Subgroups — C₁₃×#36831 #15723170

Order 3328.

1526 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2807	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2797	C₂	1	2	yes	maximal
4	C₁₃×#2776	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2748	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2746	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2738	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2727	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2722	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2654	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2611	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2606	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2598	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2594	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2479	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#401	C₂²	1	2	yes	—
28	C₁₃×#400	C₂²	1	1	yes	characteristic
29	C₁₃×#400	C₂²	1	2	yes	—
30	C₁₃×#400	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	1	yes	characteristic
33	C₁₃×#399	C₂²	1	1	yes	characteristic
34	C₁₃×#399	C₂²	1	2	yes	—
35	C₁₃×#399	C₂²	1	1	yes	characteristic
36	C₁₃×#399	C₂²	1	2	yes	—
37	C₁₃×#399	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	2	yes	—
40	C₁₃×#398	C₂²	1	2	yes	—
41	C₁₃×#398	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	1	yes	characteristic
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	1	yes	characteristic
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#394	C₂²	1	2	yes	—
52	C₁₃×#394	C₂²	1	2	yes	—
53	C₁₃×#394	C₂²	1	1	yes	characteristic
54	C₁₃×#392	C₂²	1	1	yes	characteristic
55	C₁₃×#390	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	2	yes	—
62	C₁₃×#389	C₂²	1	2	yes	—
63	C₁₃×#389	C₂²	1	2	yes	—
64	C₁₃×#389	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	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
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	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#383	C₂²	1	2	yes	—
96	C₁₃×#383	C₂²	1	1	yes	characteristic
97	C₁₃×#381	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#380	C₂²	1	2	yes	—
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
106	C₁₃×#376	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×#126	—	4	4	no	—
113	C₁₃×#126	—	4	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₁₃×#117	—	2	4	no	—
117	C₁₃×#117	—	4	2	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	—	4	2	no	—
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	1	yes	characteristic
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	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	1	yes	characteristic
192	C₁₃×#95	C₂³	1	1	yes	characteristic
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	#36831	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
203	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	4	2	no	—
207	C₂×D₄×C₁₃	—	4	2	no	—
208	C₂×D₄×C₁₃	—	4	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	4	2	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	4	2	no	—
216	C₂²×C₄×C₁₃	—	4	2	no	—
217	C₂²×C₄×C₁₃	—	4	2	no	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	4	2	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	—	4	2	no	—
249	C₁₃×C₄⋊C₄	—	4	2	no	—
250	C₁₃×C₄⋊C₄	—	4	2	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	4	2	no	—
253	C₁₃×C₄⋊C₄	—	4	2	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₄⋊C₄	—	4	2	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	2	no	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	4	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	4	2	no	—
269	C₁₃×C₂²⋊C₄	—	4	2	no	—
270	C₁₃×C₂²⋊C₄	—	4	2	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₁₃×C₂²⋊C₄	—	4	2	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	4	1	no	—
281	C₄²×C₁₃	—	4	1	no	—
282	C₄²×C₁₃	—	4	2	no	—
283	C₄²×C₁₃	—	4	2	no	—
284	C₄²×C₁₃	—	4	1	no	—
285	C₄²×C₁₃	—	4	1	no	—
286	C₄²×C₁₃	—	4	2	no	—
287	C₄²×C₁₃	#41	1	4	yes	—
288	#2852	C₂×C₁₃	1	2	yes	complemented
289	#2807	C₂×C₁₃	1	2	yes	complemented
290	#2797	C₂×C₁₃	1	2	yes	—
291	#2776	C₂×C₁₃	1	2	yes	complemented
292	#2748	C₂×C₁₃	1	2	yes	complemented
293	#2746	C₂×C₁₃	1	2	yes	complemented
294	#2738	C₂×C₁₃	1	2	yes	complemented
295	#2727	C₂×C₁₃	1	2	yes	complemented
296	#2722	C₂×C₁₃	1	2	yes	complemented
297	#2654	C₂×C₁₃	1	2	yes	complemented
298	#2611	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2606	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2598	C₂×C₁₃	1	1	yes	characteristic
301	#2594	C₂×C₁₃	1	2	yes	complemented
302	#2562	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2479	C₂×C₁₃	1	2	yes	complemented
304	#2336	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2319	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
319	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
320	D₄×C₁₃	—	4	4	no	—
321	D₄×C₁₃	—	8	4	no	—
322	C₂×C₄×C₁₃	—	2	8	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	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	2	no	—
345	C₂×C₄×C₁₃	—	2	2	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	2	no	—
352	C₂×C₄×C₁₃	—	2	2	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	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	—	8	4	no	—
368	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
369	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
370	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
372	C₂×#126	C₂²×C₁₃	1	2	yes	—
373	C₂×#126	C₂²×C₁₃	1	2	yes	—
374	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
379	#401	C₂²×C₁₃	1	2	yes	—
380	#400	C₂²×C₁₃	1	2	yes	—
381	#400	C₂²×C₁₃	1	1	yes	characteristic
382	#400	C₂²×C₁₃	1	1	yes	characteristic
383	#400	C₂²×C₁₃	1	2	yes	—
384	#400	C₂²×C₁₃	1	2	yes	—
385	#399	C₂²×C₁₃	1	1	yes	characteristic
386	#399	C₂²×C₁₃	1	1	yes	characteristic
387	#399	C₂²×C₁₃	1	2	yes	—
388	#399	C₂²×C₁₃	1	2	yes	—
389	#399	C₂²×C₁₃	1	2	yes	—
390	#398	C₂²×C₁₃	1	2	yes	—
391	#398	C₂²×C₁₃	1	2	yes	—
392	#398	C₂²×C₁₃	1	2	yes	—
393	#398	C₂²×C₁₃	1	1	yes	characteristic
394	#398	C₂²×C₁₃	1	2	yes	—
395	#398	C₂²×C₁₃	1	2	yes	—
396	#398	C₂²×C₁₃	1	2	yes	—
397	#397	C₂²×C₁₃	1	2	yes	—
398	#397	C₂²×C₁₃	1	1	yes	characteristic
399	#397	C₂²×C₁₃	1	2	yes	—
400	#397	C₂²×C₁₃	1	2	yes	—
401	#396	C₂²×C₁₃	1	2	yes	—
402	#396	C₂²×C₁₃	1	2	yes	—
403	#394	C₂²×C₁₃	1	2	yes	—
404	#394	C₂²×C₁₃	1	1	yes	characteristic
405	#394	C₂²×C₁₃	1	2	yes	—
406	#392	C₂²×C₁₃	1	1	yes	characteristic
407	#390	C₂²×C₁₃	1	2	yes	—
408	#390	C₂²×C₁₃	1	2	yes	—
409	#389	C₂²×C₁₃	1	2	yes	—
410	#389	C₂²×C₁₃	1	2	yes	—
411	#389	C₂²×C₁₃	1	2	yes	—
412	#389	C₂²×C₁₃	1	2	yes	—
413	#389	C₂²×C₁₃	1	2	yes	—
414	#389	C₂²×C₁₃	1	2	yes	—
415	#389	C₂²×C₁₃	1	2	yes	—
416	#389	C₂²×C₁₃	1	2	yes	—
417	#388	C₂²×C₁₃	1	2	yes	—
418	#388	C₂²×C₁₃	1	2	yes	—
419	#388	C₂²×C₁₃	1	2	yes	—
420	#388	C₂²×C₁₃	1	2	yes	—
421	#388	C₂²×C₁₃	1	2	yes	—
422	#388	C₂²×C₁₃	1	2	yes	—
423	#388	C₂²×C₁₃	1	2	yes	—
424	#388	C₂²×C₁₃	1	2	yes	—
425	#388	C₂²×C₁₃	1	2	yes	—
426	#388	C₂²×C₁₃	1	2	yes	—
427	#387	C₂²×C₁₃	1	2	yes	—
428	#387	C₂²×C₁₃	1	2	yes	—
429	#387	C₂²×C₁₃	1	2	yes	—
430	#387	C₂²×C₁₃	1	2	yes	—
431	#387	C₂²×C₁₃	1	2	yes	—
432	#387	C₂²×C₁₃	1	2	yes	—
433	#387	C₂²×C₁₃	1	2	yes	—
434	#387	C₂²×C₁₃	1	2	yes	—
435	#387	C₂²×C₁₃	1	2	yes	—
436	#387	C₂²×C₁₃	1	2	yes	—
437	#386	C₂²×C₁₃	1	2	yes	—
438	#386	C₂²×C₁₃	1	2	yes	—
439	#386	C₂²×C₁₃	1	2	yes	—
440	#386	C₂²×C₁₃	1	2	yes	—
441	#385	C₂²×C₁₃	1	2	yes	—
442	#385	C₂²×C₁₃	1	2	yes	—
443	#385	C₂²×C₁₃	1	2	yes	—
444	#385	C₂²×C₁₃	1	2	yes	—
445	#385	C₂²×C₁₃	1	2	yes	—
446	#385	C₂²×C₁₃	1	2	yes	—
447	#383	C₂²×C₁₃	1	1	yes	characteristic
448	#383	C₂²×C₁₃	1	2	yes	—
449	#381	C₂²×C₁₃	1	2	yes	—
450	#380	C₂²×C₁₃	1	2	yes	—
451	#380	C₂²×C₁₃	1	2	yes	—
452	#380	C₂²×C₁₃	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
458	#376	C₂²×C₁₃	1	1	yes	characteristic
459	C₂²×C₁₃	—	2	2	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	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	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂²×C₁₃	#585	1	2	yes	—
475	C₂²×C₁₃	#585	1	2	yes	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	2	no	—
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	2	2	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	2	no	—
485	C₄×C₁₃	—	4	2	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	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
497	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
498	#126	—	4	4	no	—
499	#126	—	4	4	no	—
500	#125	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	#117	—	2	4	no	—
503	#117	—	4	2	no	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₄²	—	4	2	no	—
548	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
553	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
554	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
558	#95	C₂³×C₁₃	1	1	yes	characteristic
559	#95	C₂³×C₁₃	1	1	yes	characteristic
560	#95	C₂³×C₁₃	1	2	yes	—
561	#95	C₂³×C₁₃	1	2	yes	—
562	#95	C₂³×C₁₃	1	2	yes	—
563	#95	C₂³×C₁₃	1	2	yes	—
564	#95	C₂³×C₁₃	1	2	yes	—
565	#95	C₂³×C₁₃	1	2	yes	—
566	#95	C₂³×C₁₃	1	2	yes	—
567	#95	C₂³×C₁₃	1	2	yes	—
568	#95	C₂³×C₁₃	1	2	yes	—
569	#95	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	2	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	2	yes	—
575	#95	C₂³×C₁₃	1	2	yes	—
576	#95	C₂³×C₁₃	1	2	yes	—
577	#95	C₂³×C₁₃	1	2	yes	—
578	#95	C₂³×C₁₃	1	1	yes	characteristic
579	#95	C₂³×C₁₃	1	1	yes	characteristic
580	#95	C₂³×C₁₃	1	2	yes	—
581	#95	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	2	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	C₂×C₁₃	—	4	2	no	—
588	C₂×C₁₃	—	8	2	no	—
589	C₂×C₁₃	#3455	1	1	yes	characteristic
590	C₂×C₁₃	#3492	1	1	yes	characteristic
591	C₂×C₁₃	#3510	1	1	yes	characteristic
592	C₂×C₁₃	#3539	1	2	yes	—
593	C₂×C₁₃	#3564	1	2	yes	—
594	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
595	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	4	2	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	4	1	no	—
673	C₄²	—	4	1	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	1	no	—
676	C₄²	—	4	2	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	C₁₃×#41	1	4	yes	—
680	C₁₃	#36831	1	1	yes	characteristic, direct product factor, Sylow
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
693	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
694	D₄	—	4	4	no	—
695	D₄	—	8	4	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	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	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
743	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
744	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
745	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
759	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
760	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
761	C₂²	C₁₃×#585	1	2	yes	—
762	C₂²	C₁₃×#585	1	2	yes	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₂	—	4	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₁₃×#3455	1	1	yes	characteristic
783	C₂	C₁₃×#3492	1	1	yes	characteristic
784	C₂	C₁₃×#3510	1	1	yes	characteristic
785	C₂	C₁₃×#3539	1	2	yes	—
786	C₂	C₁₃×#3564	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₁₃×#392	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×#2852	C₂	semidirect
2. C₁₃×#2807	C₂	semidirect
4. C₁₃×#2776	C₂	semidirect
5. C₁₃×#2748	C₂	semidirect
6. C₁₃×#2746	C₂	semidirect
7. C₁₃×#2738	C₂	semidirect
8. C₁₃×#2727	C₂	semidirect
9. C₁₃×#2722	C₂	semidirect
10. C₁₃×#2654	C₂	semidirect
11. C₁₃×#2611	C₂	semidirect
12. C₁₃×#2606	C₂	semidirect
14. C₁₃×#2594	C₂	semidirect
15. C₁₃×#2562	C₂	semidirect
16. C₁₃×#2479	C₂	semidirect
17. C₁₃×#2336	C₂	semidirect
18. C₁₃×#2319	C₂	semidirect
19. C₁₃×#2296	C₂	semidirect
201. #36831	C₁₃	direct (N × H)
288. #2852	C₂×C₁₃	semidirect
289. #2807	C₂×C₁₃	semidirect
291. #2776	C₂×C₁₃	semidirect
292. #2748	C₂×C₁₃	semidirect
293. #2746	C₂×C₁₃	semidirect
294. #2738	C₂×C₁₃	semidirect
295. #2727	C₂×C₁₃	semidirect
296. #2722	C₂×C₁₃	semidirect
297. #2654	C₂×C₁₃	semidirect
298. #2611	C₂×C₁₃	semidirect
299. #2606	C₂×C₁₃	semidirect
301. #2594	C₂×C₁₃	semidirect
302. #2562	C₂×C₁₃	semidirect
303. #2479	C₂×C₁₃	semidirect
304. #2336	C₂×C₁₃	semidirect
305. #2319	C₂×C₁₃	semidirect
306. #2296	C₂×C₁₃	semidirect
680. C₁₃	#36831	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×#2852	2
C₁₃×#2807	2
C₁₃×#2797	2
C₁₃×#2776	2
C₁₃×#2748	2
C₁₃×#2746	2
C₁₃×#2738	2
C₁₃×#2727	2
C₁₃×#2722	2
C₁₃×#2654	2
C₁₃×#2611	2
C₁₃×#2606	2
C₁₃×#2598	2
C₁₃×#2594	2
C₁₃×#2562	2
C₁₃×#2479	2
C₁₃×#2336	2
C₁₃×#2319	2
C₁₃×#2296	2
#36831	13

Subgroups — C13×#36831 #15723170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36831 #15723170