Subgroups — C₁₃×#60885 #15747224

Order 3328.

1682 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3243	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3096	C₂	1	2	yes	maximal
15	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	—	2	1	no	—
20	Q₈²×C₁₃	—	2	1	no	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#554	—	2	2	no	—
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#551	—	2	2	no	—
27	C₁₃×#551	—	2	2	no	—
28	D₄×Q₈×C₁₃	—	2	2	no	—
29	D₄×Q₈×C₁₃	—	2	1	no	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#544	C₂²	1	4	yes	complemented
32	C₁₃×#542	C₂²	1	2	yes	—
33	C₁₃×#542	C₂²	1	2	yes	—
34	C₁₃×#536	C₂²	1	1	yes	characteristic
35	C₁₃×#535	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	complemented
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
44	C₁₃×#520	C₂²	1	2	yes	—
45	C₁₃×#519	C₂²	1	1	yes	characteristic
46	C₁₃×#518	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#501	C₂²	1	2	yes	complemented
53	C₁₃×#501	C₂²	1	2	yes	complemented
54	C₁₃×#501	C₂²	1	2	yes	complemented
55	C₁₃×#501	C₂²	1	2	yes	complemented
56	C₁₃×#500	C₂²	1	2	yes	complemented
57	C₁₃×#498	C₂²	1	2	yes	complemented
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	4	yes	—
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	2	yes	—
63	C₁₃×#488	C₂²	1	4	yes	—
64	C₁₃×#485	C₂²	1	4	yes	complemented
65	C₁₃×#485	C₂²	1	4	yes	complemented
66	C₁₃×#484	C₂²	1	4	yes	complemented
67	C₁₃×#483	C₂²	1	4	yes	complemented
68	C₁₃×#482	C₂²	1	4	yes	—
69	C₁₃×#482	C₂²	1	4	yes	—
70	C₁₃×#481	C₂²	1	4	yes	—
71	C₁₃×#480	C₂²	1	4	yes	—
72	C₁₃×#479	C₂²	1	4	yes	complemented
73	C₁₃×#479	C₂²	1	4	yes	complemented
74	C₁₃×#478	C₂²	1	4	yes	—
75	C₁₃×#478	C₂²	1	4	yes	—
76	C₁₃×#477	C₂²	1	4	yes	complemented
77	C₁₃×#476	C₂²	1	4	yes	—
78	C₁₃×#475	C₂²	1	4	yes	complemented
79	C₁₃×#474	C₂²	1	4	yes	—
80	C₁₃×#433	C₂²	1	4	yes	complemented
81	C₁₃×#432	C₂²	1	2	yes	complemented
82	C₁₃×#432	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	C₁₃×#427	C₂²	1	2	yes	—
87	C₁₃×#424	C₂²	1	2	yes	—
88	C₁₃×#419	C₂²	1	2	yes	—
89	C₁₃×#418	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₂×C₁₃×#102	C₂²	1	2	yes	—
92	C₁₃×#408	C₂²	1	2	yes	—
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×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	1	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	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×#127	—	2	1	no	—
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	C₂³	1	4	yes	—
124	C₁₃×#125	C₂³	1	2	yes	—
125	C₁₃×#125	C₂³	1	1	yes	characteristic
126	C₁₃×#125	C₂³	1	1	yes	characteristic
127	C₁₃×#124	—	2	1	no	—
128	C₁₃×#124	—	2	1	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	4	no	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	C₂³	1	2	yes	—
154	C₁₃×#121	C₂³	1	2	yes	—
155	C₁₃×#120	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	—	2	4	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	D₄	1	2	yes	—
176	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₁₃	D₄	1	2	yes	—
178	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	C₂³	1	2	yes	—
185	C₁₃×#117	C₂³	1	1	yes	characteristic
186	C₁₃×#117	C₂³	1	1	yes	characteristic
187	C₁₃×#117	C₂³	1	4	yes	—
188	C₁₃×#117	C₂³	1	1	yes	characteristic
189	C₁₃×#117	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×#106	C₂³	1	4	yes	—
210	C₁₃×#106	C₂³	1	4	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	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	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	1	yes	characteristic
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#60885	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	8	2	no	—
241	C₂×Q₈×C₁₃	—	8	4	no	—
242	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	4	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
289	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
290	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
291	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
295	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
299	C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
314	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	1	no	—
319	C₄²×C₁₃	—	2	4	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	C₂×D₄	1	2	yes	—
323	C₄²×C₁₃	C₂×D₄	1	2	yes	—
324	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₄²×C₁₃	C₂⁴	1	2	yes	—
329	#3510	C₂×C₁₃	1	1	yes	characteristic
330	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#3244	C₂×C₁₃	1	4	yes	complemented
332	#3243	C₂×C₁₃	1	4	yes	complemented
333	#3240	C₂×C₁₃	1	2	yes	complemented
334	#3240	C₂×C₁₃	1	2	yes	complemented
335	#3239	C₂×C₁₃	1	2	yes	complemented
336	#3238	C₂×C₁₃	1	2	yes	complemented
337	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
340	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#3097	C₂×C₁₃	1	2	yes	complemented
342	#3096	C₂×C₁₃	1	2	yes	—
343	#3082	C₂×C₁₃	1	2	yes	complemented
344	#3081	C₂×C₁₃	1	2	yes	complemented
345	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	4	2	no	—
348	C₂³×C₁₃	—	8	1	no	—
349	C₂³×C₁₃	—	8	1	no	—
350	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₁₃	—	2	2	no	—
353	Q₈×C₁₃	—	2	4	no	—
354	Q₈×C₁₃	—	4	2	no	—
355	Q₈×C₁₃	—	4	2	no	—
356	Q₈×C₁₃	—	4	4	no	—
357	Q₈×C₁₃	—	4	2	no	—
358	Q₈×C₁₃	—	8	1	no	—
359	Q₈×C₁₃	—	8	1	no	—
360	Q₈×C₁₃	—	8	4	no	—
361	Q₈×C₁₃	—	8	2	no	—
362	D₄×C₁₃	—	2	4	no	—
363	D₄×C₁₃	—	2	2	no	—
364	D₄×C₁₃	—	2	4	no	—
365	D₄×C₁₃	—	4	2	no	—
366	D₄×C₁₃	—	8	2	no	—
367	D₄×C₁₃	—	8	2	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	4	2	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	2	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	2	no	—
382	C₂×C₄×C₁₃	—	8	2	no	—
383	C₂×C₄×C₁₃	—	8	2	no	—
384	C₂×C₄×C₁₃	—	8	2	no	—
385	C₂×C₄×C₁₃	—	8	4	no	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	#559	—	2	1	no	—
400	#559	—	2	1	no	—
401	Q₈²	—	2	1	no	—
402	#557	—	2	1	no	—
403	#556	—	2	1	no	—
404	#556	—	2	1	no	—
405	#554	—	2	2	no	—
406	#554	—	2	1	no	—
407	#551	—	2	2	no	—
408	#551	—	2	2	no	—
409	D₄×Q₈	—	2	2	no	—
410	D₄×Q₈	—	2	1	no	—
411	#544	C₂²×C₁₃	1	2	yes	—
412	#544	C₂²×C₁₃	1	4	yes	complemented
413	#542	C₂²×C₁₃	1	2	yes	—
414	#542	C₂²×C₁₃	1	2	yes	—
415	#536	C₂²×C₁₃	1	1	yes	characteristic
416	#535	C₂²×C₁₃	1	1	yes	characteristic
417	#533	C₂²×C₁₃	1	1	yes	characteristic
418	#533	C₂²×C₁₃	1	1	yes	characteristic
419	#533	C₂²×C₁₃	1	2	yes	complemented
420	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
422	#529	C₂²×C₁₃	1	2	yes	—
423	#529	C₂²×C₁₃	1	2	yes	—
424	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
425	#520	C₂²×C₁₃	1	2	yes	—
426	#519	C₂²×C₁₃	1	1	yes	characteristic
427	#518	C₂²×C₁₃	1	1	yes	characteristic
428	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
429	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	#501	C₂²×C₁₃	1	2	yes	complemented
434	#501	C₂²×C₁₃	1	2	yes	complemented
435	#501	C₂²×C₁₃	1	2	yes	complemented
436	#501	C₂²×C₁₃	1	2	yes	complemented
437	#500	C₂²×C₁₃	1	2	yes	complemented
438	#498	C₂²×C₁₃	1	2	yes	complemented
439	#489	C₂²×C₁₃	1	2	yes	—
440	#489	C₂²×C₁₃	1	2	yes	—
441	#489	C₂²×C₁₃	1	4	yes	—
442	#489	C₂²×C₁₃	1	2	yes	—
443	#489	C₂²×C₁₃	1	2	yes	—
444	#488	C₂²×C₁₃	1	4	yes	—
445	#485	C₂²×C₁₃	1	4	yes	complemented
446	#485	C₂²×C₁₃	1	4	yes	complemented
447	#484	C₂²×C₁₃	1	4	yes	complemented
448	#483	C₂²×C₁₃	1	4	yes	complemented
449	#482	C₂²×C₁₃	1	4	yes	—
450	#482	C₂²×C₁₃	1	4	yes	—
451	#481	C₂²×C₁₃	1	4	yes	—
452	#480	C₂²×C₁₃	1	4	yes	—
453	#479	C₂²×C₁₃	1	4	yes	complemented
454	#479	C₂²×C₁₃	1	4	yes	complemented
455	#478	C₂²×C₁₃	1	4	yes	—
456	#478	C₂²×C₁₃	1	4	yes	—
457	#477	C₂²×C₁₃	1	4	yes	complemented
458	#476	C₂²×C₁₃	1	4	yes	—
459	#475	C₂²×C₁₃	1	4	yes	complemented
460	#474	C₂²×C₁₃	1	4	yes	—
461	#433	C₂²×C₁₃	1	4	yes	complemented
462	#432	C₂²×C₁₃	1	2	yes	complemented
463	#432	C₂²×C₁₃	1	2	yes	complemented
464	#428	C₂²×C₁₃	1	2	yes	—
465	#428	C₂²×C₁₃	1	2	yes	—
466	#427	C₂²×C₁₃	1	2	yes	—
467	#427	C₂²×C₁₃	1	2	yes	—
468	#424	C₂²×C₁₃	1	2	yes	—
469	#419	C₂²×C₁₃	1	2	yes	—
470	#418	C₂²×C₁₃	1	2	yes	—
471	C₂×#103	C₂²×C₁₃	1	2	yes	—
472	C₂×#102	C₂²×C₁₃	1	2	yes	—
473	#408	C₂²×C₁₃	1	2	yes	—
474	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	2	no	—
479	C₂²×C₁₃	—	2	2	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	16	2	no	—
485	C₂²×C₁₃	#536	1	2	yes	—
486	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	1	no	—
490	C₄×C₁₃	—	2	1	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	2	1	no	—
493	C₄×C₁₃	—	2	2	no	—
494	C₄×C₁₃	—	4	4	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	1	no	—
497	C₄×C₁₃	—	4	1	no	—
498	C₄×C₁₃	—	4	1	no	—
499	C₄×C₁₃	—	4	1	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	#536	1	2	yes	—
503	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
504	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
510	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	—	2	4	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	—	2	1	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
519	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	#127	—	2	1	no	—
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#126	—	2	2	no	—
529	#126	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	4	no	—
532	#125	C₂³×C₁₃	1	1	yes	characteristic
533	#125	C₂³×C₁₃	1	1	yes	characteristic
534	#125	C₂³×C₁₃	1	2	yes	—
535	#125	C₂³×C₁₃	1	4	yes	—
536	#124	—	2	1	no	—
537	#124	—	2	1	no	—
538	#124	—	2	2	no	—
539	#124	—	2	2	no	—
540	#124	—	2	1	no	—
541	#124	—	2	1	no	—
542	#124	C₂³×C₁₃	1	2	yes	—
543	#124	C₂³×C₁₃	1	2	yes	—
544	#123	—	2	2	no	—
545	#123	—	2	2	no	—
546	#123	—	2	2	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	—	2	4	no	—
559	C₂²⋊Q₈	—	2	4	no	—
560	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
561	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
562	#121	C₂³×C₁₃	1	2	yes	—
563	#121	C₂³×C₁₃	1	2	yes	—
564	#120	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
575	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	D₄×C₁₃	1	2	yes	—
585	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
586	C₄×D₄	D₄×C₁₃	1	2	yes	—
587	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
588	C₄×D₄	C₂³×C₁₃	1	2	yes	—
589	C₄×D₄	C₂³×C₁₃	1	2	yes	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	C₂³×C₁₃	1	1	yes	characteristic
594	#117	C₂³×C₁₃	1	1	yes	characteristic
595	#117	C₂³×C₁₃	1	2	yes	—
596	#117	C₂³×C₁₃	1	4	yes	—
597	#117	C₂³×C₁₃	1	1	yes	characteristic
598	#117	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	2	no	—
606	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
608	#107	C₂³×C₁₃	1	2	yes	—
609	#107	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	2	yes	—
615	#106	C₂³×C₁₃	1	2	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	4	yes	—
625	#103	C₂³×C₁₃	1	4	yes	—
626	#102	C₂³×C₁₃	1	4	yes	—
627	#102	C₂³×C₁₃	1	4	yes	—
628	#102	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
632	#97	C₂³×C₁₃	1	1	yes	characteristic
633	#97	C₂³×C₁₃	1	1	yes	characteristic
634	#97	C₂³×C₁₃	1	2	yes	—
635	#97	C₂³×C₁₃	1	2	yes	—
636	C₄×C₈	C₂³×C₁₃	1	2	yes	—
637	C₂×C₁₃	—	2	2	no	—
638	C₂×C₁₃	—	4	2	no	—
639	C₂×C₁₃	—	8	2	no	—
640	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
641	C₂×C₁₃	#3585	1	1	yes	characteristic
642	C₂×C₁₃	#3586	1	1	yes	characteristic
643	C₂⁴	—	2	1	no	—
644	#41	—	2	4	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	4	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	8	2	no	—
655	C₂×Q₈	—	8	4	no	—
656	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
663	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	M₁₆	—	2	4	no	—
677	C₂×C₈	—	2	4	no	—
678	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
679	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
680	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
707	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	1	no	—
736	C₄²	C₂×D₄×C₁₃	1	2	yes	—
737	C₄²	C₂×D₄×C₁₃	1	2	yes	—
738	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₄²	C₂⁴×C₁₃	1	2	yes	—
743	C₁₃	#60885	1	1	yes	characteristic, direct product factor, Sylow
744	C₂³	—	2	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	8	1	no	—
747	C₂³	—	8	1	no	—
748	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
749	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	4	4	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	4	no	—
757	Q₈	—	8	2	no	—
758	Q₈	—	8	1	no	—
759	Q₈	—	8	1	no	—
760	D₄	—	2	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	4	no	—
763	D₄	—	4	2	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
793	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	2	2	no	—
796	C₈	—	2	4	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	16	2	no	—
806	C₂²	C₁₃×#536	1	2	yes	—
807	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
808	C₄	—	2	1	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	4	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	C₁₃×#536	1	2	yes	—
824	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
825	C₂	—	2	2	no	—
826	C₂	—	4	2	no	—
827	C₂	—	8	2	no	—
828	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
829	C₂	C₁₃×#3585	1	1	yes	characteristic
830	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×#535	C₂²
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
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3243	C₂	semidirect
5. C₁₃×#3240	C₂	semidirect
6. C₁₃×#3240	C₂	semidirect
7. C₁₃×#3239	C₂	semidirect
8. C₁₃×#3238	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3162	C₂	semidirect
11. C₁₃×#3140	C₂	semidirect
12. C₂×C₁₃×#489	C₂	semidirect
13. C₁₃×#3097	C₂	semidirect
15. C₁₃×#3082	C₂	semidirect
16. C₁₃×#3081	C₂	semidirect
17. C₁₃×#2923	C₂	semidirect
31. C₁₃×#544	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#501	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#501	C₂²	semidirect
53. C₁₃×#501	C₂²	semidirect
54. C₁₃×#501	C₂²	semidirect
55. C₁₃×#501	C₂²	semidirect
56. C₁₃×#500	C₂²	semidirect
57. C₁₃×#498	C₂²	semidirect
64. C₁₃×#485	C₂²	semidirect
65. C₁₃×#485	C₂²	semidirect
66. C₁₃×#484	C₂²	semidirect
67. C₁₃×#483	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
80. C₁₃×#433	C₂²	semidirect
81. C₁₃×#432	C₂²	semidirect
82. C₁₃×#432	C₂²	semidirect
228. #60885	C₁₃	direct (N × H)
330. #3503	C₂×C₁₃	semidirect
331. #3244	C₂×C₁₃	semidirect
332. #3243	C₂×C₁₃	semidirect
333. #3240	C₂×C₁₃	semidirect
334. #3240	C₂×C₁₃	semidirect
335. #3239	C₂×C₁₃	semidirect
336. #3238	C₂×C₁₃	semidirect
337. #3165	C₂×C₁₃	semidirect
338. #3162	C₂×C₁₃	semidirect
339. #3140	C₂×C₁₃	semidirect
340. C₂×#489	C₂×C₁₃	semidirect
341. #3097	C₂×C₁₃	semidirect
343. #3082	C₂×C₁₃	semidirect
344. #3081	C₂×C₁₃	semidirect
345. #2923	C₂×C₁₃	semidirect
412. #544	C₂²×C₁₃	semidirect
419. #533	C₂²×C₁₃	semidirect
421. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
429. #501	C₂²×C₁₃	semidirect
430. #501	C₂²×C₁₃	semidirect
431. #501	C₂²×C₁₃	semidirect
432. #501	C₂²×C₁₃	semidirect
433. #501	C₂²×C₁₃	semidirect
434. #501	C₂²×C₁₃	semidirect
435. #501	C₂²×C₁₃	semidirect
436. #501	C₂²×C₁₃	semidirect
437. #500	C₂²×C₁₃	semidirect
438. #498	C₂²×C₁₃	semidirect
445. #485	C₂²×C₁₃	semidirect
446. #485	C₂²×C₁₃	semidirect
447. #484	C₂²×C₁₃	semidirect
448. #483	C₂²×C₁₃	semidirect
453. #479	C₂²×C₁₃	semidirect
454. #479	C₂²×C₁₃	semidirect
457. #477	C₂²×C₁₃	semidirect
459. #475	C₂²×C₁₃	semidirect
461. #433	C₂²×C₁₃	semidirect
462. #432	C₂²×C₁₃	semidirect
463. #432	C₂²×C₁₃	semidirect
743. C₁₃	#60885	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×#3510	2
C₁₃×#3503	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3240	2
C₁₃×#3239	2
C₁₃×#3238	2
C₁₃×#3165	2
C₁₃×#3162	2
C₁₃×#3140	2
C₂×C₁₃×#489	2
C₁₃×#3097	2
C₁₃×#3096	2
C₁₃×#3082	2
C₁₃×#3081	2
C₁₃×#2923	2
#60885	13

Subgroups — C13×#60885 #15747224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60885 #15747224