Subgroups — C₁₃×#60889 #15747228

Order 3328.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3244	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3242	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3237	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3233	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×#3099	C₂	1	2	yes	maximal
12	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₃	—	2	1	no	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#554	—	2	2	no	—
21	C₁₃×#554	—	2	1	no	—
22	D₄×Q₈×C₁₃	—	2	2	no	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	C₁₃×#544	C₂²	1	2	yes	—
25	C₁₃×#544	C₂²	1	1	yes	characteristic
26	C₁₃×#544	C₂²	1	4	yes	—
27	C₁₃×#542	—	2	1	no	—
28	C₁₃×#542	C₂²	1	2	yes	—
29	C₁₃×#541	—	2	1	no	—
30	C₁₃×#541	C₂²	1	2	yes	—
31	C₁₃×#539	—	2	2	no	—
32	C₁₃×#537	C₂²	1	1	yes	characteristic
33	C₁₃×#536	C₂²	1	1	yes	characteristic
34	C₁₃×#536	C₂²	1	1	yes	characteristic
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	C₂²	1	2	yes	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	—	2	1	no	—
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₁₃×#520	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	—
49	C₁₃×#501	C₂²	1	4	yes	—
50	C₁₃×#499	C₂²	1	4	yes	—
51	C₁₃×#498	C₂²	1	4	yes	—
52	C₁₃×#491	C₂²	1	4	yes	—
53	C₁₃×#489	C₂²	1	4	yes	—
54	C₁₃×#488	C₂²	1	4	yes	—
55	C₁₃×#487	C₂²	1	4	yes	—
56	C₁₃×#485	C₂²	1	4	yes	—
57	C₁₃×#485	C₂²	1	4	yes	—
58	C₁₃×#485	C₂²	1	4	yes	—
59	C₁₃×#484	C₂²	1	4	yes	—
60	C₁₃×#483	C₂²	1	4	yes	—
61	C₁₃×#483	C₂²	1	4	yes	—
62	C₁₃×#482	C₂²	1	4	yes	—
63	C₁₃×#481	C₂²	1	4	yes	—
64	C₁₃×#479	C₂²	1	2	yes	—
65	C₁₃×#479	C₂²	1	4	yes	—
66	C₁₃×#478	C₂²	1	2	yes	—
67	C₁₃×#477	C₂²	1	1	yes	characteristic
68	C₁₃×#477	C₂²	1	2	yes	—
69	C₁₃×#477	C₂²	1	2	yes	—
70	C₁₃×#476	C₂²	1	1	yes	characteristic
71	C₁₃×#476	C₂²	1	2	yes	—
72	C₁₃×#475	C₂²	1	2	yes	—
73	C₁₃×#475	C₂²	1	2	yes	—
74	C₁₃×#475	C₂²	1	4	yes	—
75	C₁₃×#475	C₂²	1	1	yes	characteristic
76	C₁₃×#475	C₂²	1	2	yes	—
77	C₁₃×#475	C₂²	1	2	yes	—
78	C₁₃×#474	C₂²	1	1	yes	characteristic
79	C₁₃×#474	C₂²	1	2	yes	—
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×#423	C₂²	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#416	C₂²	1	2	yes	—
92	C₂×C₁₃×#103	C₂²	1	2	yes	—
93	C₁₃×#408	C₂²	1	2	yes	—
94	C₁₃×#405	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×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	1	no	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	4	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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	1	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	C₂³	1	2	yes	—
128	C₁₃×#125	C₂³	1	4	yes	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	C₂³	1	2	yes	—
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	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	—	2	4	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	D₄	1	2	yes	—
178	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	—	2	1	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	4	yes	—
187	C₁₃×#117	C₂³	1	1	yes	characteristic
188	C₁₃×#117	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₄²×C₁₃	—	2	1	no	—
196	C₂×C₄²×C₁₃	—	2	1	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	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	1	yes	characteristic
210	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#60889	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	2	no	—
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	—	2	2	no	—
232	C₁₃×#41	—	2	2	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	—	8	4	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×M₁₆	—	2	4	no	—
266	C₂×C₈×C₁₃	—	2	4	no	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	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	C₂×D₄	1	2	yes	—
316	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
317	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
318	C₄²×C₁₃	—	2	2	no	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₃	C₂×D₄	1	2	yes	—
327	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₁₃	C₂×D₄	1	2	yes	—
329	C₄²×C₁₃	C₂⁴	1	2	yes	—
330	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
332	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#3461	C₂×C₁₃	1	1	yes	characteristic
334	#3244	C₂×C₁₃	1	4	yes	complemented
335	#3242	C₂×C₁₃	1	4	yes	complemented
336	#3239	C₂×C₁₃	1	2	yes	complemented
337	#3237	C₂×C₁₃	1	2	yes	complemented
338	#3233	C₂×C₁₃	1	2	yes	complemented
339	#3229	C₂×C₁₃	1	2	yes	complemented
340	#3163	C₂×C₁₃	1	2	yes	complemented
341	#3137	C₂×C₁₃	1	2	yes	complemented
342	#3099	C₂×C₁₃	1	2	yes	—
343	#3097	C₂×C₁₃	1	2	yes	complemented
344	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
347	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₁₃	—	2	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	2	no	—
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	2	1	no	—
356	Q₈×C₁₃	—	2	1	no	—
357	Q₈×C₁₃	—	4	2	no	—
358	Q₈×C₁₃	—	4	2	no	—
359	Q₈×C₁₃	—	4	4	no	—
360	Q₈×C₁₃	—	4	2	no	—
361	Q₈×C₁₃	—	8	2	no	—
362	Q₈×C₁₃	—	8	2	no	—
363	Q₈×C₁₃	—	8	4	no	—
364	D₄×C₁₃	—	2	4	no	—
365	D₄×C₁₃	—	2	2	no	—
366	D₄×C₁₃	—	2	1	no	—
367	D₄×C₁₃	—	2	1	no	—
368	D₄×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	8	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	4	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	2	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	8	1	no	—
388	C₂×C₄×C₁₃	—	8	1	no	—
389	C₂×C₄×C₁₃	—	8	2	no	—
390	C₂×C₄×C₁₃	—	8	4	no	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
400	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
402	C₈×C₁₃	—	2	2	no	—
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	2	4	no	—
405	Q₈²	—	2	1	no	—
406	#557	—	2	1	no	—
407	#554	—	2	2	no	—
408	#554	—	2	1	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	1	yes	characteristic
413	#544	C₂²×C₁₃	1	4	yes	—
414	#542	—	2	1	no	—
415	#542	C₂²×C₁₃	1	2	yes	—
416	#541	—	2	1	no	—
417	#541	C₂²×C₁₃	1	2	yes	—
418	#539	—	2	2	no	—
419	#537	C₂²×C₁₃	1	1	yes	characteristic
420	#536	C₂²×C₁₃	1	1	yes	characteristic
421	#536	C₂²×C₁₃	1	1	yes	characteristic
422	#533	—	2	1	no	—
423	#533	C₂²×C₁₃	1	2	yes	—
424	#533	C₂²×C₁₃	1	1	yes	characteristic
425	#533	C₂²×C₁₃	1	2	yes	—
426	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
428	#529	—	2	2	no	—
429	#529	—	2	1	no	—
430	#529	C₂²×C₁₃	1	2	yes	—
431	#520	C₂²×C₁₃	1	2	yes	—
432	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
433	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	#501	C₂²×C₁₃	1	4	yes	—
436	#501	C₂²×C₁₃	1	4	yes	—
437	#499	C₂²×C₁₃	1	4	yes	—
438	#498	C₂²×C₁₃	1	4	yes	—
439	#491	C₂²×C₁₃	1	4	yes	—
440	#489	C₂²×C₁₃	1	4	yes	—
441	#488	C₂²×C₁₃	1	4	yes	—
442	#487	C₂²×C₁₃	1	4	yes	—
443	#485	C₂²×C₁₃	1	4	yes	—
444	#485	C₂²×C₁₃	1	4	yes	—
445	#485	C₂²×C₁₃	1	4	yes	—
446	#484	C₂²×C₁₃	1	4	yes	—
447	#483	C₂²×C₁₃	1	4	yes	—
448	#483	C₂²×C₁₃	1	4	yes	—
449	#482	C₂²×C₁₃	1	4	yes	—
450	#481	C₂²×C₁₃	1	4	yes	—
451	#479	C₂²×C₁₃	1	2	yes	—
452	#479	C₂²×C₁₃	1	4	yes	—
453	#478	C₂²×C₁₃	1	2	yes	—
454	#477	C₂²×C₁₃	1	1	yes	characteristic
455	#477	C₂²×C₁₃	1	2	yes	—
456	#477	C₂²×C₁₃	1	2	yes	—
457	#476	C₂²×C₁₃	1	1	yes	characteristic
458	#476	C₂²×C₁₃	1	2	yes	—
459	#475	C₂²×C₁₃	1	2	yes	—
460	#475	C₂²×C₁₃	1	2	yes	—
461	#475	C₂²×C₁₃	1	4	yes	—
462	#475	C₂²×C₁₃	1	1	yes	characteristic
463	#475	C₂²×C₁₃	1	2	yes	—
464	#475	C₂²×C₁₃	1	2	yes	—
465	#474	C₂²×C₁₃	1	1	yes	characteristic
466	#474	C₂²×C₁₃	1	2	yes	—
467	#433	C₂²×C₁₃	1	4	yes	—
468	#432	C₂²×C₁₃	1	2	yes	—
469	#431	C₂²×C₁₃	1	2	yes	—
470	#428	C₂²×C₁₃	1	2	yes	—
471	#428	C₂²×C₁₃	1	2	yes	—
472	#427	C₂²×C₁₃	1	2	yes	—
473	C₂×#106	C₂²×C₁₃	1	2	yes	—
474	#423	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
476	#419	C₂²×C₁₃	1	2	yes	—
477	#417	C₂²×C₁₃	1	2	yes	—
478	#416	C₂²×C₁₃	1	2	yes	—
479	C₂×#103	C₂²×C₁₃	1	2	yes	—
480	#408	C₂²×C₁₃	1	2	yes	—
481	#405	C₂²×C₁₃	1	2	yes	—
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	2	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	4	1	no	—
488	C₂²×C₁₃	—	4	1	no	—
489	C₂²×C₁₃	—	4	1	no	—
490	C₂²×C₁₃	#536	1	2	yes	—
491	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₄×C₁₃	—	4	1	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	1	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	—	4	4	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	#536	1	2	yes	—
507	C₄×C₁₃	#577	1	2	yes	—
508	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
509	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
510	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²×Q₈	—	2	1	no	—
513	C₂²×Q₈	—	2	2	no	—
514	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
516	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	—	2	4	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	2	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
529	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
530	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	1	no	—
538	#125	—	2	2	no	—
539	#125	—	2	4	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	C₂³×C₁₃	1	2	yes	—
543	#125	C₂³×C₁₃	1	2	yes	—
544	#125	C₂³×C₁₃	1	4	yes	—
545	#124	—	2	1	no	—
546	#124	—	2	2	no	—
547	#124	C₂³×C₁₃	1	2	yes	—
548	#123	—	2	2	no	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
568	#121	—	2	2	no	—
569	#121	—	2	1	no	—
570	#121	C₂³×C₁₃	1	2	yes	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
580	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
591	C₄×D₄	D₄×C₁₃	1	2	yes	—
592	C₄×D₄	D₄×C₁₃	1	2	yes	—
593	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
594	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
596	#117	—	2	2	no	—
597	#117	—	2	1	no	—
598	#117	—	2	2	no	—
599	#117	C₂³×C₁₃	1	1	yes	characteristic
600	#117	C₂³×C₁₃	1	2	yes	—
601	#117	C₂³×C₁₃	1	4	yes	—
602	#117	C₂³×C₁₃	1	1	yes	characteristic
603	#117	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
610	C₂×C₄²	—	2	1	no	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
614	#107	C₂³×C₁₃	1	2	yes	—
615	#107	C₂³×C₁₃	1	2	yes	—
616	#107	C₂³×C₁₃	1	4	yes	—
617	#107	C₂³×C₁₃	1	4	yes	—
618	#106	C₂³×C₁₃	1	4	yes	—
619	#106	C₂³×C₁₃	1	4	yes	—
620	#106	C₂³×C₁₃	1	2	yes	—
621	#106	C₂³×C₁₃	1	2	yes	—
622	#106	C₂³×C₁₃	1	4	yes	—
623	#106	C₂³×C₁₃	1	4	yes	—
624	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
626	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
629	#103	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	4	yes	—
631	#103	C₂³×C₁₃	1	2	yes	—
632	#103	C₂³×C₁₃	1	2	yes	—
633	#103	C₂³×C₁₃	1	4	yes	—
634	#103	C₂³×C₁₃	1	4	yes	—
635	#103	C₂³×C₁₃	1	4	yes	—
636	#102	C₂³×C₁₃	1	2	yes	—
637	#102	C₂³×C₁₃	1	2	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
641	#97	C₂³×C₁₃	1	4	yes	—
642	C₄×C₈	C₂³×C₁₃	1	4	yes	—
643	C₂×C₁₃	—	2	2	no	—
644	C₂×C₁₃	—	4	2	no	—
645	C₂×C₁₃	—	8	1	no	—
646	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
647	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
648	C₂×C₁₃	#3586	1	1	yes	characteristic
649	#41	—	2	2	no	—
650	#41	—	2	2	no	—
651	#41	—	2	2	no	—
652	#41	—	2	2	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	8	2	no	—
663	C₂×Q₈	—	8	4	no	—
664	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	M₁₆	—	2	4	no	—
686	C₂×C₈	—	2	4	no	—
687	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
688	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
689	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
720	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	4	no	—
744	C₄²	—	2	2	no	—
745	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₃	1	2	yes	—
747	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₃	1	2	yes	—
749	C₄²	C₂⁴×C₁₃	1	2	yes	—
750	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₁₃	#60889	1	1	yes	characteristic, direct product factor, Sylow
753	C₂³	—	2	1	no	—
754	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
755	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	4	no	—
767	Q₈	—	8	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	—	8	2	no	—
794	C₂×C₄	—	8	4	no	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
805	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₈	—	2	4	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₁₃×#536	1	2	yes	—
818	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	C₁₃×#536	1	2	yes	—
834	C₄	C₁₃×#577	1	2	yes	—
835	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
836	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
837	C₂	—	2	2	no	—
838	C₂	—	4	2	no	—
839	C₂	—	8	1	no	—
840	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
841	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
842	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×#537	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
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3242	C₂	semidirect
5. C₁₃×#3239	C₂	semidirect
6. C₁₃×#3237	C₂	semidirect
7. C₁₃×#3233	C₂	semidirect
8. C₁₃×#3229	C₂	semidirect
9. C₁₃×#3163	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
12. C₁₃×#3097	C₂	semidirect
13. C₁₃×#3079	C₂	semidirect
14. C₁₃×#3078	C₂	semidirect
15. C₁₃×#3076	C₂	semidirect
16. C₂×C₁₃×#475	C₂	semidirect
17. C₁₃×#2925	C₂	semidirect
228. #60889	C₁₃	direct (N × H)
332. #3503	C₂×C₁₃	semidirect
334. #3244	C₂×C₁₃	semidirect
335. #3242	C₂×C₁₃	semidirect
336. #3239	C₂×C₁₃	semidirect
337. #3237	C₂×C₁₃	semidirect
338. #3233	C₂×C₁₃	semidirect
339. #3229	C₂×C₁₃	semidirect
340. #3163	C₂×C₁₃	semidirect
341. #3137	C₂×C₁₃	semidirect
343. #3097	C₂×C₁₃	semidirect
344. #3079	C₂×C₁₃	semidirect
345. #3078	C₂×C₁₃	semidirect
346. #3076	C₂×C₁₃	semidirect
347. C₂×#475	C₂×C₁₃	semidirect
348. #2925	C₂×C₁₃	semidirect
752. C₁₃	#60889	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×#3503	2
C₁₃×#3461	2
C₁₃×#3244	2
C₁₃×#3242	2
C₁₃×#3239	2
C₁₃×#3237	2
C₁₃×#3233	2
C₁₃×#3229	2
C₁₃×#3163	2
C₁₃×#3137	2
C₁₃×#3099	2
C₁₃×#3097	2
C₁₃×#3079	2
C₁₃×#3078	2
C₁₃×#3076	2
C₂×C₁₃×#475	2
C₁₃×#2925	2
#60889	13

Subgroups — C13×#60889 #15747228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60889 #15747228