Subgroups — C₁₃×#34327 #15720666

Order 3328.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2372	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#548	C₄	1	16	yes	complemented
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
44	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	2	yes	—
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#391	C₂²	1	1	yes	characteristic
56	C₁₃×#391	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	1	yes	characteristic
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#383	C₂²	1	2	yes	—
89	C₁₃×#382	C₂²	1	1	yes	characteristic
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	1	yes	characteristic
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	2	yes	—
119	C₁₃×#376	C₂²	1	2	yes	—
120	C₂×C₁₃×#95	C₂²	1	2	yes	—
121	C₂×C₁₃×#95	C₂²	1	2	yes	—
122	C₂×C₁₃×#95	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂×C₁₃×#41	—	4	2	no	—
125	C₂×C₁₃×#41	—	4	2	no	—
126	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
127	C₂²×Q₈×C₁₃	—	4	2	no	—
128	C₂²×Q₈×C₁₃	—	4	2	no	—
129	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#124	C₂×C₄	1	8	yes	complemented
149	C₁₃×#124	C₂×C₄	1	16	yes	complemented
150	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
152	C₁₃×#121	C₂×C₄	1	8	yes	complemented
153	C₁₃×#121	C₂×C₄	1	16	yes	complemented
154	C₄×Q₈×C₁₃	—	4	2	no	—
155	C₄×Q₈×C₁₃	—	4	2	no	—
156	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	8	no	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	8	no	—
161	C₄×D₄×C₁₃	—	4	2	no	—
162	C₄×D₄×C₁₃	—	4	2	no	—
163	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
164	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
165	C₁₃×#117	—	4	2	no	—
166	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	—	4	2	no	—
202	C₂×C₄²×C₁₃	—	4	2	no	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	1	yes	characteristic
226	C₁₃×#95	C₂³	1	1	yes	characteristic
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	1	yes	characteristic
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	2	yes	—
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	2	yes	—
242	C₁₃×#95	C₂³	1	2	yes	—
243	C₁₃×#95	C₂³	1	2	yes	—
244	C₁₃×#95	C₂³	1	2	yes	—
245	C₁₃×#95	C₂³	1	2	yes	—
246	C₁₃×#95	C₂³	1	2	yes	—
247	C₁₃×#95	C₂³	1	2	yes	—
248	C₁₃×#95	C₂³	1	2	yes	—
249	C₁₃×#95	C₂³	1	2	yes	—
250	#34327	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
253	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×#41	—	4	16	no	—
255	C₂×Q₈×C₁₃	—	2	2	no	—
256	C₂×Q₈×C₁₃	—	2	2	no	—
257	C₂×Q₈×C₁₃	—	2	2	no	—
258	C₂×Q₈×C₁₃	—	2	2	no	—
259	C₂×Q₈×C₁₃	—	4	2	no	—
260	C₂×Q₈×C₁₃	—	4	2	no	—
261	C₂×Q₈×C₁₃	—	4	16	no	—
262	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
263	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
264	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	4	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	4	2	no	—
272	C₂×D₄×C₁₃	—	4	2	no	—
273	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
274	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
275	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
276	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	4	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	2	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	4	no	—
288	C₂²×C₄×C₁₃	—	2	4	no	—
289	C₂²×C₄×C₁₃	—	4	1	no	—
290	C₂²×C₄×C₁₃	—	4	1	no	—
291	C₂²×C₄×C₁₃	—	4	1	no	—
292	C₂²×C₄×C₁₃	—	4	1	no	—
293	C₂²×C₄×C₁₃	—	4	1	no	—
294	C₂²×C₄×C₁₃	—	4	1	no	—
295	C₂²×C₄×C₁₃	—	4	2	no	—
296	C₂²×C₄×C₁₃	—	4	2	no	—
297	C₂²×C₄×C₁₃	—	4	2	no	—
298	C₂²×C₄×C₁₃	—	4	2	no	—
299	C₂²×C₄×C₁₃	—	4	2	no	—
300	C₂²×C₄×C₁₃	—	4	2	no	—
301	C₂²×C₄×C₁₃	—	4	2	no	—
302	C₂²×C₄×C₁₃	—	4	2	no	—
303	C₂²×C₄×C₁₃	—	4	2	no	—
304	C₂²×C₄×C₁₃	—	4	2	no	—
305	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
306	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
307	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
308	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
309	C₂²×C₄×C₁₃	#41	1	4	yes	complemented
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	4	no	—
333	C₁₃×C₄⋊C₄	—	2	4	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	4	2	no	—
339	C₁₃×C₄⋊C₄	—	4	2	no	—
340	C₁₃×C₄⋊C₄	—	4	2	no	—
341	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
342	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
343	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
344	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	4	no	—
349	C₁₃×C₂²⋊C₄	—	2	4	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	4	no	—
352	C₁₃×C₂²⋊C₄	—	4	2	no	—
353	C₁₃×C₂²⋊C₄	—	4	2	no	—
354	C₁₃×C₂²⋊C₄	—	4	2	no	—
355	C₁₃×C₂²⋊C₄	—	4	2	no	—
356	C₁₃×C₂²⋊C₄	—	4	2	no	—
357	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
358	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
359	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
360	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
361	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
362	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
363	C₁₃×C₂²⋊C₄	#41	1	4	yes	complemented
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	2	4	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	4	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	4	1	no	—
374	C₄²×C₁₃	—	4	1	no	—
375	C₄²×C₁₃	—	4	1	no	—
376	C₄²×C₁₃	—	4	1	no	—
377	C₄²×C₁₃	—	4	1	no	—
378	C₄²×C₁₃	—	4	2	no	—
379	C₄²×C₁₃	—	4	2	no	—
380	C₄²×C₁₃	—	4	2	no	—
381	C₄²×C₁₃	—	4	2	no	—
382	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
383	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
384	C₂×#548	C₂×C₁₃	1	1	yes	characteristic
385	#2372	C₂×C₁₃	1	2	yes	complemented
386	#2368	C₂×C₁₃	1	2	yes	complemented
387	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
388	#2364	C₂×C₁₃	1	2	yes	complemented
389	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#2361	C₂×C₁₃	1	1	yes	characteristic, complemented
391	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#2353	C₂×C₁₃	1	2	yes	complemented
393	#2352	C₂×C₁₃	1	1	yes	characteristic, complemented
394	Q₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#2337	C₂×C₁₃	1	2	yes	complemented
397	#2332	C₂×C₁₃	1	2	yes	complemented
398	#2325	C₂×C₁₃	1	2	yes	complemented
399	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
400	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
401	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#2297	C₂×C₁₃	1	1	yes	characteristic, complemented
403	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
404	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#2275	C₂×C₁₃	1	2	yes	complemented
406	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
407	C₂³×C₁₃	—	2	1	no	—
408	C₂³×C₁₃	—	2	1	no	—
409	C₂³×C₁₃	—	2	1	no	—
410	C₂³×C₁₃	—	2	1	no	—
411	C₂³×C₁₃	—	2	1	no	—
412	C₂³×C₁₃	—	2	2	no	—
413	C₂³×C₁₃	—	2	2	no	—
414	C₂³×C₁₃	—	2	1	no	—
415	C₂³×C₁₃	—	2	1	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	2	no	—
418	C₂³×C₁₃	—	2	1	no	—
419	C₂³×C₁₃	—	2	2	no	—
420	C₂³×C₁₃	—	2	1	no	—
421	C₂³×C₁₃	—	2	1	no	—
422	C₂³×C₁₃	—	2	2	no	—
423	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
424	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
425	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
426	C₂³×C₁₃	C₂×#41	1	2	yes	—
427	C₂³×C₁₃	C₂×#41	1	2	yes	—
428	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
429	Q₈×C₁₃	—	2	8	no	—
430	Q₈×C₁₃	—	2	8	no	—
431	Q₈×C₁₃	—	4	8	no	—
432	D₄×C₁₃	—	2	8	no	—
433	D₄×C₁₃	—	2	16	no	—
434	D₄×C₁₃	—	2	8	no	—
435	D₄×C₁₃	—	4	8	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	1	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	2	1	no	—
457	C₂×C₄×C₁₃	—	2	1	no	—
458	C₂×C₄×C₁₃	—	2	1	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	8	no	—
461	C₂×C₄×C₁₃	—	2	8	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	1	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	1	no	—
469	C₂×C₄×C₁₃	—	2	1	no	—
470	C₂×C₄×C₁₃	—	2	1	no	—
471	C₂×C₄×C₁₃	—	2	1	no	—
472	C₂×C₄×C₁₃	—	2	2	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	2	no	—
475	C₂×C₄×C₁₃	—	2	2	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	2	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	4	8	no	—
484	C₂×C₄×C₁₃	—	4	8	no	—
485	C₂×C₄×C₁₃	—	4	4	no	—
486	C₂×C₄×C₁₃	—	4	4	no	—
487	C₂×C₄×C₁₃	—	4	4	no	—
488	C₂×C₄×C₁₃	—	4	4	no	—
489	C₂×C₄×C₁₃	—	8	4	no	—
490	C₂×C₄×C₁₃	—	8	4	no	—
491	C₂×C₄×C₁₃	—	8	4	no	—
492	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
493	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
494	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
495	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
496	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
498	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
499	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
503	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
504	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
507	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
508	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
509	#548	C₄×C₁₃	1	16	yes	complemented
510	C₂×#124	C₂²×C₁₃	1	2	yes	—
511	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
514	C₂×#121	C₂²×C₁₃	1	2	yes	—
515	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
517	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
518	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
520	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
526	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
527	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
528	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
530	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
531	#391	C₂²×C₁₃	1	2	yes	—
532	#391	C₂²×C₁₃	1	2	yes	—
533	#391	C₂²×C₁₃	1	2	yes	—
534	#391	C₂²×C₁₃	1	1	yes	characteristic
535	#391	C₂²×C₁₃	1	1	yes	characteristic
536	#391	C₂²×C₁₃	1	1	yes	characteristic
537	#391	C₂²×C₁₃	1	1	yes	characteristic
538	#391	C₂²×C₁₃	1	2	yes	—
539	#391	C₂²×C₁₃	1	1	yes	characteristic
540	#391	C₂²×C₁₃	1	1	yes	characteristic
541	#390	C₂²×C₁₃	1	1	yes	characteristic
542	#390	C₂²×C₁₃	1	1	yes	characteristic
543	#389	C₂²×C₁₃	1	1	yes	characteristic
544	#389	C₂²×C₁₃	1	1	yes	characteristic
545	#388	C₂²×C₁₃	1	2	yes	—
546	#388	C₂²×C₁₃	1	2	yes	—
547	#388	C₂²×C₁₃	1	2	yes	—
548	#388	C₂²×C₁₃	1	2	yes	—
549	#388	C₂²×C₁₃	1	2	yes	—
550	#388	C₂²×C₁₃	1	2	yes	—
551	#388	C₂²×C₁₃	1	2	yes	—
552	#388	C₂²×C₁₃	1	2	yes	—
553	#388	C₂²×C₁₃	1	2	yes	—
554	#387	C₂²×C₁₃	1	2	yes	—
555	#387	C₂²×C₁₃	1	2	yes	—
556	#387	C₂²×C₁₃	1	2	yes	—
557	#387	C₂²×C₁₃	1	2	yes	—
558	#387	C₂²×C₁₃	1	2	yes	—
559	#387	C₂²×C₁₃	1	2	yes	—
560	#387	C₂²×C₁₃	1	2	yes	—
561	#386	C₂²×C₁₃	1	2	yes	—
562	#386	C₂²×C₁₃	1	2	yes	—
563	#386	C₂²×C₁₃	1	2	yes	—
564	#386	C₂²×C₁₃	1	2	yes	—
565	#386	C₂²×C₁₃	1	2	yes	—
566	#386	C₂²×C₁₃	1	2	yes	—
567	#386	C₂²×C₁₃	1	2	yes	—
568	#385	C₂²×C₁₃	1	2	yes	—
569	#385	C₂²×C₁₃	1	2	yes	—
570	#385	C₂²×C₁₃	1	2	yes	—
571	#383	C₂²×C₁₃	1	2	yes	—
572	#382	C₂²×C₁₃	1	1	yes	characteristic
573	#381	C₂²×C₁₃	1	2	yes	—
574	#380	C₂²×C₁₃	1	2	yes	—
575	#380	C₂²×C₁₃	1	1	yes	characteristic
576	#380	C₂²×C₁₃	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
580	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
583	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
585	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
586	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
588	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
589	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
590	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
591	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
592	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
594	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
595	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
596	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
598	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
599	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
601	#376	C₂²×C₁₃	1	2	yes	—
602	#376	C₂²×C₁₃	1	2	yes	—
603	C₂×#95	C₂²×C₁₃	1	2	yes	—
604	C₂×#95	C₂²×C₁₃	1	2	yes	—
605	C₂×#95	C₂²×C₁₃	1	2	yes	—
606	C₄³	C₂²×C₁₃	1	1	yes	characteristic
607	C₂²×C₁₃	—	2	2	no	—
608	C₂²×C₁₃	—	2	2	no	—
609	C₂²×C₁₃	—	2	2	no	—
610	C₂²×C₁₃	—	2	2	no	—
611	C₂²×C₁₃	—	2	2	no	—
612	C₂²×C₁₃	—	2	2	no	—
613	C₂²×C₁₃	—	2	2	no	—
614	C₂²×C₁₃	—	2	4	no	—
615	C₂²×C₁₃	—	2	2	no	—
616	C₂²×C₁₃	—	2	4	no	—
617	C₂²×C₁₃	—	2	4	no	—
618	C₂²×C₁₃	—	2	2	no	—
619	C₂²×C₁₃	—	4	1	no	—
620	C₂²×C₁₃	—	4	2	no	—
621	C₂²×C₁₃	—	4	1	no	—
622	C₂²×C₁₃	—	4	2	no	—
623	C₂²×C₁₃	—	4	2	no	—
624	C₂²×C₁₃	—	4	1	no	—
625	C₂²×C₁₃	—	4	1	no	—
626	C₂²×C₁₃	—	4	2	no	—
627	C₂²×C₁₃	C₄×#41	1	4	yes	—
628	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
629	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
630	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
631	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
634	C₂²×C₁₃	#585	1	1	yes	characteristic
635	C₄×C₁₃	—	2	4	no	—
636	C₄×C₁₃	—	2	2	no	—
637	C₄×C₁₃	—	2	2	no	—
638	C₄×C₁₃	—	2	2	no	—
639	C₄×C₁₃	—	2	4	no	—
640	C₄×C₁₃	—	2	4	no	—
641	C₄×C₁₃	—	2	2	no	—
642	C₄×C₁₃	—	2	2	no	—
643	C₄×C₁₃	—	2	2	no	—
644	C₄×C₁₃	—	2	2	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	2	2	no	—
647	C₄×C₁₃	—	4	1	no	—
648	C₄×C₁₃	—	4	2	no	—
649	C₄×C₁₃	—	4	1	no	—
650	C₄×C₁₃	—	4	2	no	—
651	C₄×C₁₃	—	4	2	no	—
652	C₄×C₁₃	—	4	2	no	—
653	C₄×C₁₃	—	4	1	no	—
654	C₄×C₁₃	#518	1	4	yes	—
655	C₂×#41	—	4	2	no	—
656	C₂×#41	—	4	2	no	—
657	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
658	C₂²×Q₈	—	4	2	no	—
659	C₂²×Q₈	—	4	2	no	—
660	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
661	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
662	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
663	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
664	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
666	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
668	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
671	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
673	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
674	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
675	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
677	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
678	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
679	#124	C₂×C₄×C₁₃	1	8	yes	complemented
680	#124	C₂×C₄×C₁₃	1	16	yes	complemented
681	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
682	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
683	#121	C₂×C₄×C₁₃	1	8	yes	complemented
684	#121	C₂×C₄×C₁₃	1	16	yes	complemented
685	C₄×Q₈	—	4	2	no	—
686	C₄×Q₈	—	4	2	no	—
687	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
688	C₄×D₄	—	2	4	no	—
689	C₄×D₄	—	2	8	no	—
690	C₄×D₄	—	2	4	no	—
691	C₄×D₄	—	2	8	no	—
692	C₄×D₄	—	4	2	no	—
693	C₄×D₄	—	4	2	no	—
694	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
695	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
696	#117	—	4	2	no	—
697	C₂×C₄⋊C₄	—	4	2	no	—
698	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
732	C₂×C₄²	—	4	2	no	—
733	C₂×C₄²	—	4	2	no	—
734	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
738	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
739	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
744	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
745	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
746	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
748	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
754	#95	C₂³×C₁₃	1	2	yes	—
755	#95	C₂³×C₁₃	1	1	yes	characteristic
756	#95	C₂³×C₁₃	1	2	yes	—
757	#95	C₂³×C₁₃	1	2	yes	—
758	#95	C₂³×C₁₃	1	2	yes	—
759	#95	C₂³×C₁₃	1	2	yes	—
760	#95	C₂³×C₁₃	1	2	yes	—
761	#95	C₂³×C₁₃	1	2	yes	—
762	#95	C₂³×C₁₃	1	2	yes	—
763	#95	C₂³×C₁₃	1	2	yes	—
764	#95	C₂³×C₁₃	1	2	yes	—
765	#95	C₂³×C₁₃	1	1	yes	characteristic
766	#95	C₂³×C₁₃	1	2	yes	—
767	#95	C₂³×C₁₃	1	2	yes	—
768	#95	C₂³×C₁₃	1	2	yes	—
769	#95	C₂³×C₁₃	1	2	yes	—
770	#95	C₂³×C₁₃	1	2	yes	—
771	#95	C₂³×C₁₃	1	1	yes	characteristic
772	#95	C₂³×C₁₃	1	1	yes	characteristic
773	#95	C₂³×C₁₃	1	1	yes	characteristic
774	#95	C₂³×C₁₃	1	1	yes	characteristic
775	#95	C₂³×C₁₃	1	2	yes	—
776	#95	C₂³×C₁₃	1	2	yes	—
777	#95	C₂³×C₁₃	1	2	yes	—
778	#95	C₂³×C₁₃	1	2	yes	—
779	#95	C₂³×C₁₃	1	2	yes	—
780	#95	C₂³×C₁₃	1	2	yes	—
781	C₂×C₁₃	—	2	4	no	—
782	C₂×C₁₃	—	4	2	no	—
783	C₂×C₁₃	—	4	4	no	—
784	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
785	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
786	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
787	C₂×C₁₃	#3505	1	1	yes	characteristic
788	C₂×C₁₃	#3511	1	1	yes	characteristic
789	C₂×C₁₃	#3514	1	1	yes	characteristic
790	C₂×C₁₃	#3520	1	1	yes	characteristic
791	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
793	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
794	#41	—	4	16	no	—
795	C₂×Q₈	—	2	2	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	16	no	—
802	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
803	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
804	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	4	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
814	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
815	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
816	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	4	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	4	1	no	—
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	1	no	—
832	C₂²×C₄	—	4	1	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	1	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	—	4	2	no	—
841	C₂²×C₄	—	4	2	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
846	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
847	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
848	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
849	C₂²×C₄	C₁₃×#41	1	4	yes	complemented
850	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	4	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
882	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
883	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
884	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	2	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
903	C₂²⋊C₄	C₁₃×#41	1	4	yes	complemented
904	C₄²	—	2	2	no	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	4	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	4	1	no	—
914	C₄²	—	4	1	no	—
915	C₄²	—	4	1	no	—
916	C₄²	—	4	1	no	—
917	C₄²	—	4	2	no	—
918	C₄²	—	4	2	no	—
919	C₄²	—	4	2	no	—
920	C₄²	—	4	1	no	—
921	C₄²	—	4	2	no	—
922	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
923	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
924	C₁₃	#34327	1	1	yes	characteristic, direct product factor, Sylow
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	2	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
942	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
943	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
944	C₂³	C₂×C₁₃×#41	1	2	yes	—
945	C₂³	C₂×C₁₃×#41	1	2	yes	—
946	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
947	Q₈	—	2	8	no	—
948	Q₈	—	2	8	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	8	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	8	no	—
953	D₄	—	4	8	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	8	no	—
979	C₂×C₄	—	2	8	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	8	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	—	8	4	no	—
1009	C₂×C₄	—	8	4	no	—
1010	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1011	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1012	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1013	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1014	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1015	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1016	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1017	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1018	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1019	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1020	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1021	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1022	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1023	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1024	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	C₄×C₁₃×#41	1	4	yes	—
1046	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1047	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1048	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1049	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1050	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1051	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1052	C₂²	C₁₃×#585	1	1	yes	characteristic
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	4	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	4	no	—
1060	C₄	—	2	4	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	C₁₃×#518	1	4	yes	—
1073	C₂	—	2	4	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	4	4	no	—
1076	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
1077	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
1078	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1079	C₂	C₁₃×#3505	1	1	yes	characteristic
1080	C₂	C₁₃×#3511	1	1	yes	characteristic
1081	C₂	C₁₃×#3514	1	1	yes	characteristic
1082	C₂	C₁₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#548	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×#2372	C₂	semidirect
3. C₁₃×#2368	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2364	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2356	C₂	semidirect
9. C₁₃×#2353	C₂	semidirect
10. C₁₃×#2352	C₂	semidirect
11. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
12. C₁₃×#2339	C₂	semidirect
13. C₁₃×#2337	C₂	semidirect
14. C₁₃×#2332	C₂	semidirect
15. C₁₃×#2325	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₁₃×#2297	C₂	semidirect
20. C₁₃×#2295	C₂	semidirect
21. C₂×C₁₃×#391	C₂	semidirect
22. C₁₃×#2275	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
26. C₁₃×#548	C₄	semidirect
126. C₂×C₁₃×#41	C₂×C₄	semidirect
129. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
148. C₁₃×#124	C₂×C₄	semidirect
149. C₁₃×#124	C₂×C₄	semidirect
150. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
152. C₁₃×#121	C₂×C₄	semidirect
153. C₁₃×#121	C₂×C₄	semidirect
156. C₄×Q₈×C₁₃	C₂×C₄	semidirect
163. C₄×D₄×C₁₃	C₂×C₄	semidirect
164. C₄×D₄×C₁₃	C₂×C₄	semidirect
250. #34327	C₁₃	direct (N × H)
309. C₂²×C₄×C₁₃	#41	semidirect
363. C₁₃×C₂²⋊C₄	#41	semidirect
385. #2372	C₂×C₁₃	semidirect
386. #2368	C₂×C₁₃	semidirect
387. #2367	C₂×C₁₃	semidirect
388. #2364	C₂×C₁₃	semidirect
389. #2362	C₂×C₁₃	semidirect
390. #2361	C₂×C₁₃	semidirect
391. #2356	C₂×C₁₃	semidirect
392. #2353	C₂×C₁₃	semidirect
393. #2352	C₂×C₁₃	semidirect
394. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
395. #2339	C₂×C₁₃	semidirect
396. #2337	C₂×C₁₃	semidirect
397. #2332	C₂×C₁₃	semidirect
398. #2325	C₂×C₁₃	semidirect
399. C₄×#124	C₂×C₁₃	semidirect
400. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
401. C₄×#121	C₂×C₁₃	semidirect
402. #2297	C₂×C₁₃	semidirect
403. #2295	C₂×C₁₃	semidirect
404. C₂×#391	C₂×C₁₃	semidirect
405. #2275	C₂×C₁₃	semidirect
406. C₄²×D₄	C₂×C₁₃	semidirect
509. #548	C₄×C₁₃	semidirect
657. C₂×#41	C₂×C₄×C₁₃	semidirect
660. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
679. #124	C₂×C₄×C₁₃	semidirect
680. #124	C₂×C₄×C₁₃	semidirect
681. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
682. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
683. #121	C₂×C₄×C₁₃	semidirect
684. #121	C₂×C₄×C₁₃	semidirect
687. C₄×Q₈	C₂×C₄×C₁₃	semidirect
694. C₄×D₄	C₂×C₄×C₁₃	semidirect
695. C₄×D₄	C₂×C₄×C₁₃	semidirect
849. C₂²×C₄	C₁₃×#41	semidirect
903. C₂²⋊C₄	C₁₃×#41	semidirect
924. C₁₃	#34327	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×#548	2
C₁₃×#2372	2
C₁₃×#2368	2
C₁₃×#2367	2
C₁₃×#2364	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2356	2
C₁₃×#2353	2
C₁₃×#2352	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2339	2
C₁₃×#2337	2
C₁₃×#2332	2
C₁₃×#2325	2
C₄×C₁₃×#124	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₁₃×#2295	2
C₂×C₁₃×#391	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34327	13

Subgroups — C13×#34327 #15720666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34327 #15720666