Subgroups — C₁₃×#61341 #15747680

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3368	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	2	yes	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₁₃	—	2	1	no	—
23	Q₈²×C₁₃	C₂²	1	2	yes	complemented
24	C₁₃×#557	—	2	1	no	—
25	C₁₃×#557	—	2	2	no	—
26	C₁₃×#557	C₂²	1	2	yes	complemented
27	C₁₃×#557	C₂²	1	4	yes	complemented
28	C₁₃×#550	C₂²	1	2	yes	—
29	C₁₃×#550	C₂²	1	2	yes	—
30	C₁₃×#546	—	2	2	no	—
31	C₁₃×#546	—	2	2	no	—
32	C₁₃×#544	—	2	2	no	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#540	—	2	2	no	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	—	2	1	no	—
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₁₃×#518	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#490	C₂²	1	4	yes	—
47	C₁₃×#490	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#486	C₂²	1	2	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#486	C₂²	1	4	yes	complemented
53	C₁₃×#479	C₂²	1	2	yes	complemented
54	C₁₃×#478	C₂²	1	2	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	4	yes	complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#474	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	4	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#460	C₂²	1	2	yes	—
66	C₁₃×#460	C₂²	1	4	yes	—
67	C₁₃×#460	C₂²	1	2	yes	—
68	C₁₃×#460	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	4	yes	complemented
70	C₁₃×#446	C₂²	1	4	yes	complemented
71	C₁₃×#446	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₁₃×#441	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₁₃×#440	C₂²	1	4	yes	complemented
76	C₁₃×#440	C₂²	1	4	yes	complemented
77	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
79	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₃×#419	C₂²	1	1	yes	characteristic
86	C₁₃×#418	C₂²	1	2	yes	—
87	C₁₃×#418	C₂²	1	2	yes	—
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#102	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	2	no	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#137	—	2	4	no	—
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	—	2	8	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	4	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#127	—	2	1	no	—
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	C₂³	1	2	yes	—
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#127	C₂³	1	4	yes	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	D₄	1	2	yes	—
129	C₁₃×#125	C₂³	1	4	yes	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	C₂³	1	4	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	4	no	—
146	C₁₃×#121	—	2	4	no	—
147	C₁₃×#120	—	2	4	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	4	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	C₂³	1	4	yes	—
173	C₄×D₄×C₁₃	C₂³	1	4	yes	—
174	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
175	C₁₃×#117	—	2	4	no	—
176	C₁₃×#117	—	2	1	no	—
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₁₃×#117	C₂³	1	1	yes	characteristic
179	C₁₃×#117	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	—	2	1	no	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#107	C₂³	1	2	yes	—
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#102	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	#61341	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	2	no	—
217	C₁₃×#41	—	2	2	no	—
218	C₁₃×#41	—	2	2	no	—
219	C₁₃×#41	—	8	4	no	—
220	C₁₃×#41	—	8	4	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	8	2	no	—
242	C₂×D₄×C₁₃	—	8	2	no	—
243	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₁₃×Q₁₆	—	2	4	no	—
256	C₁₃×SD₁₆	—	2	8	no	—
257	C₁₃×SD₁₆	—	2	8	no	—
258	C₁₃×SD₁₆	—	2	4	no	—
259	C₁₃×M₁₆	—	2	2	no	—
260	C₁₃×M₁₆	—	2	2	no	—
261	C₂×C₈×C₁₃	—	2	4	no	—
262	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₁₃	C₂⁴	1	2	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	2	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
290	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	2	no	—
305	C₄²×C₁₃	—	2	4	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	2	no	—
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	4	yes	—
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	#3508	C₂×C₁₃	1	1	yes	characteristic
314	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3375	C₂×C₁₃	1	2	yes	complemented
316	#3371	C₂×C₁₃	1	4	yes	complemented
317	#3368	C₂×C₁₃	1	2	yes	complemented
318	#3368	C₂×C₁₃	1	4	yes	complemented
319	#3365	C₂×C₁₃	1	2	yes	complemented
320	#3362	C₂×C₁₃	1	2	yes	complemented
321	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3136	C₂×C₁₃	1	2	yes	complemented
323	#3081	C₂×C₁₃	1	2	yes	complemented
324	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3043	C₂×C₁₃	1	2	yes	complemented
326	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2949	C₂×C₁₃	1	2	yes	complemented
329	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂³×C₁₃	—	2	4	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	4	4	no	—
333	C₂³×C₁₃	—	8	2	no	—
334	C₂³×C₁₃	—	8	2	no	—
335	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₁₃	—	2	4	no	—
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	2	1	no	—
340	Q₈×C₁₃	—	2	1	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	Q₈×C₁₃	—	4	2	no	—
343	Q₈×C₁₃	—	8	1	no	—
344	Q₈×C₁₃	—	8	4	no	—
345	Q₈×C₁₃	C₂×#41	1	4	yes	—
346	D₄×C₁₃	—	2	4	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	2	4	no	—
349	D₄×C₁₃	—	2	1	no	—
350	D₄×C₁₃	—	4	4	no	—
351	D₄×C₁₃	—	4	2	no	—
352	D₄×C₁₃	—	4	4	no	—
353	D₄×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	8	2	no	—
355	D₄×C₁₃	—	8	2	no	—
356	D₄×C₁₃	—	8	4	no	—
357	D₄×C₁₃	—	8	4	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	4	2	no	—
371	C₂×C₄×C₁₃	—	8	4	no	—
372	C₂×C₄×C₁₃	—	8	4	no	—
373	C₂×C₄×C₁₃	—	8	1	no	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
382	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
384	C₈×C₁₃	—	2	2	no	—
385	C₈×C₁₃	—	2	2	no	—
386	C₈×C₁₃	—	2	2	no	—
387	C₈×C₁₃	—	2	2	no	—
388	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
390	#559	C₂²×C₁₃	1	2	yes	—
391	#559	C₂²×C₁₃	1	2	yes	—
392	Q₈²	—	2	1	no	—
393	Q₈²	C₂²×C₁₃	1	2	yes	complemented
394	#557	—	2	1	no	—
395	#557	—	2	2	no	—
396	#557	C₂²×C₁₃	1	2	yes	complemented
397	#557	C₂²×C₁₃	1	4	yes	complemented
398	#550	C₂²×C₁₃	1	2	yes	—
399	#550	C₂²×C₁₃	1	2	yes	—
400	#546	—	2	2	no	—
401	#546	—	2	2	no	—
402	#544	—	2	2	no	—
403	#544	C₂²×C₁₃	1	2	yes	—
404	#540	—	2	2	no	—
405	#535	C₂²×C₁₃	1	2	yes	—
406	#533	—	2	2	no	—
407	#533	C₂²×C₁₃	1	1	yes	characteristic
408	#533	C₂²×C₁₃	1	1	yes	characteristic
409	#532	—	2	1	no	—
410	#532	—	2	1	no	—
411	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
412	#519	C₂²×C₁₃	1	2	yes	—
413	#518	C₂²×C₁₃	1	2	yes	—
414	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
416	#490	C₂²×C₁₃	1	4	yes	—
417	#490	C₂²×C₁₃	1	4	yes	complemented
418	#489	C₂²×C₁₃	1	4	yes	complemented
419	#488	C₂²×C₁₃	1	4	yes	complemented
420	#486	C₂²×C₁₃	1	2	yes	—
421	#486	C₂²×C₁₃	1	2	yes	—
422	#486	C₂²×C₁₃	1	4	yes	complemented
423	#479	C₂²×C₁₃	1	2	yes	complemented
424	#478	C₂²×C₁₃	1	2	yes	complemented
425	#478	C₂²×C₁₃	1	4	yes	complemented
426	#478	C₂²×C₁₃	1	4	yes	complemented
427	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	#476	C₂²×C₁₃	1	4	yes	complemented
430	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#474	C₂²×C₁₃	1	4	yes	complemented
433	#464	C₂²×C₁₃	1	4	yes	complemented
434	#464	C₂²×C₁₃	1	4	yes	complemented
435	#460	C₂²×C₁₃	1	2	yes	—
436	#460	C₂²×C₁₃	1	4	yes	—
437	#460	C₂²×C₁₃	1	2	yes	—
438	#460	C₂²×C₁₃	1	4	yes	complemented
439	#460	C₂²×C₁₃	1	4	yes	complemented
440	#446	C₂²×C₁₃	1	4	yes	complemented
441	#446	C₂²×C₁₃	1	2	yes	complemented
442	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
443	#441	C₂²×C₁₃	1	2	yes	complemented
444	#440	C₂²×C₁₃	1	2	yes	complemented
445	#440	C₂²×C₁₃	1	4	yes	complemented
446	#440	C₂²×C₁₃	1	4	yes	complemented
447	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
448	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
449	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
450	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
451	#428	C₂²×C₁₃	1	1	yes	characteristic
452	#427	C₂²×C₁₃	1	2	yes	—
453	#424	C₂²×C₁₃	1	2	yes	—
454	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
455	#419	C₂²×C₁₃	1	1	yes	characteristic
456	#418	C₂²×C₁₃	1	2	yes	—
457	#418	C₂²×C₁₃	1	2	yes	—
458	#417	C₂²×C₁₃	1	1	yes	characteristic
459	#416	C₂²×C₁₃	1	2	yes	—
460	C₂×#102	C₂²×C₁₃	1	2	yes	—
461	#405	C₂²×C₁₃	1	2	yes	—
462	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
463	C₂²×C₁₃	—	2	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	4	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	4	no	—
469	C₂²×C₁₃	—	4	1	no	—
470	C₂²×C₁₃	—	4	4	no	—
471	C₂²×C₁₃	—	16	4	no	—
472	C₂²×C₁₃	#548	1	2	yes	—
473	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	2	4	no	—
477	C₄×C₁₃	—	2	4	no	—
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	4	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	#548	1	2	yes	—
487	C₄×C₁₃	#577	1	2	yes	—
488	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
489	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
497	#137	—	2	4	no	—
498	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
499	C₂×SD₁₆	—	2	8	no	—
500	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
501	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
503	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	2	4	no	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	4	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
512	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
516	#127	—	2	1	no	—
517	#127	—	2	1	no	—
518	#127	C₂³×C₁₃	1	2	yes	—
519	#127	C₂³×C₁₃	1	2	yes	—
520	#127	C₂³×C₁₃	1	4	yes	—
521	#125	—	2	4	no	—
522	#125	—	2	4	no	—
523	#125	—	2	4	no	—
524	#125	—	2	2	no	—
525	#125	D₄×C₁₃	1	2	yes	—
526	#125	C₂³×C₁₃	1	2	yes	—
527	#125	C₂³×C₁₃	1	4	yes	—
528	#124	—	2	2	no	—
529	#124	—	2	2	no	—
530	#124	C₂³×C₁₃	1	4	yes	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
537	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	2	no	—
542	#121	—	2	4	no	—
543	#121	—	2	4	no	—
544	#120	—	2	4	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	4	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
559	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
560	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
561	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₄×D₄	C₂³×C₁₃	1	4	yes	—
571	C₄×D₄	C₂³×C₁₃	1	4	yes	—
572	#117	—	2	4	no	—
573	#117	—	2	1	no	—
574	#117	C₂³×C₁₃	1	1	yes	characteristic
575	#117	C₂³×C₁₃	1	2	yes	—
576	#117	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
583	#107	C₂³×C₁₃	1	2	yes	—
584	#107	C₂³×C₁₃	1	2	yes	—
585	#107	C₂³×C₁₃	1	2	yes	—
586	#106	C₂³×C₁₃	1	2	yes	—
587	#106	C₂³×C₁₃	1	2	yes	—
588	#106	C₂³×C₁₃	1	2	yes	—
589	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
592	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
593	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
594	#103	C₂³×C₁₃	1	2	yes	—
595	#103	C₂³×C₁₃	1	2	yes	—
596	#103	C₂³×C₁₃	1	2	yes	—
597	#103	C₂³×C₁₃	1	2	yes	—
598	#103	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	4	yes	—
600	#102	C₂³×C₁₃	1	4	yes	—
601	#102	C₂³×C₁₃	1	2	yes	—
602	#102	C₂³×C₁₃	1	2	yes	—
603	#102	C₂³×C₁₃	1	2	yes	—
604	#102	C₂³×C₁₃	1	4	yes	—
605	#102	C₂³×C₁₃	1	4	yes	—
606	#102	C₂³×C₁₃	1	4	yes	—
607	#102	C₂³×C₁₃	1	4	yes	—
608	#97	C₂³×C₁₃	1	2	yes	—
609	#97	C₂³×C₁₃	1	4	yes	—
610	C₄×C₈	C₂³×C₁₃	1	2	yes	—
611	C₄×C₈	C₂³×C₁₃	1	4	yes	—
612	C₂×C₁₃	—	2	2	no	—
613	C₂×C₁₃	—	8	1	no	—
614	C₂×C₁₃	—	8	4	no	—
615	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
616	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
617	C₂×C₁₃	#3585	1	1	yes	characteristic
618	C₂⁴	—	2	2	no	—
619	#41	—	2	2	no	—
620	#41	—	2	2	no	—
621	#41	—	8	4	no	—
622	#41	—	8	4	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
629	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
630	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
631	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
632	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	8	2	no	—
644	C₂×D₄	—	8	2	no	—
645	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	Q₁₆	—	2	4	no	—
658	SD₁₆	—	2	8	no	—
659	SD₁₆	—	2	8	no	—
660	SD₁₆	—	2	4	no	—
661	M₁₆	—	2	2	no	—
662	M₁₆	—	2	2	no	—
663	C₂×C₈	—	2	4	no	—
664	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
665	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
683	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
686	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
687	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
688	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
702	C₄²	—	2	1	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₄²	C₂⁴×C₁₃	1	4	yes	—
714	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
715	C₁₃	#61341	1	1	yes	characteristic, direct product factor, Sylow
716	C₂³	—	2	4	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	4	4	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	2	no	—
721	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
722	Q₈	—	2	4	no	—
723	Q₈	—	2	4	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	Q₈	—	8	4	no	—
731	Q₈	C₂×C₁₃×#41	1	4	yes	—
732	D₄	—	2	4	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	4	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	4	no	—
739	D₄	—	4	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	2	no	—
742	D₄	—	8	4	no	—
743	D₄	—	8	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
763	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
764	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
766	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
767	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
768	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
769	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₈	—	2	2	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	16	4	no	—
783	C₂²	C₁₃×#548	1	2	yes	—
784	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
785	C₄	—	2	1	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	4	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	C₁₃×#548	1	2	yes	—
798	C₄	C₁₃×#577	1	2	yes	—
799	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
800	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	8	4	no	—
803	C₂	—	8	1	no	—
804	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
805	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
806	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3371	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3368	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3362	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3081	C₂	semidirect
12. C₁₃×#3076	C₂	semidirect
13. C₁₃×#3043	C₂	semidirect
14. C₂×C₁₃×#460	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2949	C₂	semidirect
17. C₄×C₁₃×#137	C₂	semidirect
23. Q₈²×C₁₃	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#479	C₂²	semidirect
54. C₁₃×#478	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#446	C₂²	semidirect
71. C₁₃×#446	C₂²	semidirect
72. C₈×Q₈×C₁₃	C₂²	semidirect
73. C₁₃×#441	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₁₃×#440	C₂²	semidirect
76. C₁₃×#440	C₂²	semidirect
77. C₄×C₁₃×Q₁₆	C₂²	semidirect
78. C₄×C₁₃×SD₁₆	C₂²	semidirect
79. C₄×C₁₃×SD₁₆	C₂²	semidirect
80. C₄×C₁₃×SD₁₆	C₂²	semidirect
215. #61341	C₁₃	direct (N × H)
228. C₂×Q₈×C₁₃	#41	semidirect
314. #3502	C₂×C₁₃	semidirect
315. #3375	C₂×C₁₃	semidirect
316. #3371	C₂×C₁₃	semidirect
317. #3368	C₂×C₁₃	semidirect
318. #3368	C₂×C₁₃	semidirect
319. #3365	C₂×C₁₃	semidirect
320. #3362	C₂×C₁₃	semidirect
321. #3138	C₂×C₁₃	semidirect
322. #3136	C₂×C₁₃	semidirect
323. #3081	C₂×C₁₃	semidirect
324. #3076	C₂×C₁₃	semidirect
325. #3043	C₂×C₁₃	semidirect
326. C₂×#460	C₂×C₁₃	semidirect
327. #2962	C₂×C₁₃	semidirect
328. #2949	C₂×C₁₃	semidirect
329. C₄×#137	C₂×C₁₃	semidirect
393. Q₈²	C₂²×C₁₃	semidirect
396. #557	C₂²×C₁₃	semidirect
397. #557	C₂²×C₁₃	semidirect
417. #490	C₂²×C₁₃	semidirect
418. #489	C₂²×C₁₃	semidirect
419. #488	C₂²×C₁₃	semidirect
422. #486	C₂²×C₁₃	semidirect
423. #479	C₂²×C₁₃	semidirect
424. #478	C₂²×C₁₃	semidirect
425. #478	C₂²×C₁₃	semidirect
426. #478	C₂²×C₁₃	semidirect
427. #477	C₂²×C₁₃	semidirect
428. #476	C₂²×C₁₃	semidirect
429. #476	C₂²×C₁₃	semidirect
430. #475	C₂²×C₁₃	semidirect
431. #474	C₂²×C₁₃	semidirect
432. #474	C₂²×C₁₃	semidirect
433. #464	C₂²×C₁₃	semidirect
434. #464	C₂²×C₁₃	semidirect
438. #460	C₂²×C₁₃	semidirect
439. #460	C₂²×C₁₃	semidirect
440. #446	C₂²×C₁₃	semidirect
441. #446	C₂²×C₁₃	semidirect
442. C₈×Q₈	C₂²×C₁₃	semidirect
443. #441	C₂²×C₁₃	semidirect
444. #440	C₂²×C₁₃	semidirect
445. #440	C₂²×C₁₃	semidirect
446. #440	C₂²×C₁₃	semidirect
447. C₄×Q₁₆	C₂²×C₁₃	semidirect
448. C₄×SD₁₆	C₂²×C₁₃	semidirect
449. C₄×SD₁₆	C₂²×C₁₃	semidirect
450. C₄×SD₁₆	C₂²×C₁₃	semidirect
630. C₂×Q₈	C₁₃×#41	semidirect
715. C₁₃	#61341	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×#3508	2
C₁₃×#3502	2
C₁₃×#3375	2
C₁₃×#3371	2
C₁₃×#3368	2
C₁₃×#3365	2
C₁₃×#3362	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#3081	2
C₁₃×#3076	2
C₁₃×#3043	2
C₂×C₁₃×#460	2
C₁₃×#2962	2
C₁₃×#2949	2
C₄×C₁₃×#137	2
#61341	13

Subgroups — C13×#61341 #15747680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61341 #15747680