Subgroups — C₁₃×#36930 #15723269

Order 3328.

1870 conjugacy classes of subgroups.

The subgroup lattice has 864 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×#2786	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2768	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2736	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2729	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2723	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2722	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2702	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2685	C₂	1	2	yes	maximal
11	C₁₃×#2677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2633	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2577	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2556	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2468	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2452	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
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	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	complemented
33	C₁₃×#399	C₂²	1	2	yes	—
34	C₁₃×#399	C₂²	1	1	yes	characteristic
35	C₁₃×#399	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#398	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#398	C₂²	1	2	yes	complemented
38	C₁₃×#398	C₂²	1	2	yes	complemented
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#398	C₂²	1	2	yes	complemented
41	C₁₃×#398	C₂²	1	2	yes	complemented
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	1	yes	characteristic
45	C₁₃×#397	C₂²	1	1	yes	characteristic
46	C₁₃×#397	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#397	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
53	C₁₃×#394	C₂²	1	2	yes	—
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#394	C₂²	1	2	yes	—
57	C₁₃×#393	C₂²	1	1	yes	characteristic
58	C₁₃×#393	C₂²	1	2	yes	—
59	C₁₃×#393	C₂²	1	2	yes	complemented
60	C₁₃×#391	C₂²	1	2	yes	complemented
61	C₁₃×#390	C₂²	1	2	yes	—
62	C₁₃×#390	C₂²	1	2	yes	—
63	C₁₃×#389	C₂²	1	2	yes	complemented
64	C₁₃×#389	C₂²	1	2	yes	complemented
65	C₁₃×#389	C₂²	1	2	yes	complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
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×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#387	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#387	C₂²	1	2	yes	complemented
82	C₁₃×#387	C₂²	1	2	yes	complemented
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	1	yes	characteristic
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	—
93	C₁₃×#385	C₂²	1	2	yes	complemented
94	C₁₃×#383	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#382	C₂²	1	2	yes	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×C₄⋊C₄	C₂²	1	2	yes	complemented
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	—	4	4	no	—
120	C₁₃×#126	—	2	8	no	—
121	C₁₃×#126	—	4	4	no	—
122	C₁₃×#125	—	4	2	no	—
123	C₁₃×C₂²⋊Q₈	—	4	4	no	—
124	C₁₃×C₂²⋊Q₈	—	4	4	no	—
125	C₁₃×C₂²⋊Q₈	—	4	2	no	—
126	C₁₃×C₂²⋊Q₈	—	4	4	no	—
127	C₁₃×#120	—	2	4	no	—
128	C₄×D₄×C₁₃	—	4	2	no	—
129	C₄×D₄×C₁₃	—	4	4	no	—
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×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊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	1	yes	characteristic
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×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	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
195	C₁₃×#95	C₂³	1	1	yes	characteristic
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	1	yes	characteristic
198	C₁₃×#95	C₂³	1	1	yes	characteristic
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	#36930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	—	2	2	no	—
209	C₂⁴×C₁₃	—	2	4	no	—
210	C₂⁴×C₁₃	—	4	2	no	—
211	C₂⁴×C₁₃	—	4	1	no	—
212	C₂⁴×C₁₃	—	4	1	no	—
213	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃	—	2	4	no	—
217	C₂×Q₈×C₁₃	—	4	2	no	—
218	C₂×Q₈×C₁₃	—	4	2	no	—
219	C₂×Q₈×C₁₃	—	4	1	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	2	4	no	—
224	C₂×D₄×C₁₃	—	4	2	no	—
225	C₂×D₄×C₁₃	—	4	1	no	—
226	C₂×D₄×C₁₃	—	4	1	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	1	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	16	no	—
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	4	2	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	1	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	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×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	—	4	2	no	—
288	C₁₃×C₂²⋊C₄	—	4	1	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₁₃×C₂²⋊C₄	—	4	1	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	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	#41	1	4	yes	—
303	C₄²×C₁₃	—	2	4	no	—
304	C₄²×C₁₃	—	2	2	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	C₄²×C₁₃	—	4	2	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	#2848	C₂×C₁₃	1	2	yes	complemented
310	#2786	C₂×C₁₃	1	2	yes	complemented
311	#2768	C₂×C₁₃	1	2	yes	complemented
312	#2736	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2735	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2729	C₂×C₁₃	1	2	yes	complemented
315	#2723	C₂×C₁₃	1	2	yes	complemented
316	#2722	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2702	C₂×C₁₃	1	2	yes	complemented
318	#2685	C₂×C₁₃	1	2	yes	—
319	#2677	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#2638	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2633	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2577	C₂×C₁₃	1	2	yes	complemented
323	#2556	C₂×C₁₃	1	2	yes	complemented
324	#2468	C₂×C₁₃	1	2	yes	complemented
325	#2452	C₂×C₁₃	1	2	yes	complemented
326	#2334	C₂×C₁₃	1	2	yes	complemented
327	C₄×#120	C₂×C₁₃	1	1	yes	characteristic
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	1	no	—
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	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	1	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	4	8	no	—
344	C₂³×C₁₃	—	4	4	no	—
345	C₂³×C₁₃	—	4	4	no	—
346	C₂³×C₁₃	—	4	8	no	—
347	C₂³×C₁₃	—	4	4	no	—
348	C₂³×C₁₃	C₂×#41	1	2	yes	—
349	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
350	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃	—	8	4	no	—
352	Q₈×C₁₃	—	8	2	no	—
353	D₄×C₁₃	—	4	8	no	—
354	D₄×C₁₃	—	4	4	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	1	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	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	2	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	1	no	—
382	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	4	8	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	4	no	—
399	C₂×C₄×C₁₃	—	4	8	no	—
400	C₂×C₄×C₁₃	—	8	2	no	—
401	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
402	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
404	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
406	C₂×#126	C₂²×C₁₃	1	2	yes	—
407	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
408	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
410	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
411	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
416	#400	C₂²×C₁₃	1	2	yes	complemented
417	#399	C₂²×C₁₃	1	1	yes	characteristic
418	#399	C₂²×C₁₃	1	2	yes	—
419	#399	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#398	C₂²×C₁₃	1	2	yes	complemented
421	#398	C₂²×C₁₃	1	2	yes	complemented
422	#398	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#398	C₂²×C₁₃	1	2	yes	complemented
424	#398	C₂²×C₁₃	1	2	yes	complemented
425	#398	C₂²×C₁₃	1	2	yes	complemented
426	#397	C₂²×C₁₃	1	2	yes	—
427	#397	C₂²×C₁₃	1	2	yes	—
428	#397	C₂²×C₁₃	1	1	yes	characteristic
429	#397	C₂²×C₁₃	1	1	yes	characteristic
430	#397	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#397	C₂²×C₁₃	1	2	yes	complemented
432	#396	C₂²×C₁₃	1	2	yes	—
433	#396	C₂²×C₁₃	1	2	yes	—
434	#396	C₂²×C₁₃	1	2	yes	complemented
435	#395	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#395	C₂²×C₁₃	1	2	yes	complemented
437	#394	C₂²×C₁₃	1	2	yes	—
438	#394	C₂²×C₁₃	1	2	yes	—
439	#394	C₂²×C₁₃	1	2	yes	—
440	#394	C₂²×C₁₃	1	2	yes	—
441	#393	C₂²×C₁₃	1	1	yes	characteristic
442	#393	C₂²×C₁₃	1	2	yes	—
443	#393	C₂²×C₁₃	1	2	yes	complemented
444	#391	C₂²×C₁₃	1	2	yes	complemented
445	#390	C₂²×C₁₃	1	2	yes	—
446	#390	C₂²×C₁₃	1	2	yes	—
447	#389	C₂²×C₁₃	1	2	yes	complemented
448	#389	C₂²×C₁₃	1	2	yes	complemented
449	#389	C₂²×C₁₃	1	2	yes	complemented
450	#389	C₂²×C₁₃	1	2	yes	complemented
451	#388	C₂²×C₁₃	1	2	yes	—
452	#388	C₂²×C₁₃	1	2	yes	—
453	#388	C₂²×C₁₃	1	2	yes	—
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	complemented
461	#387	C₂²×C₁₃	1	2	yes	complemented
462	#387	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	#386	C₂²×C₁₃	1	1	yes	characteristic
468	#386	C₂²×C₁₃	1	2	yes	—
469	#385	C₂²×C₁₃	1	2	yes	—
470	#385	C₂²×C₁₃	1	2	yes	—
471	#385	C₂²×C₁₃	1	2	yes	—
472	#385	C₂²×C₁₃	1	2	yes	—
473	#385	C₂²×C₁₃	1	2	yes	—
474	#385	C₂²×C₁₃	1	2	yes	—
475	#385	C₂²×C₁₃	1	1	yes	characteristic
476	#385	C₂²×C₁₃	1	2	yes	—
477	#385	C₂²×C₁₃	1	2	yes	complemented
478	#383	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#382	C₂²×C₁₃	1	2	yes	complemented
480	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#380	C₂²×C₁₃	1	2	yes	—
482	#380	C₂²×C₁₃	1	2	yes	—
483	#380	C₂²×C₁₃	1	2	yes	—
484	#379	C₂²×C₁₃	1	2	yes	—
485	#379	C₂²×C₁₃	1	2	yes	—
486	#379	C₂²×C₁₃	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
488	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
489	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	4	no	—
493	C₂²×C₁₃	—	2	4	no	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	2	4	no	—
496	C₂²×C₁₃	—	4	16	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
512	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
513	C₂²×C₁₃	#585	1	1	yes	characteristic
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	4	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
532	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	—	4	4	no	—
536	C₂³×C₄	—	4	2	no	—
537	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
538	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
542	C₄⋊Q₈	—	4	4	no	—
543	#126	—	2	8	no	—
544	#126	—	4	4	no	—
545	#125	—	4	2	no	—
546	C₂²⋊Q₈	—	4	4	no	—
547	C₂²⋊Q₈	—	4	4	no	—
548	C₂²⋊Q₈	—	4	2	no	—
549	C₂²⋊Q₈	—	4	4	no	—
550	#120	—	2	4	no	—
551	C₄×D₄	—	4	2	no	—
552	C₄×D₄	—	4	4	no	—
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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×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	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×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	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
618	#95	C₂³×C₁₃	1	1	yes	characteristic
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	1	yes	characteristic
621	#95	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	4	2	no	—
631	C₂×C₁₃	—	4	4	no	—
632	C₂×C₁₃	—	8	1	no	—
633	C₂×C₁₃	#3460	1	1	yes	characteristic
634	C₂×C₁₃	#3520	1	2	yes	—
635	C₂×C₁₃	#3532	1	1	yes	characteristic
636	C₂×C₁₃	#3538	1	1	yes	characteristic
637	C₂×C₁₃	#3541	1	2	yes	—
638	C₂⁴	—	2	2	no	—
639	C₂⁴	—	2	4	no	—
640	C₂⁴	—	4	2	no	—
641	C₂⁴	—	4	1	no	—
642	C₂⁴	—	4	1	no	—
643	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
645	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	4	2	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	—	4	1	no	—
650	C₂×Q₈	—	4	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	1	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	16	no	—
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	yes	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	1	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	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	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	2	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	2	no	—
739	C₁₃	#36930	1	1	yes	characteristic, direct product factor, Sylow
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	4	8	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	C₂×C₁₃×#41	1	2	yes	—
761	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
762	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
763	Q₈	—	8	4	no	—
764	Q₈	—	8	2	no	—
765	D₄	—	4	8	no	—
766	D₄	—	4	4	no	—
767	C₂×C₄	—	2	2	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	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	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	1	no	—
794	C₂×C₄	—	2	1	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	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
814	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
815	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	4	16	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
835	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
836	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
838	C₂²	C₁₃×#585	1	1	yes	characteristic
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	4	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₂	—	4	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₁₃×#3460	1	1	yes	characteristic
859	C₂	C₁₃×#3520	1	2	yes	—
860	C₂	C₁₃×#3532	1	1	yes	characteristic
861	C₂	C₁₃×#3538	1	1	yes	characteristic
862	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×#2786	C₂	semidirect
3. C₁₃×#2768	C₂	semidirect
4. C₁₃×#2736	C₂	semidirect
5. C₁₃×#2735	C₂	semidirect
6. C₁₃×#2729	C₂	semidirect
7. C₁₃×#2723	C₂	semidirect
8. C₁₃×#2722	C₂	semidirect
9. C₁₃×#2702	C₂	semidirect
11. C₁₃×#2677	C₂	semidirect
12. C₁₃×#2638	C₂	semidirect
13. C₁₃×#2633	C₂	semidirect
14. C₁₃×#2577	C₂	semidirect
15. C₁₃×#2556	C₂	semidirect
16. C₁₃×#2468	C₂	semidirect
17. C₁₃×#2452	C₂	semidirect
18. C₁₃×#2334	C₂	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#126	C₂²	semidirect
24. C₂×C₁₃×#125	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×#400	C₂²	semidirect
35. C₁₃×#399	C₂²	semidirect
36. C₁₃×#398	C₂²	semidirect
37. C₁₃×#398	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
47. C₁₃×#397	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
59. C₁₃×#393	C₂²	semidirect
60. C₁₃×#391	C₂²	semidirect
63. C₁₃×#389	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
76. C₁₃×#388	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
79. C₁₃×#387	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
81. C₁₃×#387	C₂²	semidirect
82. C₁₃×#387	C₂²	semidirect
93. C₁₃×#385	C₂²	semidirect
94. C₁₃×#383	C₂²	semidirect
95. C₁₃×#382	C₂²	semidirect
96. C₁₃×#381	C₂²	semidirect
103. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
104. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
207. #36930	C₁₃	direct (N × H)
309. #2848	C₂×C₁₃	semidirect
310. #2786	C₂×C₁₃	semidirect
311. #2768	C₂×C₁₃	semidirect
312. #2736	C₂×C₁₃	semidirect
313. #2735	C₂×C₁₃	semidirect
314. #2729	C₂×C₁₃	semidirect
315. #2723	C₂×C₁₃	semidirect
316. #2722	C₂×C₁₃	semidirect
317. #2702	C₂×C₁₃	semidirect
319. #2677	C₂×C₁₃	semidirect
320. #2638	C₂×C₁₃	semidirect
321. #2633	C₂×C₁₃	semidirect
322. #2577	C₂×C₁₃	semidirect
323. #2556	C₂×C₁₃	semidirect
324. #2468	C₂×C₁₃	semidirect
325. #2452	C₂×C₁₃	semidirect
326. #2334	C₂×C₁₃	semidirect
405. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
407. C₂×#126	C₂²×C₁₃	semidirect
408. C₂×#125	C₂²×C₁₃	semidirect
412. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
416. #400	C₂²×C₁₃	semidirect
419. #399	C₂²×C₁₃	semidirect
420. #398	C₂²×C₁₃	semidirect
421. #398	C₂²×C₁₃	semidirect
422. #398	C₂²×C₁₃	semidirect
423. #398	C₂²×C₁₃	semidirect
424. #398	C₂²×C₁₃	semidirect
425. #398	C₂²×C₁₃	semidirect
430. #397	C₂²×C₁₃	semidirect
431. #397	C₂²×C₁₃	semidirect
434. #396	C₂²×C₁₃	semidirect
435. #395	C₂²×C₁₃	semidirect
436. #395	C₂²×C₁₃	semidirect
443. #393	C₂²×C₁₃	semidirect
444. #391	C₂²×C₁₃	semidirect
447. #389	C₂²×C₁₃	semidirect
448. #389	C₂²×C₁₃	semidirect
449. #389	C₂²×C₁₃	semidirect
450. #389	C₂²×C₁₃	semidirect
460. #388	C₂²×C₁₃	semidirect
461. #387	C₂²×C₁₃	semidirect
462. #387	C₂²×C₁₃	semidirect
463. #387	C₂²×C₁₃	semidirect
464. #387	C₂²×C₁₃	semidirect
465. #387	C₂²×C₁₃	semidirect
466. #387	C₂²×C₁₃	semidirect
477. #385	C₂²×C₁₃	semidirect
478. #383	C₂²×C₁₃	semidirect
479. #382	C₂²×C₁₃	semidirect
480. #381	C₂²×C₁₃	semidirect
487. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
488. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
739. C₁₃	#36930	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×#2786	2
C₁₃×#2768	2
C₁₃×#2736	2
C₁₃×#2735	2
C₁₃×#2729	2
C₁₃×#2723	2
C₁₃×#2722	2
C₁₃×#2702	2
C₁₃×#2685	2
C₁₃×#2677	2
C₁₃×#2638	2
C₁₃×#2633	2
C₁₃×#2577	2
C₁₃×#2556	2
C₁₃×#2468	2
C₁₃×#2452	2
C₁₃×#2334	2
C₄×C₁₃×#120	2
#36930	13

Subgroups — C13×#36930 #15723269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36930 #15723269