Subgroups — C₁₃×#60834 #15747173

Order 3328.

2104 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3219	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3008	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#548	—	2	1	no	—
36	C₁₃×#546	—	2	2	no	—
37	C₁₃×#546	—	2	2	no	—
38	C₁₃×#546	—	2	1	no	—
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#542	—	2	1	no	—
42	C₁₃×#542	C₂²	1	2	yes	complemented
43	C₁₃×#540	—	2	1	no	—
44	C₁₃×#540	C₂²	1	2	yes	complemented
45	C₁₃×#538	—	2	2	no	—
46	C₁₃×#537	C₂²	1	1	yes	characteristic
47	C₁₃×#536	C₂²	1	1	yes	characteristic
48	C₁₃×#536	C₂²	1	2	yes	complemented
49	C₁₃×#535	C₂²	1	1	yes	characteristic
50	C₁₃×#535	C₂²	1	1	yes	characteristic
51	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#535	C₂²	1	2	yes	complemented
53	C₁₃×#532	—	2	1	no	—
54	C₁₃×#532	C₂²	1	1	yes	characteristic
55	C₁₃×#532	C₂²	1	2	yes	complemented
56	C₁₃×#532	C₂²	1	2	yes	complemented
57	C₁₃×#529	—	2	1	no	—
58	C₁₃×#529	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
61	C₁₃×#525	—	2	2	no	—
62	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#497	C₂²	1	2	yes	complemented
66	C₁₃×#496	C₂²	1	2	yes	complemented
67	C₁₃×#496	C₂²	1	2	yes	complemented
68	C₁₃×#496	C₂²	1	2	yes	complemented
69	C₁₃×#495	C₂²	1	2	yes	complemented
70	C₁₃×#495	C₂²	1	2	yes	complemented
71	C₁₃×#493	C₂²	1	2	yes	complemented
72	C₁₃×#492	C₂²	1	2	yes	complemented
73	C₁₃×#491	C₂²	1	2	yes	complemented
74	C₁₃×#490	C₂²	1	2	yes	complemented
75	C₁₃×#489	C₂²	1	2	yes	complemented
76	C₁₃×#489	C₂²	1	2	yes	complemented
77	C₁₃×#488	C₂²	1	2	yes	complemented
78	C₁₃×#488	C₂²	1	2	yes	complemented
79	C₁₃×#487	C₂²	1	2	yes	complemented
80	C₁₃×#486	C₂²	1	2	yes	complemented
81	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#464	C₂²	1	2	yes	complemented
84	C₁₃×#464	C₂²	1	2	yes	complemented
85	C₁₃×#463	C₂²	1	2	yes	complemented
86	C₁₃×#463	C₂²	1	2	yes	complemented
87	C₁₃×#463	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#463	C₂²	1	2	yes	complemented
93	C₁₃×#463	C₂²	1	2	yes	complemented
94	C₁₃×#463	C₂²	1	2	yes	complemented
95	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#461	C₂²	1	2	yes	complemented
98	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#459	C₂²	1	2	yes	complemented
101	C₁₃×#452	C₂²	1	2	yes	complemented
102	C₁₃×#452	C₂²	1	2	yes	complemented
103	C₁₃×#451	C₂²	1	2	yes	complemented
104	C₁₃×#450	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	—
106	C₁₃×#449	C₂²	1	2	yes	—
107	C₁₃×#449	C₂²	1	2	yes	complemented
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×#448	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	—
115	C₁₃×#447	C₂²	1	2	yes	—
116	C₁₃×#447	C₂²	1	2	yes	complemented
117	C₁₃×#433	C₂²	1	2	yes	complemented
118	C₁₃×#433	C₂²	1	2	yes	complemented
119	C₁₃×#432	C₂²	1	2	yes	complemented
120	C₁₃×#431	C₂²	1	2	yes	complemented
121	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#418	C₂²	1	1	yes	characteristic
125	C₁₃×#417	C₂²	1	1	yes	characteristic
126	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#416	C₂²	1	1	yes	characteristic
128	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
131	C₁₃×#408	C₂²	1	1	yes	characteristic
132	C₁₃×#408	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
134	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₁₃×2₋¹⁺⁴	—	4	2	no	—
136	C₁₃×2₋¹⁺⁴	—	4	2	no	—
137	C₁₃×H(5,𝔽₂)	—	4	2	no	—
138	C₁₃×H(5,𝔽₂)	—	4	2	no	—
139	C₂×C₁₃×#41	—	2	1	no	—
140	C₂×C₁₃×#41	—	2	2	no	—
141	C₂×C₁₃×#41	—	2	1	no	—
142	C₂×C₁₃×#41	—	2	2	no	—
143	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×#41	C₂³	1	2	yes	—
147	C₂×C₁₃×#41	C₂³	1	2	yes	—
148	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₃	—	2	1	no	—
150	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×D₄×C₁₃	—	2	2	no	—
153	C₂²×D₄×C₁₃	—	2	1	no	—
154	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
157	C₂³×C₄×C₁₃	—	2	1	no	—
158	C₁₃×#137	—	4	2	no	—
159	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
160	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
161	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
162	C₁₃×#135	—	4	2	no	—
163	C₁₃×#135	—	4	2	no	—
164	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×SD₁₆	—	4	2	no	—
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
171	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
172	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
173	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
174	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
177	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×D₈	—	4	2	no	—
179	C₂×C₁₃×D₈	C₂³	1	2	yes	—
180	C₂×C₁₃×D₈	C₂³	1	2	yes	—
181	C₂×C₁₃×D₈	C₂³	1	2	yes	—
182	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×D₈	C₂³	1	2	yes	—
184	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×D₈	C₂³	1	2	yes	—
186	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
190	C₁₃×C₄⋊Q₈	—	2	1	no	—
191	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
193	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×#127	—	2	1	no	—
195	C₁₃×#127	C₂³	1	1	yes	characteristic
196	C₁₃×#127	C₂³	1	2	yes	—
197	C₁₃×#127	C₂³	1	2	yes	—
198	C₁₃×#126	—	2	2	no	—
199	C₁₃×#126	—	2	2	no	—
200	C₁₃×#125	—	2	1	no	—
201	C₁₃×#125	C₂³	1	2	yes	—
202	C₁₃×#124	—	2	1	no	—
203	C₁₃×#124	—	2	2	no	—
204	C₁₃×#124	—	2	1	no	—
205	C₁₃×#124	—	2	1	no	—
206	C₁₃×#124	—	2	2	no	—
207	C₁₃×#124	—	2	2	no	—
208	C₁₃×#124	—	2	2	no	—
209	C₁₃×#124	C₂³	1	2	yes	—
210	C₁₃×#124	C₂³	1	2	yes	—
211	C₁₃×#124	C₂³	1	1	yes	characteristic
212	C₁₃×#124	C₂³	1	1	yes	characteristic
213	C₁₃×#124	C₂³	1	2	yes	—
214	C₁₃×#124	C₂³	1	2	yes	—
215	C₁₃×#124	C₂³	1	2	yes	—
216	C₁₃×#123	—	2	2	no	—
217	C₁₃×#123	—	2	2	no	—
218	C₁₃×#123	—	2	2	no	—
219	C₁₃×#123	—	2	2	no	—
220	C₁₃×#123	—	2	2	no	—
221	C₁₃×#123	—	2	2	no	—
222	C₁₃×#123	—	2	2	no	—
223	C₁₃×C₂²⋊Q₈	—	2	1	no	—
224	C₁₃×C₂²⋊Q₈	—	2	2	no	—
225	C₁₃×C₂²⋊Q₈	—	2	1	no	—
226	C₁₃×C₂²⋊Q₈	—	2	1	no	—
227	C₁₃×C₂²⋊Q₈	—	2	2	no	—
228	C₁₃×C₂²⋊Q₈	—	2	2	no	—
229	C₁₃×C₂²⋊Q₈	—	2	2	no	—
230	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
231	C₁₃×#121	—	2	2	no	—
232	C₁₃×#121	—	2	1	no	—
233	C₁₃×#121	—	2	1	no	—
234	C₁₃×#121	—	2	1	no	—
235	C₁₃×#121	—	2	2	no	—
236	C₁₃×#121	—	2	2	no	—
237	C₁₃×#121	—	2	2	no	—
238	C₁₃×#121	—	2	1	no	—
239	C₁₃×#121	—	2	1	no	—
240	C₁₃×#121	—	2	1	no	—
241	C₁₃×#121	—	2	1	no	—
242	C₁₃×#121	—	2	2	no	—
243	C₁₃×#121	—	2	2	no	—
244	C₁₃×#121	—	2	2	no	—
245	C₁₃×#121	—	2	2	no	—
246	C₁₃×#121	C₂³	1	2	yes	—
247	C₁₃×#121	C₂³	1	2	yes	—
248	C₁₃×#121	C₂³	1	2	yes	—
249	C₁₃×#120	—	2	2	no	—
250	C₁₃×#120	—	2	2	no	—
251	C₁₃×#120	—	2	2	no	—
252	C₁₃×#120	—	2	2	no	—
253	C₁₃×#120	—	2	2	no	—
254	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	—	2	1	no	—
259	C₄×D₄×C₁₃	—	2	1	no	—
260	C₄×D₄×C₁₃	—	2	2	no	—
261	C₄×D₄×C₁₃	—	2	1	no	—
262	C₄×D₄×C₁₃	—	2	1	no	—
263	C₄×D₄×C₁₃	—	2	2	no	—
264	C₄×D₄×C₁₃	—	2	1	no	—
265	C₄×D₄×C₁₃	—	2	1	no	—
266	C₄×D₄×C₁₃	—	2	2	no	—
267	C₄×D₄×C₁₃	—	2	2	no	—
268	C₄×D₄×C₁₃	D₄	1	2	yes	—
269	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
270	C₄×D₄×C₁₃	D₄	1	2	yes	—
271	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₁₃	C₂³	1	2	yes	—
273	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₁₃	C₂³	1	2	yes	—
275	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
276	C₁₃×#117	—	2	1	no	—
277	C₁₃×#117	—	2	2	no	—
278	C₁₃×#117	C₂³	1	1	yes	characteristic
279	C₁₃×#117	C₂³	1	1	yes	characteristic
280	C₁₃×#117	C₂³	1	2	yes	—
281	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²×C₁₃	—	2	1	no	—
288	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
290	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
294	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
295	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	1	yes	characteristic
301	C₁₃×#103	C₂³	1	1	yes	characteristic
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#103	C₂³	1	2	yes	—
304	C₁₃×#103	C₂³	1	2	yes	—
305	C₁₃×#103	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#102	C₂³	1	2	yes	—
308	C₁₃×#102	C₂³	1	1	yes	characteristic
309	C₁₃×#102	C₂³	1	1	yes	characteristic
310	C₁₃×#102	C₂³	1	1	yes	characteristic
311	C₁₃×#102	C₂³	1	1	yes	characteristic
312	C₁₃×#102	C₂³	1	2	yes	—
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×#102	C₂³	1	2	yes	—
315	C₁₃×#102	C₂³	1	2	yes	—
316	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₁₃×#97	C₂³	1	2	yes	—
321	C₁₃×#97	C₂³	1	2	yes	—
322	C₄×C₈×C₁₃	C₂³	1	2	yes	—
323	C₄×C₈×C₁₃	C₂³	1	2	yes	—
324	#60834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂⁴×C₁₃	—	2	2	no	—
326	C₂⁴×C₁₃	—	2	1	no	—
327	C₂⁴×C₁₃	—	2	1	no	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	2	no	—
330	C₁₃×#41	—	2	2	no	—
331	C₁₃×#41	—	2	2	no	—
332	C₁₃×#41	—	2	2	no	—
333	C₁₃×#41	—	2	2	no	—
334	C₁₃×#41	—	2	2	no	—
335	C₁₃×#41	—	2	2	no	—
336	C₁₃×#41	—	4	2	no	—
337	C₁₃×#41	—	4	2	no	—
338	C₁₃×#41	—	4	2	no	—
339	C₁₃×#41	—	4	2	no	—
340	C₁₃×#41	—	4	8	no	—
341	C₁₃×#41	—	4	4	no	—
342	C₁₃×#41	—	4	4	no	—
343	C₁₃×#41	—	8	4	no	—
344	C₂×Q₈×C₁₃	—	2	2	no	—
345	C₂×Q₈×C₁₃	—	2	1	no	—
346	C₂×Q₈×C₁₃	—	2	2	no	—
347	C₂×Q₈×C₁₃	—	2	2	no	—
348	C₂×Q₈×C₁₃	—	2	2	no	—
349	C₂×Q₈×C₁₃	—	4	2	no	—
350	C₂×Q₈×C₁₃	—	4	2	no	—
351	C₂×Q₈×C₁₃	—	4	4	no	—
352	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
354	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₃	—	2	1	no	—
358	C₂×D₄×C₁₃	—	2	2	no	—
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	2	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	2	2	no	—
364	C₂×D₄×C₁₃	—	2	2	no	—
365	C₂×D₄×C₁₃	—	2	1	no	—
366	C₂×D₄×C₁₃	—	2	2	no	—
367	C₂×D₄×C₁₃	—	2	1	no	—
368	C₂×D₄×C₁₃	—	2	1	no	—
369	C₂×D₄×C₁₃	—	2	2	no	—
370	C₂×D₄×C₁₃	—	2	1	no	—
371	C₂×D₄×C₁₃	—	2	2	no	—
372	C₂×D₄×C₁₃	—	2	2	no	—
373	C₂×D₄×C₁₃	—	2	2	no	—
374	C₂×D₄×C₁₃	—	2	2	no	—
375	C₂×D₄×C₁₃	—	2	2	no	—
376	C₂×D₄×C₁₃	—	2	2	no	—
377	C₂×D₄×C₁₃	—	2	2	no	—
378	C₂×D₄×C₁₃	—	4	2	no	—
379	C₂×D₄×C₁₃	—	4	2	no	—
380	C₂×D₄×C₁₃	—	4	8	no	—
381	C₂×D₄×C₁₃	—	4	4	no	—
382	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
383	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
385	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
388	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₁₃	—	2	2	no	—
390	C₂²×C₄×C₁₃	—	2	1	no	—
391	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
397	C₂²×C₄×C₁₃	—	2	2	no	—
398	C₂²×C₄×C₁₃	—	2	1	no	—
399	C₂²×C₄×C₁₃	—	2	1	no	—
400	C₂²×C₄×C₁₃	—	2	2	no	—
401	C₂²×C₄×C₁₃	—	8	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	C₂×D₄	1	2	yes	—
405	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
406	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
408	C₁₃×Q₁₆	—	4	1	no	—
409	C₁₃×Q₁₆	—	4	1	no	—
410	C₁₃×Q₁₆	—	4	2	no	—
411	C₁₃×SD₁₆	—	4	2	no	—
412	C₁₃×SD₁₆	—	4	2	no	—
413	C₁₃×SD₁₆	—	4	1	no	—
414	C₁₃×SD₁₆	—	4	1	no	—
415	C₁₃×SD₁₆	—	4	1	no	—
416	C₁₃×SD₁₆	—	4	1	no	—
417	C₁₃×SD₁₆	—	4	2	no	—
418	C₁₃×SD₁₆	—	4	2	no	—
419	C₁₃×SD₁₆	—	4	2	no	—
420	C₁₃×SD₁₆	—	4	2	no	—
421	C₁₃×D₈	—	4	2	no	—
422	C₁₃×D₈	—	4	2	no	—
423	C₁₃×D₈	—	4	1	no	—
424	C₁₃×D₈	—	4	1	no	—
425	C₁₃×D₈	—	4	2	no	—
426	C₁₃×D₈	—	4	2	no	—
427	C₁₃×D₈	—	4	2	no	—
428	C₁₃×M₁₆	—	2	2	no	—
429	C₁₃×M₁₆	—	2	2	no	—
430	C₂×C₈×C₁₃	—	2	2	no	—
431	C₂×C₈×C₁₃	—	2	2	no	—
432	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
433	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
434	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
435	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
436	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
437	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
438	C₁₃×C₄⋊C₄	—	2	1	no	—
439	C₁₃×C₄⋊C₄	—	2	1	no	—
440	C₁₃×C₄⋊C₄	—	2	1	no	—
441	C₁₃×C₄⋊C₄	—	2	2	no	—
442	C₁₃×C₄⋊C₄	—	2	2	no	—
443	C₁₃×C₄⋊C₄	—	2	1	no	—
444	C₁₃×C₄⋊C₄	—	2	2	no	—
445	C₁₃×C₄⋊C₄	—	2	1	no	—
446	C₁₃×C₄⋊C₄	—	2	2	no	—
447	C₁₃×C₄⋊C₄	—	2	2	no	—
448	C₁₃×C₄⋊C₄	—	2	2	no	—
449	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
451	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
452	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
453	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
454	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
455	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
467	C₁₃×C₂²⋊C₄	—	2	2	no	—
468	C₁₃×C₂²⋊C₄	—	2	2	no	—
469	C₁₃×C₂²⋊C₄	—	2	2	no	—
470	C₁₃×C₂²⋊C₄	—	2	1	no	—
471	C₁₃×C₂²⋊C₄	—	2	1	no	—
472	C₁₃×C₂²⋊C₄	—	2	2	no	—
473	C₁₃×C₂²⋊C₄	—	2	2	no	—
474	C₁₃×C₂²⋊C₄	—	2	1	no	—
475	C₁₃×C₂²⋊C₄	—	2	1	no	—
476	C₁₃×C₂²⋊C₄	—	2	2	no	—
477	C₁₃×C₂²⋊C₄	—	2	2	no	—
478	C₁₃×C₂²⋊C₄	—	2	2	no	—
479	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
480	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
481	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
482	C₄²×C₁₃	—	2	1	no	—
483	C₄²×C₁₃	—	2	1	no	—
484	C₄²×C₁₃	—	2	1	no	—
485	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
486	C₄²×C₁₃	C₂×D₄	1	2	yes	—
487	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
488	C₄²×C₁₃	C₂×D₄	1	2	yes	—
489	C₄²×C₁₃	C₂⁴	1	2	yes	—
490	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
491	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
492	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3225	C₂×C₁₃	1	2	yes	complemented
495	#3224	C₂×C₁₃	1	2	yes	complemented
496	#3221	C₂×C₁₃	1	2	yes	complemented
497	#3220	C₂×C₁₃	1	2	yes	complemented
498	#3219	C₂×C₁₃	1	2	yes	complemented
499	#3213	C₂×C₁₃	1	2	yes	complemented
500	#3211	C₂×C₁₃	1	2	yes	complemented
501	#3207	C₂×C₁₃	1	2	yes	complemented
502	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
503	#3154	C₂×C₁₃	1	1	yes	characteristic, complemented
504	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
505	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
506	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
507	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
508	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
509	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
510	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
511	#3012	C₂×C₁₃	1	1	yes	characteristic, complemented
512	#3010	C₂×C₁₃	1	1	yes	characteristic, complemented
513	#3008	C₂×C₁₃	1	1	yes	characteristic, complemented
514	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
515	C₂³×C₁₃	—	2	2	no	—
516	C₂³×C₁₃	—	2	2	no	—
517	C₂³×C₁₃	—	2	1	no	—
518	C₂³×C₁₃	—	2	1	no	—
519	C₂³×C₁₃	—	2	1	no	—
520	C₂³×C₁₃	—	4	4	no	—
521	C₂³×C₁₃	—	4	2	no	—
522	C₂³×C₁₃	—	4	2	no	—
523	C₂³×C₁₃	—	8	1	no	—
524	C₂³×C₁₃	—	8	1	no	—
525	C₂³×C₁₃	—	8	1	no	—
526	C₂³×C₁₃	—	8	1	no	—
527	C₂³×C₁₃	—	8	2	no	—
528	C₂³×C₁₃	—	8	2	no	—
529	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
530	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
531	Q₈×C₁₃	—	2	2	no	—
532	Q₈×C₁₃	—	2	1	no	—
533	Q₈×C₁₃	—	2	1	no	—
534	Q₈×C₁₃	—	2	2	no	—
535	Q₈×C₁₃	—	2	1	no	—
536	Q₈×C₁₃	—	2	1	no	—
537	Q₈×C₁₃	—	2	2	no	—
538	Q₈×C₁₃	—	2	1	no	—
539	Q₈×C₁₃	—	2	1	no	—
540	Q₈×C₁₃	—	4	4	no	—
541	Q₈×C₁₃	—	4	2	no	—
542	Q₈×C₁₃	—	8	2	no	—
543	D₄×C₁₃	—	2	4	no	—
544	D₄×C₁₃	—	2	2	no	—
545	D₄×C₁₃	—	2	2	no	—
546	D₄×C₁₃	—	2	2	no	—
547	D₄×C₁₃	—	2	1	no	—
548	D₄×C₁₃	—	2	1	no	—
549	D₄×C₁₃	—	2	2	no	—
550	D₄×C₁₃	—	2	1	no	—
551	D₄×C₁₃	—	2	1	no	—
552	D₄×C₁₃	—	2	2	no	—
553	D₄×C₁₃	—	2	1	no	—
554	D₄×C₁₃	—	2	1	no	—
555	D₄×C₁₃	—	4	4	no	—
556	D₄×C₁₃	—	4	4	no	—
557	D₄×C₁₃	—	4	4	no	—
558	D₄×C₁₃	—	4	2	no	—
559	D₄×C₁₃	—	4	2	no	—
560	D₄×C₁₃	—	4	2	no	—
561	D₄×C₁₃	—	4	2	no	—
562	D₄×C₁₃	—	4	2	no	—
563	D₄×C₁₃	—	8	1	no	—
564	D₄×C₁₃	—	8	2	no	—
565	D₄×C₁₃	—	8	2	no	—
566	D₄×C₁₃	—	8	1	no	—
567	D₄×C₁₃	—	8	2	no	—
568	D₄×C₁₃	—	8	2	no	—
569	D₄×C₁₃	—	8	2	no	—
570	D₄×C₁₃	—	8	2	no	—
571	D₄×C₁₃	—	8	2	no	—
572	C₂×C₄×C₁₃	—	2	2	no	—
573	C₂×C₄×C₁₃	—	2	2	no	—
574	C₂×C₄×C₁₃	—	2	1	no	—
575	C₂×C₄×C₁₃	—	2	1	no	—
576	C₂×C₄×C₁₃	—	2	1	no	—
577	C₂×C₄×C₁₃	—	2	2	no	—
578	C₂×C₄×C₁₃	—	2	1	no	—
579	C₂×C₄×C₁₃	—	2	2	no	—
580	C₂×C₄×C₁₃	—	2	1	no	—
581	C₂×C₄×C₁₃	—	4	1	no	—
582	C₂×C₄×C₁₃	—	4	1	no	—
583	C₂×C₄×C₁₃	—	4	2	no	—
584	C₂×C₄×C₁₃	—	4	2	no	—
585	C₂×C₄×C₁₃	—	4	4	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	4	no	—
590	C₂×C₄×C₁₃	—	4	2	no	—
591	C₂×C₄×C₁₃	—	4	2	no	—
592	C₂×C₄×C₁₃	—	4	2	no	—
593	C₂×C₄×C₁₃	—	4	2	no	—
594	C₂×C₄×C₁₃	—	8	1	no	—
595	C₂×C₄×C₁₃	—	8	2	no	—
596	C₂×C₄×C₁₃	—	8	1	no	—
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	1	yes	characteristic
600	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
601	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
604	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
606	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
607	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
608	C₈×C₁₃	—	2	1	no	—
609	C₈×C₁₃	—	2	1	no	—
610	C₈×C₁₃	—	2	1	no	—
611	C₈×C₁₃	—	2	1	no	—
612	C₈×C₁₃	—	2	2	no	—
613	C₈×C₁₃	—	2	2	no	—
614	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
615	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
616	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
618	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
619	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
621	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
624	#548	—	2	1	no	—
625	#548	—	2	1	no	—
626	#546	—	2	2	no	—
627	#546	—	2	2	no	—
628	#546	—	2	1	no	—
629	#546	—	2	1	no	—
630	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#542	—	2	1	no	—
632	#542	C₂²×C₁₃	1	2	yes	complemented
633	#540	—	2	1	no	—
634	#540	C₂²×C₁₃	1	2	yes	complemented
635	#538	—	2	2	no	—
636	#537	C₂²×C₁₃	1	1	yes	characteristic
637	#536	C₂²×C₁₃	1	1	yes	characteristic
638	#536	C₂²×C₁₃	1	2	yes	complemented
639	#535	C₂²×C₁₃	1	1	yes	characteristic
640	#535	C₂²×C₁₃	1	1	yes	characteristic
641	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#535	C₂²×C₁₃	1	2	yes	complemented
643	#532	—	2	1	no	—
644	#532	C₂²×C₁₃	1	1	yes	characteristic
645	#532	C₂²×C₁₃	1	2	yes	complemented
646	#532	C₂²×C₁₃	1	2	yes	complemented
647	#529	—	2	1	no	—
648	#529	C₂²×C₁₃	1	2	yes	complemented
649	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
650	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
651	#525	—	2	2	no	—
652	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
653	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#497	C₂²×C₁₃	1	2	yes	complemented
656	#496	C₂²×C₁₃	1	2	yes	complemented
657	#496	C₂²×C₁₃	1	2	yes	complemented
658	#496	C₂²×C₁₃	1	2	yes	complemented
659	#495	C₂²×C₁₃	1	2	yes	complemented
660	#495	C₂²×C₁₃	1	2	yes	complemented
661	#493	C₂²×C₁₃	1	2	yes	complemented
662	#492	C₂²×C₁₃	1	2	yes	complemented
663	#491	C₂²×C₁₃	1	2	yes	complemented
664	#490	C₂²×C₁₃	1	2	yes	complemented
665	#489	C₂²×C₁₃	1	2	yes	complemented
666	#489	C₂²×C₁₃	1	2	yes	complemented
667	#488	C₂²×C₁₃	1	2	yes	complemented
668	#488	C₂²×C₁₃	1	2	yes	complemented
669	#487	C₂²×C₁₃	1	2	yes	complemented
670	#486	C₂²×C₁₃	1	2	yes	complemented
671	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
672	#464	C₂²×C₁₃	1	2	yes	complemented
673	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
674	#464	C₂²×C₁₃	1	2	yes	complemented
675	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
676	#463	C₂²×C₁₃	1	2	yes	complemented
677	#463	C₂²×C₁₃	1	2	yes	complemented
678	#463	C₂²×C₁₃	1	2	yes	complemented
679	#463	C₂²×C₁₃	1	2	yes	complemented
680	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	#463	C₂²×C₁₃	1	2	yes	complemented
682	#463	C₂²×C₁₃	1	2	yes	complemented
683	#463	C₂²×C₁₃	1	2	yes	complemented
684	#463	C₂²×C₁₃	1	2	yes	complemented
685	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
686	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
687	#461	C₂²×C₁₃	1	2	yes	complemented
688	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
690	#459	C₂²×C₁₃	1	2	yes	complemented
691	#452	C₂²×C₁₃	1	2	yes	complemented
692	#452	C₂²×C₁₃	1	2	yes	complemented
693	#451	C₂²×C₁₃	1	2	yes	complemented
694	#450	C₂²×C₁₃	1	2	yes	complemented
695	#449	C₂²×C₁₃	1	2	yes	—
696	#449	C₂²×C₁₃	1	2	yes	—
697	#449	C₂²×C₁₃	1	2	yes	complemented
698	#449	C₂²×C₁₃	1	2	yes	complemented
699	#449	C₂²×C₁₃	1	2	yes	complemented
700	#449	C₂²×C₁₃	1	2	yes	complemented
701	#448	C₂²×C₁₃	1	2	yes	complemented
702	#448	C₂²×C₁₃	1	2	yes	complemented
703	#448	C₂²×C₁₃	1	2	yes	complemented
704	#447	C₂²×C₁₃	1	2	yes	—
705	#447	C₂²×C₁₃	1	2	yes	—
706	#447	C₂²×C₁₃	1	2	yes	complemented
707	#433	C₂²×C₁₃	1	2	yes	complemented
708	#433	C₂²×C₁₃	1	2	yes	complemented
709	#432	C₂²×C₁₃	1	2	yes	complemented
710	#431	C₂²×C₁₃	1	2	yes	complemented
711	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
712	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
713	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
714	#418	C₂²×C₁₃	1	1	yes	characteristic
715	#417	C₂²×C₁₃	1	1	yes	characteristic
716	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
717	#416	C₂²×C₁₃	1	1	yes	characteristic
718	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
719	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
720	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
721	#408	C₂²×C₁₃	1	1	yes	characteristic
722	#408	C₂²×C₁₃	1	1	yes	characteristic
723	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
724	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
725	C₂²×C₁₃	—	2	1	no	—
726	C₂²×C₁₃	—	2	1	no	—
727	C₂²×C₁₃	—	2	2	no	—
728	C₂²×C₁₃	—	2	2	no	—
729	C₂²×C₁₃	—	2	2	no	—
730	C₂²×C₁₃	—	4	1	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	2	no	—
736	C₂²×C₁₃	—	4	1	no	—
737	C₂²×C₁₃	—	4	1	no	—
738	C₂²×C₁₃	—	4	2	no	—
739	C₂²×C₁₃	—	4	1	no	—
740	C₂²×C₁₃	—	4	1	no	—
741	C₂²×C₁₃	—	4	2	no	—
742	C₂²×C₁₃	—	4	1	no	—
743	C₂²×C₁₃	—	4	1	no	—
744	C₂²×C₁₃	—	4	2	no	—
745	C₂²×C₁₃	—	8	4	no	—
746	C₂²×C₁₃	—	16	2	no	—
747	C₂²×C₁₃	—	16	4	no	—
748	C₂²×C₁₃	#535	1	2	yes	—
749	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
750	C₄×C₁₃	—	2	1	no	—
751	C₄×C₁₃	—	2	1	no	—
752	C₄×C₁₃	—	2	2	no	—
753	C₄×C₁₃	—	2	1	no	—
754	C₄×C₁₃	—	2	1	no	—
755	C₄×C₁₃	—	2	2	no	—
756	C₄×C₁₃	—	2	2	no	—
757	C₄×C₁₃	—	4	1	no	—
758	C₄×C₁₃	—	4	2	no	—
759	C₄×C₁₃	—	4	1	no	—
760	C₄×C₁₃	—	4	1	no	—
761	C₄×C₁₃	—	4	2	no	—
762	C₄×C₁₃	—	4	1	no	—
763	C₄×C₁₃	—	4	1	no	—
764	C₄×C₁₃	#535	1	2	yes	—
765	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
766	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
767	2₋¹⁺⁴	—	4	2	no	—
768	2₋¹⁺⁴	—	4	2	no	—
769	H(5,𝔽₂)	—	4	2	no	—
770	H(5,𝔽₂)	—	4	2	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	2	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	2	no	—
775	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×#41	C₂³×C₁₃	1	2	yes	—
779	C₂×#41	C₂³×C₁₃	1	2	yes	—
780	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
781	C₂²×Q₈	—	2	1	no	—
782	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
784	C₂²×D₄	—	2	2	no	—
785	C₂²×D₄	—	2	1	no	—
786	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
787	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
788	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
789	C₂³×C₄	—	2	1	no	—
790	#137	—	4	2	no	—
791	AGL(1,ℤ/8)	—	4	2	no	—
792	AGL(1,ℤ/8)	—	4	2	no	—
793	AGL(1,ℤ/8)	—	4	2	no	—
794	#135	—	4	2	no	—
795	#135	—	4	2	no	—
796	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
797	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
798	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
799	C₂×SD₁₆	—	4	2	no	—
800	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
805	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
806	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
807	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
808	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
809	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
810	C₂×D₈	—	4	2	no	—
811	C₂×D₈	C₂³×C₁₃	1	2	yes	—
812	C₂×D₈	C₂³×C₁₃	1	2	yes	—
813	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
814	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₂×D₈	C₂³×C₁₃	1	2	yes	—
816	C₂×D₈	C₂³×C₁₃	1	2	yes	—
817	C₂×D₈	C₂³×C₁₃	1	2	yes	—
818	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
819	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
820	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
821	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
822	C₄⋊Q₈	—	2	1	no	—
823	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
825	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
826	#127	—	2	1	no	—
827	#127	C₂³×C₁₃	1	1	yes	characteristic
828	#127	C₂³×C₁₃	1	2	yes	—
829	#127	C₂³×C₁₃	1	2	yes	—
830	#126	—	2	2	no	—
831	#126	—	2	2	no	—
832	#125	—	2	1	no	—
833	#125	C₂³×C₁₃	1	2	yes	—
834	#124	—	2	1	no	—
835	#124	—	2	2	no	—
836	#124	—	2	1	no	—
837	#124	—	2	1	no	—
838	#124	—	2	2	no	—
839	#124	—	2	2	no	—
840	#124	—	2	2	no	—
841	#124	C₂³×C₁₃	1	2	yes	—
842	#124	C₂³×C₁₃	1	2	yes	—
843	#124	C₂³×C₁₃	1	1	yes	characteristic
844	#124	C₂³×C₁₃	1	2	yes	—
845	#124	C₂³×C₁₃	1	2	yes	—
846	#124	C₂³×C₁₃	1	2	yes	—
847	#124	C₂³×C₁₃	1	1	yes	characteristic
848	#123	—	2	2	no	—
849	#123	—	2	2	no	—
850	#123	—	2	2	no	—
851	#123	—	2	2	no	—
852	#123	—	2	2	no	—
853	#123	—	2	2	no	—
854	#123	—	2	2	no	—
855	C₂²⋊Q₈	—	2	1	no	—
856	C₂²⋊Q₈	—	2	2	no	—
857	C₂²⋊Q₈	—	2	1	no	—
858	C₂²⋊Q₈	—	2	1	no	—
859	C₂²⋊Q₈	—	2	2	no	—
860	C₂²⋊Q₈	—	2	2	no	—
861	C₂²⋊Q₈	—	2	2	no	—
862	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
863	#121	—	2	2	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	—	2	2	no	—
868	#121	—	2	2	no	—
869	#121	—	2	2	no	—
870	#121	—	2	1	no	—
871	#121	—	2	1	no	—
872	#121	—	2	1	no	—
873	#121	—	2	1	no	—
874	#121	—	2	2	no	—
875	#121	—	2	2	no	—
876	#121	—	2	2	no	—
877	#121	—	2	2	no	—
878	#121	C₂³×C₁₃	1	2	yes	—
879	#121	C₂³×C₁₃	1	2	yes	—
880	#121	C₂³×C₁₃	1	2	yes	—
881	#120	—	2	2	no	—
882	#120	—	2	2	no	—
883	#120	—	2	2	no	—
884	#120	—	2	2	no	—
885	#120	—	2	2	no	—
886	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
887	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
888	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
889	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	2	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	2	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	2	no	—
899	C₄×D₄	—	2	2	no	—
900	C₄×D₄	D₄×C₁₃	1	2	yes	—
901	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
902	C₄×D₄	D₄×C₁₃	1	2	yes	—
903	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₁₃	1	2	yes	—
905	C₄×D₄	C₂³×C₁₃	1	2	yes	—
906	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
908	#117	—	2	1	no	—
909	#117	—	2	2	no	—
910	#117	C₂³×C₁₃	1	1	yes	characteristic
911	#117	C₂³×C₁₃	1	1	yes	characteristic
912	#117	C₂³×C₁₃	1	2	yes	—
913	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
914	C₂×C₂²⋊C₄	—	2	1	no	—
915	C₂×C₂²⋊C₄	—	2	1	no	—
916	C₂×C₂²⋊C₄	—	2	1	no	—
917	C₂×C₂²⋊C₄	—	2	2	no	—
918	C₂×C₂²⋊C₄	—	2	2	no	—
919	C₂×C₄²	—	2	1	no	—
920	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
921	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
922	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
923	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
924	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
925	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
926	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
927	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
928	#103	C₂³×C₁₃	1	2	yes	—
929	#103	C₂³×C₁₃	1	2	yes	—
930	#103	C₂³×C₁₃	1	1	yes	characteristic
931	#103	C₂³×C₁₃	1	1	yes	characteristic
932	#103	C₂³×C₁₃	1	1	yes	characteristic
933	#103	C₂³×C₁₃	1	1	yes	characteristic
934	#103	C₂³×C₁₃	1	2	yes	—
935	#103	C₂³×C₁₃	1	2	yes	—
936	#103	C₂³×C₁₃	1	2	yes	—
937	#103	C₂³×C₁₃	1	2	yes	—
938	#102	C₂³×C₁₃	1	2	yes	—
939	#102	C₂³×C₁₃	1	2	yes	—
940	#102	C₂³×C₁₃	1	1	yes	characteristic
941	#102	C₂³×C₁₃	1	1	yes	characteristic
942	#102	C₂³×C₁₃	1	1	yes	characteristic
943	#102	C₂³×C₁₃	1	1	yes	characteristic
944	#102	C₂³×C₁₃	1	2	yes	—
945	#102	C₂³×C₁₃	1	2	yes	—
946	#102	C₂³×C₁₃	1	2	yes	—
947	#102	C₂³×C₁₃	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
952	#97	C₂³×C₁₃	1	2	yes	—
953	#97	C₂³×C₁₃	1	2	yes	—
954	C₄×C₈	C₂³×C₁₃	1	2	yes	—
955	C₄×C₈	C₂³×C₁₃	1	2	yes	—
956	C₂×C₁₃	—	2	2	no	—
957	C₂×C₁₃	—	4	2	no	—
958	C₂×C₁₃	—	8	1	no	—
959	C₂×C₁₃	—	8	1	no	—
960	C₂×C₁₃	—	8	2	no	—
961	C₂×C₁₃	—	8	2	no	—
962	C₂×C₁₃	—	8	1	no	—
963	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
964	C₂×C₁₃	#3584	1	1	yes	characteristic
965	C₂×C₁₃	#3585	1	1	yes	characteristic
966	C₂⁴	—	2	2	no	—
967	C₂⁴	—	2	1	no	—
968	C₂⁴	—	2	1	no	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	2	2	no	—
973	#41	—	2	2	no	—
974	#41	—	2	2	no	—
975	#41	—	2	2	no	—
976	#41	—	2	2	no	—
977	#41	—	4	2	no	—
978	#41	—	4	2	no	—
979	#41	—	4	2	no	—
980	#41	—	4	2	no	—
981	#41	—	4	8	no	—
982	#41	—	4	4	no	—
983	#41	—	4	4	no	—
984	#41	—	8	4	no	—
985	C₂×Q₈	—	2	2	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	—	2	2	no	—
990	C₂×Q₈	—	4	2	no	—
991	C₂×Q₈	—	4	2	no	—
992	C₂×Q₈	—	4	4	no	—
993	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
994	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
995	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	2	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	2	2	no	—
1015	C₂×D₄	—	2	2	no	—
1016	C₂×D₄	—	2	2	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	4	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	8	no	—
1022	C₂×D₄	—	4	4	no	—
1023	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1025	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1026	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1027	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1028	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
1029	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	2	no	—
1039	C₂²×C₄	—	2	1	no	—
1040	C₂²×C₄	—	2	1	no	—
1041	C₂²×C₄	—	2	2	no	—
1042	C₂²×C₄	—	8	2	no	—
1043	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1046	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
1047	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1048	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1049	Q₁₆	—	4	1	no	—
1050	Q₁₆	—	4	1	no	—
1051	Q₁₆	—	4	2	no	—
1052	SD₁₆	—	4	2	no	—
1053	SD₁₆	—	4	2	no	—
1054	SD₁₆	—	4	1	no	—
1055	SD₁₆	—	4	1	no	—
1056	SD₁₆	—	4	1	no	—
1057	SD₁₆	—	4	1	no	—
1058	SD₁₆	—	4	2	no	—
1059	SD₁₆	—	4	2	no	—
1060	SD₁₆	—	4	2	no	—
1061	SD₁₆	—	4	2	no	—
1062	D₈	—	4	2	no	—
1063	D₈	—	4	2	no	—
1064	D₈	—	4	1	no	—
1065	D₈	—	4	1	no	—
1066	D₈	—	4	2	no	—
1067	D₈	—	4	2	no	—
1068	D₈	—	4	2	no	—
1069	M₁₆	—	2	2	no	—
1070	M₁₆	—	2	2	no	—
1071	C₂×C₈	—	2	2	no	—
1072	C₂×C₈	—	2	2	no	—
1073	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1074	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1075	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1076	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1077	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1078	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	2	no	—
1089	C₄⋊C₄	—	2	2	no	—
1090	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1091	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1092	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1093	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1094	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1096	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1097	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	2	no	—
1118	C₂²⋊C₄	—	2	2	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1121	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1122	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1127	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1128	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1129	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1130	C₄²	C₂⁴×C₁₃	1	2	yes	—
1131	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1132	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1133	C₁₃	#60834	1	1	yes	characteristic, direct product factor, Sylow
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	1	no	—
1137	C₂³	—	2	1	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	2	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1149	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1150	Q₈	—	2	2	no	—
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	2	2	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	4	4	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	8	2	no	—
1162	D₄	—	2	4	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	2	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	4	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	4	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	4	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	2	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1220	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1221	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1223	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1224	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1225	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1226	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	1	no	—
1230	C₈	—	2	1	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	8	4	no	—
1254	C₂²	—	16	2	no	—
1255	C₂²	—	16	4	no	—
1256	C₂²	C₁₃×#535	1	2	yes	—
1257	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	2	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	C₁₃×#535	1	2	yes	—
1273	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1274	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1275	C₂	—	2	2	no	—
1276	C₂	—	4	2	no	—
1277	C₂	—	8	2	no	—
1278	C₂	—	8	2	no	—
1279	C₂	—	8	1	no	—
1280	C₂	—	8	1	no	—
1281	C₂	—	8	1	no	—
1282	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
1283	C₂	C₁₃×#3584	1	1	yes	characteristic
1284	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3500	C₂	semidirect
2. C₁₃×#3460	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3224	C₂	semidirect
5. C₁₃×#3221	C₂	semidirect
6. C₁₃×#3220	C₂	semidirect
7. C₁₃×#3219	C₂	semidirect
8. C₁₃×#3213	C₂	semidirect
9. C₁₃×#3211	C₂	semidirect
10. C₁₃×#3207	C₂	semidirect
11. C₁₃×#3155	C₂	semidirect
12. C₁₃×#3154	C₂	semidirect
13. C₁₃×#3137	C₂	semidirect
14. C₁₃×#3136	C₂	semidirect
15. C₁₃×#3040	C₂	semidirect
16. C₁₃×#3036	C₂	semidirect
17. C₁₃×#3035	C₂	semidirect
18. C₂×C₁₃×#463	C₂	semidirect
19. C₁₃×#3013	C₂	semidirect
20. C₁₃×#3012	C₂	semidirect
21. C₁₃×#3010	C₂	semidirect
22. C₁₃×#3008	C₂	semidirect
23. C₁₃×#2925	C₂	semidirect
26. C₂×C₁₃×#137	C₂²	semidirect
29. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
31. C₂×C₁₃×#135	C₂²	semidirect
32. C₂²×C₁₃×SD₁₆	C₂²	semidirect
40. C₁₃×#544	C₂²	semidirect
42. C₁₃×#542	C₂²	semidirect
44. C₁₃×#540	C₂²	semidirect
48. C₁₃×#536	C₂²	semidirect
51. C₁₃×#535	C₂²	semidirect
52. C₁₃×#535	C₂²	semidirect
55. C₁₃×#532	C₂²	semidirect
56. C₁₃×#532	C₂²	semidirect
58. C₁₃×#529	C₂²	semidirect
60. C₂×C₁₃×#124	C₂²	semidirect
63. C₄×C₁₃×#41	C₂²	semidirect
64. C₂×C₄×D₄×C₁₃	C₂²	semidirect
65. C₁₃×#497	C₂²	semidirect
66. C₁₃×#496	C₂²	semidirect
67. C₁₃×#496	C₂²	semidirect
68. C₁₃×#496	C₂²	semidirect
69. C₁₃×#495	C₂²	semidirect
70. C₁₃×#495	C₂²	semidirect
71. C₁₃×#493	C₂²	semidirect
72. C₁₃×#492	C₂²	semidirect
73. C₁₃×#491	C₂²	semidirect
74. C₁₃×#490	C₂²	semidirect
75. C₁₃×#489	C₂²	semidirect
76. C₁₃×#489	C₂²	semidirect
77. C₁₃×#488	C₂²	semidirect
78. C₁₃×#488	C₂²	semidirect
79. C₁₃×#487	C₂²	semidirect
80. C₁₃×#486	C₂²	semidirect
81. C₁₃×#464	C₂²	semidirect
82. C₁₃×#464	C₂²	semidirect
83. C₁₃×#464	C₂²	semidirect
84. C₁₃×#464	C₂²	semidirect
85. C₁₃×#463	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
87. C₁₃×#463	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#463	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#463	C₂²	semidirect
93. C₁₃×#463	C₂²	semidirect
94. C₁₃×#463	C₂²	semidirect
95. C₁₃×#462	C₂²	semidirect
96. C₁₃×#461	C₂²	semidirect
97. C₁₃×#461	C₂²	semidirect
98. C₁₃×#460	C₂²	semidirect
99. C₁₃×#459	C₂²	semidirect
100. C₁₃×#459	C₂²	semidirect
101. C₁₃×#452	C₂²	semidirect
102. C₁₃×#452	C₂²	semidirect
103. C₁₃×#451	C₂²	semidirect
104. C₁₃×#450	C₂²	semidirect
107. C₁₃×#449	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×#448	C₂²	semidirect
116. C₁₃×#447	C₂²	semidirect
117. C₁₃×#433	C₂²	semidirect
118. C₁₃×#433	C₂²	semidirect
119. C₁₃×#432	C₂²	semidirect
120. C₁₃×#431	C₂²	semidirect
121. C₁₃×#423	C₂²	semidirect
122. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
123. C₁₃×#419	C₂²	semidirect
126. C₁₃×#417	C₂²	semidirect
128. C₁₃×#416	C₂²	semidirect
129. C₂×C₁₃×#103	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₁₃×#405	C₂²	semidirect
324. #60834	C₁₃	direct (N × H)
492. #3500	C₂×C₁₃	semidirect
493. #3460	C₂×C₁₃	semidirect
494. #3225	C₂×C₁₃	semidirect
495. #3224	C₂×C₁₃	semidirect
496. #3221	C₂×C₁₃	semidirect
497. #3220	C₂×C₁₃	semidirect
498. #3219	C₂×C₁₃	semidirect
499. #3213	C₂×C₁₃	semidirect
500. #3211	C₂×C₁₃	semidirect
501. #3207	C₂×C₁₃	semidirect
502. #3155	C₂×C₁₃	semidirect
503. #3154	C₂×C₁₃	semidirect
504. #3137	C₂×C₁₃	semidirect
505. #3136	C₂×C₁₃	semidirect
506. #3040	C₂×C₁₃	semidirect
507. #3036	C₂×C₁₃	semidirect
508. #3035	C₂×C₁₃	semidirect
509. C₂×#463	C₂×C₁₃	semidirect
510. #3013	C₂×C₁₃	semidirect
511. #3012	C₂×C₁₃	semidirect
512. #3010	C₂×C₁₃	semidirect
513. #3008	C₂×C₁₃	semidirect
514. #2925	C₂×C₁₃	semidirect
616. C₂×#137	C₂²×C₁₃	semidirect
619. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
621. C₂×#135	C₂²×C₁₃	semidirect
622. C₂²×SD₁₆	C₂²×C₁₃	semidirect
630. #544	C₂²×C₁₃	semidirect
632. #542	C₂²×C₁₃	semidirect
634. #540	C₂²×C₁₃	semidirect
638. #536	C₂²×C₁₃	semidirect
641. #535	C₂²×C₁₃	semidirect
642. #535	C₂²×C₁₃	semidirect
645. #532	C₂²×C₁₃	semidirect
646. #532	C₂²×C₁₃	semidirect
648. #529	C₂²×C₁₃	semidirect
650. C₂×#124	C₂²×C₁₃	semidirect
653. C₄×#41	C₂²×C₁₃	semidirect
654. C₂×C₄×D₄	C₂²×C₁₃	semidirect
655. #497	C₂²×C₁₃	semidirect
656. #496	C₂²×C₁₃	semidirect
657. #496	C₂²×C₁₃	semidirect
658. #496	C₂²×C₁₃	semidirect
659. #495	C₂²×C₁₃	semidirect
660. #495	C₂²×C₁₃	semidirect
661. #493	C₂²×C₁₃	semidirect
662. #492	C₂²×C₁₃	semidirect
663. #491	C₂²×C₁₃	semidirect
664. #490	C₂²×C₁₃	semidirect
665. #489	C₂²×C₁₃	semidirect
666. #489	C₂²×C₁₃	semidirect
667. #488	C₂²×C₁₃	semidirect
668. #488	C₂²×C₁₃	semidirect
669. #487	C₂²×C₁₃	semidirect
670. #486	C₂²×C₁₃	semidirect
671. #464	C₂²×C₁₃	semidirect
672. #464	C₂²×C₁₃	semidirect
673. #464	C₂²×C₁₃	semidirect
674. #464	C₂²×C₁₃	semidirect
675. #463	C₂²×C₁₃	semidirect
676. #463	C₂²×C₁₃	semidirect
677. #463	C₂²×C₁₃	semidirect
678. #463	C₂²×C₁₃	semidirect
679. #463	C₂²×C₁₃	semidirect
680. #463	C₂²×C₁₃	semidirect
681. #463	C₂²×C₁₃	semidirect
682. #463	C₂²×C₁₃	semidirect
683. #463	C₂²×C₁₃	semidirect
684. #463	C₂²×C₁₃	semidirect
685. #462	C₂²×C₁₃	semidirect
686. #461	C₂²×C₁₃	semidirect
687. #461	C₂²×C₁₃	semidirect
688. #460	C₂²×C₁₃	semidirect
689. #459	C₂²×C₁₃	semidirect
690. #459	C₂²×C₁₃	semidirect
691. #452	C₂²×C₁₃	semidirect
692. #452	C₂²×C₁₃	semidirect
693. #451	C₂²×C₁₃	semidirect
694. #450	C₂²×C₁₃	semidirect
697. #449	C₂²×C₁₃	semidirect
698. #449	C₂²×C₁₃	semidirect
699. #449	C₂²×C₁₃	semidirect
700. #449	C₂²×C₁₃	semidirect
701. #448	C₂²×C₁₃	semidirect
702. #448	C₂²×C₁₃	semidirect
703. #448	C₂²×C₁₃	semidirect
706. #447	C₂²×C₁₃	semidirect
707. #433	C₂²×C₁₃	semidirect
708. #433	C₂²×C₁₃	semidirect
709. #432	C₂²×C₁₃	semidirect
710. #431	C₂²×C₁₃	semidirect
711. #423	C₂²×C₁₃	semidirect
712. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
713. #419	C₂²×C₁₃	semidirect
716. #417	C₂²×C₁₃	semidirect
718. #416	C₂²×C₁₃	semidirect
719. C₂×#103	C₂²×C₁₃	semidirect
723. #405	C₂²×C₁₃	semidirect
724. #405	C₂²×C₁₃	semidirect
1133. C₁₃	#60834	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×#3500	2
C₁₃×#3460	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3221	2
C₁₃×#3220	2
C₁₃×#3219	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3207	2
C₁₃×#3155	2
C₁₃×#3154	2
C₁₃×#3137	2
C₁₃×#3136	2
C₁₃×#3040	2
C₁₃×#3036	2
C₁₃×#3035	2
C₂×C₁₃×#463	2
C₁₃×#3013	2
C₁₃×#3012	2
C₁₃×#3010	2
C₁₃×#3008	2
C₁₃×#2925	2
#60834	13

Subgroups — C13×#60834 #15747173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60834 #15747173