Subgroups — C₁₃×#60871 #15747210

Order 3328.

1742 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3243	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3241	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3226	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3164	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#555	—	2	1	no	—
19	C₁₃×#553	—	2	1	no	—
20	C₁₃×#553	—	2	1	no	—
21	C₁₃×#551	—	2	2	no	—
22	C₁₃×#547	—	2	1	no	—
23	C₁₃×#546	—	2	2	no	—
24	C₁₃×#544	—	2	2	no	—
25	C₁₃×#544	—	2	1	no	—
26	C₁₃×#544	—	2	1	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#544	C₂²	1	2	yes	—
29	C₁₃×#544	C₂²	1	1	yes	characteristic
30	C₁₃×#544	C₂²	1	4	yes	complemented
31	C₁₃×#542	C₂²	1	2	yes	—
32	C₁₃×#540	C₂²	1	2	yes	—
33	C₁₃×#535	C₂²	1	1	yes	characteristic
34	C₁₃×#532	C₂²	1	2	yes	—
35	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₂×C₁₃×#125	—	2	1	no	—
39	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
40	C₁₃×#525	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₁₃×#520	C₂²	1	1	yes	characteristic
44	C₁₃×#518	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
47	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#501	C₂²	1	4	yes	complemented
50	C₁₃×#500	C₂²	1	4	yes	complemented
51	C₁₃×#499	C₂²	1	4	yes	complemented
52	C₁₃×#490	C₂²	1	4	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#488	C₂²	1	4	yes	complemented
55	C₁₃×#486	C₂²	1	4	yes	complemented
56	C₁₃×#485	C₂²	1	2	yes	complemented
57	C₁₃×#484	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#484	C₂²	1	2	yes	complemented
59	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#483	C₂²	1	2	yes	complemented
61	C₁₃×#482	C₂²	1	4	yes	—
62	C₁₃×#482	C₂²	1	2	yes	complemented
63	C₁₃×#481	C₂²	1	2	yes	—
64	C₁₃×#481	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#481	C₂²	1	2	yes	complemented
66	C₁₃×#480	C₂²	1	2	yes	—
67	C₁₃×#480	C₂²	1	2	yes	—
68	C₁₃×#480	C₂²	1	4	yes	—
69	C₁₃×#480	C₂²	1	2	yes	—
70	C₁₃×#480	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#480	C₂²	1	2	yes	complemented
72	C₁₃×#479	C₂²	1	4	yes	complemented
73	C₁₃×#478	C₂²	1	4	yes	complemented
74	C₁₃×#478	C₂²	1	4	yes	complemented
75	C₁₃×#478	C₂²	1	4	yes	complemented
76	C₁₃×#477	C₂²	1	4	yes	complemented
77	C₁₃×#476	C₂²	1	4	yes	complemented
78	C₁₃×#474	C₂²	1	4	yes	complemented
79	C₁₃×#474	C₂²	1	4	yes	complemented
80	C₁₃×#433	C₂²	1	4	yes	complemented
81	C₁₃×#432	C₂²	1	2	yes	complemented
82	C₁₃×#431	C₂²	1	2	yes	complemented
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	2	yes	—
85	C₁₃×#427	C₂²	1	2	yes	—
86	C₂×C₁₃×#107	C₂²	1	2	yes	—
87	C₁₃×#424	C₂²	1	2	yes	—
88	C₁₃×#418	C₂²	1	2	yes	—
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#416	C₂²	1	2	yes	—
91	C₂×C₁₃×#102	C₂²	1	2	yes	—
92	C₁₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	4	no	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×#127	C₂³	1	2	yes	—
114	C₁₃×#126	—	2	2	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	—	2	2	no	—
118	C₁₃×#125	—	2	4	no	—
119	C₁₃×#125	—	2	1	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	C₂³	1	4	yes	—
123	C₁₃×#125	C₂³	1	4	yes	—
124	C₁₃×#125	C₂³	1	2	yes	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	C₂³	1	2	yes	—
128	C₁₃×#123	—	2	1	no	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	2	yes	—
150	C₁₃×#121	C₂³	1	1	yes	characteristic
151	C₁₃×#121	C₂³	1	1	yes	characteristic
152	C₁₃×#120	—	2	1	no	—
153	C₁₃×#120	—	2	2	no	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	—	2	1	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₁₃×#117	—	2	1	no	—
166	C₁₃×#117	—	2	1	no	—
167	C₁₃×#117	—	2	1	no	—
168	C₁₃×#117	—	2	2	no	—
169	C₁₃×#117	D₄	1	2	yes	—
170	C₁₃×#117	D₄	1	1	yes	characteristic
171	C₁₃×#117	D₄	1	1	yes	characteristic
172	C₁₃×#117	C₂³	1	2	yes	—
173	C₁₃×#117	C₂³	1	1	yes	characteristic
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₁₃×#117	C₂³	1	1	yes	characteristic
176	C₁₃×#117	C₂³	1	1	yes	characteristic
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
186	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
197	C₂×C₄²×C₁₃	—	2	1	no	—
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₁₃×#107	C₂³	1	4	yes	—
200	C₁₃×#107	C₂³	1	4	yes	—
201	C₁₃×#107	C₂³	1	2	yes	—
202	C₁₃×#107	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	2	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#60871	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	8	4	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	4	no	—
235	C₂×Q₈×C₁₃	—	2	4	no	—
236	C₂×Q₈×C₁₃	—	8	4	no	—
237	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	8	2	no	—
248	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	8	2	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₁₃×M₁₆	—	2	4	no	—
271	C₂×C₈×C₁₃	—	2	4	no	—
272	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₄	—	2	1	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	C₂×D₄	1	2	yes	—
329	C₄²×C₁₃	C₂⁴	1	2	yes	—
330	C₄²×C₁₃	C₂⁴	1	2	yes	—
331	#3494	C₂×C₁₃	1	1	yes	characteristic
332	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#3243	C₂×C₁₃	1	4	yes	complemented
334	#3241	C₂×C₁₃	1	4	yes	complemented
335	#3238	C₂×C₁₃	1	2	yes	complemented
336	#3234	C₂×C₁₃	1	2	yes	complemented
337	#3232	C₂×C₁₃	1	2	yes	complemented
338	#3226	C₂×C₁₃	1	2	yes	complemented
339	#3164	C₂×C₁₃	1	2	yes	complemented
340	#3136	C₂×C₁₃	1	2	yes	complemented
341	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3092	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3091	C₂×C₁₃	1	1	yes	characteristic, complemented
344	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3083	C₂×C₁₃	1	2	yes	complemented
346	#3081	C₂×C₁₃	1	2	yes	complemented
347	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	4	1	no	—
353	C₂³×C₁₃	—	4	2	no	—
354	C₂³×C₁₃	—	8	1	no	—
355	C₂³×C₁₃	—	8	1	no	—
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	8	4	no	—
361	Q₈×C₁₃	—	8	4	no	—
362	Q₈×C₁₃	—	8	2	no	—
363	D₄×C₁₃	—	2	4	no	—
364	D₄×C₁₃	—	2	2	no	—
365	D₄×C₁₃	—	4	2	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	2	no	—
368	D₄×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	8	2	no	—
370	D₄×C₁₃	—	8	2	no	—
371	D₄×C₁₃	—	8	1	no	—
372	D₄×C₁₃	—	8	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	8	2	no	—
392	C₂×C₄×C₁₃	—	8	2	no	—
393	C₂×C₄×C₁₃	—	8	2	no	—
394	C₂×C₄×C₁₃	—	8	2	no	—
395	C₂×C₄×C₁₃	—	8	2	no	—
396	C₂×C₄×C₁₃	—	8	1	no	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
405	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₁₃	—	2	2	no	—
407	C₈×C₁₃	—	2	2	no	—
408	C₈×C₁₃	—	2	4	no	—
409	#555	—	2	1	no	—
410	#553	—	2	1	no	—
411	#553	—	2	1	no	—
412	#551	—	2	2	no	—
413	#547	—	2	1	no	—
414	#546	—	2	2	no	—
415	#544	—	2	2	no	—
416	#544	—	2	1	no	—
417	#544	—	2	1	no	—
418	#544	C₂²×C₁₃	1	2	yes	—
419	#544	C₂²×C₁₃	1	2	yes	—
420	#544	C₂²×C₁₃	1	1	yes	characteristic
421	#544	C₂²×C₁₃	1	4	yes	complemented
422	#542	C₂²×C₁₃	1	2	yes	—
423	#540	C₂²×C₁₃	1	2	yes	—
424	#535	C₂²×C₁₃	1	1	yes	characteristic
425	#532	C₂²×C₁₃	1	2	yes	—
426	C₂×C₄⋊Q₈	—	2	1	no	—
427	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
428	#529	C₂²×C₁₃	1	2	yes	—
429	C₂×#125	—	2	1	no	—
430	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
431	#525	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	—	2	2	no	—
433	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
434	#520	C₂²×C₁₃	1	1	yes	characteristic
435	#518	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
439	#501	C₂²×C₁₃	1	4	yes	complemented
440	#501	C₂²×C₁₃	1	4	yes	complemented
441	#500	C₂²×C₁₃	1	4	yes	complemented
442	#499	C₂²×C₁₃	1	4	yes	complemented
443	#490	C₂²×C₁₃	1	4	yes	complemented
444	#489	C₂²×C₁₃	1	4	yes	complemented
445	#488	C₂²×C₁₃	1	4	yes	complemented
446	#486	C₂²×C₁₃	1	4	yes	complemented
447	#485	C₂²×C₁₃	1	2	yes	complemented
448	#484	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#484	C₂²×C₁₃	1	2	yes	complemented
450	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#483	C₂²×C₁₃	1	2	yes	complemented
452	#482	C₂²×C₁₃	1	4	yes	—
453	#482	C₂²×C₁₃	1	2	yes	complemented
454	#481	C₂²×C₁₃	1	2	yes	—
455	#481	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#481	C₂²×C₁₃	1	2	yes	complemented
457	#480	C₂²×C₁₃	1	2	yes	—
458	#480	C₂²×C₁₃	1	2	yes	—
459	#480	C₂²×C₁₃	1	4	yes	—
460	#480	C₂²×C₁₃	1	2	yes	—
461	#480	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#480	C₂²×C₁₃	1	2	yes	complemented
463	#479	C₂²×C₁₃	1	4	yes	complemented
464	#478	C₂²×C₁₃	1	4	yes	complemented
465	#478	C₂²×C₁₃	1	4	yes	complemented
466	#478	C₂²×C₁₃	1	4	yes	complemented
467	#477	C₂²×C₁₃	1	4	yes	complemented
468	#476	C₂²×C₁₃	1	4	yes	complemented
469	#474	C₂²×C₁₃	1	4	yes	complemented
470	#474	C₂²×C₁₃	1	4	yes	complemented
471	#433	C₂²×C₁₃	1	4	yes	complemented
472	#432	C₂²×C₁₃	1	2	yes	complemented
473	#431	C₂²×C₁₃	1	2	yes	complemented
474	#428	C₂²×C₁₃	1	2	yes	—
475	#428	C₂²×C₁₃	1	2	yes	—
476	#427	C₂²×C₁₃	1	2	yes	—
477	C₂×#107	C₂²×C₁₃	1	2	yes	—
478	#424	C₂²×C₁₃	1	2	yes	—
479	#418	C₂²×C₁₃	1	2	yes	—
480	#417	C₂²×C₁₃	1	2	yes	—
481	#416	C₂²×C₁₃	1	2	yes	—
482	C₂×#102	C₂²×C₁₃	1	2	yes	—
483	#407	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
485	#405	C₂²×C₁₃	1	2	yes	—
486	C₂²×C₁₃	—	2	1	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	4	4	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	16	2	no	—
501	C₂²×C₁₃	#536	1	2	yes	—
502	C₂²×C₁₃	#576	1	2	yes	—
503	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	2	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	—	4	1	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	4	4	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	#536	1	2	yes	—
518	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
521	C₂²×Q₈	—	2	2	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
527	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
528	C₄⋊Q₈	—	2	2	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	4	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
535	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
536	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
537	#127	C₂³×C₁₃	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	4	no	—
543	#125	—	2	1	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	C₂³×C₁₃	1	4	yes	—
547	#125	C₂³×C₁₃	1	4	yes	—
548	#125	C₂³×C₁₃	1	2	yes	—
549	#124	—	2	2	no	—
550	#124	—	2	2	no	—
551	#124	C₂³×C₁₃	1	2	yes	—
552	#123	—	2	1	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	2	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	C₂³×C₁₃	1	2	yes	—
573	#121	C₂³×C₁₃	1	2	yes	—
574	#121	C₂³×C₁₃	1	1	yes	characteristic
575	#121	C₂³×C₁₃	1	1	yes	characteristic
576	#120	—	2	1	no	—
577	#120	—	2	2	no	—
578	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	C₂³×C₁₃	1	2	yes	—
587	C₄×D₄	C₂³×C₁₃	1	2	yes	—
588	C₄×D₄	C₂³×C₁₃	1	2	yes	—
589	#117	—	2	1	no	—
590	#117	—	2	1	no	—
591	#117	—	2	1	no	—
592	#117	—	2	2	no	—
593	#117	D₄×C₁₃	1	2	yes	—
594	#117	D₄×C₁₃	1	1	yes	characteristic
595	#117	D₄×C₁₃	1	1	yes	characteristic
596	#117	C₂³×C₁₃	1	2	yes	—
597	#117	C₂³×C₁₃	1	2	yes	—
598	#117	C₂³×C₁₃	1	1	yes	characteristic
599	#117	C₂³×C₁₃	1	1	yes	characteristic
600	#117	C₂³×C₁₃	1	1	yes	characteristic
601	#117	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
623	#107	C₂³×C₁₃	1	4	yes	—
624	#107	C₂³×C₁₃	1	4	yes	—
625	#107	C₂³×C₁₃	1	2	yes	—
626	#107	C₂³×C₁₃	1	2	yes	—
627	#107	C₂³×C₁₃	1	4	yes	—
628	#107	C₂³×C₁₃	1	4	yes	—
629	#106	C₂³×C₁₃	1	2	yes	—
630	#106	C₂³×C₁₃	1	2	yes	—
631	#106	C₂³×C₁₃	1	4	yes	—
632	#106	C₂³×C₁₃	1	4	yes	—
633	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
634	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
635	#103	C₂³×C₁₃	1	2	yes	—
636	#103	C₂³×C₁₃	1	2	yes	—
637	#103	C₂³×C₁₃	1	4	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	#102	C₂³×C₁₃	1	2	yes	—
641	#102	C₂³×C₁₃	1	2	yes	—
642	#102	C₂³×C₁₃	1	4	yes	—
643	#102	C₂³×C₁₃	1	4	yes	—
644	#102	C₂³×C₁₃	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
646	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
647	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
648	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
650	#97	C₂³×C₁₃	1	4	yes	—
651	C₄×C₈	C₂³×C₁₃	1	4	yes	—
652	C₂×C₁₃	—	2	2	no	—
653	C₂×C₁₃	—	2	2	no	—
654	C₂×C₁₃	—	4	1	no	—
655	C₂×C₁₃	—	8	1	no	—
656	C₂×C₁₃	—	8	2	no	—
657	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
658	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
659	C₂×C₁₃	#3586	1	1	yes	characteristic
660	C₂⁴	—	2	1	no	—
661	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
662	#41	—	2	4	no	—
663	#41	—	8	4	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	4	no	—
667	C₂×Q₈	—	8	4	no	—
668	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	8	2	no	—
679	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	8	2	no	—
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	M₁₆	—	2	4	no	—
702	C₂×C₈	—	2	4	no	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
705	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
732	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	1	no	—
758	C₄²	C₂×D₄×C₁₃	1	2	yes	—
759	C₄²	C₂×D₄×C₁₃	1	2	yes	—
760	C₄²	C₂⁴×C₁₃	1	2	yes	—
761	C₄²	C₂⁴×C₁₃	1	2	yes	—
762	C₁₃	#60871	1	1	yes	characteristic, direct product factor, Sylow
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	Q₈	—	2	2	no	—
775	Q₈	—	8	4	no	—
776	Q₈	—	8	4	no	—
777	Q₈	—	8	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	2	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
820	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	—	2	4	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	16	2	no	—
839	C₂²	C₁₃×#536	1	2	yes	—
840	C₂²	C₁₃×#576	1	2	yes	—
841	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	4	4	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	C₁₃×#536	1	2	yes	—
856	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
857	C₂	—	2	2	no	—
858	C₂	—	2	2	no	—
859	C₂	—	4	1	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
863	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
864	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#544	C₂	semidirect
3. C₁₃×#3243	C₂	semidirect
4. C₁₃×#3241	C₂	semidirect
5. C₁₃×#3238	C₂	semidirect
6. C₁₃×#3234	C₂	semidirect
7. C₁₃×#3232	C₂	semidirect
8. C₁₃×#3226	C₂	semidirect
9. C₁₃×#3164	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3094	C₂	semidirect
12. C₁₃×#3092	C₂	semidirect
13. C₁₃×#3091	C₂	semidirect
14. C₂×C₁₃×#480	C₂	semidirect
15. C₁₃×#3083	C₂	semidirect
16. C₁₃×#3081	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
30. C₁₃×#544	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#125	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#500	C₂²	semidirect
51. C₁₃×#499	C₂²	semidirect
52. C₁₃×#490	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
55. C₁₃×#486	C₂²	semidirect
56. C₁₃×#485	C₂²	semidirect
57. C₁₃×#484	C₂²	semidirect
58. C₁₃×#484	C₂²	semidirect
59. C₁₃×#483	C₂²	semidirect
60. C₁₃×#483	C₂²	semidirect
62. C₁₃×#482	C₂²	semidirect
64. C₁₃×#481	C₂²	semidirect
65. C₁₃×#481	C₂²	semidirect
70. C₁₃×#480	C₂²	semidirect
71. C₁₃×#480	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#478	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#474	C₂²	semidirect
80. C₁₃×#433	C₂²	semidirect
81. C₁₃×#432	C₂²	semidirect
82. C₁₃×#431	C₂²	semidirect
228. #60871	C₁₃	direct (N × H)
332. C₂×#544	C₂×C₁₃	semidirect
333. #3243	C₂×C₁₃	semidirect
334. #3241	C₂×C₁₃	semidirect
335. #3238	C₂×C₁₃	semidirect
336. #3234	C₂×C₁₃	semidirect
337. #3232	C₂×C₁₃	semidirect
338. #3226	C₂×C₁₃	semidirect
339. #3164	C₂×C₁₃	semidirect
340. #3136	C₂×C₁₃	semidirect
341. #3094	C₂×C₁₃	semidirect
342. #3092	C₂×C₁₃	semidirect
343. #3091	C₂×C₁₃	semidirect
344. C₂×#480	C₂×C₁₃	semidirect
345. #3083	C₂×C₁₃	semidirect
346. #3081	C₂×C₁₃	semidirect
347. #2924	C₂×C₁₃	semidirect
421. #544	C₂²×C₁₃	semidirect
427. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
430. C₂×#125	C₂²×C₁₃	semidirect
439. #501	C₂²×C₁₃	semidirect
440. #501	C₂²×C₁₃	semidirect
441. #500	C₂²×C₁₃	semidirect
442. #499	C₂²×C₁₃	semidirect
443. #490	C₂²×C₁₃	semidirect
444. #489	C₂²×C₁₃	semidirect
445. #488	C₂²×C₁₃	semidirect
446. #486	C₂²×C₁₃	semidirect
447. #485	C₂²×C₁₃	semidirect
448. #484	C₂²×C₁₃	semidirect
449. #484	C₂²×C₁₃	semidirect
450. #483	C₂²×C₁₃	semidirect
451. #483	C₂²×C₁₃	semidirect
453. #482	C₂²×C₁₃	semidirect
455. #481	C₂²×C₁₃	semidirect
456. #481	C₂²×C₁₃	semidirect
461. #480	C₂²×C₁₃	semidirect
462. #480	C₂²×C₁₃	semidirect
463. #479	C₂²×C₁₃	semidirect
464. #478	C₂²×C₁₃	semidirect
465. #478	C₂²×C₁₃	semidirect
466. #478	C₂²×C₁₃	semidirect
467. #477	C₂²×C₁₃	semidirect
468. #476	C₂²×C₁₃	semidirect
469. #474	C₂²×C₁₃	semidirect
470. #474	C₂²×C₁₃	semidirect
471. #433	C₂²×C₁₃	semidirect
472. #432	C₂²×C₁₃	semidirect
473. #431	C₂²×C₁₃	semidirect
762. C₁₃	#60871	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×#3494	2
C₂×C₁₃×#544	2
C₁₃×#3243	2
C₁₃×#3241	2
C₁₃×#3238	2
C₁₃×#3234	2
C₁₃×#3232	2
C₁₃×#3226	2
C₁₃×#3164	2
C₁₃×#3136	2
C₁₃×#3094	2
C₁₃×#3092	2
C₁₃×#3091	2
C₂×C₁₃×#480	2
C₁₃×#3083	2
C₁₃×#3081	2
C₁₃×#2924	2
#60871	13

Subgroups — C13×#60871 #15747210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60871 #15747210