Subgroups — C₁₃×#34495 #15720834

Order 3328.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1124 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	C₁₃×#2376	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2363	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×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2312	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2293	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	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×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	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#390	C₂²	1	2	yes	—
55	C₁₃×#390	C₂²	1	1	yes	characteristic
56	C₁₃×#390	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#390	C₂²	1	2	yes	complemented
60	C₁₃×#390	C₂²	1	2	yes	complemented
61	C₁₃×#390	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#388	C₂²	1	1	yes	characteristic
68	C₁₃×#388	C₂²	1	1	yes	characteristic
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	complemented
75	C₁₃×#388	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#388	C₂²	1	1	yes	characteristic, complemented
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×#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×#387	C₂²	1	2	yes	complemented
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	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	2	yes	complemented
97	C₁₃×#385	C₂²	1	2	yes	complemented
98	C₁₃×#385	C₂²	1	2	yes	complemented
99	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#381	C₂²	1	2	yes	complemented
101	C₁₃×#380	C₂²	1	1	yes	characteristic
102	C₁₃×#380	C₂²	1	2	yes	complemented
103	C₁₃×#380	C₂²	1	2	yes	complemented
104	C₁₃×#380	C₂²	1	2	yes	complemented
105	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#379	C₂²	1	2	yes	—
107	C₁₃×#379	C₂²	1	2	yes	—
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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, 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	2	yes	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	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₁₃	C₂³	1	2	yes	—
125	C₂×C₁₃×#41	—	4	2	no	—
126	C₂×C₁₃×#41	—	4	2	no	—
127	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃	—	4	2	no	—
130	C₂²×D₄×C₁₃	—	4	2	no	—
131	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
145	C₁₃×#124	C₂×C₄	1	8	yes	complemented
146	C₁₃×#123	C₂×C₄	1	16	yes	complemented
147	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
148	C₁₃×#121	C₂×C₄	1	8	yes	—
149	C₁₃×#121	C₂×C₄	1	16	yes	complemented
150	C₁₃×#120	C₂×C₄	1	16	yes	complemented
151	C₄×Q₈×C₁₃	—	4	2	no	—
152	C₄×Q₈×C₁₃	—	4	2	no	—
153	C₄×D₄×C₁₃	—	4	2	no	—
154	C₄×D₄×C₁₃	—	4	2	no	—
155	C₄×D₄×C₁₃	—	4	4	no	—
156	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
158	C₁₃×#117	—	4	2	no	—
159	C₁₃×#117	—	4	2	no	—
160	C₁₃×#117	—	4	4	no	—
161	C₁₃×#117	—	4	2	no	—
162	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	4	4	no	—
182	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
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	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
205	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	1	yes	characteristic
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	1	yes	characteristic
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	#34495	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂⁴×C₁₃	—	4	2	no	—
251	C₂⁴×C₁₃	—	4	2	no	—
252	C₂⁴×C₁₃	—	4	2	no	—
253	C₂⁴×C₁₃	—	4	2	no	—
254	C₂⁴×C₁₃	—	4	2	no	—
255	C₂⁴×C₁₃	—	4	2	no	—
256	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
257	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
259	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
260	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₁₃×#41	—	4	16	no	—
262	C₂×Q₈×C₁₃	—	2	2	no	—
263	C₂×Q₈×C₁₃	—	2	2	no	—
264	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	4	16	no	—
270	C₂×D₄×C₁₃	—	4	2	no	—
271	C₂×D₄×C₁₃	—	4	2	no	—
272	C₂×D₄×C₁₃	—	4	2	no	—
273	C₂×D₄×C₁₃	—	4	1	no	—
274	C₂×D₄×C₁₃	—	4	1	no	—
275	C₂×D₄×C₁₃	—	4	2	no	—
276	C₂×D₄×C₁₃	—	4	2	no	—
277	C₂×D₄×C₁₃	—	4	2	no	—
278	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
281	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
282	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
283	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
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	2	no	—
288	C₂²×C₄×C₁₃	—	2	4	no	—
289	C₂²×C₄×C₁₃	—	4	2	no	—
290	C₂²×C₄×C₁₃	—	4	2	no	—
291	C₂²×C₄×C₁₃	—	4	2	no	—
292	C₂²×C₄×C₁₃	—	4	2	no	—
293	C₂²×C₄×C₁₃	—	4	2	no	—
294	C₂²×C₄×C₁₃	—	4	2	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	C₂²×C₄	1	4	yes	—
302	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
303	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	4	2	no	—
330	C₁₃×C₄⋊C₄	—	4	1	no	—
331	C₁₃×C₄⋊C₄	—	4	1	no	—
332	C₁₃×C₄⋊C₄	—	4	2	no	—
333	C₁₃×C₄⋊C₄	—	4	1	no	—
334	C₁₃×C₄⋊C₄	—	4	1	no	—
335	C₁₃×C₄⋊C₄	—	4	1	no	—
336	C₁₃×C₄⋊C₄	—	4	1	no	—
337	C₁₃×C₄⋊C₄	—	4	2	no	—
338	C₁₃×C₄⋊C₄	—	4	2	no	—
339	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
340	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
341	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	4	2	no	—
346	C₁₃×C₂²⋊C₄	—	4	2	no	—
347	C₁₃×C₂²⋊C₄	—	4	1	no	—
348	C₁₃×C₂²⋊C₄	—	4	2	no	—
349	C₁₃×C₂²⋊C₄	—	4	2	no	—
350	C₁₃×C₂²⋊C₄	—	4	2	no	—
351	C₁₃×C₂²⋊C₄	—	4	1	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	—	4	2	no	—
358	C₁₃×C₂²⋊C₄	—	4	1	no	—
359	C₁₃×C₂²⋊C₄	—	4	1	no	—
360	C₁₃×C₂²⋊C₄	—	4	1	no	—
361	C₁₃×C₂²⋊C₄	—	4	1	no	—
362	C₁₃×C₂²⋊C₄	—	4	2	no	—
363	C₁₃×C₂²⋊C₄	—	4	2	no	—
364	C₁₃×C₂²⋊C₄	—	4	2	no	—
365	C₁₃×C₂²⋊C₄	—	4	2	no	—
366	C₁₃×C₂²⋊C₄	—	4	2	no	—
367	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
368	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
369	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
370	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
371	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
372	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
373	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	—	2	2	no	—
376	C₄²×C₁₃	—	2	2	no	—
377	C₄²×C₁₃	—	2	2	no	—
378	C₄²×C₁₃	—	2	2	no	—
379	C₄²×C₁₃	—	4	1	no	—
380	C₄²×C₁₃	—	4	1	no	—
381	C₄²×C₁₃	—	4	1	no	—
382	C₄²×C₁₃	—	4	2	no	—
383	C₄²×C₁₃	—	4	2	no	—
384	C₄²×C₁₃	—	4	2	no	—
385	C₄²×C₁₃	—	4	2	no	—
386	C₄²×C₁₃	—	4	2	no	—
387	C₄²×C₁₃	—	4	2	no	—
388	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
389	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
390	#2376	C₂×C₁₃	1	2	yes	complemented
391	#2375	C₂×C₁₃	1	2	yes	complemented
392	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#2363	C₂×C₁₃	1	2	yes	complemented
394	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#2361	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#2357	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#2352	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#2342	C₂×C₁₃	1	2	yes	complemented
399	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
400	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
401	#2335	C₂×C₁₃	1	2	yes	complemented
402	#2333	C₂×C₁₃	1	2	yes	complemented
403	#2324	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#2323	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#2321	C₂×C₁₃	1	2	yes	complemented
406	#2312	C₂×C₁₃	1	2	yes	complemented
407	#2311	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#2309	C₂×C₁₃	1	1	yes	characteristic, complemented
409	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
411	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
412	C₂³×C₁₃	—	2	2	no	—
413	C₂³×C₁₃	—	2	1	no	—
414	C₂³×C₁₃	—	2	1	no	—
415	C₂³×C₁₃	—	2	1	no	—
416	C₂³×C₁₃	—	2	1	no	—
417	C₂³×C₁₃	—	2	1	no	—
418	C₂³×C₁₃	—	2	2	no	—
419	C₂³×C₁₃	—	2	2	no	—
420	C₂³×C₁₃	—	2	2	no	—
421	C₂³×C₁₃	—	2	1	no	—
422	C₂³×C₁₃	—	2	2	no	—
423	C₂³×C₁₃	—	2	2	no	—
424	C₂³×C₁₃	—	2	1	no	—
425	C₂³×C₁₃	—	2	2	no	—
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	2	no	—
428	C₂³×C₁₃	—	2	2	no	—
429	C₂³×C₁₃	—	2	2	no	—
430	C₂³×C₁₃	—	2	1	no	—
431	C₂³×C₁₃	—	2	2	no	—
432	C₂³×C₁₃	—	2	1	no	—
433	C₂³×C₁₃	—	2	1	no	—
434	C₂³×C₁₃	—	2	1	no	—
435	C₂³×C₁₃	—	2	1	no	—
436	C₂³×C₁₃	—	4	8	no	—
437	C₂³×C₁₃	—	4	8	no	—
438	C₂³×C₁₃	—	4	8	no	—
439	C₂³×C₁₃	—	8	4	no	—
440	C₂³×C₁₃	—	8	4	no	—
441	C₂³×C₁₃	—	8	4	no	—
442	C₂³×C₁₃	—	8	4	no	—
443	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
444	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
445	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
446	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
447	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
448	Q₈×C₁₃	—	2	8	no	—
449	D₄×C₁₃	—	2	8	no	—
450	D₄×C₁₃	—	2	8	no	—
451	D₄×C₁₃	—	4	8	no	—
452	D₄×C₁₃	—	4	4	no	—
453	D₄×C₁₃	—	4	8	no	—
454	D₄×C₁₃	—	4	8	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	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	1	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	1	no	—
466	C₂×C₄×C₁₃	—	2	1	no	—
467	C₂×C₄×C₁₃	—	2	1	no	—
468	C₂×C₄×C₁₃	—	2	2	no	—
469	C₂×C₄×C₁₃	—	2	8	no	—
470	C₂×C₄×C₁₃	—	2	8	no	—
471	C₂×C₄×C₁₃	—	2	1	no	—
472	C₂×C₄×C₁₃	—	2	1	no	—
473	C₂×C₄×C₁₃	—	2	1	no	—
474	C₂×C₄×C₁₃	—	2	1	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	2	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	2	2	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	1	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	1	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	2	no	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	2	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	4	8	no	—
505	C₂×C₄×C₁₃	—	4	8	no	—
506	C₂×C₄×C₁₃	—	8	4	no	—
507	C₂×C₄×C₁₃	—	8	4	no	—
508	C₂×C₄×C₁₃	—	8	4	no	—
509	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
510	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
512	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
513	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
514	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
516	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
517	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
519	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
520	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
521	#546	C₄×C₁₃	1	16	yes	complemented
522	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
523	C₂×#123	C₂²×C₁₃	1	2	yes	—
524	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
525	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
526	C₂×#121	C₂²×C₁₃	1	2	yes	—
527	C₂×#120	C₂²×C₁₃	1	2	yes	—
528	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
529	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
531	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
533	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
534	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
535	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
536	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
537	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
539	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
540	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
541	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
542	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
543	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	#390	C₂²×C₁₃	1	1	yes	characteristic
545	#390	C₂²×C₁₃	1	1	yes	characteristic
546	#390	C₂²×C₁₃	1	2	yes	—
547	#390	C₂²×C₁₃	1	1	yes	characteristic
548	#390	C₂²×C₁₃	1	1	yes	characteristic
549	#390	C₂²×C₁₃	1	2	yes	—
550	#390	C₂²×C₁₃	1	1	yes	characteristic
551	#390	C₂²×C₁₃	1	1	yes	characteristic
552	#390	C₂²×C₁₃	1	1	yes	characteristic
553	#390	C₂²×C₁₃	1	1	yes	characteristic
554	#390	C₂²×C₁₃	1	2	yes	complemented
555	#390	C₂²×C₁₃	1	2	yes	complemented
556	#390	C₂²×C₁₃	1	2	yes	complemented
557	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	#389	C₂²×C₁₃	1	2	yes	complemented
559	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	#388	C₂²×C₁₃	1	1	yes	characteristic
563	#388	C₂²×C₁₃	1	2	yes	—
564	#388	C₂²×C₁₃	1	2	yes	—
565	#388	C₂²×C₁₃	1	2	yes	—
566	#388	C₂²×C₁₃	1	2	yes	—
567	#388	C₂²×C₁₃	1	2	yes	—
568	#388	C₂²×C₁₃	1	1	yes	characteristic
569	#388	C₂²×C₁₃	1	2	yes	complemented
570	#388	C₂²×C₁₃	1	2	yes	complemented
571	#388	C₂²×C₁₃	1	2	yes	complemented
572	#388	C₂²×C₁₃	1	2	yes	complemented
573	#388	C₂²×C₁₃	1	2	yes	complemented
574	#388	C₂²×C₁₃	1	2	yes	complemented
575	#388	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#388	C₂²×C₁₃	1	2	yes	complemented
577	#388	C₂²×C₁₃	1	2	yes	complemented
578	#388	C₂²×C₁₃	1	1	yes	characteristic, complemented
579	#388	C₂²×C₁₃	1	2	yes	complemented
580	#388	C₂²×C₁₃	1	2	yes	complemented
581	#387	C₂²×C₁₃	1	2	yes	complemented
582	#387	C₂²×C₁₃	1	2	yes	complemented
583	#387	C₂²×C₁₃	1	2	yes	complemented
584	#386	C₂²×C₁₃	1	2	yes	—
585	#386	C₂²×C₁₃	1	2	yes	—
586	#386	C₂²×C₁₃	1	2	yes	—
587	#386	C₂²×C₁₃	1	2	yes	complemented
588	#386	C₂²×C₁₃	1	2	yes	complemented
589	#386	C₂²×C₁₃	1	2	yes	complemented
590	#386	C₂²×C₁₃	1	2	yes	complemented
591	#385	C₂²×C₁₃	1	2	yes	complemented
592	#385	C₂²×C₁₃	1	2	yes	complemented
593	#385	C₂²×C₁₃	1	2	yes	complemented
594	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
595	#381	C₂²×C₁₃	1	2	yes	complemented
596	#380	C₂²×C₁₃	1	1	yes	characteristic
597	#380	C₂²×C₁₃	1	2	yes	complemented
598	#380	C₂²×C₁₃	1	2	yes	complemented
599	#380	C₂²×C₁₃	1	2	yes	complemented
600	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#379	C₂²×C₁₃	1	2	yes	—
602	#379	C₂²×C₁₃	1	2	yes	—
603	#379	C₂²×C₁₃	1	2	yes	—
604	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
607	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
610	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
611	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
612	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
613	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
614	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
615	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
616	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
618	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	C₂²×C₁₃	—	2	2	no	—
620	C₂²×C₁₃	—	2	2	no	—
621	C₂²×C₁₃	—	2	4	no	—
622	C₂²×C₁₃	—	2	4	no	—
623	C₂²×C₁₃	—	2	2	no	—
624	C₂²×C₁₃	—	2	2	no	—
625	C₂²×C₁₃	—	2	4	no	—
626	C₂²×C₁₃	—	2	4	no	—
627	C₂²×C₁₃	—	2	4	no	—
628	C₂²×C₁₃	—	2	2	no	—
629	C₂²×C₁₃	—	2	4	no	—
630	C₂²×C₁₃	—	2	2	no	—
631	C₂²×C₁₃	—	4	2	no	—
632	C₂²×C₁₃	—	4	1	no	—
633	C₂²×C₁₃	—	4	2	no	—
634	C₂²×C₁₃	—	4	1	no	—
635	C₂²×C₁₃	—	4	1	no	—
636	C₂²×C₁₃	—	4	2	no	—
637	C₂²×C₁₃	—	4	2	no	—
638	C₂²×C₁₃	—	4	1	no	—
639	C₂²×C₁₃	—	4	1	no	—
640	C₂²×C₁₃	—	4	2	no	—
641	C₂²×C₁₃	—	4	2	no	—
642	C₂²×C₁₃	—	4	1	no	—
643	C₂²×C₁₃	—	4	1	no	—
644	C₂²×C₁₃	—	4	2	no	—
645	C₂²×C₁₃	—	4	2	no	—
646	C₂²×C₁₃	—	4	1	no	—
647	C₂²×C₁₃	—	8	16	no	—
648	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
649	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
650	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
651	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂²×C₁₃	#585	1	1	yes	characteristic
653	C₂²×C₁₃	#585	1	1	yes	characteristic
654	C₂²×C₁₃	#585	1	1	yes	characteristic
655	C₄×C₁₃	—	2	2	no	—
656	C₄×C₁₃	—	2	2	no	—
657	C₄×C₁₃	—	2	4	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	2	2	no	—
660	C₄×C₁₃	—	2	4	no	—
661	C₄×C₁₃	—	2	2	no	—
662	C₄×C₁₃	—	4	1	no	—
663	C₄×C₁₃	—	4	1	no	—
664	C₄×C₁₃	—	4	2	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	1	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	1	no	—
669	C₄×C₁₃	—	4	2	no	—
670	C₄×C₁₃	—	4	2	no	—
671	C₄×C₁₃	—	4	1	no	—
672	C₄×C₁₃	—	4	2	no	—
673	C₄×C₁₃	#518	1	4	yes	—
674	C₂⁵	C₂³×C₁₃	1	2	yes	—
675	C₂×#41	—	4	2	no	—
676	C₂×#41	—	4	2	no	—
677	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
678	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
679	C₂²×D₄	—	4	2	no	—
680	C₂²×D₄	—	4	2	no	—
681	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
682	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
685	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
686	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
687	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
688	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
692	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
693	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
694	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
695	#124	C₂×C₄×C₁₃	1	8	yes	complemented
696	#123	C₂×C₄×C₁₃	1	16	yes	complemented
697	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
698	#121	C₂×C₄×C₁₃	1	8	yes	—
699	#121	C₂×C₄×C₁₃	1	16	yes	complemented
700	#120	C₂×C₄×C₁₃	1	16	yes	complemented
701	C₄×Q₈	—	4	2	no	—
702	C₄×Q₈	—	4	2	no	—
703	C₄×D₄	—	4	2	no	—
704	C₄×D₄	—	4	2	no	—
705	C₄×D₄	—	4	4	no	—
706	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
707	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
708	#117	—	4	2	no	—
709	#117	—	4	2	no	—
710	#117	—	4	4	no	—
711	#117	—	4	2	no	—
712	C₂×C₄⋊C₄	—	4	2	no	—
713	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
731	C₂×C₂²⋊C₄	—	4	4	no	—
732	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
733	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
765	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
771	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
772	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
773	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
774	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
775	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
779	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
780	#95	C₂³×C₁₃	1	1	yes	characteristic
781	#95	C₂³×C₁₃	1	1	yes	characteristic
782	#95	C₂³×C₁₃	1	2	yes	—
783	#95	C₂³×C₁₃	1	1	yes	characteristic
784	#95	C₂³×C₁₃	1	1	yes	characteristic
785	#95	C₂³×C₁₃	1	1	yes	characteristic
786	#95	C₂³×C₁₃	1	2	yes	—
787	#95	C₂³×C₁₃	1	2	yes	—
788	#95	C₂³×C₁₃	1	1	yes	characteristic
789	#95	C₂³×C₁₃	1	2	yes	—
790	#95	C₂³×C₁₃	1	2	yes	—
791	#95	C₂³×C₁₃	1	2	yes	—
792	#95	C₂³×C₁₃	1	2	yes	—
793	#95	C₂³×C₁₃	1	2	yes	—
794	#95	C₂³×C₁₃	1	2	yes	—
795	#95	C₂³×C₁₃	1	2	yes	—
796	#95	C₂³×C₁₃	1	2	yes	—
797	#95	C₂³×C₁₃	1	2	yes	—
798	#95	C₂³×C₁₃	1	2	yes	—
799	C₂×C₁₃	—	4	2	no	—
800	C₂×C₁₃	—	4	4	no	—
801	C₂×C₁₃	—	4	4	no	—
802	C₂×C₁₃	—	4	2	no	—
803	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
804	C₂×C₁₃	#3428	1	1	yes	characteristic
805	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
806	C₂×C₁₃	#3546	1	1	yes	characteristic
807	C₂×C₁₃	#3551	1	1	yes	characteristic
808	C₂×C₁₃	#3558	1	1	yes	characteristic
809	C₂×C₁₃	#3562	1	1	yes	characteristic
810	C₂⁴	—	4	2	no	—
811	C₂⁴	—	4	2	no	—
812	C₂⁴	—	4	2	no	—
813	C₂⁴	—	4	2	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
817	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
819	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
820	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
821	#41	—	4	16	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	2	2	no	—
824	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	4	16	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	1	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
839	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
840	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
841	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
842	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
843	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
862	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
863	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
864	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
879	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	4	2	no	—
890	C₄⋊C₄	—	4	2	no	—
891	C₄⋊C₄	—	4	1	no	—
892	C₄⋊C₄	—	4	1	no	—
893	C₄⋊C₄	—	4	1	no	—
894	C₄⋊C₄	—	4	1	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	1	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
900	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
901	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	1	no	—
908	C₂²⋊C₄	—	4	1	no	—
909	C₂²⋊C₄	—	4	1	no	—
910	C₂²⋊C₄	—	4	1	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	—	4	1	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	1	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
928	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
929	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
930	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
931	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
932	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
933	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	4	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	—	4	2	no	—
943	C₄²	—	4	2	no	—
944	C₄²	—	4	1	no	—
945	C₄²	—	4	1	no	—
946	C₄²	—	4	1	no	—
947	C₄²	—	4	2	no	—
948	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
949	C₁₃	#34495	1	1	yes	characteristic, direct product factor, Sylow
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	4	8	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	8	no	—
977	C₂³	—	8	4	no	—
978	C₂³	—	8	4	no	—
979	C₂³	—	8	4	no	—
980	C₂³	—	8	4	no	—
981	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
982	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
983	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
984	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
985	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
986	Q₈	—	2	8	no	—
987	D₄	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	4	8	no	—
990	D₄	—	4	4	no	—
991	D₄	—	4	8	no	—
992	D₄	—	4	8	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	8	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	8	4	no	—
1045	C₂×C₄	—	8	4	no	—
1046	C₂×C₄	—	8	4	no	—
1047	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1048	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1049	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1050	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1051	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1052	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1053	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1054	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1055	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1056	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	4	no	—
1060	C₂²	—	2	4	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	2	4	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	8	16	no	—
1086	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1087	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1089	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1090	C₂²	C₁₃×#585	1	1	yes	characteristic
1091	C₂²	C₁₃×#585	1	1	yes	characteristic
1092	C₂²	C₁₃×#585	1	1	yes	characteristic
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	4	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	4	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	C₁₃×#518	1	4	yes	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	4	no	—
1114	C₂	—	4	4	no	—
1115	C₂	—	4	2	no	—
1116	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
1117	C₂	C₁₃×#3428	1	1	yes	characteristic
1118	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1119	C₂	C₁₃×#3546	1	1	yes	characteristic
1120	C₂	C₁₃×#3551	1	1	yes	characteristic
1121	C₂	C₁₃×#3558	1	1	yes	characteristic
1122	C₂	C₁₃×#3562	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. C₁₃×#2376	C₂	semidirect
3. C₁₃×#2375	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2357	C₂	semidirect
9. C₁₃×#2352	C₂	semidirect
10. C₁₃×#2342	C₂	semidirect
11. C₁₃×#2341	C₂	semidirect
12. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
13. C₁₃×#2335	C₂	semidirect
14. C₁₃×#2333	C₂	semidirect
15. C₁₃×#2324	C₂	semidirect
16. C₁₃×#2323	C₂	semidirect
17. C₁₃×#2321	C₂	semidirect
18. C₁₃×#2312	C₂	semidirect
19. C₁₃×#2311	C₂	semidirect
20. C₁₃×#2309	C₂	semidirect
21. C₄×C₁₃×#124	C₂	semidirect
22. C₁₃×#2293	C₂	semidirect
23. C₁₃×#2293	C₂	semidirect
26. C₁₃×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
42. C₂×C₁₃×#117	C₂²	semidirect
43. C₂×C₁₃×#117	C₂²	semidirect
44. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₁₃×#391	C₂²	semidirect
48. C₁₃×#391	C₂²	semidirect
59. C₁₃×#390	C₂²	semidirect
60. C₁₃×#390	C₂²	semidirect
61. C₁₃×#390	C₂²	semidirect
62. C₁₃×#389	C₂²	semidirect
63. C₁₃×#389	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
74. C₁₃×#388	C₂²	semidirect
75. C₁₃×#388	C₂²	semidirect
76. C₁₃×#388	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×#388	C₂²	semidirect
85. C₁₃×#388	C₂²	semidirect
86. C₁₃×#387	C₂²	semidirect
87. C₁₃×#387	C₂²	semidirect
88. 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×#382	C₂²	semidirect
100. C₁₃×#381	C₂²	semidirect
102. C₁₃×#380	C₂²	semidirect
103. C₁₃×#380	C₂²	semidirect
104. C₁₃×#380	C₂²	semidirect
105. 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
115. C₄×C₁₃×C₂²⋊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. C₄³×C₁₃	C₂²	semidirect
127. C₂×C₁₃×#41	C₂×C₄	semidirect
131. C₂²×D₄×C₁₃	C₂×C₄	semidirect
145. C₁₃×#124	C₂×C₄	semidirect
146. C₁₃×#123	C₂×C₄	semidirect
147. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
149. C₁₃×#121	C₂×C₄	semidirect
150. C₁₃×#120	C₂×C₄	semidirect
156. C₄×D₄×C₁₃	C₂×C₄	semidirect
157. C₄×D₄×C₁₃	C₂×C₄	semidirect
182. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
249. #34495	C₁₃	direct (N × H)
390. #2376	C₂×C₁₃	semidirect
391. #2375	C₂×C₁₃	semidirect
392. #2367	C₂×C₁₃	semidirect
393. #2363	C₂×C₁₃	semidirect
394. #2362	C₂×C₁₃	semidirect
395. #2361	C₂×C₁₃	semidirect
396. #2357	C₂×C₁₃	semidirect
397. #2352	C₂×C₁₃	semidirect
398. #2342	C₂×C₁₃	semidirect
399. #2341	C₂×C₁₃	semidirect
400. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
401. #2335	C₂×C₁₃	semidirect
402. #2333	C₂×C₁₃	semidirect
403. #2324	C₂×C₁₃	semidirect
404. #2323	C₂×C₁₃	semidirect
405. #2321	C₂×C₁₃	semidirect
406. #2312	C₂×C₁₃	semidirect
407. #2311	C₂×C₁₃	semidirect
408. #2309	C₂×C₁₃	semidirect
409. C₄×#124	C₂×C₁₃	semidirect
410. #2293	C₂×C₁₃	semidirect
411. #2293	C₂×C₁₃	semidirect
521. #546	C₄×C₁₃	semidirect
528. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
529. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
534. C₂×C₄×D₄	C₂²×C₁₃	semidirect
537. C₂×#117	C₂²×C₁₃	semidirect
538. C₂×#117	C₂²×C₁₃	semidirect
539. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
542. #391	C₂²×C₁₃	semidirect
543. #391	C₂²×C₁₃	semidirect
554. #390	C₂²×C₁₃	semidirect
555. #390	C₂²×C₁₃	semidirect
556. #390	C₂²×C₁₃	semidirect
557. #389	C₂²×C₁₃	semidirect
558. #389	C₂²×C₁₃	semidirect
559. #389	C₂²×C₁₃	semidirect
560. #389	C₂²×C₁₃	semidirect
561. #389	C₂²×C₁₃	semidirect
569. #388	C₂²×C₁₃	semidirect
570. #388	C₂²×C₁₃	semidirect
571. #388	C₂²×C₁₃	semidirect
572. #388	C₂²×C₁₃	semidirect
573. #388	C₂²×C₁₃	semidirect
574. #388	C₂²×C₁₃	semidirect
575. #388	C₂²×C₁₃	semidirect
576. #388	C₂²×C₁₃	semidirect
577. #388	C₂²×C₁₃	semidirect
578. #388	C₂²×C₁₃	semidirect
579. #388	C₂²×C₁₃	semidirect
580. #388	C₂²×C₁₃	semidirect
581. #387	C₂²×C₁₃	semidirect
582. #387	C₂²×C₁₃	semidirect
583. #387	C₂²×C₁₃	semidirect
587. #386	C₂²×C₁₃	semidirect
588. #386	C₂²×C₁₃	semidirect
589. #386	C₂²×C₁₃	semidirect
590. #386	C₂²×C₁₃	semidirect
591. #385	C₂²×C₁₃	semidirect
592. #385	C₂²×C₁₃	semidirect
593. #385	C₂²×C₁₃	semidirect
594. #382	C₂²×C₁₃	semidirect
595. #381	C₂²×C₁₃	semidirect
597. #380	C₂²×C₁₃	semidirect
598. #380	C₂²×C₁₃	semidirect
599. #380	C₂²×C₁₃	semidirect
600. #380	C₂²×C₁₃	semidirect
604. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
605. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
606. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
607. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
608. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
610. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
611. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
612. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
613. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
614. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
615. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
616. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
617. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
618. C₄³	C₂²×C₁₃	semidirect
677. C₂×#41	C₂×C₄×C₁₃	semidirect
681. C₂²×D₄	C₂×C₄×C₁₃	semidirect
695. #124	C₂×C₄×C₁₃	semidirect
696. #123	C₂×C₄×C₁₃	semidirect
697. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
699. #121	C₂×C₄×C₁₃	semidirect
700. #120	C₂×C₄×C₁₃	semidirect
706. C₄×D₄	C₂×C₄×C₁₃	semidirect
707. C₄×D₄	C₂×C₄×C₁₃	semidirect
732. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
949. C₁₃	#34495	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×#546	2
C₁₃×#2376	2
C₁₃×#2375	2
C₁₃×#2367	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2361	2
C₁₃×#2357	2
C₁₃×#2352	2
C₁₃×#2342	2
C₁₃×#2341	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2335	2
C₁₃×#2333	2
C₁₃×#2324	2
C₁₃×#2323	2
C₁₃×#2321	2
C₁₃×#2312	2
C₁₃×#2311	2
C₁₃×#2309	2
C₄×C₁₃×#124	2
C₁₃×#2293	2
#34495	13

Subgroups — C13×#34495 #15720834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34495 #15720834