Subgroups — C₁₃×#34292 #15720631

Order 3328.

3296 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2358	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#546	C₄	1	16	yes	complemented
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#123	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₁₃×#518	—	2	8	no	—
34	C₄×C₁₃×#41	—	2	8	no	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
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	2	yes	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
50	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
53	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
55	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
56	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
60	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#390	C₂²	1	1	yes	characteristic
64	C₁₃×#390	C₂²	1	2	yes	—
65	C₁₃×#390	C₂²	1	1	yes	characteristic
66	C₁₃×#390	C₂²	1	2	yes	complemented
67	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#389	C₂²	1	2	yes	complemented
70	C₁₃×#388	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	complemented
78	C₁₃×#388	C₂²	1	2	yes	complemented
79	C₁₃×#388	C₂²	1	2	yes	complemented
80	C₁₃×#388	C₂²	1	2	yes	complemented
81	C₁₃×#388	C₂²	1	2	yes	complemented
82	C₁₃×#388	C₂²	1	2	yes	complemented
83	C₁₃×#388	C₂²	1	2	yes	complemented
84	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#387	C₂²	1	2	yes	complemented
87	C₁₃×#387	C₂²	1	2	yes	complemented
88	C₁₃×#386	C₂²	1	1	yes	characteristic
89	C₁₃×#386	C₂²	1	1	yes	characteristic
90	C₁₃×#386	C₂²	1	2	yes	—
91	C₁₃×#386	C₂²	1	2	yes	—
92	C₁₃×#386	C₂²	1	2	yes	complemented
93	C₁₃×#386	C₂²	1	2	yes	complemented
94	C₁₃×#386	C₂²	1	2	yes	complemented
95	C₁₃×#386	C₂²	1	2	yes	complemented
96	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#385	C₂²	1	2	yes	complemented
99	C₁₃×#385	C₂²	1	2	yes	complemented
100	C₁₃×#385	C₂²	1	2	yes	complemented
101	C₁₃×#385	C₂²	1	2	yes	complemented
102	C₁₃×#385	C₂²	1	2	yes	complemented
103	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#381	C₂²	1	2	yes	complemented
105	C₁₃×#380	C₂²	1	1	yes	characteristic
106	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#380	C₂²	1	2	yes	complemented
108	C₁₃×#379	C₂²	1	2	yes	—
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
125	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
126	C₂⁵×C₁₃	C₂³	1	2	yes	—
127	C₂×C₁₃×#41	—	2	4	no	—
128	C₂×C₁₃×#41	—	2	4	no	—
129	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃	—	2	4	no	—
132	C₂²×D₄×C₁₃	—	2	4	no	—
133	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
148	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
152	C₁₃×#124	C₂×C₄	1	8	yes	complemented
153	C₁₃×#123	C₂×C₄	1	16	yes	complemented
154	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
155	C₁₃×#121	C₂×C₄	1	8	yes	complemented
156	C₁₃×#121	C₂×C₄	1	16	yes	complemented
157	C₁₃×#120	C₂×C₄	1	16	yes	complemented
158	C₄×Q₈×C₁₃	—	2	4	no	—
159	C₄×Q₈×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₄×D₄×C₁₃	—	2	4	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	8	no	—
164	C₄×D₄×C₁₃	—	2	8	no	—
165	C₄×D₄×C₁₃	—	2	4	no	—
166	C₄×D₄×C₁₃	—	2	8	no	—
167	C₄×D₄×C₁₃	—	2	8	no	—
168	C₄×D₄×C₁₃	—	2	4	no	—
169	C₄×D₄×C₁₃	—	4	4	no	—
170	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
171	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
172	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
173	C₁₃×#117	—	2	4	no	—
174	C₁₃×#117	—	2	4	no	—
175	C₁₃×#117	—	2	8	no	—
176	C₁₃×#117	—	2	4	no	—
177	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
198	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	—	2	8	no	—
227	C₂×C₄²×C₁₃	—	2	4	no	—
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
237	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
239	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
242	C₁₃×#95	C₂³	1	1	yes	characteristic
243	C₁₃×#95	C₂³	1	1	yes	characteristic
244	C₁₃×#95	C₂³	1	1	yes	characteristic
245	C₁₃×#95	C₂³	1	1	yes	characteristic
246	C₁₃×#95	C₂³	1	1	yes	characteristic
247	C₁₃×#95	C₂³	1	1	yes	characteristic
248	C₁₃×#95	C₂³	1	1	yes	characteristic
249	C₁₃×#95	C₂³	1	2	yes	—
250	C₁₃×#95	C₂³	1	2	yes	—
251	C₁₃×#95	C₂³	1	2	yes	—
252	C₁₃×#95	C₂³	1	2	yes	—
253	C₁₃×#95	C₂³	1	2	yes	—
254	C₁₃×#95	C₂³	1	2	yes	—
255	C₁₃×#95	C₂³	1	2	yes	—
256	C₁₃×#95	C₂³	1	1	yes	characteristic
257	C₁₃×#95	C₂³	1	2	yes	—
258	C₁₃×#95	C₂³	1	2	yes	—
259	C₁₃×#95	C₂³	1	1	yes	characteristic
260	C₁₃×#95	C₂³	1	2	yes	—
261	C₁₃×#95	C₂³	1	1	yes	characteristic
262	C₁₃×#95	C₂³	1	2	yes	—
263	#34292	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂⁴×C₁₃	—	2	4	no	—
265	C₂⁴×C₁₃	—	2	4	no	—
266	C₂⁴×C₁₃	—	4	2	no	—
267	C₂⁴×C₁₃	—	4	2	no	—
268	C₂⁴×C₁₃	—	4	2	no	—
269	C₂⁴×C₁₃	—	4	2	no	—
270	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
271	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
273	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
275	C₁₃×#41	—	2	32	no	—
276	C₂×Q₈×C₁₃	—	2	2	no	—
277	C₂×Q₈×C₁₃	—	2	2	no	—
278	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₁₃	—	2	4	no	—
280	C₂×D₄×C₁₃	—	2	4	no	—
281	C₂×D₄×C₁₃	—	2	4	no	—
282	C₂×D₄×C₁₃	—	2	4	no	—
283	C₂×D₄×C₁₃	—	2	32	no	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	—	2	2	no	—
286	C₂×D₄×C₁₃	—	4	2	no	—
287	C₂×D₄×C₁₃	—	4	1	no	—
288	C₂×D₄×C₁₃	—	4	2	no	—
289	C₂×D₄×C₁₃	—	4	1	no	—
290	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
291	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
292	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
293	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
294	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
295	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
296	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
297	C₂×D₄×C₁₃	#41	1	4	yes	—
298	C₂²×C₄×C₁₃	—	2	4	no	—
299	C₂²×C₄×C₁₃	—	2	4	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	2	2	no	—
302	C₂²×C₄×C₁₃	—	2	2	no	—
303	C₂²×C₄×C₁₃	—	2	2	no	—
304	C₂²×C₄×C₁₃	—	2	4	no	—
305	C₂²×C₄×C₁₃	—	2	4	no	—
306	C₂²×C₄×C₁₃	—	2	4	no	—
307	C₂²×C₄×C₁₃	—	2	2	no	—
308	C₂²×C₄×C₁₃	—	2	2	no	—
309	C₂²×C₄×C₁₃	—	2	4	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	4	no	—
312	C₂²×C₄×C₁₃	—	2	4	no	—
313	C₂²×C₄×C₁₃	—	4	2	no	—
314	C₂²×C₄×C₁₃	—	4	2	no	—
315	C₂²×C₄×C₁₃	—	4	2	no	—
316	C₂²×C₄×C₁₃	—	4	2	no	—
317	C₂²×C₄×C₁₃	—	4	1	no	—
318	C₂²×C₄×C₁₃	—	4	1	no	—
319	C₂²×C₄×C₁₃	—	4	2	no	—
320	C₂²×C₄×C₁₃	—	4	1	no	—
321	C₂²×C₄×C₁₃	—	4	2	no	—
322	C₂²×C₄×C₁₃	—	4	2	no	—
323	C₂²×C₄×C₁₃	—	4	2	no	—
324	C₂²×C₄×C₁₃	—	4	2	no	—
325	C₂²×C₄×C₁₃	—	4	2	no	—
326	C₂²×C₄×C₁₃	—	4	2	no	—
327	C₂²×C₄×C₁₃	—	4	2	no	—
328	C₂²×C₄×C₁₃	—	4	2	no	—
329	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
330	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
331	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
332	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
333	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
334	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	4	no	—
357	C₁₃×C₄⋊C₄	—	2	4	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	4	no	—
362	C₁₃×C₄⋊C₄	—	4	2	no	—
363	C₁₃×C₄⋊C₄	—	4	2	no	—
364	C₁₃×C₄⋊C₄	—	4	2	no	—
365	C₁₃×C₄⋊C₄	—	4	1	no	—
366	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
367	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
368	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
369	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
370	C₁₃×C₂²⋊C₄	—	2	4	no	—
371	C₁₃×C₂²⋊C₄	—	2	4	no	—
372	C₁₃×C₂²⋊C₄	—	2	4	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	4	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	4	no	—
377	C₁₃×C₂²⋊C₄	—	2	4	no	—
378	C₁₃×C₂²⋊C₄	—	2	4	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	4	no	—
381	C₁₃×C₂²⋊C₄	—	4	2	no	—
382	C₁₃×C₂²⋊C₄	—	4	2	no	—
383	C₁₃×C₂²⋊C₄	—	4	1	no	—
384	C₁₃×C₂²⋊C₄	—	4	2	no	—
385	C₁₃×C₂²⋊C₄	—	4	2	no	—
386	C₁₃×C₂²⋊C₄	—	4	1	no	—
387	C₁₃×C₂²⋊C₄	—	4	1	no	—
388	C₁₃×C₂²⋊C₄	—	4	2	no	—
389	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
390	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
391	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
392	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
393	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
394	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
395	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
396	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	—	2	4	no	—
399	C₄²×C₁₃	—	2	2	no	—
400	C₄²×C₁₃	—	2	4	no	—
401	C₄²×C₁₃	—	2	2	no	—
402	C₄²×C₁₃	—	2	4	no	—
403	C₄²×C₁₃	—	2	4	no	—
404	C₄²×C₁₃	—	2	2	no	—
405	C₄²×C₁₃	—	2	2	no	—
406	C₄²×C₁₃	—	4	2	no	—
407	C₄²×C₁₃	—	4	2	no	—
408	C₄²×C₁₃	—	4	2	no	—
409	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
410	C₄²×C₁₃	C₂×D₄	1	4	yes	—
411	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
412	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
413	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
416	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#2361	C₂×C₁₃	1	2	yes	complemented
418	#2359	C₂×C₁₃	1	2	yes	complemented
419	#2358	C₂×C₁₃	1	2	yes	complemented
420	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
421	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#2342	C₂×C₁₃	1	2	yes	complemented
423	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
424	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
425	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
426	#2325	C₂×C₁₃	1	2	yes	complemented
427	#2323	C₂×C₁₃	1	1	yes	characteristic, complemented
428	#2321	C₂×C₁₃	1	2	yes	complemented
429	C₄×#123	C₂×C₁₃	1	2	yes	complemented
430	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
431	#2290	C₂×C₁₃	1	1	yes	characteristic, complemented
432	C₂×#388	C₂×C₁₃	1	2	yes	complemented
433	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
434	C₂³×C₁₃	—	2	2	no	—
435	C₂³×C₁₃	—	2	2	no	—
436	C₂³×C₁₃	—	2	2	no	—
437	C₂³×C₁₃	—	2	2	no	—
438	C₂³×C₁₃	—	2	1	no	—
439	C₂³×C₁₃	—	2	1	no	—
440	C₂³×C₁₃	—	2	2	no	—
441	C₂³×C₁₃	—	2	1	no	—
442	C₂³×C₁₃	—	2	1	no	—
443	C₂³×C₁₃	—	2	2	no	—
444	C₂³×C₁₃	—	2	1	no	—
445	C₂³×C₁₃	—	2	2	no	—
446	C₂³×C₁₃	—	2	1	no	—
447	C₂³×C₁₃	—	2	1	no	—
448	C₂³×C₁₃	—	2	1	no	—
449	C₂³×C₁₃	—	2	2	no	—
450	C₂³×C₁₃	—	2	2	no	—
451	C₂³×C₁₃	—	2	1	no	—
452	C₂³×C₁₃	—	2	1	no	—
453	C₂³×C₁₃	—	2	2	no	—
454	C₂³×C₁₃	—	2	1	no	—
455	C₂³×C₁₃	—	2	1	no	—
456	C₂³×C₁₃	—	2	16	no	—
457	C₂³×C₁₃	—	4	8	no	—
458	C₂³×C₁₃	—	4	8	no	—
459	C₂³×C₁₃	—	8	4	no	—
460	C₂³×C₁₃	—	8	4	no	—
461	C₂³×C₁₃	—	8	4	no	—
462	C₂³×C₁₃	—	8	4	no	—
463	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
464	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
465	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
466	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
467	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
468	C₂³×C₁₃	C₂×#41	1	4	yes	—
469	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
470	Q₈×C₁₃	—	2	8	no	—
471	D₄×C₁₃	—	2	16	no	—
472	D₄×C₁₃	—	2	16	no	—
473	D₄×C₁₃	—	2	8	no	—
474	D₄×C₁₃	—	4	4	no	—
475	D₄×C₁₃	—	4	8	no	—
476	D₄×C₁₃	C₄×D₄	1	16	yes	complemented
477	C₂×C₄×C₁₃	—	2	16	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	1	no	—
481	C₂×C₄×C₁₃	—	2	2	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	1	no	—
486	C₂×C₄×C₁₃	—	2	2	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	1	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	2	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	8	no	—
499	C₂×C₄×C₁₃	—	2	8	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	2	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	1	no	—
507	C₂×C₄×C₁₃	—	2	2	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	2	2	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	2	2	no	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	1	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	2	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	4	8	no	—
525	C₂×C₄×C₁₃	—	4	8	no	—
526	C₂×C₄×C₁₃	—	4	4	no	—
527	C₂×C₄×C₁₃	—	4	8	no	—
528	C₂×C₄×C₁₃	—	4	4	no	—
529	C₂×C₄×C₁₃	—	8	4	no	—
530	C₂×C₄×C₁₃	—	8	4	no	—
531	C₂×C₄×C₁₃	—	8	4	no	—
532	C₂×C₄×C₁₃	—	8	4	no	—
533	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
534	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
535	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
536	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
538	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
539	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
540	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
542	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
545	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
546	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
547	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
548	#546	C₄×C₁₃	1	16	yes	complemented
549	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
550	C₂×#123	C₂²×C₁₃	1	2	yes	—
551	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
552	C₂×#121	C₂²×C₁₃	1	2	yes	—
553	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
554	C₂×#120	C₂²×C₁₃	1	2	yes	—
555	#518	—	2	8	no	—
556	C₄×#41	—	2	8	no	—
557	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
560	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
565	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
566	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
569	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
570	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
571	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
572	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
573	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
574	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
575	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
577	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
578	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
579	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
580	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
581	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
582	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
583	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#390	C₂²×C₁₃	1	2	yes	—
586	#390	C₂²×C₁₃	1	1	yes	characteristic
587	#390	C₂²×C₁₃	1	1	yes	characteristic
588	#390	C₂²×C₁₃	1	2	yes	complemented
589	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	#389	C₂²×C₁₃	1	2	yes	complemented
591	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	#388	C₂²×C₁₃	1	2	yes	—
593	#388	C₂²×C₁₃	1	2	yes	—
594	#388	C₂²×C₁₃	1	2	yes	—
595	#388	C₂²×C₁₃	1	1	yes	characteristic
596	#388	C₂²×C₁₃	1	2	yes	—
597	#388	C₂²×C₁₃	1	2	yes	—
598	#388	C₂²×C₁₃	1	1	yes	characteristic
599	#388	C₂²×C₁₃	1	2	yes	complemented
600	#388	C₂²×C₁₃	1	2	yes	complemented
601	#388	C₂²×C₁₃	1	2	yes	complemented
602	#388	C₂²×C₁₃	1	2	yes	complemented
603	#388	C₂²×C₁₃	1	2	yes	complemented
604	#388	C₂²×C₁₃	1	2	yes	complemented
605	#388	C₂²×C₁₃	1	2	yes	complemented
606	#387	C₂²×C₁₃	1	2	yes	complemented
607	#387	C₂²×C₁₃	1	2	yes	complemented
608	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#386	C₂²×C₁₃	1	1	yes	characteristic
611	#386	C₂²×C₁₃	1	2	yes	—
612	#386	C₂²×C₁₃	1	2	yes	—
613	#386	C₂²×C₁₃	1	1	yes	characteristic
614	#386	C₂²×C₁₃	1	2	yes	complemented
615	#386	C₂²×C₁₃	1	2	yes	complemented
616	#386	C₂²×C₁₃	1	2	yes	complemented
617	#386	C₂²×C₁₃	1	2	yes	complemented
618	#385	C₂²×C₁₃	1	2	yes	complemented
619	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#385	C₂²×C₁₃	1	2	yes	complemented
621	#385	C₂²×C₁₃	1	2	yes	complemented
622	#385	C₂²×C₁₃	1	2	yes	complemented
623	#385	C₂²×C₁₃	1	2	yes	complemented
624	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
625	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#381	C₂²×C₁₃	1	2	yes	complemented
627	#380	C₂²×C₁₃	1	1	yes	characteristic
628	#380	C₂²×C₁₃	1	2	yes	complemented
629	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#379	C₂²×C₁₃	1	2	yes	—
631	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
634	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
636	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
639	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
641	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
642	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
643	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
644	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
645	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
647	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
648	C₂²×C₁₃	—	2	4	no	—
649	C₂²×C₁₃	—	2	4	no	—
650	C₂²×C₁₃	—	2	4	no	—
651	C₂²×C₁₃	—	2	4	no	—
652	C₂²×C₁₃	—	2	4	no	—
653	C₂²×C₁₃	—	2	4	no	—
654	C₂²×C₁₃	—	2	2	no	—
655	C₂²×C₁₃	—	2	2	no	—
656	C₂²×C₁₃	—	2	4	no	—
657	C₂²×C₁₃	—	2	2	no	—
658	C₂²×C₁₃	—	2	2	no	—
659	C₂²×C₁₃	—	2	4	no	—
660	C₂²×C₁₃	—	2	2	no	—
661	C₂²×C₁₃	—	2	4	no	—
662	C₂²×C₁₃	—	2	2	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	4	2	no	—
665	C₂²×C₁₃	—	4	1	no	—
666	C₂²×C₁₃	—	4	1	no	—
667	C₂²×C₁₃	—	4	2	no	—
668	C₂²×C₁₃	—	4	1	no	—
669	C₂²×C₁₃	—	4	1	no	—
670	C₂²×C₁₃	—	4	2	no	—
671	C₂²×C₁₃	—	4	1	no	—
672	C₂²×C₁₃	—	4	1	no	—
673	C₂²×C₁₃	—	4	2	no	—
674	C₂²×C₁₃	—	4	1	no	—
675	C₂²×C₁₃	—	8	16	no	—
676	C₂²×C₁₃	C₂×C₄×D₄	1	8	yes	—
677	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
678	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
679	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
680	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂²×C₁₃	#585	1	1	yes	characteristic
682	C₂²×C₁₃	#585	1	1	yes	characteristic
683	C₂²×C₁₃	#585	1	1	yes	characteristic
684	C₄×C₁₃	—	2	2	no	—
685	C₄×C₁₃	—	2	2	no	—
686	C₄×C₁₃	—	2	4	no	—
687	C₄×C₁₃	—	2	2	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	2	4	no	—
690	C₄×C₁₃	—	2	2	no	—
691	C₄×C₁₃	—	2	4	no	—
692	C₄×C₁₃	—	2	2	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	—	4	2	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	2	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	1	no	—
702	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
703	C₂⁵	C₂³×C₁₃	1	2	yes	—
704	C₂×#41	—	2	4	no	—
705	C₂×#41	—	2	4	no	—
706	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
707	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
708	C₂²×D₄	—	2	4	no	—
709	C₂²×D₄	—	2	4	no	—
710	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
711	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
714	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
716	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
718	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
720	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
722	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
723	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
724	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
725	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
726	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
727	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
728	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
729	#124	C₂×C₄×C₁₃	1	8	yes	complemented
730	#123	C₂×C₄×C₁₃	1	16	yes	complemented
731	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
732	#121	C₂×C₄×C₁₃	1	8	yes	complemented
733	#121	C₂×C₄×C₁₃	1	16	yes	complemented
734	#120	C₂×C₄×C₁₃	1	16	yes	complemented
735	C₄×Q₈	—	2	4	no	—
736	C₄×Q₈	—	2	4	no	—
737	C₄×D₄	—	2	4	no	—
738	C₄×D₄	—	2	4	no	—
739	C₄×D₄	—	2	4	no	—
740	C₄×D₄	—	2	8	no	—
741	C₄×D₄	—	2	8	no	—
742	C₄×D₄	—	2	4	no	—
743	C₄×D₄	—	2	8	no	—
744	C₄×D₄	—	2	8	no	—
745	C₄×D₄	—	2	4	no	—
746	C₄×D₄	—	4	4	no	—
747	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
748	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
749	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
750	#117	—	2	4	no	—
751	#117	—	2	4	no	—
752	#117	—	2	8	no	—
753	#117	—	2	4	no	—
754	C₂×C₄⋊C₄	—	4	4	no	—
755	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
772	C₂×C₂²⋊C₄	—	2	8	no	—
773	C₂×C₂²⋊C₄	—	2	8	no	—
774	C₂×C₂²⋊C₄	—	4	4	no	—
775	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
776	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
796	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
803	C₂×C₄²	—	2	8	no	—
804	C₂×C₄²	—	2	4	no	—
805	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
807	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
809	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
812	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
813	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
815	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
816	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
817	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
818	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
819	#95	C₂³×C₁₃	1	1	yes	characteristic
820	#95	C₂³×C₁₃	1	1	yes	characteristic
821	#95	C₂³×C₁₃	1	2	yes	—
822	#95	C₂³×C₁₃	1	2	yes	—
823	#95	C₂³×C₁₃	1	2	yes	—
824	#95	C₂³×C₁₃	1	2	yes	—
825	#95	C₂³×C₁₃	1	2	yes	—
826	#95	C₂³×C₁₃	1	2	yes	—
827	#95	C₂³×C₁₃	1	1	yes	characteristic
828	#95	C₂³×C₁₃	1	1	yes	characteristic
829	#95	C₂³×C₁₃	1	1	yes	characteristic
830	#95	C₂³×C₁₃	1	1	yes	characteristic
831	#95	C₂³×C₁₃	1	1	yes	characteristic
832	#95	C₂³×C₁₃	1	1	yes	characteristic
833	#95	C₂³×C₁₃	1	1	yes	characteristic
834	#95	C₂³×C₁₃	1	2	yes	—
835	#95	C₂³×C₁₃	1	2	yes	—
836	#95	C₂³×C₁₃	1	2	yes	—
837	#95	C₂³×C₁₃	1	2	yes	—
838	#95	C₂³×C₁₃	1	2	yes	—
839	#95	C₂³×C₁₃	1	1	yes	characteristic
840	C₂×C₁₃	—	2	8	no	—
841	C₂×C₁₃	—	4	2	no	—
842	C₂×C₁₃	—	4	4	no	—
843	C₂×C₁₃	—	4	2	no	—
844	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
845	C₂×C₁₃	#3428	1	1	yes	characteristic
846	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
847	C₂×C₁₃	#3485	1	1	yes	characteristic
848	C₂×C₁₃	#3488	1	1	yes	characteristic
849	C₂×C₁₃	#3514	1	1	yes	characteristic
850	C₂×C₁₃	#3521	1	1	yes	characteristic
851	C₂⁴	—	2	4	no	—
852	C₂⁴	—	2	4	no	—
853	C₂⁴	—	4	2	no	—
854	C₂⁴	—	4	2	no	—
855	C₂⁴	—	4	2	no	—
856	C₂⁴	—	4	2	no	—
857	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
858	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
860	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
861	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
862	#41	—	2	32	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
866	C₂×D₄	—	2	4	no	—
867	C₂×D₄	—	2	4	no	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	32	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	4	1	no	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	1	no	—
877	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
878	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
879	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
880	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
881	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
882	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
883	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
884	C₂×D₄	C₁₃×#41	1	4	yes	—
885	C₂²×C₄	—	2	4	no	—
886	C₂²×C₄	—	2	4	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	4	no	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	4	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	4	no	—
899	C₂²×C₄	—	2	4	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	2	no	—
903	C₂²×C₄	—	4	2	no	—
904	C₂²×C₄	—	4	1	no	—
905	C₂²×C₄	—	4	1	no	—
906	C₂²×C₄	—	4	2	no	—
907	C₂²×C₄	—	4	1	no	—
908	C₂²×C₄	—	4	2	no	—
909	C₂²×C₄	—	4	2	no	—
910	C₂²×C₄	—	4	2	no	—
911	C₂²×C₄	—	4	2	no	—
912	C₂²×C₄	—	4	2	no	—
913	C₂²×C₄	—	4	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
917	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
918	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
919	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
920	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
921	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
927	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	4	no	—
944	C₄⋊C₄	—	2	4	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	4	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	1	no	—
953	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
954	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
955	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
956	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	4	no	—
964	C₂²⋊C₄	—	2	4	no	—
965	C₂²⋊C₄	—	2	4	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	4	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	1	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	1	no	—
975	C₂²⋊C₄	—	4	1	no	—
976	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
978	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
981	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
982	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
983	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	4	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	4	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	4	no	—
990	C₄²	—	2	4	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	4	2	no	—
994	C₄²	—	4	2	no	—
995	C₄²	—	4	2	no	—
996	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
997	C₄²	C₂×D₄×C₁₃	1	4	yes	—
998	C₁₃	#34292	1	1	yes	characteristic, direct product factor, Sylow
999	C₂³	—	2	2	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	16	no	—
1022	C₂³	—	4	8	no	—
1023	C₂³	—	4	8	no	—
1024	C₂³	—	8	4	no	—
1025	C₂³	—	8	4	no	—
1026	C₂³	—	8	4	no	—
1027	C₂³	—	8	4	no	—
1028	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
1029	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
1030	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
1031	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
1032	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
1033	C₂³	C₂×C₁₃×#41	1	4	yes	—
1034	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1035	Q₈	—	2	8	no	—
1036	D₄	—	2	16	no	—
1037	D₄	—	2	16	no	—
1038	D₄	—	2	8	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	8	no	—
1041	D₄	C₄×D₄×C₁₃	1	16	yes	complemented
1042	C₂×C₄	—	2	16	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	8	no	—
1064	C₂×C₄	—	2	8	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	8	no	—
1090	C₂×C₄	—	4	8	no	—
1091	C₂×C₄	—	4	4	no	—
1092	C₂×C₄	—	4	8	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	8	4	no	—
1095	C₂×C₄	—	8	4	no	—
1096	C₂×C₄	—	8	4	no	—
1097	C₂×C₄	—	8	4	no	—
1098	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1100	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1101	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1102	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1103	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1104	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
1107	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1109	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1110	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1111	C₂²	—	2	4	no	—
1112	C₂²	—	2	4	no	—
1113	C₂²	—	2	4	no	—
1114	C₂²	—	2	4	no	—
1115	C₂²	—	2	4	no	—
1116	C₂²	—	2	4	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	4	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	4	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	8	16	no	—
1139	C₂²	C₂×C₄×D₄×C₁₃	1	8	yes	—
1140	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1141	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1142	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1143	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1144	C₂²	C₁₃×#585	1	1	yes	characteristic
1145	C₂²	C₁₃×#585	1	1	yes	characteristic
1146	C₂²	C₁₃×#585	1	1	yes	characteristic
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	4	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	4	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	4	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
1166	C₂	—	2	8	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	4	no	—
1169	C₂	—	4	2	no	—
1170	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
1171	C₂	C₁₃×#3428	1	1	yes	characteristic
1172	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂	C₁₃×#3485	1	1	yes	characteristic
1174	C₂	C₁₃×#3488	1	1	yes	characteristic
1175	C₂	C₁₃×#3514	1	1	yes	characteristic
1176	C₂	C₁₃×#3521	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×#546	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. C₂×C₁₃×#518	C₂	semidirect
3. C₂×C₄×C₁₃×#41	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2359	C₂	semidirect
9. C₁₃×#2358	C₂	semidirect
10. C₁₃×#2354	C₂	semidirect
11. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₁₃×#2342	C₂	semidirect
13. C₁₃×#2339	C₂	semidirect
14. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
15. C₁₃×#2326	C₂	semidirect
16. C₁₃×#2325	C₂	semidirect
17. C₁₃×#2323	C₂	semidirect
18. C₁₃×#2321	C₂	semidirect
19. C₄×C₁₃×#123	C₂	semidirect
20. C₄×C₁₃×#121	C₂	semidirect
21. C₁₃×#2290	C₂	semidirect
22. C₂×C₁₃×#388	C₂	semidirect
23. C₁₃×#2275	C₂	semidirect
26. C₁₃×#546	C₄	semidirect
35. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
47. C₂×C₄×D₄×C₁₃	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
49. C₂×C₄×D₄×C₁₃	C₂²	semidirect
52. C₂×C₁₃×#117	C₂²	semidirect
53. C₂×C₁₃×#117	C₂²	semidirect
54. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₂²×C₄²×C₁₃	C₂²	semidirect
60. C₂²×C₄²×C₁₃	C₂²	semidirect
61. C₁₃×#391	C₂²	semidirect
62. C₁₃×#391	C₂²	semidirect
66. C₁₃×#390	C₂²	semidirect
67. C₁₃×#389	C₂²	semidirect
68. C₁₃×#389	C₂²	semidirect
69. C₁₃×#389	C₂²	semidirect
77. C₁₃×#388	C₂²	semidirect
78. C₁₃×#388	C₂²	semidirect
79. C₁₃×#388	C₂²	semidirect
80. C₁₃×#388	C₂²	semidirect
81. C₁₃×#388	C₂²	semidirect
82. C₁₃×#388	C₂²	semidirect
83. C₁₃×#388	C₂²	semidirect
84. C₁₃×#387	C₂²	semidirect
85. C₁₃×#387	C₂²	semidirect
86. C₁₃×#387	C₂²	semidirect
87. C₁₃×#387	C₂²	semidirect
92. C₁₃×#386	C₂²	semidirect
93. C₁₃×#386	C₂²	semidirect
94. C₁₃×#386	C₂²	semidirect
95. C₁₃×#386	C₂²	semidirect
96. C₁₃×#385	C₂²	semidirect
97. C₁₃×#385	C₂²	semidirect
98. C₁₃×#385	C₂²	semidirect
99. C₁₃×#385	C₂²	semidirect
100. C₁₃×#385	C₂²	semidirect
101. C₁₃×#385	C₂²	semidirect
102. C₁₃×#385	C₂²	semidirect
103. C₁₃×#384	C₂²	semidirect
104. C₁₃×#381	C₂²	semidirect
106. C₁₃×#380	C₂²	semidirect
107. C₁₃×#380	C₂²	semidirect
109. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
110. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
111. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
112. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
113. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
114. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
116. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
117. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
119. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
123. C₁₃×#376	C₂²	semidirect
124. C₂×C₁₃×#95	C₂²	semidirect
125. C₂×C₁₃×#95	C₂²	semidirect
129. C₂×C₁₃×#41	C₂×C₄	semidirect
133. C₂²×D₄×C₁₃	C₂×C₄	semidirect
152. C₁₃×#124	C₂×C₄	semidirect
153. C₁₃×#123	C₂×C₄	semidirect
154. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
155. C₁₃×#121	C₂×C₄	semidirect
156. C₁₃×#121	C₂×C₄	semidirect
157. C₁₃×#120	C₂×C₄	semidirect
170. C₄×D₄×C₁₃	C₂×C₄	semidirect
171. C₄×D₄×C₁₃	C₂×C₄	semidirect
172. C₄×D₄×C₁₃	D₄	semidirect
198. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
263. #34292	C₁₃	direct (N × H)
412. C₂×#518	C₂×C₁₃	semidirect
413. C₂×C₄×#41	C₂×C₁₃	semidirect
414. #2367	C₂×C₁₃	semidirect
415. #2363	C₂×C₁₃	semidirect
416. #2362	C₂×C₁₃	semidirect
417. #2361	C₂×C₁₃	semidirect
418. #2359	C₂×C₁₃	semidirect
419. #2358	C₂×C₁₃	semidirect
420. #2354	C₂×C₁₃	semidirect
421. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
422. #2342	C₂×C₁₃	semidirect
423. #2339	C₂×C₁₃	semidirect
424. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
425. #2326	C₂×C₁₃	semidirect
426. #2325	C₂×C₁₃	semidirect
427. #2323	C₂×C₁₃	semidirect
428. #2321	C₂×C₁₃	semidirect
429. C₄×#123	C₂×C₁₃	semidirect
430. C₄×#121	C₂×C₁₃	semidirect
431. #2290	C₂×C₁₃	semidirect
432. C₂×#388	C₂×C₁₃	semidirect
433. #2275	C₂×C₁₃	semidirect
476. D₄×C₁₃	C₄×D₄	semidirect
548. #546	C₄×C₁₃	semidirect
557. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
558. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
569. C₂×C₄×D₄	C₂²×C₁₃	semidirect
570. C₂×C₄×D₄	C₂²×C₁₃	semidirect
571. C₂×C₄×D₄	C₂²×C₁₃	semidirect
574. C₂×#117	C₂²×C₁₃	semidirect
575. C₂×#117	C₂²×C₁₃	semidirect
576. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
581. C₂²×C₄²	C₂²×C₁₃	semidirect
582. C₂²×C₄²	C₂²×C₁₃	semidirect
583. #391	C₂²×C₁₃	semidirect
584. #391	C₂²×C₁₃	semidirect
588. #390	C₂²×C₁₃	semidirect
589. #389	C₂²×C₁₃	semidirect
590. #389	C₂²×C₁₃	semidirect
591. #389	C₂²×C₁₃	semidirect
599. #388	C₂²×C₁₃	semidirect
600. #388	C₂²×C₁₃	semidirect
601. #388	C₂²×C₁₃	semidirect
602. #388	C₂²×C₁₃	semidirect
603. #388	C₂²×C₁₃	semidirect
604. #388	C₂²×C₁₃	semidirect
605. #388	C₂²×C₁₃	semidirect
606. #387	C₂²×C₁₃	semidirect
607. #387	C₂²×C₁₃	semidirect
608. #387	C₂²×C₁₃	semidirect
609. #387	C₂²×C₁₃	semidirect
614. #386	C₂²×C₁₃	semidirect
615. #386	C₂²×C₁₃	semidirect
616. #386	C₂²×C₁₃	semidirect
617. #386	C₂²×C₁₃	semidirect
618. #385	C₂²×C₁₃	semidirect
619. #385	C₂²×C₁₃	semidirect
620. #385	C₂²×C₁₃	semidirect
621. #385	C₂²×C₁₃	semidirect
622. #385	C₂²×C₁₃	semidirect
623. #385	C₂²×C₁₃	semidirect
624. #385	C₂²×C₁₃	semidirect
625. #384	C₂²×C₁₃	semidirect
626. #381	C₂²×C₁₃	semidirect
628. #380	C₂²×C₁₃	semidirect
629. #380	C₂²×C₁₃	semidirect
631. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
632. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
633. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
634. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
635. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
636. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
638. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
639. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
640. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
641. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
642. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
643. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
644. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
645. #376	C₂²×C₁₃	semidirect
646. C₂×#95	C₂²×C₁₃	semidirect
647. C₂×#95	C₂²×C₁₃	semidirect
706. C₂×#41	C₂×C₄×C₁₃	semidirect
710. C₂²×D₄	C₂×C₄×C₁₃	semidirect
729. #124	C₂×C₄×C₁₃	semidirect
730. #123	C₂×C₄×C₁₃	semidirect
731. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
732. #121	C₂×C₄×C₁₃	semidirect
733. #121	C₂×C₄×C₁₃	semidirect
734. #120	C₂×C₄×C₁₃	semidirect
747. C₄×D₄	C₂×C₄×C₁₃	semidirect
748. C₄×D₄	C₂×C₄×C₁₃	semidirect
749. C₄×D₄	D₄×C₁₃	semidirect
775. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
998. C₁₃	#34292	direct (N × H)
1041. D₄	C₄×D₄×C₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#546	2
C₂×C₁₃×#518	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2367	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2359	2
C₁₃×#2358	2
C₁₃×#2354	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2342	2
C₁₃×#2339	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2326	2
C₁₃×#2325	2
C₁₃×#2323	2
C₁₃×#2321	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2290	2
C₂×C₁₃×#388	2
C₁₃×#2275	2
#34292	13

Subgroups — C13×#34292 #15720631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34292 #15720631