Subgroups — C₁₃×#60886 #15747225

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3504	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×#3237	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3236	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3235	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3098	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#555	—	2	1	no	—
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	—	2	1	no	—
24	C₁₃×#554	—	2	2	no	—
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	—	2	1	no	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#548	—	2	2	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#544	C₂²	1	1	yes	characteristic
31	C₁₃×#544	C₂²	1	1	yes	characteristic
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#542	C₂²	1	4	yes	—
35	C₁₃×#537	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	2	yes	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#125	C₂²	1	2	yes	—
44	C₁₃×#520	C₂²	1	2	yes	—
45	C₁₃×#520	C₂²	1	1	yes	characteristic
46	C₁₃×#520	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	2	yes	—
49	C₁₃×#501	C₂²	1	2	yes	—
50	C₁₃×#501	C₂²	1	4	yes	—
51	C₁₃×#501	C₂²	1	2	yes	—
52	C₁₃×#501	C₂²	1	2	yes	—
53	C₁₃×#500	C₂²	1	2	yes	—
54	C₁₃×#498	C₂²	1	2	yes	—
55	C₁₃×#491	C₂²	1	1	yes	characteristic
56	C₁₃×#491	C₂²	1	1	yes	characteristic
57	C₁₃×#491	C₂²	1	2	yes	—
58	C₁₃×#490	C₂²	1	1	yes	characteristic
59	C₁₃×#490	C₂²	1	1	yes	characteristic
60	C₁₃×#490	C₂²	1	2	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	—
65	C₁₃×#485	C₂²	1	4	yes	—
66	C₁₃×#484	C₂²	1	4	yes	—
67	C₁₃×#483	C₂²	1	4	yes	—
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	—
73	C₁₃×#479	C₂²	1	4	yes	—
74	C₁₃×#478	C₂²	1	4	yes	—
75	C₁₃×#478	C₂²	1	4	yes	—
76	C₁₃×#477	C₂²	1	4	yes	—
77	C₁₃×#476	C₂²	1	4	yes	—
78	C₁₃×#475	C₂²	1	4	yes	—
79	C₁₃×#474	C₂²	1	4	yes	—
80	C₁₃×#433	C₂²	1	4	yes	—
81	C₁₃×#432	C₂²	1	2	yes	—
82	C₁₃×#432	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	2	yes	—
85	C₂×C₁₃×#107	C₂²	1	2	yes	—
86	C₂×C₁₃×#106	C₂²	1	2	yes	—
87	C₁₃×#424	C₂²	1	2	yes	—
88	C₁₃×#417	C₂²	1	2	yes	—
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#416	C₂²	1	2	yes	—
91	C₁₃×#416	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	—	2	2	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	—	2	1	no	—
102	C₁₃×C₄⋊Q₈	—	2	1	no	—
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	C₂³	1	1	yes	characteristic
115	C₁₃×#126	—	2	4	no	—
116	C₁₃×#125	—	2	1	no	—
117	C₁₃×#125	—	2	1	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	1	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	C₂³	1	2	yes	—
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×#125	C₂³	1	2	yes	—
128	C₁₃×#125	C₂³	1	1	yes	characteristic
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#125	C₂³	1	1	yes	characteristic
131	C₁₃×#124	—	2	4	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	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	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	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	C₂³	1	4	yes	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	4	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	4	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₁₃	D₄	1	2	yes	—
175	C₄×D₄×C₁₃	D₄	1	2	yes	—
176	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₁₃	C₂³	1	4	yes	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	C₂³	1	1	yes	characteristic
181	C₁₃×#117	C₂³	1	1	yes	characteristic
182	C₁₃×#117	C₂³	1	2	yes	—
183	C₁₃×#117	C₂³	1	2	yes	—
184	C₁₃×#117	C₂³	1	1	yes	characteristic
185	C₁₃×#117	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	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	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	2	yes	—
210	C₁₃×#103	C₂³	1	2	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	2	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	2	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	#60886	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	2	4	no	—
230	C₁₃×#41	—	2	8	no	—
231	C₁₃×#41	—	8	4	no	—
232	C₂×Q₈×C₁₃	—	2	2	no	—
233	C₂×Q₈×C₁₃	—	2	2	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	—	8	2	no	—
239	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	1	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₁₃×M₁₆	—	2	4	no	—
262	C₂×C₈×C₁₃	—	2	4	no	—
263	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	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	2	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₁₃×C₂²⋊C₄	—	2	4	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	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	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	4	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	2	no	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	C₂×D₄	1	2	yes	—
322	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₃	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₁₃	C₂⁴	1	2	yes	—
328	#3511	C₂×C₁₃	1	1	yes	characteristic
329	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3244	C₂×C₁₃	1	4	yes	complemented
331	#3243	C₂×C₁₃	1	4	yes	complemented
332	#3237	C₂×C₁₃	1	2	yes	complemented
333	#3236	C₂×C₁₃	1	2	yes	complemented
334	#3235	C₂×C₁₃	1	2	yes	complemented
335	#3234	C₂×C₁₃	1	2	yes	complemented
336	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3099	C₂×C₁₃	1	2	yes	complemented
341	#3098	C₂×C₁₃	1	2	yes	complemented
342	#3084	C₂×C₁₃	1	2	yes	complemented
343	#3083	C₂×C₁₃	1	2	yes	complemented
344	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
347	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₁₃	—	2	2	no	—
349	Q₈×C₁₃	—	2	4	no	—
350	Q₈×C₁₃	—	4	4	no	—
351	Q₈×C₁₃	—	8	2	no	—
352	Q₈×C₁₃	—	8	1	no	—
353	Q₈×C₁₃	—	8	2	no	—
354	Q₈×C₁₃	—	8	1	no	—
355	Q₈×C₁₃	—	8	2	no	—
356	D₄×C₁₃	—	2	4	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	4	no	—
359	D₄×C₁₃	—	4	2	no	—
360	D₄×C₁₃	—	4	2	no	—
361	D₄×C₁₃	—	4	4	no	—
362	D₄×C₁₃	—	8	4	no	—
363	C₂×C₄×C₁₃	—	2	4	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	—	8	1	no	—
379	C₂×C₄×C₁₃	—	8	2	no	—
380	C₂×C₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	—	8	2	no	—
382	C₂×C₄×C₁₃	—	8	2	no	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	2₋¹⁺⁴	1	4	yes	—
392	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	2	2	no	—
395	C₈×C₁₃	—	2	4	no	—
396	#557	—	2	1	no	—
397	#557	—	2	1	no	—
398	#556	—	2	1	no	—
399	#555	—	2	1	no	—
400	#554	—	2	1	no	—
401	#554	—	2	1	no	—
402	#554	—	2	2	no	—
403	#554	—	2	2	no	—
404	#554	—	2	1	no	—
405	#553	—	2	2	no	—
406	#548	—	2	2	no	—
407	#547	—	2	1	no	—
408	#544	C₂²×C₁₃	1	1	yes	characteristic
409	#544	C₂²×C₁₃	1	1	yes	characteristic
410	#544	C₂²×C₁₃	1	2	yes	—
411	#544	C₂²×C₁₃	1	2	yes	—
412	#542	C₂²×C₁₃	1	4	yes	—
413	#537	C₂²×C₁₃	1	2	yes	—
414	#533	C₂²×C₁₃	1	2	yes	—
415	#533	C₂²×C₁₃	1	1	yes	characteristic
416	#533	C₂²×C₁₃	1	2	yes	—
417	#532	C₂²×C₁₃	1	1	yes	characteristic
418	#532	C₂²×C₁₃	1	2	yes	—
419	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#125	C₂²×C₁₃	1	2	yes	—
422	#520	C₂²×C₁₃	1	2	yes	—
423	#520	C₂²×C₁₃	1	1	yes	characteristic
424	#520	C₂²×C₁₃	1	1	yes	characteristic
425	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
426	#501	C₂²×C₁₃	1	2	yes	—
427	#501	C₂²×C₁₃	1	2	yes	—
428	#501	C₂²×C₁₃	1	4	yes	—
429	#501	C₂²×C₁₃	1	2	yes	—
430	#501	C₂²×C₁₃	1	2	yes	—
431	#500	C₂²×C₁₃	1	2	yes	—
432	#498	C₂²×C₁₃	1	2	yes	—
433	#491	C₂²×C₁₃	1	1	yes	characteristic
434	#491	C₂²×C₁₃	1	1	yes	characteristic
435	#491	C₂²×C₁₃	1	2	yes	—
436	#490	C₂²×C₁₃	1	1	yes	characteristic
437	#490	C₂²×C₁₃	1	1	yes	characteristic
438	#490	C₂²×C₁₃	1	2	yes	—
439	#489	C₂²×C₁₃	1	2	yes	—
440	#489	C₂²×C₁₃	1	2	yes	—
441	#488	C₂²×C₁₃	1	4	yes	—
442	#485	C₂²×C₁₃	1	4	yes	—
443	#485	C₂²×C₁₃	1	4	yes	—
444	#484	C₂²×C₁₃	1	4	yes	—
445	#483	C₂²×C₁₃	1	4	yes	—
446	#482	C₂²×C₁₃	1	4	yes	—
447	#482	C₂²×C₁₃	1	4	yes	—
448	#481	C₂²×C₁₃	1	4	yes	—
449	#480	C₂²×C₁₃	1	4	yes	—
450	#479	C₂²×C₁₃	1	4	yes	—
451	#479	C₂²×C₁₃	1	4	yes	—
452	#478	C₂²×C₁₃	1	4	yes	—
453	#478	C₂²×C₁₃	1	4	yes	—
454	#477	C₂²×C₁₃	1	4	yes	—
455	#476	C₂²×C₁₃	1	4	yes	—
456	#475	C₂²×C₁₃	1	4	yes	—
457	#474	C₂²×C₁₃	1	4	yes	—
458	#433	C₂²×C₁₃	1	4	yes	—
459	#432	C₂²×C₁₃	1	2	yes	—
460	#432	C₂²×C₁₃	1	2	yes	—
461	#428	C₂²×C₁₃	1	2	yes	—
462	#428	C₂²×C₁₃	1	2	yes	—
463	C₂×#107	C₂²×C₁₃	1	2	yes	—
464	C₂×#106	C₂²×C₁₃	1	2	yes	—
465	#424	C₂²×C₁₃	1	2	yes	—
466	#417	C₂²×C₁₃	1	2	yes	—
467	#417	C₂²×C₁₃	1	2	yes	—
468	#416	C₂²×C₁₃	1	2	yes	—
469	#416	C₂²×C₁₃	1	2	yes	—
470	#408	C₂²×C₁₃	1	2	yes	—
471	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₁₃	—	2	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	2	no	—
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	2	2	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	#536	1	2	yes	—
482	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	2	1	no	—
487	C₄×C₁₃	—	2	2	no	—
488	C₄×C₁₃	—	2	1	no	—
489	C₄×C₁₃	—	2	2	no	—
490	C₄×C₁₃	—	4	4	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	1	no	—
493	C₄×C₁₃	—	4	1	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	1	no	—
496	C₄×C₁₃	—	4	1	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	#536	1	2	yes	—
499	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	C₂³×C₁₃	1	2	yes	—
502	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
505	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
519	#127	C₂³×C₁₃	1	1	yes	characteristic
520	#126	—	2	4	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	—	2	2	no	—
524	#125	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	—	2	1	no	—
527	#125	—	2	1	no	—
528	#125	—	2	2	no	—
529	#125	—	2	2	no	—
530	#125	C₂³×C₁₃	1	2	yes	—
531	#125	C₂³×C₁₃	1	1	yes	characteristic
532	#125	C₂³×C₁₃	1	2	yes	—
533	#125	C₂³×C₁₃	1	2	yes	—
534	#125	C₂³×C₁₃	1	2	yes	—
535	#125	C₂³×C₁₃	1	1	yes	characteristic
536	#124	—	2	4	no	—
537	#124	—	2	2	no	—
538	#124	C₂³×C₁₃	1	2	yes	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
554	#121	—	2	2	no	—
555	#121	—	2	4	no	—
556	#121	—	2	1	no	—
557	#121	—	2	1	no	—
558	#121	—	2	2	no	—
559	#121	C₂³×C₁₃	1	4	yes	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
568	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
569	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	4	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
579	C₄×D₄	D₄×C₁₃	1	2	yes	—
580	C₄×D₄	D₄×C₁₃	1	2	yes	—
581	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
582	C₄×D₄	C₂³×C₁₃	1	4	yes	—
583	#117	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	C₂³×C₁₃	1	1	yes	characteristic
586	#117	C₂³×C₁₃	1	1	yes	characteristic
587	#117	C₂³×C₁₃	1	2	yes	—
588	#117	C₂³×C₁₃	1	2	yes	—
589	#117	C₂³×C₁₃	1	1	yes	characteristic
590	#117	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×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×C₄²	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
604	#107	C₂³×C₁₃	1	4	yes	—
605	#107	C₂³×C₁₃	1	4	yes	—
606	#107	C₂³×C₁₃	1	4	yes	—
607	#107	C₂³×C₁₃	1	4	yes	—
608	#106	C₂³×C₁₃	1	4	yes	—
609	#106	C₂³×C₁₃	1	4	yes	—
610	#106	C₂³×C₁₃	1	4	yes	—
611	#106	C₂³×C₁₃	1	4	yes	—
612	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
613	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
614	#103	C₂³×C₁₃	1	2	yes	—
615	#103	C₂³×C₁₃	1	2	yes	—
616	#103	C₂³×C₁₃	1	2	yes	—
617	#103	C₂³×C₁₃	1	2	yes	—
618	#103	C₂³×C₁₃	1	4	yes	—
619	#103	C₂³×C₁₃	1	4	yes	—
620	#102	C₂³×C₁₃	1	2	yes	—
621	#102	C₂³×C₁₃	1	2	yes	—
622	#102	C₂³×C₁₃	1	2	yes	—
623	#102	C₂³×C₁₃	1	2	yes	—
624	#102	C₂³×C₁₃	1	4	yes	—
625	#102	C₂³×C₁₃	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
627	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
628	#97	C₂³×C₁₃	1	1	yes	characteristic
629	#97	C₂³×C₁₃	1	1	yes	characteristic
630	#97	C₂³×C₁₃	1	2	yes	—
631	#97	C₂³×C₁₃	1	2	yes	—
632	C₄×C₈	C₂³×C₁₃	1	2	yes	—
633	C₂×C₁₃	—	2	2	no	—
634	C₂×C₁₃	—	4	2	no	—
635	C₂×C₁₃	—	8	2	no	—
636	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
637	C₂×C₁₃	#3585	1	1	yes	characteristic
638	C₂×C₁₃	#3586	1	1	yes	characteristic
639	#41	—	2	4	no	—
640	#41	—	2	8	no	—
641	#41	—	8	4	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	8	2	no	—
649	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	M₁₆	—	2	4	no	—
672	C₂×C₈	—	2	4	no	—
673	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
674	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	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	—	2	2	no	—
703	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	yes	—
712	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	1	no	—
730	C₄²	—	2	1	no	—
731	C₄²	C₂×D₄×C₁₃	1	2	yes	—
732	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₁₃	1	2	yes	—
735	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₄²	C₂⁴×C₁₃	1	2	yes	—
738	C₁₃	#60886	1	1	yes	characteristic, direct product factor, Sylow
739	C₂³	—	2	2	no	—
740	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
741	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
742	Q₈	—	2	2	no	—
743	Q₈	—	2	4	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	8	2	no	—
746	Q₈	—	8	2	no	—
747	Q₈	—	8	1	no	—
748	Q₈	—	8	2	no	—
749	Q₈	—	8	1	no	—
750	D₄	—	2	4	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	8	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	8	4	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	2	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
785	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
786	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	C₁₃×#536	1	2	yes	—
799	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
800	C₄	—	2	1	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	2	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	2	no	—
807	C₄	—	4	4	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	C₁₃×#536	1	2	yes	—
816	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
817	C₂	—	2	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
821	C₂	C₁₃×#3585	1	1	yes	characteristic
822	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×#3511	C₂
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×#3504	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3243	C₂	semidirect
5. C₁₃×#3237	C₂	semidirect
6. C₁₃×#3236	C₂	semidirect
7. C₁₃×#3235	C₂	semidirect
8. C₁₃×#3234	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₂×C₁₃×#501	C₂	semidirect
11. C₁₃×#3142	C₂	semidirect
12. C₁₃×#3135	C₂	semidirect
13. C₁₃×#3099	C₂	semidirect
14. C₁₃×#3098	C₂	semidirect
15. C₁₃×#3084	C₂	semidirect
16. C₁₃×#3083	C₂	semidirect
17. C₁₃×#2923	C₂	semidirect
228. #60886	C₁₃	direct (N × H)
329. #3504	C₂×C₁₃	semidirect
330. #3244	C₂×C₁₃	semidirect
331. #3243	C₂×C₁₃	semidirect
332. #3237	C₂×C₁₃	semidirect
333. #3236	C₂×C₁₃	semidirect
334. #3235	C₂×C₁₃	semidirect
335. #3234	C₂×C₁₃	semidirect
336. #3165	C₂×C₁₃	semidirect
337. C₂×#501	C₂×C₁₃	semidirect
338. #3142	C₂×C₁₃	semidirect
339. #3135	C₂×C₁₃	semidirect
340. #3099	C₂×C₁₃	semidirect
341. #3098	C₂×C₁₃	semidirect
342. #3084	C₂×C₁₃	semidirect
343. #3083	C₂×C₁₃	semidirect
344. #2923	C₂×C₁₃	semidirect
738. C₁₃	#60886	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×#3511	2
C₁₃×#3504	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3237	2
C₁₃×#3236	2
C₁₃×#3235	2
C₁₃×#3234	2
C₁₃×#3165	2
C₂×C₁₃×#501	2
C₁₃×#3142	2
C₁₃×#3135	2
C₁₃×#3099	2
C₁₃×#3098	2
C₁₃×#3084	2
C₁₃×#3083	2
C₁₃×#2923	2
#60886	13

Subgroups — C13×#60886 #15747225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60886 #15747225