Subgroups — C₁₃×#36929 #15723268

Order 3328.

1892 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2788	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2750	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2735	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2728	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2720	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2717	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2697	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2690	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2684	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2683	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2652	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2530	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2465	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2460	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2449	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#400	C₂²	1	2	yes	complemented
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#400	C₂²	1	2	yes	complemented
37	C₁₃×#400	C₂²	1	2	yes	complemented
38	C₁₃×#399	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#398	C₂²	1	2	yes	complemented
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	complemented
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	complemented
51	C₁₃×#395	C₂²	1	2	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#395	C₂²	1	2	yes	complemented
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#393	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	2	yes	complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	2	yes	complemented
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	2	yes	complemented
73	C₁₃×#387	C₂²	1	2	yes	complemented
74	C₁₃×#387	C₂²	1	2	yes	complemented
75	C₁₃×#387	C₂²	1	2	yes	complemented
76	C₁₃×#387	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	1	yes	characteristic
82	C₁₃×#386	C₂²	1	1	yes	characteristic
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	1	yes	characteristic
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	complemented
93	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#385	C₂²	1	2	yes	complemented
95	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#381	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#379	C₂²	1	1	yes	characteristic
101	C₁₃×#379	C₂²	1	2	yes	—
102	C₁₃×#379	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	—	4	4	no	—
113	C₂³×C₄×C₁₃	—	4	2	no	—
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#125	—	4	4	no	—
122	C₁₃×#124	—	2	4	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	—	4	4	no	—
125	C₁₃×C₂²⋊Q₈	—	4	4	no	—
126	C₁₃×C₂²⋊Q₈	—	4	4	no	—
127	C₁₃×C₂²⋊Q₈	—	4	4	no	—
128	C₁₃×#120	—	2	4	no	—
129	C₄×Q₈×C₁₃	—	4	2	no	—
130	C₄×D₄×C₁₃	—	4	2	no	—
131	C₄×D₄×C₁₃	—	4	4	no	—
132	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₂²⋊C₄	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	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	#36929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂⁴×C₁₃	—	2	2	no	—
210	C₂⁴×C₁₃	—	2	4	no	—
211	C₂⁴×C₁₃	—	4	2	no	—
212	C₂⁴×C₁₃	—	4	1	no	—
213	C₂⁴×C₁₃	—	4	1	no	—
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	4	no	—
219	C₂×Q₈×C₁₃	—	4	1	no	—
220	C₂×Q₈×C₁₃	—	4	1	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	—	4	2	no	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	4	1	no	—
226	C₂×D₄×C₁₃	—	4	2	no	—
227	C₂×D₄×C₁₃	—	4	1	no	—
228	C₂×D₄×C₁₃	#41	1	4	yes	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	4	1	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	1	no	—
243	C₂²×C₄×C₁₃	—	4	1	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	16	no	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	no	—
283	C₁₃×C₄⋊C₄	—	4	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	1	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	1	no	—
298	C₁₃×C₂²⋊C₄	—	4	1	no	—
299	C₁₃×C₂²⋊C₄	—	4	1	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	2	no	—
303	C₁₃×C₂²⋊C₄	—	4	2	no	—
304	C₁₃×C₂²⋊C₄	—	4	2	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	2	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	—	2	2	no	—
310	C₄²×C₁₃	—	4	1	no	—
311	C₄²×C₁₃	—	4	2	no	—
312	C₄²×C₁₃	—	4	2	no	—
313	C₄²×C₁₃	—	4	2	no	—
314	#2848	C₂×C₁₃	1	2	yes	complemented
315	#2788	C₂×C₁₃	1	2	yes	complemented
316	#2750	C₂×C₁₃	1	2	yes	complemented
317	#2735	C₂×C₁₃	1	2	yes	complemented
318	#2728	C₂×C₁₃	1	2	yes	complemented
319	#2720	C₂×C₁₃	1	2	yes	complemented
320	#2717	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2697	C₂×C₁₃	1	1	yes	characteristic
322	#2690	C₂×C₁₃	1	2	yes	complemented
323	#2684	C₂×C₁₃	1	1	yes	characteristic
324	#2683	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2652	C₂×C₁₃	1	2	yes	complemented
326	#2530	C₂×C₁₃	1	2	yes	complemented
327	#2465	C₂×C₁₃	1	2	yes	complemented
328	#2460	C₂×C₁₃	1	2	yes	complemented
329	#2449	C₂×C₁₃	1	2	yes	complemented
330	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#2322	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₄×#120	C₂×C₁₃	1	1	yes	characteristic
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	1	no	—
346	C₂³×C₁₃	—	2	1	no	—
347	C₂³×C₁₃	—	4	8	no	—
348	C₂³×C₁₃	—	4	4	no	—
349	C₂³×C₁₃	—	4	4	no	—
350	C₂³×C₁₃	—	4	8	no	—
351	C₂³×C₁₃	—	4	4	no	—
352	C₂³×C₁₃	C₂×#41	1	2	yes	—
353	C₂³×C₁₃	C₂×#41	1	2	yes	—
354	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
355	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
356	Q₈×C₁₃	—	4	4	no	—
357	Q₈×C₁₃	—	8	4	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	4	8	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	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	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	2	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	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	8	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	8	2	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
409	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
410	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
411	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
413	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
419	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
423	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	#400	C₂²×C₁₃	1	2	yes	complemented
425	#400	C₂²×C₁₃	1	2	yes	complemented
426	#400	C₂²×C₁₃	1	2	yes	complemented
427	#400	C₂²×C₁₃	1	2	yes	complemented
428	#400	C₂²×C₁₃	1	2	yes	complemented
429	#399	C₂²×C₁₃	1	2	yes	—
430	#398	C₂²×C₁₃	1	2	yes	complemented
431	#398	C₂²×C₁₃	1	2	yes	complemented
432	#397	C₂²×C₁₃	1	2	yes	—
433	#397	C₂²×C₁₃	1	2	yes	—
434	#397	C₂²×C₁₃	1	2	yes	—
435	#397	C₂²×C₁₃	1	2	yes	—
436	#397	C₂²×C₁₃	1	2	yes	—
437	#397	C₂²×C₁₃	1	2	yes	complemented
438	#396	C₂²×C₁₃	1	2	yes	—
439	#396	C₂²×C₁₃	1	2	yes	—
440	#396	C₂²×C₁₃	1	2	yes	—
441	#396	C₂²×C₁₃	1	2	yes	complemented
442	#395	C₂²×C₁₃	1	2	yes	complemented
443	#395	C₂²×C₁₃	1	2	yes	complemented
444	#395	C₂²×C₁₃	1	2	yes	complemented
445	#394	C₂²×C₁₃	1	2	yes	—
446	#394	C₂²×C₁₃	1	2	yes	—
447	#393	C₂²×C₁₃	1	2	yes	—
448	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#391	C₂²×C₁₃	1	2	yes	complemented
450	#390	C₂²×C₁₃	1	1	yes	characteristic
451	#389	C₂²×C₁₃	1	2	yes	complemented
452	#389	C₂²×C₁₃	1	2	yes	complemented
453	#389	C₂²×C₁₃	1	2	yes	complemented
454	#388	C₂²×C₁₃	1	2	yes	—
455	#388	C₂²×C₁₃	1	2	yes	—
456	#388	C₂²×C₁₃	1	2	yes	—
457	#388	C₂²×C₁₃	1	2	yes	—
458	#388	C₂²×C₁₃	1	2	yes	—
459	#388	C₂²×C₁₃	1	2	yes	—
460	#388	C₂²×C₁₃	1	2	yes	—
461	#388	C₂²×C₁₃	1	2	yes	—
462	#388	C₂²×C₁₃	1	2	yes	complemented
463	#387	C₂²×C₁₃	1	2	yes	complemented
464	#387	C₂²×C₁₃	1	2	yes	complemented
465	#387	C₂²×C₁₃	1	2	yes	complemented
466	#387	C₂²×C₁₃	1	2	yes	complemented
467	#387	C₂²×C₁₃	1	2	yes	complemented
468	#387	C₂²×C₁₃	1	2	yes	complemented
469	#387	C₂²×C₁₃	1	2	yes	complemented
470	#386	C₂²×C₁₃	1	1	yes	characteristic
471	#386	C₂²×C₁₃	1	1	yes	characteristic
472	#386	C₂²×C₁₃	1	2	yes	—
473	#386	C₂²×C₁₃	1	2	yes	—
474	#386	C₂²×C₁₃	1	2	yes	—
475	#385	C₂²×C₁₃	1	2	yes	—
476	#385	C₂²×C₁₃	1	2	yes	—
477	#385	C₂²×C₁₃	1	2	yes	—
478	#385	C₂²×C₁₃	1	2	yes	—
479	#385	C₂²×C₁₃	1	2	yes	—
480	#385	C₂²×C₁₃	1	2	yes	—
481	#385	C₂²×C₁₃	1	1	yes	characteristic
482	#385	C₂²×C₁₃	1	2	yes	—
483	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#385	C₂²×C₁₃	1	2	yes	complemented
485	#385	C₂²×C₁₃	1	2	yes	complemented
486	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	#380	C₂²×C₁₃	1	2	yes	—
489	#380	C₂²×C₁₃	1	2	yes	—
490	#380	C₂²×C₁₃	1	2	yes	—
491	#379	C₂²×C₁₃	1	2	yes	—
492	#379	C₂²×C₁₃	1	2	yes	—
493	#379	C₂²×C₁₃	1	1	yes	characteristic
494	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
495	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	2	2	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	2	4	no	—
502	C₂²×C₁₃	—	2	4	no	—
503	C₂²×C₁₃	—	2	4	no	—
504	C₂²×C₁₃	—	2	4	no	—
505	C₂²×C₁₃	—	4	16	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
517	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
519	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
520	C₂²×C₁₃	#585	1	1	yes	characteristic
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	4	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	1	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
540	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
541	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	—	4	4	no	—
543	C₂³×C₄	—	4	2	no	—
544	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
545	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
550	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
551	#125	—	4	4	no	—
552	#124	—	2	4	no	—
553	#123	—	2	4	no	—
554	C₂²⋊Q₈	—	4	4	no	—
555	C₂²⋊Q₈	—	4	4	no	—
556	C₂²⋊Q₈	—	4	4	no	—
557	C₂²⋊Q₈	—	4	4	no	—
558	#120	—	2	4	no	—
559	C₄×Q₈	—	4	2	no	—
560	C₄×D₄	—	4	2	no	—
561	C₄×D₄	—	4	4	no	—
562	C₂×C₄⋊C₄	—	4	2	no	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	#95	C₂³×C₁₃	1	2	yes	—
615	#95	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	2	yes	—
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	#95	C₂³×C₁₃	1	2	yes	—
627	#95	C₂³×C₁₃	1	2	yes	—
628	#95	C₂³×C₁₃	1	2	yes	—
629	#95	C₂³×C₁₃	1	2	yes	—
630	#95	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	C₂×C₁₃	—	4	2	no	—
639	C₂×C₁₃	—	4	2	no	—
640	C₂×C₁₃	—	4	4	no	—
641	C₂×C₁₃	#3459	1	1	yes	characteristic
642	C₂×C₁₃	#3520	1	2	yes	—
643	C₂×C₁₃	#3532	1	1	yes	characteristic
644	C₂×C₁₃	#3538	1	1	yes	characteristic
645	C₂×C₁₃	#3541	1	2	yes	—
646	C₂⁴	—	2	2	no	—
647	C₂⁴	—	2	4	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	—	4	1	no	—
651	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	4	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	4	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	—	4	1	no	—
665	C₂×D₄	C₁₃×#41	1	4	yes	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	16	no	—
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	4	1	no	—
732	C₂²⋊C₄	—	4	1	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	4	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	1	no	—
751	C₁₃	#36929	1	1	yes	characteristic, direct product factor, Sylow
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	4	8	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	8	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	4	no	—
771	C₂³	C₂×C₁₃×#41	1	2	yes	—
772	C₂³	C₂×C₁₃×#41	1	2	yes	—
773	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
774	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	8	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	8	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	4	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	4	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
828	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
829	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	4	16	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
849	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
850	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
851	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
852	C₂²	C₁₃×#585	1	1	yes	characteristic
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₂	—	4	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	2	no	—
872	C₂	C₁₃×#3459	1	1	yes	characteristic
873	C₂	C₁₃×#3520	1	2	yes	—
874	C₂	C₁₃×#3532	1	1	yes	characteristic
875	C₂	C₁₃×#3538	1	1	yes	characteristic
876	C₂	C₁₃×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#120	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2848	C₂	semidirect
2. C₁₃×#2788	C₂	semidirect
3. C₁₃×#2750	C₂	semidirect
4. C₁₃×#2735	C₂	semidirect
5. C₁₃×#2728	C₂	semidirect
6. C₁₃×#2720	C₂	semidirect
7. C₁₃×#2717	C₂	semidirect
9. C₁₃×#2690	C₂	semidirect
11. C₁₃×#2683	C₂	semidirect
12. C₁₃×#2652	C₂	semidirect
13. C₁₃×#2530	C₂	semidirect
14. C₁₃×#2465	C₂	semidirect
15. C₁₃×#2460	C₂	semidirect
16. C₁₃×#2449	C₂	semidirect
17. C₁₃×#2326	C₂	semidirect
18. C₁₃×#2322	C₂	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#400	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
53. C₁₃×#395	C₂²	semidirect
57. C₁₃×#391	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
60. C₁₃×#389	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
62. C₁₃×#389	C₂²	semidirect
71. C₁₃×#388	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
73. C₁₃×#387	C₂²	semidirect
74. C₁₃×#387	C₂²	semidirect
75. C₁₃×#387	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
92. C₁₃×#385	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#385	C₂²	semidirect
95. C₁₃×#384	C₂²	semidirect
96. C₁₃×#381	C₂²	semidirect
105. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
106. C₁₃×#376	C₂²	semidirect
208. #36929	C₁₃	direct (N × H)
314. #2848	C₂×C₁₃	semidirect
315. #2788	C₂×C₁₃	semidirect
316. #2750	C₂×C₁₃	semidirect
317. #2735	C₂×C₁₃	semidirect
318. #2728	C₂×C₁₃	semidirect
319. #2720	C₂×C₁₃	semidirect
320. #2717	C₂×C₁₃	semidirect
322. #2690	C₂×C₁₃	semidirect
324. #2683	C₂×C₁₃	semidirect
325. #2652	C₂×C₁₃	semidirect
326. #2530	C₂×C₁₃	semidirect
327. #2465	C₂×C₁₃	semidirect
328. #2460	C₂×C₁₃	semidirect
329. #2449	C₂×C₁₃	semidirect
330. #2326	C₂×C₁₃	semidirect
331. #2322	C₂×C₁₃	semidirect
412. C₂×#125	C₂²×C₁₃	semidirect
418. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
420. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
423. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
424. #400	C₂²×C₁₃	semidirect
425. #400	C₂²×C₁₃	semidirect
426. #400	C₂²×C₁₃	semidirect
427. #400	C₂²×C₁₃	semidirect
428. #400	C₂²×C₁₃	semidirect
430. #398	C₂²×C₁₃	semidirect
431. #398	C₂²×C₁₃	semidirect
437. #397	C₂²×C₁₃	semidirect
441. #396	C₂²×C₁₃	semidirect
442. #395	C₂²×C₁₃	semidirect
443. #395	C₂²×C₁₃	semidirect
444. #395	C₂²×C₁₃	semidirect
448. #391	C₂²×C₁₃	semidirect
449. #391	C₂²×C₁₃	semidirect
451. #389	C₂²×C₁₃	semidirect
452. #389	C₂²×C₁₃	semidirect
453. #389	C₂²×C₁₃	semidirect
462. #388	C₂²×C₁₃	semidirect
463. #387	C₂²×C₁₃	semidirect
464. #387	C₂²×C₁₃	semidirect
465. #387	C₂²×C₁₃	semidirect
466. #387	C₂²×C₁₃	semidirect
467. #387	C₂²×C₁₃	semidirect
468. #387	C₂²×C₁₃	semidirect
469. #387	C₂²×C₁₃	semidirect
483. #385	C₂²×C₁₃	semidirect
484. #385	C₂²×C₁₃	semidirect
485. #385	C₂²×C₁₃	semidirect
486. #384	C₂²×C₁₃	semidirect
487. #381	C₂²×C₁₃	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
497. #376	C₂²×C₁₃	semidirect
751. C₁₃	#36929	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×#2848	2
C₁₃×#2788	2
C₁₃×#2750	2
C₁₃×#2735	2
C₁₃×#2728	2
C₁₃×#2720	2
C₁₃×#2717	2
C₁₃×#2697	2
C₁₃×#2690	2
C₁₃×#2684	2
C₁₃×#2683	2
C₁₃×#2652	2
C₁₃×#2530	2
C₁₃×#2465	2
C₁₃×#2460	2
C₁₃×#2449	2
C₁₃×#2326	2
C₁₃×#2322	2
C₄×C₁₃×#120	2
#36929	13

Subgroups — C13×#36929 #15723268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36929 #15723268