Subgroups — C₁₃×#34503 #15720842

Order 3328.

2140 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2381	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2367	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2314	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₁₃×#555	C₄	1	16	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
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
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	2	yes	—
43	C₁₃×#388	C₂²	1	2	yes	—
44	C₁₃×#388	C₂²	1	2	yes	—
45	C₁₃×#388	C₂²	1	2	yes	—
46	C₁₃×#388	C₂²	1	2	yes	—
47	C₁₃×#388	C₂²	1	2	yes	—
48	C₁₃×#388	C₂²	1	2	yes	—
49	C₁₃×#388	C₂²	1	2	yes	—
50	C₁₃×#388	C₂²	1	2	yes	—
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
55	C₁₃×#387	C₂²	1	2	yes	—
56	C₁₃×#387	C₂²	1	2	yes	—
57	C₁₃×#387	C₂²	1	2	yes	—
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	2	yes	—
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#386	C₂²	1	2	yes	—
71	C₁₃×#386	C₂²	1	2	yes	—
72	C₁₃×#386	C₂²	1	2	yes	—
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	2	yes	—
75	C₁₃×#385	C₂²	1	2	yes	—
76	C₁₃×#385	C₂²	1	2	yes	—
77	C₁₃×#385	C₂²	1	2	yes	—
78	C₁₃×#385	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#384	C₂²	1	1	yes	characteristic
82	C₁₃×#383	C₂²	1	2	yes	—
83	C₁₃×#383	C₂²	1	2	yes	—
84	C₁₃×#382	C₂²	1	1	yes	characteristic
85	C₁₃×#382	C₂²	1	2	yes	—
86	C₁₃×#382	C₂²	1	1	yes	characteristic
87	C₁₃×#381	C₂²	1	2	yes	—
88	C₁₃×#381	C₂²	1	2	yes	—
89	C₁₃×#380	C₂²	1	2	yes	—
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₁₃×#376	C₂²	1	2	yes	—
103	C₁₃×#376	C₂²	1	1	yes	characteristic
104	C₁₃×#376	C₂²	1	1	yes	characteristic
105	C₂×C₁₃×#95	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₄³×C₁₃	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
121	C₁₃×#124	C₂×C₄	1	8	yes	complemented
122	C₁₃×#124	C₂×C₄	1	8	yes	complemented
123	C₁₃×#124	C₂×C₄	1	16	yes	complemented
124	C₁₃×#121	C₂×C₄	1	16	yes	complemented
125	C₁₃×#121	C₂×C₄	1	16	yes	complemented
126	C₄×Q₈×C₁₃	—	4	2	no	—
127	C₄×Q₈×C₁₃	—	4	2	no	—
128	C₄×D₄×C₁₃	—	4	2	no	—
129	C₄×D₄×C₁₃	—	4	2	no	—
130	C₄×D₄×C₁₃	—	4	4	no	—
131	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
132	C₁₃×#117	C₂×C₄	1	16	yes	complemented
133	C₁₃×#117	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×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×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	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	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	C₁₃×#95	C₂³	1	2	yes	—
209	#34503	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
211	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
212	C₂×Q₈×C₁₃	—	4	1	no	—
213	C₂×Q₈×C₁₃	—	4	1	no	—
214	C₂×Q₈×C₁₃	—	4	1	no	—
215	C₂×Q₈×C₁₃	—	4	1	no	—
216	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
217	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
218	C₂×D₄×C₁₃	—	4	1	no	—
219	C₂×D₄×C₁₃	—	4	1	no	—
220	C₂×D₄×C₁₃	—	4	2	no	—
221	C₂×D₄×C₁₃	—	4	1	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	—	4	2	no	—
224	C₂×D₄×C₁₃	—	4	2	no	—
225	C₂×D₄×C₁₃	—	4	2	no	—
226	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
227	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
228	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
229	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	2	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
247	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	2	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	1	no	—
272	C₁₃×C₄⋊C₄	—	4	1	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
278	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
279	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	4	2	no	—
284	C₁₃×C₂²⋊C₄	—	4	2	no	—
285	C₁₃×C₂²⋊C₄	—	4	2	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	—	4	2	no	—
288	C₁₃×C₂²⋊C₄	—	4	2	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
293	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
294	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
295	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
296	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
297	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
298	C₄²×C₁₃	—	2	2	no	—
299	C₄²×C₁₃	—	2	2	no	—
300	C₄²×C₁₃	—	2	2	no	—
301	C₄²×C₁₃	—	4	2	no	—
302	C₄²×C₁₃	—	4	2	no	—
303	C₄²×C₁₃	—	4	2	no	—
304	C₄²×C₁₃	—	4	2	no	—
305	C₄²×C₁₃	—	4	1	no	—
306	C₄²×C₁₃	—	4	1	no	—
307	C₄²×C₁₃	—	4	1	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	C₄²×C₁₃	—	4	2	no	—
310	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
311	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
312	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
313	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
314	C₂×#555	C₂×C₁₃	1	1	yes	characteristic
315	#2381	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#2379	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2377	C₂×C₁₃	1	2	yes	complemented
318	#2372	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#2367	C₂×C₁₃	1	2	yes	complemented
320	#2364	C₂×C₁₃	1	2	yes	complemented
321	#2353	C₂×C₁₃	1	2	yes	complemented
322	#2343	C₂×C₁₃	1	2	yes	complemented
323	#2343	C₂×C₁₃	1	2	yes	complemented
324	#2337	C₂×C₁₃	1	2	yes	complemented
325	#2333	C₂×C₁₃	1	2	yes	complemented
326	#2327	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2325	C₂×C₁₃	1	2	yes	complemented
329	#2318	C₂×C₁₃	1	2	yes	complemented
330	#2314	C₂×C₁₃	1	2	yes	complemented
331	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2298	C₂×C₁₃	1	2	yes	complemented
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	2	no	—
339	C₂³×C₁₃	—	2	2	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	C₂³×C₄	1	4	yes	—
346	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
347	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
348	Q₈×C₁₃	—	4	4	no	—
349	Q₈×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	8	no	—
351	D₄×C₁₃	—	4	4	no	—
352	D₄×C₁₃	—	4	4	no	—
353	D₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	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	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	2	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	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	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	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
394	C₂×C₄×C₁₃	—	4	8	no	—
395	C₂×C₄×C₁₃	—	8	4	no	—
396	C₂×C₄×C₁₃	—	8	4	no	—
397	C₂×C₄×C₁₃	—	8	4	no	—
398	C₂×C₄×C₁₃	—	8	4	no	—
399	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
401	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
404	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
407	#555	C₄×C₁₃	1	16	yes	complemented
408	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#124	C₂²×C₁₃	1	2	yes	—
411	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#121	C₂²×C₁₃	1	2	yes	—
413	C₂×#121	C₂²×C₁₃	1	2	yes	—
414	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
420	C₂×#117	C₂²×C₁₃	1	2	yes	—
421	C₂×#117	C₂²×C₁₃	1	2	yes	—
422	#391	C₂²×C₁₃	1	1	yes	characteristic
423	#391	C₂²×C₁₃	1	1	yes	characteristic
424	#391	C₂²×C₁₃	1	1	yes	characteristic
425	#391	C₂²×C₁₃	1	2	yes	—
426	#391	C₂²×C₁₃	1	1	yes	characteristic
427	#390	C₂²×C₁₃	1	1	yes	characteristic
428	#390	C₂²×C₁₃	1	2	yes	—
429	#390	C₂²×C₁₃	1	1	yes	characteristic
430	#388	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	2	yes	—
432	#388	C₂²×C₁₃	1	2	yes	—
433	#388	C₂²×C₁₃	1	2	yes	—
434	#388	C₂²×C₁₃	1	2	yes	—
435	#388	C₂²×C₁₃	1	2	yes	—
436	#388	C₂²×C₁₃	1	2	yes	—
437	#388	C₂²×C₁₃	1	2	yes	—
438	#388	C₂²×C₁₃	1	2	yes	—
439	#388	C₂²×C₁₃	1	2	yes	—
440	#388	C₂²×C₁₃	1	2	yes	—
441	#388	C₂²×C₁₃	1	2	yes	—
442	#387	C₂²×C₁₃	1	2	yes	—
443	#387	C₂²×C₁₃	1	2	yes	—
444	#387	C₂²×C₁₃	1	2	yes	—
445	#387	C₂²×C₁₃	1	2	yes	—
446	#387	C₂²×C₁₃	1	2	yes	—
447	#387	C₂²×C₁₃	1	2	yes	—
448	#387	C₂²×C₁₃	1	2	yes	—
449	#387	C₂²×C₁₃	1	2	yes	—
450	#387	C₂²×C₁₃	1	2	yes	—
451	#387	C₂²×C₁₃	1	2	yes	—
452	#387	C₂²×C₁₃	1	2	yes	—
453	#387	C₂²×C₁₃	1	2	yes	—
454	#386	C₂²×C₁₃	1	2	yes	—
455	#386	C₂²×C₁₃	1	2	yes	—
456	#386	C₂²×C₁₃	1	2	yes	—
457	#386	C₂²×C₁₃	1	2	yes	—
458	#386	C₂²×C₁₃	1	2	yes	—
459	#386	C₂²×C₁₃	1	2	yes	—
460	#386	C₂²×C₁₃	1	2	yes	—
461	#386	C₂²×C₁₃	1	2	yes	—
462	#385	C₂²×C₁₃	1	2	yes	—
463	#385	C₂²×C₁₃	1	2	yes	—
464	#385	C₂²×C₁₃	1	2	yes	—
465	#385	C₂²×C₁₃	1	2	yes	—
466	#385	C₂²×C₁₃	1	2	yes	—
467	#385	C₂²×C₁₃	1	2	yes	—
468	#384	C₂²×C₁₃	1	1	yes	characteristic
469	#383	C₂²×C₁₃	1	2	yes	—
470	#383	C₂²×C₁₃	1	2	yes	—
471	#382	C₂²×C₁₃	1	2	yes	—
472	#382	C₂²×C₁₃	1	1	yes	characteristic
473	#382	C₂²×C₁₃	1	1	yes	characteristic
474	#381	C₂²×C₁₃	1	2	yes	—
475	#381	C₂²×C₁₃	1	2	yes	—
476	#380	C₂²×C₁₃	1	2	yes	—
477	#380	C₂²×C₁₃	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
489	#376	C₂²×C₁₃	1	1	yes	characteristic
490	#376	C₂²×C₁₃	1	1	yes	characteristic
491	#376	C₂²×C₁₃	1	2	yes	—
492	C₂×#95	C₂²×C₁₃	1	2	yes	—
493	C₂×#95	C₂²×C₁₃	1	2	yes	—
494	C₄³	C₂²×C₁₃	1	1	yes	characteristic
495	C₂²×C₁₃	—	2	4	no	—
496	C₂²×C₁₃	—	2	4	no	—
497	C₂²×C₁₃	—	2	4	no	—
498	C₂²×C₁₃	—	2	4	no	—
499	C₂²×C₁₃	—	2	4	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
510	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂²×C₁₃	#585	1	2	yes	—
512	C₂²×C₁₃	#585	1	2	yes	—
513	C₂²×C₁₃	#585	1	1	yes	characteristic
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	2	4	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
541	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
542	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
543	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
544	#124	C₂×C₄×C₁₃	1	8	yes	complemented
545	#124	C₂×C₄×C₁₃	1	16	yes	complemented
546	#124	C₂×C₄×C₁₃	1	8	yes	complemented
547	#121	C₂×C₄×C₁₃	1	16	yes	complemented
548	#121	C₂×C₄×C₁₃	1	16	yes	complemented
549	C₄×Q₈	—	4	2	no	—
550	C₄×Q₈	—	4	2	no	—
551	C₄×D₄	—	4	2	no	—
552	C₄×D₄	—	4	2	no	—
553	C₄×D₄	—	4	4	no	—
554	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
555	#117	C₂×C₄×C₁₃	1	16	yes	complemented
556	#117	C₂×C₄×C₁₃	1	16	yes	complemented
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊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	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	2	yes	—
610	#95	C₂³×C₁₃	1	2	yes	—
611	#95	C₂³×C₁₃	1	2	yes	—
612	#95	C₂³×C₁₃	1	2	yes	—
613	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	4	4	no	—
633	C₂×C₁₃	—	4	4	no	—
634	C₂×C₁₃	#3428	1	2	yes	—
635	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×C₁₃	#3545	1	1	yes	characteristic
637	C₂×C₁₃	#3551	1	1	yes	characteristic
638	C₂×C₁₃	#3566	1	2	yes	—
639	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
640	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	1	no	—
645	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
646	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	1	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
656	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
657	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
658	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
659	C₂²×C₄	—	2	4	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	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
676	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	1	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
707	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
708	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	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	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
722	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
723	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
724	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
725	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
726	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	4	2	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	1	no	—
737	C₄²	—	4	1	no	—
738	C₄²	—	4	1	no	—
739	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
740	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
741	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
742	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
743	C₁₃	#34503	1	1	yes	characteristic, direct product factor, Sylow
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
757	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
758	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
759	Q₈	—	4	4	no	—
760	Q₈	—	4	4	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	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	2	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	—	4	8	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	—	8	4	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
811	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
812	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
815	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
816	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
817	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
833	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
834	C₂²	C₁₃×#585	1	2	yes	—
835	C₂²	C₁₃×#585	1	2	yes	—
836	C₂²	C₁₃×#585	1	1	yes	characteristic
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	4	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₂	—	4	4	no	—
855	C₂	—	4	4	no	—
856	C₂	C₁₃×#3428	1	2	yes	—
857	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂	C₁₃×#3545	1	1	yes	characteristic
859	C₂	C₁₃×#3551	1	1	yes	characteristic
860	C₂	C₁₃×#3566	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#555	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2381	C₂	semidirect
3. C₁₃×#2379	C₂	semidirect
4. C₁₃×#2377	C₂	semidirect
5. C₁₃×#2372	C₂	semidirect
6. C₁₃×#2367	C₂	semidirect
7. C₁₃×#2364	C₂	semidirect
8. C₁₃×#2353	C₂	semidirect
9. C₁₃×#2343	C₂	semidirect
10. C₁₃×#2343	C₂	semidirect
11. C₁₃×#2337	C₂	semidirect
12. C₁₃×#2333	C₂	semidirect
13. C₁₃×#2327	C₂	semidirect
14. C₁₃×#2326	C₂	semidirect
15. C₁₃×#2325	C₂	semidirect
16. C₁₃×#2318	C₂	semidirect
17. C₁₃×#2314	C₂	semidirect
18. C₄×C₁₃×#124	C₂	semidirect
19. C₁₃×#2298	C₂	semidirect
20. C₁₃×#555	C₄	semidirect
120. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
121. C₁₃×#124	C₂×C₄	semidirect
122. C₁₃×#124	C₂×C₄	semidirect
123. C₁₃×#124	C₂×C₄	semidirect
124. C₁₃×#121	C₂×C₄	semidirect
125. C₁₃×#121	C₂×C₄	semidirect
131. C₄×D₄×C₁₃	C₂×C₄	semidirect
132. C₁₃×#117	C₂×C₄	semidirect
133. C₁₃×#117	C₂×C₄	semidirect
209. #34503	C₁₃	direct (N × H)
315. #2381	C₂×C₁₃	semidirect
316. #2379	C₂×C₁₃	semidirect
317. #2377	C₂×C₁₃	semidirect
318. #2372	C₂×C₁₃	semidirect
319. #2367	C₂×C₁₃	semidirect
320. #2364	C₂×C₁₃	semidirect
321. #2353	C₂×C₁₃	semidirect
322. #2343	C₂×C₁₃	semidirect
323. #2343	C₂×C₁₃	semidirect
324. #2337	C₂×C₁₃	semidirect
325. #2333	C₂×C₁₃	semidirect
326. #2327	C₂×C₁₃	semidirect
327. #2326	C₂×C₁₃	semidirect
328. #2325	C₂×C₁₃	semidirect
329. #2318	C₂×C₁₃	semidirect
330. #2314	C₂×C₁₃	semidirect
331. C₄×#124	C₂×C₁₃	semidirect
332. #2298	C₂×C₁₃	semidirect
407. #555	C₄×C₁₃	semidirect
543. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
544. #124	C₂×C₄×C₁₃	semidirect
545. #124	C₂×C₄×C₁₃	semidirect
546. #124	C₂×C₄×C₁₃	semidirect
547. #121	C₂×C₄×C₁₃	semidirect
548. #121	C₂×C₄×C₁₃	semidirect
554. C₄×D₄	C₂×C₄×C₁₃	semidirect
555. #117	C₂×C₄×C₁₃	semidirect
556. #117	C₂×C₄×C₁₃	semidirect
743. C₁₃	#34503	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×#555	2
C₁₃×#2381	2
C₁₃×#2379	2
C₁₃×#2377	2
C₁₃×#2372	2
C₁₃×#2367	2
C₁₃×#2364	2
C₁₃×#2353	2
C₁₃×#2343	2
C₁₃×#2337	2
C₁₃×#2333	2
C₁₃×#2327	2
C₁₃×#2326	2
C₁₃×#2325	2
C₁₃×#2318	2
C₁₃×#2314	2
C₄×C₁₃×#124	2
C₁₃×#2298	2
#34503	13

Subgroups — C13×#34503 #15720842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34503 #15720842