Subgroups — C₁₃×#36740 #15723079

Order 3328.

2262 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2700	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2698	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2689	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2687	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2681	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2680	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2674	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2672	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2564	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2417	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#543	—	2	8	no	—
21	C₁₃×#538	—	2	8	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#126	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	2	yes	—
40	C₂×C₁₃×#120	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#400	C₂²	1	2	yes	complemented
49	C₁₃×#400	C₂²	1	2	yes	complemented
50	C₁₃×#399	C₂²	1	2	yes	complemented
51	C₁₃×#398	C₂²	1	2	yes	complemented
52	C₁₃×#398	C₂²	1	2	yes	complemented
53	C₁₃×#398	C₂²	1	2	yes	complemented
54	C₁₃×#398	C₂²	1	2	yes	complemented
55	C₁₃×#397	C₂²	1	2	yes	—
56	C₁₃×#397	C₂²	1	2	yes	—
57	C₁₃×#397	C₂²	1	2	yes	—
58	C₁₃×#397	C₂²	1	2	yes	—
59	C₁₃×#397	C₂²	1	2	yes	complemented
60	C₁₃×#396	C₂²	1	2	yes	complemented
61	C₁₃×#396	C₂²	1	2	yes	complemented
62	C₁₃×#395	C₂²	1	2	yes	complemented
63	C₁₃×#395	C₂²	1	2	yes	complemented
64	C₁₃×#395	C₂²	1	2	yes	complemented
65	C₁₃×#394	C₂²	1	2	yes	—
66	C₁₃×#394	C₂²	1	2	yes	—
67	C₁₃×#394	C₂²	1	2	yes	—
68	C₁₃×#394	C₂²	1	2	yes	—
69	C₁₃×#394	C₂²	1	2	yes	complemented
70	C₁₃×#393	C₂²	1	2	yes	complemented
71	C₁₃×#393	C₂²	1	2	yes	complemented
72	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#391	C₂²	1	2	yes	complemented
76	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#389	C₂²	1	2	yes	complemented
78	C₁₃×#389	C₂²	1	2	yes	complemented
79	C₁₃×#389	C₂²	1	2	yes	complemented
80	C₁₃×#388	C₂²	1	2	yes	—
81	C₁₃×#388	C₂²	1	2	yes	—
82	C₁₃×#388	C₂²	1	2	yes	—
83	C₁₃×#388	C₂²	1	2	yes	—
84	C₁₃×#388	C₂²	1	2	yes	complemented
85	C₁₃×#388	C₂²	1	2	yes	complemented
86	C₁₃×#387	C₂²	1	2	yes	complemented
87	C₁₃×#387	C₂²	1	2	yes	complemented
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#386	C₂²	1	2	yes	—
90	C₁₃×#386	C₂²	1	2	yes	—
91	C₁₃×#386	C₂²	1	2	yes	—
92	C₁₃×#386	C₂²	1	2	yes	—
93	C₁₃×#386	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#385	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	2	yes	complemented
97	C₁₃×#385	C₂²	1	2	yes	complemented
98	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#381	C₂²	1	2	yes	—
101	C₁₃×#381	C₂²	1	2	yes	—
102	C₁₃×#380	C₂²	1	2	yes	—
103	C₁₃×#380	C₂²	1	2	yes	—
104	C₁₃×#380	C₂²	1	2	yes	—
105	C₁₃×#380	C₂²	1	2	yes	—
106	C₁₃×#380	C₂²	1	2	yes	complemented
107	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
108	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
109	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	—	4	2	no	—
128	C₁₃×#126	—	2	8	no	—
129	C₁₃×#124	—	2	8	no	—
130	C₁₃×#124	—	4	2	no	—
131	C₁₃×#123	—	2	8	no	—
132	C₁₃×#123	—	4	4	no	—
133	C₁₃×#123	—	4	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	8	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	8	no	—
139	C₁₃×C₂²⋊Q₈	—	2	8	no	—
140	C₁₃×C₂²⋊Q₈	—	2	8	no	—
141	C₁₃×C₂²⋊Q₈	—	2	8	no	—
142	C₁₃×C₂²⋊Q₈	—	4	4	no	—
143	C₁₃×#121	—	2	4	no	—
144	C₁₃×#121	—	2	8	no	—
145	C₁₃×#120	—	2	8	no	—
146	C₄×D₄×C₁₃	—	2	8	no	—
147	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	—	4	2	no	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	#36740	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂⁴×C₁₃	—	2	2	no	—
224	C₂⁴×C₁₃	—	2	2	no	—
225	C₂⁴×C₁₃	—	4	1	no	—
226	C₂⁴×C₁₃	—	4	1	no	—
227	C₂⁴×C₁₃	—	4	1	no	—
228	C₂⁴×C₁₃	—	4	1	no	—
229	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
230	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
231	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
232	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×Q₈×C₁₃	—	2	4	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	—	4	1	no	—
239	C₂×Q₈×C₁₃	—	4	1	no	—
240	C₂×Q₈×C₁₃	—	4	1	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	—	4	1	no	—
243	C₂×Q₈×C₁₃	—	4	1	no	—
244	C₂×Q₈×C₁₃	—	4	1	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	1	no	—
254	C₂×D₄×C₁₃	—	4	1	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	4	no	—
266	C₂²×C₄×C₁₃	—	4	1	no	—
267	C₂²×C₄×C₁₃	—	4	1	no	—
268	C₂²×C₄×C₁₃	—	4	1	no	—
269	C₂²×C₄×C₁₃	—	4	1	no	—
270	C₂²×C₄×C₁₃	—	4	1	no	—
271	C₂²×C₄×C₁₃	—	4	1	no	—
272	C₂²×C₄×C₁₃	—	4	1	no	—
273	C₂²×C₄×C₁₃	—	4	1	no	—
274	C₂²×C₄×C₁₃	—	4	1	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	1	no	—
280	C₂²×C₄×C₁₃	—	4	2	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
283	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	4	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	4	no	—
312	C₁₃×C₄⋊C₄	—	2	4	no	—
313	C₁₃×C₄⋊C₄	—	2	4	no	—
314	C₁₃×C₄⋊C₄	—	4	2	no	—
315	C₁₃×C₄⋊C₄	—	4	2	no	—
316	C₁₃×C₄⋊C₄	—	4	2	no	—
317	C₁₃×C₄⋊C₄	—	4	2	no	—
318	C₁₃×C₄⋊C₄	—	4	2	no	—
319	C₁₃×C₄⋊C₄	—	4	2	no	—
320	C₁₃×C₄⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₁₃×C₂²⋊C₄	—	4	2	no	—
336	C₁₃×C₂²⋊C₄	—	4	2	no	—
337	C₁₃×C₂²⋊C₄	—	4	2	no	—
338	C₁₃×C₂²⋊C₄	—	4	2	no	—
339	C₁₃×C₂²⋊C₄	—	4	2	no	—
340	C₁₃×C₂²⋊C₄	—	4	2	no	—
341	C₁₃×C₂²⋊C₄	—	4	2	no	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
344	C₄²×C₁₃	—	2	4	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	4	1	no	—
348	C₄²×C₁₃	—	4	1	no	—
349	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#538	C₂×C₁₃	1	1	yes	characteristic
351	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2850	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2700	C₂×C₁₃	1	2	yes	complemented
354	#2698	C₂×C₁₃	1	2	yes	complemented
355	#2689	C₂×C₁₃	1	2	yes	complemented
356	#2687	C₂×C₁₃	1	2	yes	complemented
357	#2681	C₂×C₁₃	1	2	yes	complemented
358	#2680	C₂×C₁₃	1	2	yes	complemented
359	#2674	C₂×C₁₃	1	2	yes	complemented
360	#2672	C₂×C₁₃	1	2	yes	complemented
361	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2639	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2564	C₂×C₁₃	1	2	yes	complemented
364	#2417	C₂×C₁₃	1	2	yes	complemented
365	#2412	C₂×C₁₃	1	2	yes	complemented
366	#2412	C₂×C₁₃	1	2	yes	complemented
367	C₂×#388	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	1	no	—
369	C₂³×C₁₃	—	2	1	no	—
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	8	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	4	4	no	—
387	C₂³×C₁₃	—	4	4	no	—
388	C₂³×C₁₃	—	8	2	no	—
389	C₂³×C₁₃	—	8	2	no	—
390	C₂³×C₁₃	—	8	2	no	—
391	C₂³×C₁₃	—	8	2	no	—
392	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
393	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
395	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
396	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
397	Q₈×C₁₃	—	8	4	no	—
398	Q₈×C₁₃	—	8	2	no	—
399	Q₈×C₁₃	—	8	2	no	—
400	Q₈×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	4	8	no	—
402	D₄×C₁₃	—	8	2	no	—
403	D₄×C₁₃	—	8	4	no	—
404	D₄×C₁₃	—	8	4	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	4	4	no	—
451	C₂×C₄×C₁₃	—	4	4	no	—
452	C₂×C₄×C₁₃	—	8	4	no	—
453	C₂×C₄×C₁₃	—	8	4	no	—
454	C₂×C₄×C₁₃	—	8	4	no	—
455	C₂×C₄×C₁₃	—	8	2	no	—
456	C₂×C₄×C₁₃	—	8	2	no	—
457	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
461	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
462	#543	—	2	8	no	—
463	#538	—	2	8	no	—
464	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂×#126	C₂²×C₁₃	1	2	yes	—
466	C₂×#124	C₂²×C₁₃	1	2	yes	—
467	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	C₂×#123	C₂²×C₁₃	1	2	yes	—
469	C₂×#123	C₂²×C₁₃	1	2	yes	—
470	C₂×#123	C₂²×C₁₃	1	2	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
477	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
479	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
480	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#121	C₂²×C₁₃	1	2	yes	—
482	C₂×#120	C₂²×C₁₃	1	2	yes	—
483	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
484	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
485	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
490	#400	C₂²×C₁₃	1	2	yes	complemented
491	#400	C₂²×C₁₃	1	2	yes	complemented
492	#399	C₂²×C₁₃	1	2	yes	complemented
493	#398	C₂²×C₁₃	1	2	yes	complemented
494	#398	C₂²×C₁₃	1	2	yes	complemented
495	#398	C₂²×C₁₃	1	2	yes	complemented
496	#398	C₂²×C₁₃	1	2	yes	complemented
497	#397	C₂²×C₁₃	1	2	yes	—
498	#397	C₂²×C₁₃	1	2	yes	—
499	#397	C₂²×C₁₃	1	2	yes	—
500	#397	C₂²×C₁₃	1	2	yes	—
501	#397	C₂²×C₁₃	1	2	yes	complemented
502	#396	C₂²×C₁₃	1	2	yes	complemented
503	#396	C₂²×C₁₃	1	2	yes	complemented
504	#395	C₂²×C₁₃	1	2	yes	complemented
505	#395	C₂²×C₁₃	1	2	yes	complemented
506	#395	C₂²×C₁₃	1	2	yes	complemented
507	#394	C₂²×C₁₃	1	2	yes	—
508	#394	C₂²×C₁₃	1	2	yes	—
509	#394	C₂²×C₁₃	1	2	yes	—
510	#394	C₂²×C₁₃	1	2	yes	—
511	#394	C₂²×C₁₃	1	2	yes	complemented
512	#393	C₂²×C₁₃	1	2	yes	complemented
513	#393	C₂²×C₁₃	1	2	yes	complemented
514	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#391	C₂²×C₁₃	1	2	yes	complemented
518	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#389	C₂²×C₁₃	1	2	yes	complemented
520	#389	C₂²×C₁₃	1	2	yes	complemented
521	#389	C₂²×C₁₃	1	2	yes	complemented
522	#388	C₂²×C₁₃	1	2	yes	—
523	#388	C₂²×C₁₃	1	2	yes	—
524	#388	C₂²×C₁₃	1	2	yes	—
525	#388	C₂²×C₁₃	1	2	yes	—
526	#388	C₂²×C₁₃	1	2	yes	complemented
527	#388	C₂²×C₁₃	1	2	yes	complemented
528	#387	C₂²×C₁₃	1	2	yes	complemented
529	#387	C₂²×C₁₃	1	2	yes	complemented
530	#386	C₂²×C₁₃	1	2	yes	—
531	#386	C₂²×C₁₃	1	2	yes	—
532	#386	C₂²×C₁₃	1	2	yes	—
533	#386	C₂²×C₁₃	1	2	yes	—
534	#386	C₂²×C₁₃	1	2	yes	—
535	#386	C₂²×C₁₃	1	2	yes	—
536	#385	C₂²×C₁₃	1	2	yes	—
537	#385	C₂²×C₁₃	1	2	yes	—
538	#385	C₂²×C₁₃	1	2	yes	complemented
539	#385	C₂²×C₁₃	1	2	yes	complemented
540	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
542	#381	C₂²×C₁₃	1	2	yes	—
543	#381	C₂²×C₁₃	1	2	yes	—
544	#380	C₂²×C₁₃	1	2	yes	—
545	#380	C₂²×C₁₃	1	2	yes	—
546	#380	C₂²×C₁₃	1	2	yes	—
547	#380	C₂²×C₁₃	1	2	yes	—
548	#380	C₂²×C₁₃	1	2	yes	complemented
549	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
550	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	2	2	no	—
555	C₂²×C₁₃	—	2	2	no	—
556	C₂²×C₁₃	—	2	2	no	—
557	C₂²×C₁₃	—	2	4	no	—
558	C₂²×C₁₃	—	2	4	no	—
559	C₂²×C₁₃	—	2	4	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	2	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	8	8	no	—
572	C₂²×C₁₃	#536	1	4	yes	—
573	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
574	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
577	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
578	C₂²×C₁₃	#585	1	1	yes	characteristic
579	C₂²×C₁₃	#585	1	1	yes	characteristic
580	C₄×C₁₃	—	2	4	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	2	no	—
583	C₄×C₁₃	—	2	2	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	—	4	1	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
604	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
609	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
610	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₄⋊Q₈	—	4	2	no	—
615	#126	—	2	8	no	—
616	#124	—	2	8	no	—
617	#124	—	4	2	no	—
618	#123	—	2	8	no	—
619	#123	—	4	4	no	—
620	#123	—	4	4	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	2	8	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	8	no	—
626	C₂²⋊Q₈	—	2	8	no	—
627	C₂²⋊Q₈	—	2	8	no	—
628	C₂²⋊Q₈	—	2	8	no	—
629	C₂²⋊Q₈	—	4	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	8	no	—
632	#120	—	2	8	no	—
633	C₄×D₄	—	2	8	no	—
634	C₂×C₄⋊C₄	—	4	2	no	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	—	2	8	no	—
657	C₂×C₂²⋊C₄	—	4	2	no	—
658	C₂×C₂²⋊C₄	—	4	2	no	—
659	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
683	C₂×C₄²	—	4	2	no	—
684	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
689	#95	C₂³×C₁₃	1	2	yes	—
690	#95	C₂³×C₁₃	1	2	yes	—
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	2	yes	—
700	#95	C₂³×C₁₃	1	2	yes	—
701	#95	C₂³×C₁₃	1	2	yes	—
702	#95	C₂³×C₁₃	1	2	yes	—
703	#95	C₂³×C₁₃	1	2	yes	—
704	#95	C₂³×C₁₃	1	2	yes	—
705	#95	C₂³×C₁₃	1	2	yes	—
706	#95	C₂³×C₁₃	1	2	yes	—
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	2	yes	—
709	C₂×C₁₃	—	2	4	no	—
710	C₂×C₁₃	—	4	4	no	—
711	C₂×C₁₃	—	8	2	no	—
712	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
713	C₂×C₁₃	#3496	1	1	yes	characteristic
714	C₂×C₁₃	#3496	1	1	yes	characteristic
715	C₂×C₁₃	#3535	1	1	yes	characteristic
716	C₂×C₁₃	#3536	1	1	yes	characteristic
717	C₂×C₁₃	#3561	1	1	yes	characteristic
718	C₂×C₁₃	#3564	1	1	yes	characteristic
719	C₂⁴	—	2	2	no	—
720	C₂⁴	—	2	2	no	—
721	C₂⁴	—	4	1	no	—
722	C₂⁴	—	4	1	no	—
723	C₂⁴	—	4	1	no	—
724	C₂⁴	—	4	1	no	—
725	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
726	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
727	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
728	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₂×Q₈	—	2	4	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	—	4	1	no	—
735	C₂×Q₈	—	4	1	no	—
736	C₂×Q₈	—	4	1	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×Q₈	—	4	1	no	—
739	C₂×Q₈	—	4	1	no	—
740	C₂×Q₈	—	4	1	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	1	no	—
750	C₂×D₄	—	4	1	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	1	no	—
764	C₂²×C₄	—	4	1	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	1	no	—
768	C₂²×C₄	—	4	1	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	1	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
779	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
780	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
785	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	4	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
839	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
840	C₄²	—	2	4	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	4	1	no	—
844	C₄²	—	4	1	no	—
845	C₁₃	#36740	1	1	yes	characteristic, direct product factor, Sylow
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	8	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	—	8	2	no	—
868	C₂³	—	8	2	no	—
869	C₂³	—	8	2	no	—
870	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
871	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
873	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
874	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
875	Q₈	—	8	4	no	—
876	Q₈	—	8	2	no	—
877	Q₈	—	8	2	no	—
878	Q₈	—	8	2	no	—
879	D₄	—	4	8	no	—
880	D₄	—	8	2	no	—
881	D₄	—	8	4	no	—
882	D₄	—	8	4	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	4	no	—
934	C₂×C₄	—	8	4	no	—
935	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
936	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
938	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
939	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	8	8	no	—
961	C₂²	C₁₃×#536	1	4	yes	—
962	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
963	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
964	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
965	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
966	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
967	C₂²	C₁₃×#585	1	1	yes	characteristic
968	C₂²	C₁₃×#585	1	1	yes	characteristic
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₂	—	2	4	no	—
986	C₂	—	4	4	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
989	C₂	C₁₃×#3496	1	1	yes	characteristic
990	C₂	C₁₃×#3496	1	1	yes	characteristic
991	C₂	C₁₃×#3535	1	1	yes	characteristic
992	C₂	C₁₃×#3536	1	1	yes	characteristic
993	C₂	C₁₃×#3561	1	1	yes	characteristic
994	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#538	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#543	C₂	semidirect
3. C₁₃×#2857	C₂	semidirect
4. C₁₃×#2850	C₂	semidirect
5. C₁₃×#2700	C₂	semidirect
6. C₁₃×#2698	C₂	semidirect
7. C₁₃×#2689	C₂	semidirect
8. C₁₃×#2687	C₂	semidirect
9. C₁₃×#2681	C₂	semidirect
10. C₁₃×#2680	C₂	semidirect
11. C₁₃×#2674	C₂	semidirect
12. C₁₃×#2672	C₂	semidirect
13. C₁₃×#2659	C₂	semidirect
14. C₁₃×#2639	C₂	semidirect
15. C₁₃×#2564	C₂	semidirect
16. C₁₃×#2417	C₂	semidirect
17. C₁₃×#2412	C₂	semidirect
18. C₁₃×#2412	C₂	semidirect
19. C₂×C₁₃×#388	C₂	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×#124	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
48. C₁₃×#400	C₂²	semidirect
49. C₁₃×#400	C₂²	semidirect
50. C₁₃×#399	C₂²	semidirect
51. C₁₃×#398	C₂²	semidirect
52. C₁₃×#398	C₂²	semidirect
53. C₁₃×#398	C₂²	semidirect
54. C₁₃×#398	C₂²	semidirect
59. C₁₃×#397	C₂²	semidirect
60. C₁₃×#396	C₂²	semidirect
61. C₁₃×#396	C₂²	semidirect
62. C₁₃×#395	C₂²	semidirect
63. C₁₃×#395	C₂²	semidirect
64. C₁₃×#395	C₂²	semidirect
69. C₁₃×#394	C₂²	semidirect
70. C₁₃×#393	C₂²	semidirect
71. C₁₃×#393	C₂²	semidirect
72. C₁₃×#391	C₂²	semidirect
73. C₁₃×#391	C₂²	semidirect
74. C₁₃×#391	C₂²	semidirect
75. C₁₃×#391	C₂²	semidirect
76. C₁₃×#390	C₂²	semidirect
77. C₁₃×#389	C₂²	semidirect
78. C₁₃×#389	C₂²	semidirect
79. C₁₃×#389	C₂²	semidirect
84. C₁₃×#388	C₂²	semidirect
85. C₁₃×#388	C₂²	semidirect
86. C₁₃×#387	C₂²	semidirect
87. C₁₃×#387	C₂²	semidirect
96. C₁₃×#385	C₂²	semidirect
97. C₁₃×#385	C₂²	semidirect
98. C₁₃×#384	C₂²	semidirect
99. C₁₃×#382	C₂²	semidirect
106. C₁₃×#380	C₂²	semidirect
222. #36740	C₁₃	direct (N × H)
349. C₂×#543	C₂×C₁₃	semidirect
351. #2857	C₂×C₁₃	semidirect
352. #2850	C₂×C₁₃	semidirect
353. #2700	C₂×C₁₃	semidirect
354. #2698	C₂×C₁₃	semidirect
355. #2689	C₂×C₁₃	semidirect
356. #2687	C₂×C₁₃	semidirect
357. #2681	C₂×C₁₃	semidirect
358. #2680	C₂×C₁₃	semidirect
359. #2674	C₂×C₁₃	semidirect
360. #2672	C₂×C₁₃	semidirect
361. #2659	C₂×C₁₃	semidirect
362. #2639	C₂×C₁₃	semidirect
363. #2564	C₂×C₁₃	semidirect
364. #2417	C₂×C₁₃	semidirect
365. #2412	C₂×C₁₃	semidirect
366. #2412	C₂×C₁₃	semidirect
367. C₂×#388	C₂×C₁₃	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
467. C₂×#124	C₂²×C₁₃	semidirect
479. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
490. #400	C₂²×C₁₃	semidirect
491. #400	C₂²×C₁₃	semidirect
492. #399	C₂²×C₁₃	semidirect
493. #398	C₂²×C₁₃	semidirect
494. #398	C₂²×C₁₃	semidirect
495. #398	C₂²×C₁₃	semidirect
496. #398	C₂²×C₁₃	semidirect
501. #397	C₂²×C₁₃	semidirect
502. #396	C₂²×C₁₃	semidirect
503. #396	C₂²×C₁₃	semidirect
504. #395	C₂²×C₁₃	semidirect
505. #395	C₂²×C₁₃	semidirect
506. #395	C₂²×C₁₃	semidirect
511. #394	C₂²×C₁₃	semidirect
512. #393	C₂²×C₁₃	semidirect
513. #393	C₂²×C₁₃	semidirect
514. #391	C₂²×C₁₃	semidirect
515. #391	C₂²×C₁₃	semidirect
516. #391	C₂²×C₁₃	semidirect
517. #391	C₂²×C₁₃	semidirect
518. #390	C₂²×C₁₃	semidirect
519. #389	C₂²×C₁₃	semidirect
520. #389	C₂²×C₁₃	semidirect
521. #389	C₂²×C₁₃	semidirect
526. #388	C₂²×C₁₃	semidirect
527. #388	C₂²×C₁₃	semidirect
528. #387	C₂²×C₁₃	semidirect
529. #387	C₂²×C₁₃	semidirect
538. #385	C₂²×C₁₃	semidirect
539. #385	C₂²×C₁₃	semidirect
540. #384	C₂²×C₁₃	semidirect
541. #382	C₂²×C₁₃	semidirect
548. #380	C₂²×C₁₃	semidirect
845. C₁₃	#36740	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×#543	2
C₂×C₁₃×#538	2
C₁₃×#2857	2
C₁₃×#2850	2
C₁₃×#2700	2
C₁₃×#2698	2
C₁₃×#2689	2
C₁₃×#2687	2
C₁₃×#2681	2
C₁₃×#2680	2
C₁₃×#2674	2
C₁₃×#2672	2
C₁₃×#2659	2
C₁₃×#2639	2
C₁₃×#2564	2
C₁₃×#2417	2
C₁₃×#2412	2
C₂×C₁₃×#388	2
#36740	13

Subgroups — C13×#36740 #15723079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36740 #15723079