Subgroups — C₁₃×#34910 #15721249

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2602	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2601	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2431	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2392	C₂	1	4	yes	maximal, complemented
14	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2290	C₂	1	4	yes	maximal, complemented
19	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₁₃×#529	—	2	8	no	—
24	C₂×C₁₃×#126	C₂²	1	2	yes	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#123	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×#41	—	2	8	no	—
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#117	C₂²	1	2	yes	—
45	C₂×C₁₃×#117	C₂²	1	2	yes	—
46	C₂×C₁₃×#117	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
48	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#398	C₂²	1	4	yes	—
50	C₁₃×#397	C₂²	1	4	yes	—
51	C₁₃×#396	C₂²	1	4	yes	—
52	C₁₃×#396	C₂²	1	4	yes	—
53	C₁₃×#394	C₂²	1	4	yes	—
54	C₁₃×#394	C₂²	1	4	yes	—
55	C₁₃×#394	C₂²	1	4	yes	—
56	C₁₃×#392	C₂²	1	4	yes	—
57	C₁₃×#391	C₂²	1	1	yes	characteristic
58	C₁₃×#391	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#391	C₂²	1	1	yes	characteristic
61	C₁₃×#390	C₂²	1	1	yes	characteristic
62	C₁₃×#390	C₂²	1	1	yes	characteristic
63	C₁₃×#390	C₂²	1	1	yes	characteristic
64	C₁₃×#390	C₂²	1	1	yes	characteristic
65	C₁₃×#390	C₂²	1	4	yes	—
66	C₁₃×#389	C₂²	1	4	yes	—
67	C₁₃×#388	C₂²	1	4	yes	—
68	C₁₃×#388	C₂²	1	4	yes	—
69	C₁₃×#388	C₂²	1	4	yes	—
70	C₁₃×#388	C₂²	1	4	yes	—
71	C₁₃×#387	C₂²	1	4	yes	—
72	C₁₃×#387	C₂²	1	4	yes	—
73	C₁₃×#386	C₂²	1	4	yes	—
74	C₁₃×#386	C₂²	1	4	yes	—
75	C₁₃×#385	C₂²	1	4	yes	—
76	C₁₃×#385	C₂²	1	4	yes	—
77	C₁₃×#384	C₂²	1	1	yes	characteristic
78	C₁₃×#384	C₂²	1	1	yes	characteristic
79	C₁₃×#382	C₂²	1	1	yes	characteristic
80	C₁₃×#382	C₂²	1	1	yes	characteristic
81	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
84	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
85	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
87	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
89	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₁₃×#376	C₂²	1	2	yes	—
91	C₄³×C₁₃	C₂²	1	1	yes	characteristic
92	C₄³×C₁₃	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	4	no	—
94	C₂×C₁₃×#41	—	2	4	no	—
95	C₂×C₁₃×#41	—	2	4	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	—	2	4	no	—
111	C₁₃×#127	—	2	4	no	—
112	C₁₃×#126	—	2	8	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#124	—	2	4	no	—
115	C₁₃×#124	—	2	4	no	—
116	C₁₃×#124	—	2	4	no	—
117	C₁₃×#123	—	2	8	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×#121	—	2	4	no	—
120	C₄×Q₈×C₁₃	—	2	4	no	—
121	C₄×Q₈×C₁₃	—	2	4	no	—
122	C₄×Q₈×C₁₃	—	2	4	no	—
123	C₄×D₄×C₁₃	—	2	8	no	—
124	C₄×D₄×C₁₃	—	2	8	no	—
125	C₄×D₄×C₁₃	—	2	8	no	—
126	C₄×D₄×C₁₃	—	2	4	no	—
127	C₄×D₄×C₁₃	—	2	4	no	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	16	no	—
130	C₁₃×#117	—	2	4	no	—
131	C₁₃×#117	—	2	8	no	—
132	C₁₃×#117	—	2	8	no	—
133	C₁₃×#117	—	2	8	no	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₄²×C₁₃	—	2	8	no	—
166	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	4	yes	—
188	C₁₃×#95	C₂³	1	4	yes	—
189	C₁₃×#95	C₂³	1	4	yes	—
190	C₁₃×#95	C₂³	1	4	yes	—
191	C₁₃×#95	C₂³	1	4	yes	—
192	C₁₃×#95	C₂³	1	4	yes	—
193	#34910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
195	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
197	C₁₃×#41	—	2	32	no	—
198	C₂×Q₈×C₁₃	—	2	2	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	#41	1	4	yes	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	8	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	8	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	#41	1	4	yes	—
218	C₂²×C₄×C₁₃	—	2	4	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	8	no	—
228	C₂²×C₄×C₁₃	—	2	8	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	8	no	—
263	C₁₃×C₄⋊C₄	—	2	8	no	—
264	C₁₃×C₄⋊C₄	—	4	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	8	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	8	no	—
277	C₁₃×C₂²⋊C₄	—	2	8	no	—
278	C₁₃×C₂²⋊C₄	—	2	8	no	—
279	C₁₃×C₂²⋊C₄	—	4	4	no	—
280	C₁₃×C₂²⋊C₄	—	4	4	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	2	no	—
290	C₄²×C₁₃	—	4	2	no	—
291	C₄²×C₁₃	—	4	2	no	—
292	C₄²×C₁₃	C₂×D₄	1	4	yes	—
293	C₄²×C₁₃	C₂×D₄	1	4	yes	—
294	C₄²×C₁₃	C₂×D₄	1	4	yes	—
295	C₄²×C₁₃	C₂×D₄	1	4	yes	—
296	C₄²×C₁₃	#41	1	8	yes	complemented
297	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2602	C₂×C₁₃	1	4	yes	complemented
300	#2601	C₂×C₁₃	1	4	yes	complemented
301	#2566	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2565	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2545	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2544	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2500	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#2499	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2432	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#2431	C₂×C₁₃	1	1	yes	characteristic
309	#2392	C₂×C₁₃	1	4	yes	complemented
310	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2290	C₂×C₁₃	1	4	yes	complemented
315	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	4	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	4	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	4	no	—
327	C₂³×C₁₃	—	2	2	no	—
328	C₂³×C₁₃	—	2	4	no	—
329	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂³×C₁₃	C₂×#41	1	4	yes	—
331	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
332	Q₈×C₁₃	—	2	8	no	—
333	Q₈×C₁₃	—	4	4	no	—
334	D₄×C₁₃	—	2	16	no	—
335	D₄×C₁₃	—	2	8	no	—
336	D₄×C₁₃	—	4	16	no	—
337	D₄×C₁₃	—	4	8	no	—
338	D₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	2	16	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	8	no	—
352	C₂×C₄×C₁₃	—	2	8	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	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	4	no	—
364	C₂×C₄×C₁₃	—	2	4	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	4	8	no	—
372	C₂×C₄×C₁₃	—	4	8	no	—
373	C₂×C₄×C₁₃	—	4	8	no	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
381	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
382	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
383	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
385	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
386	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
389	#529	—	2	8	no	—
390	C₂×#126	C₂²×C₁₃	1	2	yes	—
391	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#123	C₂²×C₁₃	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
398	C₄×#41	—	2	8	no	—
399	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
403	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
409	C₂×#117	C₂²×C₁₃	1	2	yes	—
410	C₂×#117	C₂²×C₁₃	1	2	yes	—
411	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#117	C₂²×C₁₃	1	2	yes	—
413	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
414	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
415	#398	C₂²×C₁₃	1	4	yes	—
416	#397	C₂²×C₁₃	1	4	yes	—
417	#396	C₂²×C₁₃	1	4	yes	—
418	#396	C₂²×C₁₃	1	4	yes	—
419	#394	C₂²×C₁₃	1	4	yes	—
420	#394	C₂²×C₁₃	1	4	yes	—
421	#394	C₂²×C₁₃	1	4	yes	—
422	#392	C₂²×C₁₃	1	4	yes	—
423	#391	C₂²×C₁₃	1	1	yes	characteristic
424	#391	C₂²×C₁₃	1	1	yes	characteristic
425	#391	C₂²×C₁₃	1	1	yes	characteristic
426	#391	C₂²×C₁₃	1	1	yes	characteristic
427	#390	C₂²×C₁₃	1	1	yes	characteristic
428	#390	C₂²×C₁₃	1	4	yes	—
429	#390	C₂²×C₁₃	1	1	yes	characteristic
430	#390	C₂²×C₁₃	1	1	yes	characteristic
431	#390	C₂²×C₁₃	1	1	yes	characteristic
432	#389	C₂²×C₁₃	1	4	yes	—
433	#388	C₂²×C₁₃	1	4	yes	—
434	#388	C₂²×C₁₃	1	4	yes	—
435	#388	C₂²×C₁₃	1	4	yes	—
436	#388	C₂²×C₁₃	1	4	yes	—
437	#387	C₂²×C₁₃	1	4	yes	—
438	#387	C₂²×C₁₃	1	4	yes	—
439	#386	C₂²×C₁₃	1	4	yes	—
440	#386	C₂²×C₁₃	1	4	yes	—
441	#385	C₂²×C₁₃	1	4	yes	—
442	#385	C₂²×C₁₃	1	4	yes	—
443	#384	C₂²×C₁₃	1	1	yes	characteristic
444	#384	C₂²×C₁₃	1	1	yes	characteristic
445	#382	C₂²×C₁₃	1	1	yes	characteristic
446	#382	C₂²×C₁₃	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
448	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
456	#376	C₂²×C₁₃	1	2	yes	—
457	C₄³	C₂²×C₁₃	1	1	yes	characteristic
458	C₄³	C₂²×C₁₃	1	1	yes	characteristic
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	2	8	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	4	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	4	no	—
473	C₂²×C₁₃	—	4	4	no	—
474	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
475	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₁₃	C₂²×#41	1	2	yes	—
478	C₂²×C₁₃	#585	1	2	yes	—
479	C₄×C₁₃	—	2	2	no	—
480	C₄×C₁₃	—	2	4	no	—
481	C₄×C₁₃	—	2	2	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	4	no	—
485	C₄×C₁₃	—	2	4	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	#525	1	4	yes	—
494	C₄×C₁₃	#532	1	4	yes	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	2	4	no	—
498	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
501	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
503	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
506	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
507	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₄⋊Q₈	—	2	4	no	—
513	#127	—	2	4	no	—
514	#126	—	2	8	no	—
515	#125	—	2	4	no	—
516	#124	—	2	4	no	—
517	#124	—	2	4	no	—
518	#124	—	2	4	no	—
519	#123	—	2	8	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	#121	—	2	4	no	—
522	C₄×Q₈	—	2	4	no	—
523	C₄×Q₈	—	2	4	no	—
524	C₄×Q₈	—	2	4	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	16	no	—
532	#117	—	2	4	no	—
533	#117	—	2	8	no	—
534	#117	—	2	8	no	—
535	#117	—	2	8	no	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₄²	—	2	8	no	—
568	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
569	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	4	yes	—
590	#95	C₂³×C₁₃	1	4	yes	—
591	#95	C₂³×C₁₃	1	4	yes	—
592	#95	C₂³×C₁₃	1	4	yes	—
593	#95	C₂³×C₁₃	1	4	yes	—
594	#95	C₂³×C₁₃	1	4	yes	—
595	C₂×C₁₃	—	4	2	no	—
596	C₂×C₁₃	—	4	4	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
599	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
600	C₂×C₁₃	#3449	1	1	yes	characteristic
601	C₂×C₁₃	#3475	1	2	yes	—
602	C₂×C₁₃	#3480	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
604	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
606	#41	—	2	32	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	C₁₃×#41	1	4	yes	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	C₁₃×#41	1	4	yes	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	8	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	4	no	—
640	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
641	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	8	no	—
672	C₄⋊C₄	—	2	8	no	—
673	C₄⋊C₄	—	4	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	8	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	8	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	8	no	—
688	C₂²⋊C₄	—	4	4	no	—
689	C₂²⋊C₄	—	4	4	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	C₂×D₄×C₁₃	1	4	yes	—
702	C₄²	C₂×D₄×C₁₃	1	4	yes	—
703	C₄²	C₂×D₄×C₁₃	1	4	yes	—
704	C₄²	C₂×D₄×C₁₃	1	4	yes	—
705	C₄²	C₁₃×#41	1	8	yes	complemented
706	C₁₃	#34910	1	1	yes	characteristic, direct product factor, Sylow
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	4	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	4	no	—
720	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
721	C₂³	C₂×C₁₃×#41	1	4	yes	—
722	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
723	Q₈	—	2	8	no	—
724	Q₈	—	4	4	no	—
725	D₄	—	2	16	no	—
726	D₄	—	2	8	no	—
727	D₄	—	4	16	no	—
728	D₄	—	4	8	no	—
729	D₄	—	4	4	no	—
730	C₂×C₄	—	2	16	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	2	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	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	8	no	—
765	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
768	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
771	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
772	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
773	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
774	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
775	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
776	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
793	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
794	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
795	C₂²	C₂²×C₁₃×#41	1	2	yes	—
796	C₂²	C₁₃×#585	1	2	yes	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	4	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	C₁₃×#525	1	4	yes	—
812	C₄	C₁₃×#532	1	4	yes	—
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
817	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
818	C₂	C₁₃×#3449	1	1	yes	characteristic
819	C₂	C₁₃×#3475	1	2	yes	—
820	C₂	C₁₃×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2431	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₂×C₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#2602	C₂	semidirect
4. C₁₃×#2601	C₂	semidirect
5. C₁₃×#2566	C₂	semidirect
6. C₁₃×#2565	C₂	semidirect
7. C₁₃×#2545	C₂	semidirect
8. C₁₃×#2544	C₂	semidirect
9. C₁₃×#2500	C₂	semidirect
10. C₁₃×#2499	C₂	semidirect
11. C₁₃×#2432	C₂	semidirect
13. C₁₃×#2392	C₂	semidirect
14. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
15. C₄×C₁₃×#127	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₄×C₁₃×#124	C₂	semidirect
18. C₁₃×#2290	C₂	semidirect
19. C₄×C₁₃×#117	C₂	semidirect
166. C₂×C₄²×C₁₃	D₄	semidirect
193. #34910	C₁₃	direct (N × H)
296. C₄²×C₁₃	#41	semidirect
297. C₂×#529	C₂×C₁₃	semidirect
298. C₂×C₄×#41	C₂×C₁₃	semidirect
299. #2602	C₂×C₁₃	semidirect
300. #2601	C₂×C₁₃	semidirect
301. #2566	C₂×C₁₃	semidirect
302. #2565	C₂×C₁₃	semidirect
303. #2545	C₂×C₁₃	semidirect
304. #2544	C₂×C₁₃	semidirect
305. #2500	C₂×C₁₃	semidirect
306. #2499	C₂×C₁₃	semidirect
307. #2432	C₂×C₁₃	semidirect
309. #2392	C₂×C₁₃	semidirect
310. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
311. C₄×#127	C₂×C₁₃	semidirect
312. C₄×#124	C₂×C₁₃	semidirect
313. C₄×#124	C₂×C₁₃	semidirect
314. #2290	C₂×C₁₃	semidirect
315. C₄×#117	C₂×C₁₃	semidirect
568. C₂×C₄²	D₄×C₁₃	semidirect
705. C₄²	C₁₃×#41	semidirect
706. C₁₃	#34910	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#529	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2602	2
C₁₃×#2601	2
C₁₃×#2566	2
C₁₃×#2565	2
C₁₃×#2545	2
C₁₃×#2544	2
C₁₃×#2500	2
C₁₃×#2499	2
C₁₃×#2432	2
C₁₃×#2431	2
C₁₃×#2392	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#127	2
C₄×C₁₃×#124	2
C₁₃×#2290	2
C₄×C₁₃×#117	2
#34910	13

Subgroups — C13×#34910 #15721249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34910 #15721249