Subgroups — C₁₃×#60872 #15747211

Order 3328.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3242	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3236	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3232	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3229	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3092	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#3091	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#556	—	2	1	no	—
19	C₁₃×#554	—	2	1	no	—
20	C₁₃×#552	—	2	2	no	—
21	C₁₃×#552	—	2	1	no	—
22	C₁₃×#552	—	2	1	no	—
23	C₁₃×#551	—	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	—
31	C₁₃×#542	C₂²	1	2	yes	—
32	C₁₃×#541	C₂²	1	2	yes	—
33	C₁₃×#536	C₂²	1	1	yes	characteristic
34	C₁₃×#533	C₂²	1	2	yes	—
35	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₂×C₁₃×#125	—	2	1	no	—
39	C₂×C₁₃×#125	C₂²	1	2	yes	—
40	C₁₃×#525	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#520	C₂²	1	1	yes	characteristic
44	C₁₃×#519	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×#499	C₂²	1	4	yes	complemented
51	C₁₃×#498	C₂²	1	4	yes	complemented
52	C₁₃×#491	C₂²	1	4	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#488	C₂²	1	4	yes	complemented
55	C₁₃×#487	C₂²	1	4	yes	complemented
56	C₁₃×#485	C₂²	1	2	yes	—
57	C₁₃×#485	C₂²	1	4	yes	—
58	C₁₃×#484	C₂²	1	1	yes	characteristic
59	C₁₃×#484	C₂²	1	2	yes	—
60	C₁₃×#484	C₂²	1	2	yes	—
61	C₁₃×#483	C₂²	1	2	yes	—
62	C₁₃×#483	C₂²	1	2	yes	—
63	C₁₃×#483	C₂²	1	4	yes	—
64	C₁₃×#483	C₂²	1	1	yes	characteristic
65	C₁₃×#483	C₂²	1	2	yes	—
66	C₁₃×#483	C₂²	1	2	yes	—
67	C₁₃×#482	C₂²	1	2	yes	—
68	C₁₃×#481	C₂²	1	1	yes	characteristic
69	C₁₃×#481	C₂²	1	2	yes	—
70	C₁₃×#480	C₂²	1	1	yes	characteristic
71	C₁₃×#480	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	4	yes	complemented
73	C₁₃×#479	C₂²	1	4	yes	complemented
74	C₁₃×#479	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×#475	C₂²	1	4	yes	complemented
79	C₁₃×#475	C₂²	1	4	yes	complemented
80	C₁₃×#433	C₂²	1	4	yes	—
81	C₁₃×#432	C₂²	1	2	yes	—
82	C₁₃×#431	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	2	yes	—
85	C₁₃×#427	C₂²	1	2	yes	—
86	C₂×C₁₃×#106	C₂²	1	2	yes	—
87	C₁₃×#424	C₂²	1	2	yes	—
88	C₁₃×#419	C₂²	1	2	yes	—
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#416	C₂²	1	2	yes	—
91	C₂×C₁₃×#103	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	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	2	no	—
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	4	no	—
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#126	—	2	2	no	—
114	C₁₃×#126	—	2	2	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	—	2	4	no	—
118	C₁₃×#125	—	2	2	no	—
119	C₁₃×#125	—	2	2	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	1	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	C₂³	1	4	yes	—
126	C₁₃×#125	C₂³	1	4	yes	—
127	C₁₃×#125	C₂³	1	2	yes	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	C₂³	1	2	yes	—
130	C₁₃×#123	—	2	1	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
149	C₁₃×#121	C₂³	1	1	yes	characteristic
150	C₁₃×#121	C₂³	1	1	yes	characteristic
151	C₁₃×#120	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	C₁₃×#117	—	2	1	no	—
164	C₁₃×#117	—	2	1	no	—
165	C₁₃×#117	—	2	2	no	—
166	C₁₃×#117	—	2	1	no	—
167	C₁₃×#117	—	2	2	no	—
168	C₁₃×#117	—	2	2	no	—
169	C₁₃×#117	D₄	1	1	yes	characteristic
170	C₁₃×#117	D₄	1	2	yes	—
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	—	2	1	no	—
186	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	1	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	2	yes	—
200	C₁₃×#107	C₂³	1	2	yes	—
201	C₁₃×#107	C₂³	1	4	yes	—
202	C₁₃×#107	C₂³	1	4	yes	—
203	C₁₃×#106	C₂³	1	4	yes	—
204	C₁₃×#106	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	4	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	2	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	#60872	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₁₃×#41	—	2	4	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	2	no	—
233	C₂×Q₈×C₁₃	—	2	4	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	2	yes	—
238	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	8	2	no	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₁₃×M₁₆	—	2	4	no	—
263	C₂×C₈×C₁₃	—	2	4	no	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
293	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	1	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
316	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
317	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	1	no	—
325	C₄²×C₁₃	C₂×D₄	1	2	yes	—
326	C₄²×C₁₃	C₂×D₄	1	2	yes	—
327	C₄²×C₁₃	C₂⁴	1	2	yes	—
328	C₄²×C₁₃	C₂⁴	1	2	yes	—
329	#3495	C₂×C₁₃	1	1	yes	characteristic
330	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#3244	C₂×C₁₃	1	4	yes	complemented
332	#3242	C₂×C₁₃	1	4	yes	complemented
333	#3238	C₂×C₁₃	1	2	yes	complemented
334	#3236	C₂×C₁₃	1	2	yes	complemented
335	#3232	C₂×C₁₃	1	2	yes	complemented
336	#3229	C₂×C₁₃	1	2	yes	complemented
337	#3163	C₂×C₁₃	1	2	yes	complemented
338	#3137	C₂×C₁₃	1	2	yes	complemented
339	#3095	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3092	C₂×C₁₃	1	1	yes	characteristic
341	#3091	C₂×C₁₃	1	1	yes	characteristic
342	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3084	C₂×C₁₃	1	2	yes	complemented
344	#3082	C₂×C₁₃	1	2	yes	complemented
345	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	1	no	—
349	C₂³×C₁₃	—	4	1	no	—
350	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₁₃	—	2	4	no	—
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	4	2	no	—
356	Q₈×C₁₃	—	8	2	no	—
357	Q₈×C₁₃	—	8	4	no	—
358	Q₈×C₁₃	—	8	4	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	4	2	no	—
361	D₄×C₁₃	—	4	2	no	—
362	D₄×C₁₃	—	8	1	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	4	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	4	2	no	—
378	C₂×C₄×C₁₃	—	4	2	no	—
379	C₂×C₄×C₁₃	—	4	2	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	4	2	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	8	2	no	—
384	C₂×C₄×C₁₃	—	8	1	no	—
385	C₂×C₄×C₁₃	—	8	2	no	—
386	C₂×C₄×C₁₃	—	8	2	no	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
395	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
396	C₈×C₁₃	—	2	2	no	—
397	C₈×C₁₃	—	2	2	no	—
398	C₈×C₁₃	—	2	4	no	—
399	#556	—	2	1	no	—
400	#554	—	2	1	no	—
401	#552	—	2	2	no	—
402	#552	—	2	1	no	—
403	#552	—	2	1	no	—
404	#551	—	2	2	no	—
405	#544	—	2	2	no	—
406	#544	—	2	1	no	—
407	#544	—	2	1	no	—
408	#544	C₂²×C₁₃	1	2	yes	—
409	#544	C₂²×C₁₃	1	2	yes	—
410	#544	C₂²×C₁₃	1	1	yes	characteristic
411	#544	C₂²×C₁₃	1	4	yes	—
412	#542	C₂²×C₁₃	1	2	yes	—
413	#541	C₂²×C₁₃	1	2	yes	—
414	#536	C₂²×C₁₃	1	1	yes	characteristic
415	#533	C₂²×C₁₃	1	2	yes	—
416	C₂×C₄⋊Q₈	—	2	1	no	—
417	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
418	#529	C₂²×C₁₃	1	2	yes	—
419	C₂×#125	—	2	1	no	—
420	C₂×#125	C₂²×C₁₃	1	2	yes	—
421	#525	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊Q₈	—	2	2	no	—
423	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
424	#520	C₂²×C₁₃	1	1	yes	characteristic
425	#519	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
429	#501	C₂²×C₁₃	1	4	yes	complemented
430	#501	C₂²×C₁₃	1	4	yes	complemented
431	#499	C₂²×C₁₃	1	4	yes	complemented
432	#498	C₂²×C₁₃	1	4	yes	complemented
433	#491	C₂²×C₁₃	1	4	yes	complemented
434	#489	C₂²×C₁₃	1	4	yes	complemented
435	#488	C₂²×C₁₃	1	4	yes	complemented
436	#487	C₂²×C₁₃	1	4	yes	complemented
437	#485	C₂²×C₁₃	1	2	yes	—
438	#485	C₂²×C₁₃	1	4	yes	—
439	#484	C₂²×C₁₃	1	1	yes	characteristic
440	#484	C₂²×C₁₃	1	2	yes	—
441	#484	C₂²×C₁₃	1	2	yes	—
442	#483	C₂²×C₁₃	1	2	yes	—
443	#483	C₂²×C₁₃	1	2	yes	—
444	#483	C₂²×C₁₃	1	4	yes	—
445	#483	C₂²×C₁₃	1	1	yes	characteristic
446	#483	C₂²×C₁₃	1	2	yes	—
447	#483	C₂²×C₁₃	1	2	yes	—
448	#482	C₂²×C₁₃	1	2	yes	—
449	#481	C₂²×C₁₃	1	1	yes	characteristic
450	#481	C₂²×C₁₃	1	2	yes	—
451	#480	C₂²×C₁₃	1	1	yes	characteristic
452	#480	C₂²×C₁₃	1	2	yes	—
453	#479	C₂²×C₁₃	1	4	yes	complemented
454	#479	C₂²×C₁₃	1	4	yes	complemented
455	#479	C₂²×C₁₃	1	4	yes	complemented
456	#478	C₂²×C₁₃	1	4	yes	complemented
457	#477	C₂²×C₁₃	1	4	yes	complemented
458	#476	C₂²×C₁₃	1	4	yes	complemented
459	#475	C₂²×C₁₃	1	4	yes	complemented
460	#475	C₂²×C₁₃	1	4	yes	complemented
461	#433	C₂²×C₁₃	1	4	yes	—
462	#432	C₂²×C₁₃	1	2	yes	—
463	#431	C₂²×C₁₃	1	2	yes	—
464	#428	C₂²×C₁₃	1	2	yes	—
465	#428	C₂²×C₁₃	1	2	yes	—
466	#427	C₂²×C₁₃	1	2	yes	—
467	C₂×#106	C₂²×C₁₃	1	2	yes	—
468	#424	C₂²×C₁₃	1	2	yes	—
469	#419	C₂²×C₁₃	1	2	yes	—
470	#417	C₂²×C₁₃	1	2	yes	—
471	#416	C₂²×C₁₃	1	2	yes	—
472	C₂×#103	C₂²×C₁₃	1	2	yes	—
473	#407	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
475	#405	C₂²×C₁₃	1	2	yes	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	2	1	no	—
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	4	4	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	4	1	no	—
487	C₂²×C₁₃	#536	1	2	yes	—
488	C₂²×C₁₃	#577	1	2	yes	—
489	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	2	1	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	2	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	1	no	—
499	C₄×C₁₃	—	4	1	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	4	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	#536	1	2	yes	—
505	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
506	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
513	C₄⋊Q₈	—	2	2	no	—
514	C₄⋊Q₈	—	2	2	no	—
515	C₄⋊Q₈	—	2	4	no	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
522	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#126	—	2	2	no	—
526	#126	—	2	2	no	—
527	#125	—	2	2	no	—
528	#125	—	2	4	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	1	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	C₂³×C₁₃	1	4	yes	—
537	#125	C₂³×C₁₃	1	4	yes	—
538	#125	C₂³×C₁₃	1	2	yes	—
539	#124	—	2	2	no	—
540	#124	C₂³×C₁₃	1	2	yes	—
541	#123	—	2	1	no	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	2	4	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	#121	C₂³×C₁₃	1	1	yes	characteristic
561	#121	C₂³×C₁₃	1	1	yes	characteristic
562	#120	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
567	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
568	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	C₂³×C₁₃	1	2	yes	—
574	#117	—	2	1	no	—
575	#117	—	2	1	no	—
576	#117	—	2	2	no	—
577	#117	—	2	1	no	—
578	#117	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	D₄×C₁₃	1	1	yes	characteristic
581	#117	D₄×C₁₃	1	2	yes	—
582	#117	D₄×C₁₃	1	1	yes	characteristic
583	#117	C₂³×C₁₃	1	2	yes	—
584	#117	C₂³×C₁₃	1	2	yes	—
585	#117	C₂³×C₁₃	1	1	yes	characteristic
586	#117	C₂³×C₁₃	1	1	yes	characteristic
587	#117	C₂³×C₁₃	1	1	yes	characteristic
588	#117	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	2	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
608	C₂×C₄²	—	2	1	no	—
609	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
610	#107	C₂³×C₁₃	1	2	yes	—
611	#107	C₂³×C₁₃	1	2	yes	—
612	#107	C₂³×C₁₃	1	4	yes	—
613	#107	C₂³×C₁₃	1	4	yes	—
614	#106	C₂³×C₁₃	1	4	yes	—
615	#106	C₂³×C₁₃	1	4	yes	—
616	#106	C₂³×C₁₃	1	2	yes	—
617	#106	C₂³×C₁₃	1	2	yes	—
618	#106	C₂³×C₁₃	1	4	yes	—
619	#106	C₂³×C₁₃	1	4	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	#103	C₂³×C₁₃	1	4	yes	—
623	#103	C₂³×C₁₃	1	4	yes	—
624	#103	C₂³×C₁₃	1	2	yes	—
625	#103	C₂³×C₁₃	1	2	yes	—
626	#103	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	2	yes	—
630	#102	C₂³×C₁₃	1	2	yes	—
631	#102	C₂³×C₁₃	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
633	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
634	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
637	#97	C₂³×C₁₃	1	4	yes	—
638	C₄×C₈	C₂³×C₁₃	1	4	yes	—
639	C₂×C₁₃	—	2	2	no	—
640	C₂×C₁₃	—	2	2	no	—
641	C₂×C₁₃	—	4	1	no	—
642	C₂×C₁₃	—	8	1	no	—
643	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
644	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
645	C₂×C₁₃	#3586	1	1	yes	characteristic
646	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
647	#41	—	2	4	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	8	4	no	—
654	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
655	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	8	2	no	—
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
679	M₁₆	—	2	4	no	—
680	C₂×C₈	—	2	4	no	—
681	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
682	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
683	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	1	no	—
742	C₄²	C₂×D₄×C₁₃	1	2	yes	—
743	C₄²	C₂×D₄×C₁₃	1	2	yes	—
744	C₄²	C₂⁴×C₁₃	1	2	yes	—
745	C₄²	C₂⁴×C₁₃	1	2	yes	—
746	C₁₃	#60872	1	1	yes	characteristic, direct product factor, Sylow
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
754	Q₈	—	2	4	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	8	4	no	—
758	Q₈	—	8	4	no	—
759	Q₈	—	8	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	8	2	no	—
785	C₂×C₄	—	8	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
796	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
797	C₈	—	2	2	no	—
798	C₈	—	2	2	no	—
799	C₈	—	2	4	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	C₁₃×#536	1	2	yes	—
812	C₂²	C₁₃×#577	1	2	yes	—
813	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	2	no	—
828	C₄	C₁₃×#536	1	2	yes	—
829	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
835	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
836	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×#525	C₂²
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×#3244	C₂	semidirect
4. C₁₃×#3242	C₂	semidirect
5. C₁₃×#3238	C₂	semidirect
6. C₁₃×#3236	C₂	semidirect
7. C₁₃×#3232	C₂	semidirect
8. C₁₃×#3229	C₂	semidirect
9. C₁₃×#3163	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3095	C₂	semidirect
14. C₂×C₁₃×#483	C₂	semidirect
15. C₁₃×#3084	C₂	semidirect
16. C₁₃×#3082	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#499	C₂²	semidirect
51. C₁₃×#498	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
55. C₁₃×#487	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
228. #60872	C₁₃	direct (N × H)
330. C₂×#544	C₂×C₁₃	semidirect
331. #3244	C₂×C₁₃	semidirect
332. #3242	C₂×C₁₃	semidirect
333. #3238	C₂×C₁₃	semidirect
334. #3236	C₂×C₁₃	semidirect
335. #3232	C₂×C₁₃	semidirect
336. #3229	C₂×C₁₃	semidirect
337. #3163	C₂×C₁₃	semidirect
338. #3137	C₂×C₁₃	semidirect
339. #3095	C₂×C₁₃	semidirect
342. C₂×#483	C₂×C₁₃	semidirect
343. #3084	C₂×C₁₃	semidirect
344. #3082	C₂×C₁₃	semidirect
345. #2924	C₂×C₁₃	semidirect
429. #501	C₂²×C₁₃	semidirect
430. #501	C₂²×C₁₃	semidirect
431. #499	C₂²×C₁₃	semidirect
432. #498	C₂²×C₁₃	semidirect
433. #491	C₂²×C₁₃	semidirect
434. #489	C₂²×C₁₃	semidirect
435. #488	C₂²×C₁₃	semidirect
436. #487	C₂²×C₁₃	semidirect
453. #479	C₂²×C₁₃	semidirect
454. #479	C₂²×C₁₃	semidirect
455. #479	C₂²×C₁₃	semidirect
456. #478	C₂²×C₁₃	semidirect
457. #477	C₂²×C₁₃	semidirect
458. #476	C₂²×C₁₃	semidirect
459. #475	C₂²×C₁₃	semidirect
460. #475	C₂²×C₁₃	semidirect
746. C₁₃	#60872	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×#3495	2
C₂×C₁₃×#544	2
C₁₃×#3244	2
C₁₃×#3242	2
C₁₃×#3238	2
C₁₃×#3236	2
C₁₃×#3232	2
C₁₃×#3229	2
C₁₃×#3163	2
C₁₃×#3137	2
C₁₃×#3095	2
C₁₃×#3092	2
C₁₃×#3091	2
C₂×C₁₃×#483	2
C₁₃×#3084	2
C₁₃×#3082	2
C₁₃×#2924	2
#60872	13

Subgroups — C13×#60872 #15747211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60872 #15747211