Subgroups — C₁₃×#36840 #15723179

Order 3328.

1988 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2765	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2760	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2746	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2710	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2709	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2708	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2697	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2684	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2669	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2653	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2527	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2459	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2457	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2443	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2328	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, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#120	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#401	C₂²	1	2	yes	complemented
34	C₁₃×#401	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#400	C₂²	1	2	yes	complemented
37	C₁₃×#399	C₂²	1	2	yes	complemented
38	C₁₃×#398	C₂²	1	2	yes	complemented
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#397	C₂²	1	2	yes	—
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	complemented
44	C₁₃×#396	C₂²	1	2	yes	—
45	C₁₃×#394	C₂²	1	2	yes	—
46	C₁₃×#394	C₂²	1	2	yes	—
47	C₁₃×#394	C₂²	1	2	yes	—
48	C₁₃×#394	C₂²	1	2	yes	—
49	C₁₃×#394	C₂²	1	2	yes	complemented
50	C₁₃×#394	C₂²	1	2	yes	complemented
51	C₁₃×#393	C₂²	1	2	yes	—
52	C₁₃×#393	C₂²	1	2	yes	—
53	C₁₃×#393	C₂²	1	2	yes	complemented
54	C₁₃×#393	C₂²	1	2	yes	complemented
55	C₁₃×#392	C₂²	1	2	yes	—
56	C₁₃×#392	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	2	yes	complemented
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#388	C₂²	1	2	yes	—
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	complemented
67	C₁₃×#388	C₂²	1	2	yes	complemented
68	C₁₃×#388	C₂²	1	2	yes	complemented
69	C₁₃×#387	C₂²	1	2	yes	complemented
70	C₁₃×#387	C₂²	1	2	yes	complemented
71	C₁₃×#387	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	2	yes	complemented
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	1	yes	characteristic
78	C₁₃×#386	C₂²	1	1	yes	characteristic
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	complemented
85	C₁₃×#386	C₂²	1	2	yes	complemented
86	C₁₃×#386	C₂²	1	2	yes	complemented
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	1	yes	characteristic
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	complemented
94	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#381	C₂²	1	2	yes	—
97	C₁₃×#381	C₂²	1	2	yes	—
98	C₁₃×#381	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#381	C₂²	1	2	yes	complemented
100	C₁₃×#380	C₂²	1	2	yes	complemented
101	C₁₃×#379	C₂²	1	1	yes	characteristic
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	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	—	4	2	no	—
117	C₂³×C₄×C₁₃	—	4	4	no	—
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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×#127	—	2	4	no	—
127	C₁₃×#124	—	4	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	4	4	no	—
130	C₁₃×#123	—	4	4	no	—
131	C₁₃×#121	—	4	4	no	—
132	C₁₃×#120	—	2	4	no	—
133	C₁₃×#120	—	4	4	no	—
134	C₄×D₄×C₁₃	—	4	2	no	—
135	C₄×D₄×C₁₃	—	4	2	no	—
136	C₄×D₄×C₁₃	—	4	4	no	—
137	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
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	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	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₂²⋊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	2	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	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	#36840	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	1	no	—
212	C₂⁴×C₁₃	—	4	2	no	—
213	C₂⁴×C₁₃	—	4	1	no	—
214	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
218	C₂×Q₈×C₁₃	—	4	2	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	4	1	no	—
229	C₂×D₄×C₁₃	—	4	1	no	—
230	C₂×D₄×C₁₃	—	4	1	no	—
231	C₂×D₄×C₁₃	—	4	1	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	—	4	2	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	2	no	—
241	C₂×D₄×C₁₃	#41	1	4	yes	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	4	1	no	—
249	C₂²×C₄×C₁₃	—	4	2	no	—
250	C₂²×C₄×C₁₃	—	4	2	no	—
251	C₂²×C₄×C₁₃	—	4	2	no	—
252	C₂²×C₄×C₁₃	—	4	2	no	—
253	C₂²×C₄×C₁₃	—	4	1	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	1	no	—
256	C₂²×C₄×C₁₃	—	4	1	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	2	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	16	no	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
284	C₁₃×C₄⋊C₄	—	4	1	no	—
285	C₁₃×C₄⋊C₄	—	4	2	no	—
286	C₁₃×C₄⋊C₄	—	4	2	no	—
287	C₁₃×C₄⋊C₄	—	4	2	no	—
288	C₁₃×C₄⋊C₄	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	1	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	1	no	—
307	C₁₃×C₂²⋊C₄	—	4	1	no	—
308	C₁₃×C₂²⋊C₄	—	4	1	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	4	1	no	—
322	C₄²×C₁₃	—	4	2	no	—
323	C₄²×C₁₃	—	4	2	no	—
324	#2849	C₂×C₁₃	1	2	yes	complemented
325	#2804	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2765	C₂×C₁₃	1	2	yes	complemented
327	#2760	C₂×C₁₃	1	2	yes	complemented
328	#2746	C₂×C₁₃	1	2	yes	complemented
329	#2710	C₂×C₁₃	1	2	yes	complemented
330	#2709	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#2708	C₂×C₁₃	1	2	yes	complemented
332	#2697	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#2684	C₂×C₁₃	1	2	yes	complemented
334	#2669	C₂×C₁₃	1	1	yes	characteristic
335	#2653	C₂×C₁₃	1	2	yes	complemented
336	#2527	C₂×C₁₃	1	2	yes	complemented
337	#2459	C₂×C₁₃	1	2	yes	complemented
338	#2457	C₂×C₁₃	1	2	yes	complemented
339	#2443	C₂×C₁₃	1	2	yes	complemented
340	#2328	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2322	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₄×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	1	no	—
345	C₂³×C₁₃	—	2	1	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	2	2	no	—
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	4	4	no	—
365	C₂³×C₁₃	—	4	8	no	—
366	C₂³×C₁₃	—	4	4	no	—
367	C₂³×C₁₃	—	4	8	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	C₂×#41	1	2	yes	—
370	C₂³×C₁₃	C₂×#41	1	2	yes	—
371	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
372	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
373	Q₈×C₁₃	—	8	4	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	8	no	—
377	D₄×C₁₃	—	8	4	no	—
378	D₄×C₁₃	—	8	4	no	—
379	D₄×C₁₃	—	8	4	no	—
380	D₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	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	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	4	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	8	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	8	2	no	—
426	C₂×C₄×C₁₃	—	8	2	no	—
427	C₂×C₄×C₁₃	—	8	4	no	—
428	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
429	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
430	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#124	C₂²×C₁₃	1	2	yes	—
433	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#123	C₂²×C₁₃	1	2	yes	—
435	C₂×#123	C₂²×C₁₃	1	2	yes	—
436	C₂×#121	C₂²×C₁₃	1	2	yes	—
437	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#120	C₂²×C₁₃	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	#401	C₂²×C₁₃	1	2	yes	complemented
444	#401	C₂²×C₁₃	1	2	yes	complemented
445	#400	C₂²×C₁₃	1	2	yes	complemented
446	#400	C₂²×C₁₃	1	2	yes	complemented
447	#399	C₂²×C₁₃	1	2	yes	complemented
448	#398	C₂²×C₁₃	1	2	yes	complemented
449	#398	C₂²×C₁₃	1	2	yes	complemented
450	#397	C₂²×C₁₃	1	2	yes	—
451	#397	C₂²×C₁₃	1	2	yes	—
452	#397	C₂²×C₁₃	1	2	yes	—
453	#397	C₂²×C₁₃	1	2	yes	complemented
454	#396	C₂²×C₁₃	1	2	yes	—
455	#394	C₂²×C₁₃	1	2	yes	—
456	#394	C₂²×C₁₃	1	2	yes	—
457	#394	C₂²×C₁₃	1	2	yes	—
458	#394	C₂²×C₁₃	1	2	yes	—
459	#394	C₂²×C₁₃	1	2	yes	complemented
460	#394	C₂²×C₁₃	1	2	yes	complemented
461	#393	C₂²×C₁₃	1	2	yes	—
462	#393	C₂²×C₁₃	1	2	yes	—
463	#393	C₂²×C₁₃	1	2	yes	complemented
464	#393	C₂²×C₁₃	1	2	yes	complemented
465	#392	C₂²×C₁₃	1	2	yes	—
466	#392	C₂²×C₁₃	1	2	yes	—
467	#391	C₂²×C₁₃	1	2	yes	complemented
468	#391	C₂²×C₁₃	1	2	yes	complemented
469	#390	C₂²×C₁₃	1	1	yes	characteristic
470	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	#389	C₂²×C₁₃	1	2	yes	complemented
472	#388	C₂²×C₁₃	1	2	yes	—
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#388	C₂²×C₁₃	1	2	yes	—
476	#388	C₂²×C₁₃	1	2	yes	complemented
477	#388	C₂²×C₁₃	1	2	yes	complemented
478	#388	C₂²×C₁₃	1	2	yes	complemented
479	#387	C₂²×C₁₃	1	2	yes	complemented
480	#387	C₂²×C₁₃	1	2	yes	complemented
481	#387	C₂²×C₁₃	1	2	yes	complemented
482	#387	C₂²×C₁₃	1	2	yes	complemented
483	#386	C₂²×C₁₃	1	1	yes	characteristic
484	#386	C₂²×C₁₃	1	2	yes	—
485	#386	C₂²×C₁₃	1	2	yes	—
486	#386	C₂²×C₁₃	1	2	yes	—
487	#386	C₂²×C₁₃	1	2	yes	—
488	#386	C₂²×C₁₃	1	2	yes	—
489	#386	C₂²×C₁₃	1	2	yes	—
490	#386	C₂²×C₁₃	1	2	yes	—
491	#386	C₂²×C₁₃	1	2	yes	—
492	#386	C₂²×C₁₃	1	2	yes	—
493	#386	C₂²×C₁₃	1	1	yes	characteristic
494	#386	C₂²×C₁₃	1	2	yes	complemented
495	#386	C₂²×C₁₃	1	2	yes	complemented
496	#386	C₂²×C₁₃	1	2	yes	complemented
497	#385	C₂²×C₁₃	1	2	yes	—
498	#385	C₂²×C₁₃	1	2	yes	—
499	#385	C₂²×C₁₃	1	2	yes	—
500	#385	C₂²×C₁₃	1	2	yes	—
501	#385	C₂²×C₁₃	1	2	yes	—
502	#385	C₂²×C₁₃	1	1	yes	characteristic
503	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#385	C₂²×C₁₃	1	2	yes	complemented
505	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	#381	C₂²×C₁₃	1	2	yes	—
507	#381	C₂²×C₁₃	1	2	yes	—
508	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#381	C₂²×C₁₃	1	2	yes	complemented
510	#380	C₂²×C₁₃	1	2	yes	complemented
511	#379	C₂²×C₁₃	1	2	yes	—
512	#379	C₂²×C₁₃	1	1	yes	characteristic
513	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
514	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
515	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	4	no	—
520	C₂²×C₁₃	—	2	4	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	4	16	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	1	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	1	no	—
533	C₂²×C₁₃	—	4	1	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	2	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	2	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
543	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
545	C₂²×C₁₃	#585	1	1	yes	characteristic
546	C₂²×C₁₃	#585	1	2	yes	—
547	C₄×C₁₃	—	2	2	no	—
548	C₄×C₁₃	—	2	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₄×C₁₃	—	4	1	no	—
555	C₄×C₁₃	—	4	1	no	—
556	C₄×C₁₃	—	4	2	no	—
557	C₄×C₁₃	—	4	2	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	—	4	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
564	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
565	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
567	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
568	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
569	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
570	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂³×C₄	—	4	2	no	—
572	C₂³×C₄	—	4	4	no	—
573	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
574	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
578	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
580	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
581	#127	—	2	4	no	—
582	#124	—	4	4	no	—
583	#123	—	2	4	no	—
584	#123	—	4	4	no	—
585	#123	—	4	4	no	—
586	#121	—	4	4	no	—
587	#120	—	2	4	no	—
588	#120	—	4	4	no	—
589	C₄×D₄	—	4	2	no	—
590	C₄×D₄	—	4	2	no	—
591	C₄×D₄	—	4	4	no	—
592	C₂×C₄⋊C₄	—	4	2	no	—
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	2	yes	—
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	2	yes	—
661	#95	C₂³×C₁₃	1	2	yes	—
662	#95	C₂³×C₁₃	1	2	yes	—
663	C₂×C₁₃	—	4	2	no	—
664	C₂×C₁₃	—	4	2	no	—
665	C₂×C₁₃	—	4	4	no	—
666	C₂×C₁₃	—	8	2	no	—
667	C₂×C₁₃	#3459	1	1	yes	characteristic
668	C₂×C₁₃	#3513	1	2	yes	—
669	C₂×C₁₃	#3532	1	1	yes	characteristic
670	C₂×C₁₃	#3533	1	2	yes	—
671	C₂×C₁₃	#3540	1	1	yes	characteristic
672	C₂⁴	—	2	2	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	1	no	—
675	C₂⁴	—	4	2	no	—
676	C₂⁴	—	4	1	no	—
677	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
678	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	C₁₃×#41	1	4	yes	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	16	no	—
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	1	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	1	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	1	no	—
787	C₁₃	#36840	1	1	yes	characteristic, direct product factor, Sylow
788	C₂³	—	2	2	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	4	4	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	8	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	4	4	no	—
814	C₂³	C₂×C₁₃×#41	1	2	yes	—
815	C₂³	C₂×C₁₃×#41	1	2	yes	—
816	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
817	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
818	Q₈	—	8	4	no	—
819	D₄	—	4	4	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	8	4	no	—
823	D₄	—	8	4	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	4	no	—
873	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
874	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	4	16	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
901	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
902	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
903	C₂²	C₁₃×#585	1	1	yes	characteristic
904	C₂²	C₁₃×#585	1	2	yes	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₂	—	4	4	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	2	no	—
923	C₂	—	8	2	no	—
924	C₂	C₁₃×#3459	1	1	yes	characteristic
925	C₂	C₁₃×#3513	1	2	yes	—
926	C₂	C₁₃×#3532	1	1	yes	characteristic
927	C₂	C₁₃×#3533	1	2	yes	—
928	C₂	C₁₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₁₃×#2669	C₂
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×#2849	C₂	semidirect
2. C₁₃×#2804	C₂	semidirect
3. C₁₃×#2765	C₂	semidirect
4. C₁₃×#2760	C₂	semidirect
5. C₁₃×#2746	C₂	semidirect
6. C₁₃×#2710	C₂	semidirect
7. C₁₃×#2709	C₂	semidirect
8. C₁₃×#2708	C₂	semidirect
9. C₁₃×#2697	C₂	semidirect
10. C₁₃×#2684	C₂	semidirect
12. C₁₃×#2653	C₂	semidirect
13. C₁₃×#2527	C₂	semidirect
14. C₁₃×#2459	C₂	semidirect
15. C₁₃×#2457	C₂	semidirect
16. C₁₃×#2443	C₂	semidirect
17. C₁₃×#2328	C₂	semidirect
18. C₁₃×#2322	C₂	semidirect
19. C₄×C₁₃×#120	C₂	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
33. C₁₃×#401	C₂²	semidirect
34. C₁₃×#401	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#400	C₂²	semidirect
37. C₁₃×#399	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
53. C₁₃×#393	C₂²	semidirect
54. C₁₃×#393	C₂²	semidirect
57. C₁₃×#391	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
60. C₁₃×#390	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
66. C₁₃×#388	C₂²	semidirect
67. C₁₃×#388	C₂²	semidirect
68. C₁₃×#388	C₂²	semidirect
69. C₁₃×#387	C₂²	semidirect
70. C₁₃×#387	C₂²	semidirect
71. C₁₃×#387	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
84. C₁₃×#386	C₂²	semidirect
85. C₁₃×#386	C₂²	semidirect
86. C₁₃×#386	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#385	C₂²	semidirect
95. C₁₃×#382	C₂²	semidirect
98. C₁₃×#381	C₂²	semidirect
99. C₁₃×#381	C₂²	semidirect
100. C₁₃×#380	C₂²	semidirect
105. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
106. C₁₃×#376	C₂²	semidirect
208. #36840	C₁₃	direct (N × H)
324. #2849	C₂×C₁₃	semidirect
325. #2804	C₂×C₁₃	semidirect
326. #2765	C₂×C₁₃	semidirect
327. #2760	C₂×C₁₃	semidirect
328. #2746	C₂×C₁₃	semidirect
329. #2710	C₂×C₁₃	semidirect
330. #2709	C₂×C₁₃	semidirect
331. #2708	C₂×C₁₃	semidirect
332. #2697	C₂×C₁₃	semidirect
333. #2684	C₂×C₁₃	semidirect
335. #2653	C₂×C₁₃	semidirect
336. #2527	C₂×C₁₃	semidirect
337. #2459	C₂×C₁₃	semidirect
338. #2457	C₂×C₁₃	semidirect
339. #2443	C₂×C₁₃	semidirect
340. #2328	C₂×C₁₃	semidirect
341. #2322	C₂×C₁₃	semidirect
342. C₄×#120	C₂×C₁₃	semidirect
441. C₂×C₄×D₄	C₂²×C₁₃	semidirect
442. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
443. #401	C₂²×C₁₃	semidirect
444. #401	C₂²×C₁₃	semidirect
445. #400	C₂²×C₁₃	semidirect
446. #400	C₂²×C₁₃	semidirect
447. #399	C₂²×C₁₃	semidirect
448. #398	C₂²×C₁₃	semidirect
449. #398	C₂²×C₁₃	semidirect
453. #397	C₂²×C₁₃	semidirect
459. #394	C₂²×C₁₃	semidirect
460. #394	C₂²×C₁₃	semidirect
463. #393	C₂²×C₁₃	semidirect
464. #393	C₂²×C₁₃	semidirect
467. #391	C₂²×C₁₃	semidirect
468. #391	C₂²×C₁₃	semidirect
470. #390	C₂²×C₁₃	semidirect
471. #389	C₂²×C₁₃	semidirect
476. #388	C₂²×C₁₃	semidirect
477. #388	C₂²×C₁₃	semidirect
478. #388	C₂²×C₁₃	semidirect
479. #387	C₂²×C₁₃	semidirect
480. #387	C₂²×C₁₃	semidirect
481. #387	C₂²×C₁₃	semidirect
482. #387	C₂²×C₁₃	semidirect
494. #386	C₂²×C₁₃	semidirect
495. #386	C₂²×C₁₃	semidirect
496. #386	C₂²×C₁₃	semidirect
503. #385	C₂²×C₁₃	semidirect
504. #385	C₂²×C₁₃	semidirect
505. #382	C₂²×C₁₃	semidirect
508. #381	C₂²×C₁₃	semidirect
509. #381	C₂²×C₁₃	semidirect
510. #380	C₂²×C₁₃	semidirect
515. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
516. #376	C₂²×C₁₃	semidirect
787. C₁₃	#36840	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×#2849	2
C₁₃×#2804	2
C₁₃×#2765	2
C₁₃×#2760	2
C₁₃×#2746	2
C₁₃×#2710	2
C₁₃×#2709	2
C₁₃×#2708	2
C₁₃×#2697	2
C₁₃×#2684	2
C₁₃×#2669	2
C₁₃×#2653	2
C₁₃×#2527	2
C₁₃×#2459	2
C₁₃×#2457	2
C₁₃×#2443	2
C₁₃×#2328	2
C₁₃×#2322	2
C₄×C₁₃×#120	2
#36840	13

Subgroups — C13×#36840 #15723179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36840 #15723179