Subgroups — C₁₃×#36748 #15723087

Order 3328.

1858 conjugacy classes of subgroups.

The subgroup lattice has 852 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
2	C₁₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2790	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2788	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2768	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2729	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2720	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2704	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2569	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2549	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2442	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2440	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2312	C₂	1	2	yes	maximal
19	C₂×C₁₃×#385	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×#125	C₂²	1	2	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₁₃×#400	C₂²	1	2	yes	complemented
32	C₁₃×#400	C₂²	1	2	yes	complemented
33	C₁₃×#400	C₂²	1	2	yes	complemented
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#399	C₂²	1	1	yes	characteristic
36	C₁₃×#399	C₂²	1	1	yes	characteristic
37	C₁₃×#399	C₂²	1	1	yes	characteristic
38	C₁₃×#399	C₂²	1	1	yes	characteristic
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×#398	C₂²	1	2	yes	complemented
43	C₁₃×#398	C₂²	1	2	yes	complemented
44	C₁₃×#398	C₂²	1	2	yes	complemented
45	C₁₃×#398	C₂²	1	2	yes	complemented
46	C₁₃×#398	C₂²	1	2	yes	complemented
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#395	C₂²	1	2	yes	complemented
54	C₁₃×#395	C₂²	1	2	yes	complemented
55	C₁₃×#393	C₂²	1	1	yes	characteristic
56	C₁₃×#393	C₂²	1	1	yes	characteristic
57	C₁₃×#393	C₂²	1	1	yes	characteristic
58	C₁₃×#393	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	2	yes	complemented
60	C₁₃×#391	C₂²	1	2	yes	complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	2	yes	complemented
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×#387	C₂²	1	2	yes	complemented
76	C₁₃×#387	C₂²	1	2	yes	complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	1	yes	characteristic
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	1	yes	characteristic
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	1	yes	characteristic
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×#384	C₂²	1	2	yes	complemented
94	C₁₃×#382	C₂²	1	2	yes	complemented
95	C₁₃×#380	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	2	yes	—
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	1	yes	characteristic
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#380	C₂²	1	2	yes	—
101	C₁₃×#380	C₂²	1	1	yes	characteristic
102	C₁₃×#379	C₂²	1	2	yes	—
103	C₁₃×#379	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	—	4	4	no	—
112	C₂³×C₄×C₁₃	—	4	2	no	—
113	C₂³×C₄×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	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	—	4	4	no	—
121	C₁₃×#125	—	4	4	no	—
122	C₁₃×C₂²⋊Q₈	—	4	4	no	—
123	C₁₃×C₂²⋊Q₈	—	4	2	no	—
124	C₁₃×C₂²⋊Q₈	—	4	2	no	—
125	C₁₃×C₂²⋊Q₈	—	4	4	no	—
126	C₁₃×C₂²⋊Q₈	—	4	4	no	—
127	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
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×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
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×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	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	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	2	yes	—
184	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
194	C₁₃×#95	C₂³	1	1	yes	characteristic
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	1	yes	characteristic
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	#36748	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂⁴×C₁₃	—	2	2	no	—
208	C₂⁴×C₁₃	—	2	2	no	—
209	C₂⁴×C₁₃	—	4	2	no	—
210	C₂⁴×C₁₃	—	4	2	no	—
211	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
212	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂×Q₈×C₁₃	—	2	4	no	—
216	C₂×Q₈×C₁₃	—	4	2	no	—
217	C₂×Q₈×C₁₃	—	4	2	no	—
218	C₂×Q₈×C₁₃	—	4	1	no	—
219	C₂×Q₈×C₁₃	—	4	1	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	4	2	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	2	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	1	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	16	no	—
239	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
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	2	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	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	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	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	—	4	2	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	2	no	—
272	C₁₃×C₄⋊C₄	—	4	1	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	4	1	no	—
288	C₁₃×C₂²⋊C₄	—	4	1	no	—
289	C₁₃×C₂²⋊C₄	—	4	1	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	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	C₂×Q₈	1	4	yes	—
300	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
301	C₁₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
302	C₄²×C₁₃	—	4	2	no	—
303	C₄²×C₁₃	—	4	2	no	—
304	C₄²×C₁₃	—	4	2	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	#2848	C₂×C₁₃	1	2	yes	—
307	#2807	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#2790	C₂×C₁₃	1	2	yes	complemented
309	#2788	C₂×C₁₃	1	2	yes	complemented
310	#2768	C₂×C₁₃	1	2	yes	complemented
311	#2763	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2742	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2729	C₂×C₁₃	1	2	yes	complemented
314	#2720	C₂×C₁₃	1	2	yes	complemented
315	#2704	C₂×C₁₃	1	2	yes	complemented
316	#2677	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2626	C₂×C₁₃	1	1	yes	characteristic
318	#2626	C₂×C₁₃	1	1	yes	characteristic
319	#2569	C₂×C₁₃	1	2	yes	complemented
320	#2549	C₂×C₁₃	1	2	yes	complemented
321	#2442	C₂×C₁₃	1	2	yes	complemented
322	#2440	C₂×C₁₃	1	2	yes	complemented
323	#2312	C₂×C₁₃	1	2	yes	—
324	C₂×#385	C₂×C₁₃	1	1	yes	characteristic
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	8	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	1	no	—
333	C₂³×C₁₃	—	2	1	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	4	8	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	4	no	—
339	C₂³×C₁₃	—	4	8	no	—
340	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
341	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
342	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
343	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
344	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
345	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
346	Q₈×C₁₃	—	8	4	no	—
347	Q₈×C₁₃	—	8	2	no	—
348	Q₈×C₁₃	—	8	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	1	no	—
364	C₂×C₄×C₁₃	—	2	1	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	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	—	4	8	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	—	4	8	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	8	2	no	—
396	C₂×C₄×C₁₃	—	8	2	no	—
397	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
398	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
399	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
400	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
402	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
403	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
405	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
409	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	#400	C₂²×C₁₃	1	2	yes	complemented
412	#400	C₂²×C₁₃	1	2	yes	complemented
413	#400	C₂²×C₁₃	1	2	yes	complemented
414	#400	C₂²×C₁₃	1	2	yes	complemented
415	#399	C₂²×C₁₃	1	1	yes	characteristic
416	#399	C₂²×C₁₃	1	1	yes	characteristic
417	#399	C₂²×C₁₃	1	1	yes	characteristic
418	#399	C₂²×C₁₃	1	1	yes	characteristic
419	#398	C₂²×C₁₃	1	2	yes	complemented
420	#398	C₂²×C₁₃	1	2	yes	complemented
421	#398	C₂²×C₁₃	1	2	yes	complemented
422	#398	C₂²×C₁₃	1	2	yes	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	#398	C₂²×C₁₃	1	2	yes	complemented
427	#396	C₂²×C₁₃	1	2	yes	—
428	#396	C₂²×C₁₃	1	2	yes	—
429	#396	C₂²×C₁₃	1	2	yes	—
430	#396	C₂²×C₁₃	1	2	yes	—
431	#395	C₂²×C₁₃	1	2	yes	complemented
432	#395	C₂²×C₁₃	1	2	yes	complemented
433	#395	C₂²×C₁₃	1	2	yes	complemented
434	#395	C₂²×C₁₃	1	2	yes	complemented
435	#393	C₂²×C₁₃	1	1	yes	characteristic
436	#393	C₂²×C₁₃	1	1	yes	characteristic
437	#393	C₂²×C₁₃	1	1	yes	characteristic
438	#393	C₂²×C₁₃	1	1	yes	characteristic
439	#391	C₂²×C₁₃	1	2	yes	complemented
440	#391	C₂²×C₁₃	1	2	yes	complemented
441	#389	C₂²×C₁₃	1	2	yes	complemented
442	#389	C₂²×C₁₃	1	2	yes	complemented
443	#389	C₂²×C₁₃	1	2	yes	complemented
444	#389	C₂²×C₁₃	1	2	yes	complemented
445	#389	C₂²×C₁₃	1	2	yes	complemented
446	#389	C₂²×C₁₃	1	2	yes	complemented
447	#388	C₂²×C₁₃	1	2	yes	—
448	#388	C₂²×C₁₃	1	2	yes	—
449	#388	C₂²×C₁₃	1	2	yes	—
450	#388	C₂²×C₁₃	1	2	yes	—
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	#387	C₂²×C₁₃	1	2	yes	complemented
456	#387	C₂²×C₁₃	1	2	yes	complemented
457	#387	C₂²×C₁₃	1	2	yes	complemented
458	#387	C₂²×C₁₃	1	2	yes	complemented
459	#385	C₂²×C₁₃	1	2	yes	—
460	#385	C₂²×C₁₃	1	2	yes	—
461	#385	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	1	yes	characteristic
468	#385	C₂²×C₁₃	1	1	yes	characteristic
469	#385	C₂²×C₁₃	1	2	yes	—
470	#385	C₂²×C₁₃	1	2	yes	—
471	#385	C₂²×C₁₃	1	1	yes	characteristic
472	#385	C₂²×C₁₃	1	1	yes	characteristic
473	#384	C₂²×C₁₃	1	2	yes	complemented
474	#382	C₂²×C₁₃	1	2	yes	complemented
475	#380	C₂²×C₁₃	1	2	yes	—
476	#380	C₂²×C₁₃	1	2	yes	—
477	#380	C₂²×C₁₃	1	1	yes	characteristic
478	#380	C₂²×C₁₃	1	2	yes	—
479	#380	C₂²×C₁₃	1	2	yes	—
480	#380	C₂²×C₁₃	1	2	yes	—
481	#380	C₂²×C₁₃	1	1	yes	characteristic
482	#379	C₂²×C₁₃	1	2	yes	—
483	#379	C₂²×C₁₃	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₂×#95	C₂²×C₁₃	1	2	yes	—
487	C₂²×C₁₃	—	2	4	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	4	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	4	no	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	4	16	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	#544	1	4	yes	—
503	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
504	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
506	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
507	C₂²×C₁₃	#585	1	2	yes	—
508	C₄×C₁₃	—	2	4	no	—
509	C₄×C₁₃	—	2	4	no	—
510	C₄×C₁₃	—	2	4	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	—	4	1	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
526	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₂³×C₄	—	4	4	no	—
529	C₂³×C₄	—	4	2	no	—
530	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
531	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
537	C₄⋊Q₈	—	4	4	no	—
538	#125	—	4	4	no	—
539	C₂²⋊Q₈	—	4	4	no	—
540	C₂²⋊Q₈	—	4	2	no	—
541	C₂²⋊Q₈	—	4	2	no	—
542	C₂²⋊Q₈	—	4	4	no	—
543	C₂²⋊Q₈	—	4	4	no	—
544	C₂×C₄⋊C₄	—	4	4	no	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	—	4	2	no	—
573	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
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	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	#95	C₂³×C₁₃	1	2	yes	—
598	#95	C₂³×C₁₃	1	2	yes	—
599	#95	C₂³×C₁₃	1	2	yes	—
600	#95	C₂³×C₁₃	1	2	yes	—
601	#95	C₂³×C₁₃	1	2	yes	—
602	#95	C₂³×C₁₃	1	2	yes	—
603	#95	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	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	1	yes	characteristic
615	#95	C₂³×C₁₃	1	1	yes	characteristic
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	2	4	no	—
624	C₂×C₁₃	—	4	2	no	—
625	C₂×C₁₃	—	4	2	no	—
626	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
627	C₂×C₁₃	#3501	1	2	yes	—
628	C₂×C₁₃	#3532	1	1	yes	characteristic
629	C₂×C₁₃	#3533	1	1	yes	characteristic
630	C₂×C₁₃	#3541	1	2	yes	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
636	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×Q₈	—	4	2	no	—
645	C₂×Q₈	—	4	2	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	1	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	16	no	—
663	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	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	2	no	—
700	C₄⋊C₄	—	4	2	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	—	4	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	4	1	no	—
712	C₂²⋊C₄	—	4	1	no	—
713	C₂²⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	4	1	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	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
724	C₂²⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
725	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
726	C₄²	—	4	2	no	—
727	C₄²	—	4	2	no	—
728	C₄²	—	4	2	no	—
729	C₄²	—	4	2	no	—
730	C₁₃	#36748	1	1	yes	characteristic, direct product factor, Sylow
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	8	no	—
746	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
747	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
748	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
749	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
750	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
751	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
752	Q₈	—	8	4	no	—
753	Q₈	—	8	2	no	—
754	Q₈	—	8	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	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	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	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
804	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
805	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	4	16	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	C₁₃×#544	1	4	yes	—
822	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
823	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
825	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
826	C₂²	C₁₃×#585	1	2	yes	—
827	C₄	—	2	4	no	—
828	C₄	—	2	4	no	—
829	C₄	—	2	4	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₂	—	2	4	no	—
844	C₂	—	4	2	no	—
845	C₂	—	4	2	no	—
846	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
847	C₂	C₁₃×#3501	1	2	yes	—
848	C₂	C₁₃×#3532	1	1	yes	characteristic
849	C₂	C₁₃×#3533	1	1	yes	characteristic
850	C₂	C₁₃×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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
2. C₁₃×#2807	C₂	semidirect
3. C₁₃×#2790	C₂	semidirect
4. C₁₃×#2788	C₂	semidirect
5. C₁₃×#2768	C₂	semidirect
6. C₁₃×#2763	C₂	semidirect
7. C₁₃×#2742	C₂	semidirect
8. C₁₃×#2729	C₂	semidirect
9. C₁₃×#2720	C₂	semidirect
10. C₁₃×#2704	C₂	semidirect
11. C₁₃×#2677	C₂	semidirect
14. C₁₃×#2569	C₂	semidirect
15. C₁₃×#2549	C₂	semidirect
16. C₁₃×#2442	C₂	semidirect
17. C₁₃×#2440	C₂	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
31. C₁₃×#400	C₂²	semidirect
32. C₁₃×#400	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
42. C₁₃×#398	C₂²	semidirect
43. C₁₃×#398	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#398	C₂²	semidirect
46. C₁₃×#398	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
53. C₁₃×#395	C₂²	semidirect
54. C₁₃×#395	C₂²	semidirect
59. C₁₃×#391	C₂²	semidirect
60. C₁₃×#391	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
62. C₁₃×#389	C₂²	semidirect
63. C₁₃×#389	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
75. C₁₃×#387	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
93. C₁₃×#384	C₂²	semidirect
94. C₁₃×#382	C₂²	semidirect
156. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
206. #36748	C₁₃	direct (N × H)
307. #2807	C₂×C₁₃	semidirect
308. #2790	C₂×C₁₃	semidirect
309. #2788	C₂×C₁₃	semidirect
310. #2768	C₂×C₁₃	semidirect
311. #2763	C₂×C₁₃	semidirect
312. #2742	C₂×C₁₃	semidirect
313. #2729	C₂×C₁₃	semidirect
314. #2720	C₂×C₁₃	semidirect
315. #2704	C₂×C₁₃	semidirect
316. #2677	C₂×C₁₃	semidirect
319. #2569	C₂×C₁₃	semidirect
320. #2549	C₂×C₁₃	semidirect
321. #2442	C₂×C₁₃	semidirect
322. #2440	C₂×C₁₃	semidirect
401. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
402. C₂×#125	C₂²×C₁₃	semidirect
411. #400	C₂²×C₁₃	semidirect
412. #400	C₂²×C₁₃	semidirect
413. #400	C₂²×C₁₃	semidirect
414. #400	C₂²×C₁₃	semidirect
419. #398	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
426. #398	C₂²×C₁₃	semidirect
431. #395	C₂²×C₁₃	semidirect
432. #395	C₂²×C₁₃	semidirect
433. #395	C₂²×C₁₃	semidirect
434. #395	C₂²×C₁₃	semidirect
439. #391	C₂²×C₁₃	semidirect
440. #391	C₂²×C₁₃	semidirect
441. #389	C₂²×C₁₃	semidirect
442. #389	C₂²×C₁₃	semidirect
443. #389	C₂²×C₁₃	semidirect
444. #389	C₂²×C₁₃	semidirect
445. #389	C₂²×C₁₃	semidirect
446. #389	C₂²×C₁₃	semidirect
455. #387	C₂²×C₁₃	semidirect
456. #387	C₂²×C₁₃	semidirect
457. #387	C₂²×C₁₃	semidirect
458. #387	C₂²×C₁₃	semidirect
473. #384	C₂²×C₁₃	semidirect
474. #382	C₂²×C₁₃	semidirect
573. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
730. C₁₃	#36748	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×#2807	2
C₁₃×#2790	2
C₁₃×#2788	2
C₁₃×#2768	2
C₁₃×#2763	2
C₁₃×#2742	2
C₁₃×#2729	2
C₁₃×#2720	2
C₁₃×#2704	2
C₁₃×#2677	2
C₁₃×#2626	2
C₁₃×#2569	2
C₁₃×#2549	2
C₁₃×#2442	2
C₁₃×#2440	2
C₁₃×#2312	2
C₂×C₁₃×#385	2
#36748	13

Subgroups — C13×#36748 #15723087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36748 #15723087