575	C₂×C₄×C₁₃	—	4	4	no	—
576	C₂×C₄×C₁₃	—	4	4	no	—
577	C₂×C₄×C₁₃	—	4	2	no	—
578	C₂×C₄×C₁₃	—	4	2	no	—
579	C₂×C₄×C₁₃	—	4	2	no	—
580	C₂×C₄×C₁₃	—	8	2	no	—
581	C₂×C₄×C₁₃	—	8	2	no	—
582	C₂×C₄×C₁₃	—	8	2	no	—
583	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
586	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
587	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
588	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
589	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
590	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
591	C₈×C₁₃	—	2	1	no	—
592	C₈×C₁₃	—	2	1	no	—
593	C₈×C₁₃	—	2	2	no	—
594	C₈×C₁₃	—	2	2	no	—
595	C₈×C₁₃	—	2	1	no	—
596	C₈×C₁₃	—	2	1	no	—
597	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
598	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
599	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
600	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
601	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
602	#562	—	2	2	no	—
603	#555	—	2	1	no	—
604	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#553	—	2	1	no	—
607	#552	C₂²×C₁₃	1	2	yes	complemented
608	#550	C₂²×C₁₃	1	1	yes	characteristic
609	#550	C₂²×C₁₃	1	2	yes	—
610	#550	C₂²×C₁₃	1	1	yes	characteristic
611	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#548	C₂²×C₁₃	1	2	yes	complemented
613	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	D₄²	—	2	1	no	—
615	D₄²	—	2	1	no	—
616	D₄²	—	2	2	no	—
617	D₄²	C₂²×C₁₃	1	2	yes	—
618	D₄²	C₂²×C₁₃	1	1	yes	characteristic
619	D₄²	C₂²×C₁₃	1	1	yes	characteristic
620	#544	—	2	1	no	—
621	#542	—	2	2	no	—
622	#540	—	2	1	no	—
623	#537	C₂²×C₁₃	1	2	yes	complemented
624	#536	C₂²×C₁₃	1	2	yes	complemented
625	#535	—	2	2	no	—
626	#535	C₂²×C₁₃	1	2	yes	—
627	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#532	—	2	1	no	—
629	#532	C₂²×C₁₃	1	1	yes	characteristic
630	C₂×#127	—	2	1	no	—
631	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
632	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
634	#496	C₂²×C₁₃	1	2	yes	complemented
635	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#490	C₂²×C₁₃	1	2	yes	complemented
638	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#485	C₂²×C₁₃	1	2	yes	complemented
642	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#482	C₂²×C₁₃	1	2	yes	complemented
644	#482	C₂²×C₁₃	1	2	yes	complemented
645	#481	C₂²×C₁₃	1	2	yes	complemented
646	#480	C₂²×C₁₃	1	2	yes	complemented
647	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#469	C₂²×C₁₃	1	2	yes	complemented
652	#468	C₂²×C₁₃	1	2	yes	complemented
653	#468	C₂²×C₁₃	1	2	yes	complemented
654	#468	C₂²×C₁₃	1	2	yes	complemented
655	#466	C₂²×C₁₃	1	2	yes	complemented
656	#465	C₂²×C₁₃	1	2	yes	complemented
657	#465	C₂²×C₁₃	1	2	yes	complemented
658	#465	C₂²×C₁₃	1	2	yes	complemented
659	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	#460	C₂²×C₁₃	1	2	yes	complemented
665	#460	C₂²×C₁₃	1	2	yes	complemented
666	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	#452	C₂²×C₁₃	1	1	yes	characteristic
670	#452	C₂²×C₁₃	1	2	yes	—
671	#452	C₂²×C₁₃	1	2	yes	complemented
672	#452	C₂²×C₁₃	1	2	yes	complemented
673	#452	C₂²×C₁₃	1	2	yes	complemented
674	#450	C₂²×C₁₃	1	2	yes	complemented
675	#450	C₂²×C₁₃	1	2	yes	complemented
676	#450	C₂²×C₁₃	1	2	yes	complemented
677	#450	C₂²×C₁₃	1	2	yes	complemented
678	#450	C₂²×C₁₃	1	2	yes	complemented
679	#450	C₂²×C₁₃	1	2	yes	complemented
680	#449	C₂²×C₁₃	1	1	yes	characteristic
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	#448	C₂²×C₁₃	1	2	yes	complemented
685	#448	C₂²×C₁₃	1	2	yes	complemented
686	#447	C₂²×C₁₃	1	2	yes	complemented
687	#447	C₂²×C₁₃	1	2	yes	complemented
688	#441	C₂²×C₁₃	1	2	yes	complemented
689	#440	C₂²×C₁₃	1	2	yes	complemented
690	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
694	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
695	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
696	#435	C₂²×C₁₃	1	2	yes	complemented
697	#435	C₂²×C₁₃	1	2	yes	complemented
698	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
699	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
700	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
701	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
702	#418	C₂²×C₁₃	1	2	yes	complemented
703	#417	C₂²×C₁₃	1	2	yes	complemented
704	#416	C₂²×C₁₃	1	2	yes	complemented
705	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
706	#408	C₂²×C₁₃	1	2	yes	complemented
707	#408	C₂²×C₁₃	1	2	yes	complemented
708	C₂²×C₁₃	—	2	1	no	—
709	C₂²×C₁₃	—	2	2	no	—
710	C₂²×C₁₃	—	2	2	no	—
711	C₂²×C₁₃	—	2	2	no	—
712	C₂²×C₁₃	—	2	1	no	—
713	C₂²×C₁₃	—	2	2	no	—
714	C₂²×C₁₃	—	2	2	no	—
715	C₂²×C₁₃	—	2	1	no	—
716	C₂²×C₁₃	—	2	2	no	—
717	C₂²×C₁₃	—	2	2	no	—
718	C₂²×C₁₃	—	4	1	no	—
719	C₂²×C₁₃	—	4	1	no	—
720	C₂²×C₁₃	—	4	2	no	—
721	C₂²×C₁₃	—	4	2	no	—
722	C₂²×C₁₃	—	4	1	no	—
723	C₂²×C₁₃	—	4	2	no	—
724	C₂²×C₁₃	—	4	2	no	—
725	C₂²×C₁₃	—	4	1	no	—
726	C₂²×C₁₃	—	4	1	no	—
727	C₂²×C₁₃	—	4	2	no	—
728	C₂²×C₁₃	—	4	2	no	—
729	C₂²×C₁₃	—	16	4	no	—
730	C₂²×C₁₃	—	16	4	no	—
731	C₂²×C₁₃	—	16	4	no	—
732	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
733	C₄×C₁₃	—	2	1	no	—
734	C₄×C₁₃	—	2	1	no	—
735	C₄×C₁₃	—	2	1	no	—
736	C₄×C₁₃	—	2	2	no	—
737	C₄×C₁₃	—	2	2	no	—
738	C₄×C₁₃	—	2	2	no	—
739	C₄×C₁₃	—	2	1	no	—
740	C₄×C₁₃	—	4	1	no	—
741	C₄×C₁₃	—	4	1	no	—
742	C₄×C₁₃	—	4	2	no	—
743	C₄×C₁₃	—	4	2	no	—
744	C₄×C₁₃	—	4	1	no	—
745	C₄×C₁₃	—	4	1	no	—
746	C₄×C₁₃	—	4	1	no	—
747	C₄×C₁₃	#577	1	2	yes	—
748	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
750	H(5,𝔽₂)	—	4	4	no	—
751	H(5,𝔽₂)	—	4	4	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
754	C₂×#41	C₂³×C₁₃	1	2	yes	—
755	C₂×#41	C₂³×C₁₃	1	2	yes	—
756	C₂×#41	C₂³×C₁₃	1	2	yes	—
757	C₂×#41	C₂³×C₁₃	1	2	yes	—
758	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
759	C₂²×D₄	—	2	2	no	—
760	C₂²×D₄	—	2	2	no	—
761	C₂²×D₄	—	2	2	no	—
762	C₂²×D₄	—	2	1	no	—
763	C₂²×D₄	—	2	1	no	—
764	C₂²×D₄	—	2	2	no	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	—	2	1	no	—
767	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
768	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
769	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
770	#137	—	4	4	no	—
771	AGL(1,ℤ/8)	—	4	4	no	—
772	#135	—	4	4	no	—
773	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
774	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
775	C₂×SD₁₆	—	4	4	no	—
776	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
781	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
785	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×D₈	C₂³×C₁₃	1	2	yes	—
787	C₂×D₈	C₂³×C₁₃	1	2	yes	—
788	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
789	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
790	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
791	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
792	C₄⋊Q₈	—	2	2	no	—
793	C₄⋊Q₈	—	2	1	no	—
794	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
797	#127	—	2	2	no	—
798	#127	—	2	1	no	—
799	#127	—	2	1	no	—
800	#127	—	2	2	no	—
801	#127	—	2	1	no	—
802	#127	—	2	1	no	—
803	#127	D₄×C₁₃	1	1	yes	characteristic
804	#127	C₂³×C₁₃	1	1	yes	characteristic
805	#127	C₂³×C₁₃	1	1	yes	characteristic
806	#127	C₂³×C₁₃	1	2	yes	—
807	#126	—	2	2	no	—
808	#126	—	2	1	no	—
809	#125	—	2	2	no	—
810	#125	—	2	1	no	—
811	#125	—	2	1	no	—
812	#125	C₂³×C₁₃	1	1	yes	characteristic
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	—	2	2	no	—
817	#124	D₄×C₁₃	1	2	yes	—
818	#124	C₂³×C₁₃	1	1	yes	characteristic
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	1	no	—
823	#123	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
833	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	1	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	2	no	—
845	#121	—	2	2	no	—
846	#121	—	2	2	no	—
847	#121	D₄×C₁₃	1	1	yes	characteristic
848	#121	D₄×C₁₃	1	1	yes	characteristic
849	#121	D₄×C₁₃	1	2	yes	—
850	#121	C₂³×C₁₃	1	1	yes	characteristic
851	#121	C₂³×C₁₃	1	2	yes	—
852	#121	C₂³×C₁₃	1	2	yes	—
853	#121	C₂³×C₁₃	1	2	yes	—
854	#121	C₂³×C₁₃	1	2	yes	—
855	#121	C₂³×C₁₃	1	2	yes	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	#120	—	2	2	no	—
859	#120	—	2	2	no	—
860	#120	—	2	2	no	—
861	#120	—	2	2	no	—
862	C₄×Q₈	—	2	1	no	—
863	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
866	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	2	no	—
876	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
878	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×D₄	C₂³×C₁₃	1	2	yes	—
881	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
882	#117	—	2	1	no	—
883	#117	—	2	1	no	—
884	#117	—	2	2	no	—
885	#117	—	2	1	no	—
886	#117	—	2	1	no	—
887	#117	C₂³×C₁₃	1	1	yes	characteristic
888	#117	C₂³×C₁₃	1	2	yes	—
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
893	#107	C₂³×C₁₃	1	1	yes	characteristic
894	#107	C₂³×C₁₃	1	1	yes	characteristic
895	#107	C₂³×C₁₃	1	2	yes	—
896	#106	C₂³×C₁₃	1	1	yes	characteristic
897	#106	C₂³×C₁₃	1	1	yes	characteristic
898	#106	C₂³×C₁₃	1	2	yes	—
899	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
903	#103	C₂³×C₁₃	1	1	yes	characteristic
904	#103	C₂³×C₁₃	1	2	yes	—
905	#103	C₂³×C₁₃	1	1	yes	characteristic
906	#103	C₂³×C₁₃	1	1	yes	characteristic
907	#103	C₂³×C₁₃	1	1	yes	characteristic
908	#103	C₂³×C₁₃	1	2	yes	—
909	#103	C₂³×C₁₃	1	2	yes	—
910	#102	C₂³×C₁₃	1	1	yes	characteristic
911	#102	C₂³×C₁₃	1	2	yes	—
912	#102	C₂³×C₁₃	1	2	yes	—
913	#102	C₂³×C₁₃	1	2	yes	—
914	#102	C₂³×C₁₃	1	2	yes	—
915	#102	C₂³×C₁₃	1	2	yes	—
916	#102	C₂³×C₁₃	1	2	yes	—
917	#102	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
922	#102	C₂³×C₁₃	1	1	yes	characteristic
923	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
930	#97	C₂³×C₁₃	1	2	yes	—
931	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
933	C₂×C₁₃	—	4	2	no	—
934	C₂×C₁₃	—	4	2	no	—
935	C₂×C₁₃	—	4	1	no	—
936	C₂×C₁₃	—	4	2	no	—
937	C₂×C₁₃	—	8	1	no	—
938	C₂×C₁₃	—	8	2	no	—
939	C₂×C₁₃	—	8	2	no	—
940	C₂×C₁₃	#3484	1	1	yes	characteristic
941	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
942	C₂×C₁₃	#3585	1	1	yes	characteristic
943	C₂⁴	—	2	2	no	—
944	C₂⁴	—	2	2	no	—
945	C₂⁴	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	4	no	—
950	#41	—	4	2	no	—
951	#41	—	4	2	no	—
952	#41	—	4	2	no	—
953	#41	—	4	2	no	—
954	#41	—	4	8	no	—
955	#41	—	4	2	no	—
956	#41	—	4	2	no	—
957	C₂×Q₈	—	2	1	no	—
958	C₂×Q₈	—	2	2	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
964	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	4	no	—
967	C₂×D₄	—	2	4	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	4	2	no	—
987	C₂×D₄	—	4	2	no	—
988	C₂×D₄	—	4	2	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	4	8	no	—
991	C₂×D₄	—	4	8	no	—
992	C₂×D₄	—	4	8	no	—
993	C₂×D₄	—	8	2	no	—
994	C₂×D₄	—	8	2	no	—
995	C₂×D₄	—	8	2	no	—
996	C₂×D₄	—	8	2	no	—
997	C₂×D₄	—	8	4	no	—
998	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1001	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1002	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1003	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1004	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1005	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1006	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1007	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1021	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1022	Q₁₆	—	2	4	no	—
1023	Q₁₆	—	2	2	no	—
1024	SD₁₆	—	2	2	no	—
1025	SD₁₆	—	2	2	no	—
1026	SD₁₆	—	2	4	no	—
1027	SD₁₆	—	4	2	no	—
1028	SD₁₆	—	4	2	no	—
1029	SD₁₆	—	4	2	no	—
1030	SD₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	D₈	—	2	2	no	—
1034	D₈	—	4	2	no	—
1035	D₈	—	4	2	no	—
1036	M₁₆	—	4	2	no	—
1037	M₁₆	—	4	2	no	—
1038	C₂×C₈	—	4	2	no	—
1039	C₂×C₈	—	4	2	no	—
1040	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1044	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1045	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1064	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1066	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1088	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1091	C₄²	—	2	1	no	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	2	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	1	no	—
1097	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1098	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1099	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1100	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1101	C₁₃	#61689	1	1	yes	characteristic, direct product factor, Sylow
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	4	4	no	—
1107	C₂³	—	4	4	no	—
1108	C₂³	—	4	4	no	—
1109	C₂³	—	8	2	no	—
1110	C₂³	—	8	2	no	—
1111	C₂³	—	8	2	no	—
1112	C₂³	—	8	2	no	—
1113	C₂³	—	8	2	no	—
1114	C₂³	—	8	2	no	—
1115	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1116	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1117	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	2	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	8	2	no	—
1125	Q₈	—	8	1	no	—
1126	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	2	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	2	2	no	—
1135	D₄	—	2	2	no	—
1136	D₄	—	2	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	4	no	—
1142	D₄	—	4	4	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	4	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	8	2	no	—
1150	D₄	—	8	1	no	—
1151	D₄	—	8	1	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	2	no	—
1155	D₄	—	8	2	no	—
1156	D₄	—	8	1	no	—
1157	D₄	—	8	2	no	—
1158	D₄	—	8	2	no	—
1159	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1160	C₂×C₄	—	2	4	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	2	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	2	no	—
1185	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1189	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1192	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1193	C₈	—	2	1	no	—
1194	C₈	—	2	1	no	—
1195	C₈	—	2	2	no	—
1196	C₈	—	2	2	no	—
1197	C₈	—	2	1	no	—
1198	C₈	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	2	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	2	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	16	4	no	—
1221	C₂²	—	16	4	no	—
1222	C₂²	—	16	4	no	—
1223	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	C₁₃×#577	1	2	yes	—
1239	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1240	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1241	C₂	—	4	1	no	—
1242	C₂	—	4	2	no	—
1243	C₂	—	4	2	no	—
1244	C₂	—	4	2	no	—
1245	C₂	—	8	2	no	—
1246	C₂	—	8	2	no	—
1247	C₂	—	8	1	no	—
1248	C₂	C₁₃×#3484	1	1	yes	characteristic
1249	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1250	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×#3547	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3325	C₂	semidirect
5. C₁₃×#3317	C₂	semidirect
6. C₁₃×#3310	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3284	C₂	semidirect
10. D₄×C₁₃×SD₁₆	C₂	semidirect
11. C₁₃×#3278	C₂	semidirect
12. C₁₃×#3272	C₂	semidirect
13. C₁₃×#3271	C₂	semidirect
14. C₁₃×#3265	C₂	semidirect
15. C₁₃×#3217	C₂	semidirect
16. C₁₃×#3208	C₂	semidirect
17. C₁₃×#3200	C₂	semidirect
18. C₁₃×#3198	C₂	semidirect
19. C₁₃×#3116	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3012	C₂	semidirect
22. C₁₃×#3009	C₂	semidirect
23. C₁₃×#2981	C₂	semidirect
25. C₂×C₁₃×#137	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#548	C₂²	semidirect
40. C₁₃×#547	C₂²	semidirect
50. C₁₃×#537	C₂²	semidirect
51. C₁₃×#536	C₂²	semidirect
54. C₁₃×#533	C₂²	semidirect
59. C₁₃×#529	C₂²	semidirect
61. C₁₃×#496	C₂²	semidirect
62. C₁₃×#492	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#486	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	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×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#469	C₂²	semidirect
79. C₁₃×#468	C₂²	semidirect
80. C₁₃×#468	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#466	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#462	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#460	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#459	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
98. C₁₃×#452	C₂²	semidirect
99. C₁₃×#452	C₂²	semidirect
100. C₁₃×#452	C₂²	semidirect
101. C₁₃×#450	C₂²	semidirect
102. C₁₃×#450	C₂²	semidirect
103. C₁₃×#450	C₂²	semidirect
104. C₁₃×#450	C₂²	semidirect
105. C₁₃×#450	C₂²	semidirect
106. C₁₃×#450	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#448	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#447	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₁₃×#441	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. #61689	C₁₃	direct (N × H)
477. #3547	C₂×C₁₃	semidirect
478. #3498	C₂×C₁₃	semidirect
479. #3333	C₂×C₁₃	semidirect
480. #3325	C₂×C₁₃	semidirect
481. #3317	C₂×C₁₃	semidirect
482. #3310	C₂×C₁₃	semidirect
483. #3305	C₂×C₁₃	semidirect
484. #3295	C₂×C₁₃	semidirect
485. #3284	C₂×C₁₃	semidirect
486. D₄×SD₁₆	C₂×C₁₃	semidirect
487. #3278	C₂×C₁₃	semidirect
488. #3272	C₂×C₁₃	semidirect
489. #3271	C₂×C₁₃	semidirect
490. #3265	C₂×C₁₃	semidirect
491. #3217	C₂×C₁₃	semidirect
492. #3208	C₂×C₁₃	semidirect
493. #3200	C₂×C₁₃	semidirect
494. #3198	C₂×C₁₃	semidirect
495. #3116	C₂×C₁₃	semidirect
496. #3102	C₂×C₁₃	semidirect
497. #3012	C₂×C₁₃	semidirect
498. #3009	C₂×C₁₃	semidirect
499. #2981	C₂×C₁₃	semidirect
598. C₂×#137	C₂²×C₁₃	semidirect
599. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
600. C₂×#135	C₂²×C₁₃	semidirect
601. C₂²×SD₁₆	C₂²×C₁₃	semidirect
604. #555	C₂²×C₁₃	semidirect
605. #554	C₂²×C₁₃	semidirect
607. #552	C₂²×C₁₃	semidirect
611. D₄×Q₈	C₂²×C₁₃	semidirect
612. #548	C₂²×C₁₃	semidirect
613. #547	C₂²×C₁₃	semidirect
623. #537	C₂²×C₁₃	semidirect
624. #536	C₂²×C₁₃	semidirect
627. #533	C₂²×C₁₃	semidirect
632. #529	C₂²×C₁₃	semidirect
634. #496	C₂²×C₁₃	semidirect
635. #492	C₂²×C₁₃	semidirect
636. #492	C₂²×C₁₃	semidirect
637. #490	C₂²×C₁₃	semidirect
638. #486	C₂²×C₁₃	semidirect
639. #486	C₂²×C₁₃	semidirect
640. #485	C₂²×C₁₃	semidirect
641. #485	C₂²×C₁₃	semidirect
642. #482	C₂²×C₁₃	semidirect
643. #482	C₂²×C₁₃	semidirect
644. #482	C₂²×C₁₃	semidirect
645. #481	C₂²×C₁₃	semidirect
646. #480	C₂²×C₁₃	semidirect
647. #479	C₂²×C₁₃	semidirect
648. #478	C₂²×C₁₃	semidirect
649. #477	C₂²×C₁₃	semidirect
650. #476	C₂²×C₁₃	semidirect
651. #469	C₂²×C₁₃	semidirect
652. #468	C₂²×C₁₃	semidirect
653. #468	C₂²×C₁₃	semidirect
654. #468	C₂²×C₁₃	semidirect
655. #466	C₂²×C₁₃	semidirect
656. #465	C₂²×C₁₃	semidirect
657. #465	C₂²×C₁₃	semidirect
658. #465	C₂²×C₁₃	semidirect
659. #464	C₂²×C₁₃	semidirect
660. #463	C₂²×C₁₃	semidirect
661. #462	C₂²×C₁₃	semidirect
662. #461	C₂²×C₁₃	semidirect
663. #460	C₂²×C₁₃	semidirect
664. #460	C₂²×C₁₃	semidirect
665. #460	C₂²×C₁₃	semidirect
666. #460	C₂²×C₁₃	semidirect
667. #459	C₂²×C₁₃	semidirect
668. #459	C₂²×C₁₃	semidirect
671. #452	C₂²×C₁₃	semidirect
672. #452	C₂²×C₁₃	semidirect
673. #452	C₂²×C₁₃	semidirect
674. #450	C₂²×C₁₃	semidirect
675. #450	C₂²×C₁₃	semidirect
676. #450	C₂²×C₁₃	semidirect
677. #450	C₂²×C₁₃	semidirect
678. #450	C₂²×C₁₃	semidirect
679. #450	C₂²×C₁₃	semidirect
681. #449	C₂²×C₁₃	semidirect
682. #449	C₂²×C₁₃	semidirect
683. #449	C₂²×C₁₃	semidirect
684. #448	C₂²×C₁₃	semidirect
685. #448	C₂²×C₁₃	semidirect
686. #447	C₂²×C₁₃	semidirect
687. #447	C₂²×C₁₃	semidirect
688. #441	C₂²×C₁₃	semidirect
689. #440	C₂²×C₁₃	semidirect
690. C₄×Q₁₆	C₂²×C₁₃	semidirect
691. C₄×SD₁₆	C₂²×C₁₃	semidirect
692. C₄×SD₁₆	C₂²×C₁₃	semidirect
693. C₄×D₈	C₂²×C₁₃	semidirect
694. #436	C₂²×C₁₃	semidirect
695. #436	C₂²×C₁₃	semidirect
696. #435	C₂²×C₁₃	semidirect
697. #435	C₂²×C₁₃	semidirect
698. C₈×D₄	C₂²×C₁₃	semidirect
699. C₈×D₄	C₂²×C₁₃	semidirect
700. #432	C₂²×C₁₃	semidirect
701. #431	C₂²×C₁₃	semidirect
702. #418	C₂²×C₁₃	semidirect
703. #417	C₂²×C₁₃	semidirect
704. #416	C₂²×C₁₃	semidirect
705. C₂×#102	C₂²×C₁₃	semidirect
706. #408	C₂²×C₁₃	semidirect
707. #408	C₂²×C₁₃	semidirect
1101. C₁₃	#61689	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×#3547	2
C₁₃×#3498	2
C₁₃×#3333	2
C₁₃×#3325	2
C₁₃×#3317	2
C₁₃×#3310	2
C₁₃×#3305	2
C₁₃×#3295	2
C₁₃×#3284	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3278	2
C₁₃×#3272	2
C₁₃×#3271	2
C₁₃×#3265	2
C₁₃×#3217	2
C₁₃×#3208	2
C₁₃×#3200	2
C₁₃×#3198	2
C₁₃×#3116	2
C₁₃×#3102	2
C₁₃×#3012	2
C₁₃×#3009	2
C₁₃×#2981	2
#61689	13

Subgroups — C13×#61689 #15748028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61689 #15748028