Subgroups — C₁₃×#34261 #15720600

Order 3328.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2342	C₂	1	2	yes	maximal, complemented
12	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2312	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
22	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#518	C₄	1	16	yes	complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
46	C₁₃×#390	C₂²	1	1	yes	characteristic
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#388	C₂²	1	1	yes	characteristic
55	C₁₃×#388	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	1	yes	characteristic
59	C₁₃×#388	C₂²	1	1	yes	characteristic
60	C₁₃×#388	C₂²	1	1	yes	characteristic
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	complemented
65	C₁₃×#388	C₂²	1	2	yes	complemented
66	C₁₃×#388	C₂²	1	2	yes	complemented
67	C₁₃×#388	C₂²	1	2	yes	complemented
68	C₁₃×#388	C₂²	1	2	yes	complemented
69	C₁₃×#388	C₂²	1	2	yes	complemented
70	C₁₃×#388	C₂²	1	2	yes	complemented
71	C₁₃×#388	C₂²	1	2	yes	complemented
72	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#387	C₂²	1	2	yes	complemented
74	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#387	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#387	C₂²	1	2	yes	complemented
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×#385	C₂²	1	2	yes	complemented
83	C₁₃×#385	C₂²	1	2	yes	complemented
84	C₁₃×#385	C₂²	1	2	yes	complemented
85	C₁₃×#385	C₂²	1	2	yes	complemented
86	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#383	C₂²	1	2	yes	complemented
88	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#382	C₂²	1	2	yes	complemented
90	C₁₃×#381	C₂²	1	2	yes	complemented
91	C₁₃×#381	C₂²	1	2	yes	complemented
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	1	yes	characteristic
94	C₁₃×#380	C₂²	1	2	yes	complemented
95	C₁₃×#380	C₂²	1	2	yes	complemented
96	C₁₃×#380	C₂²	1	2	yes	complemented
97	C₁₃×#380	C₂²	1	2	yes	complemented
98	C₁₃×#379	C₂²	1	2	yes	—
99	C₁₃×#379	C₂²	1	2	yes	—
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
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	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
120	C₁₃×#376	C₂²	1	2	yes	complemented
121	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
122	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	—	2	4	no	—
126	C₂²×D₄×C₁₃	—	2	4	no	—
127	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₄×D₄×C₁₃	—	2	4	no	—
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
145	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
147	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
148	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
149	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
150	C₁₃×#117	—	4	4	no	—
151	C₁₃×#117	—	4	4	no	—
152	C₁₃×#117	C₂×C₄	1	8	yes	complemented
153	C₁₃×#117	C₂×C₄	1	8	yes	complemented
154	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	4	4	no	—
174	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
175	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
176	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	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	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₁₃	—	4	4	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	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	1	yes	characteristic
221	C₁₃×#95	C₂³	1	1	yes	characteristic
222	C₁₃×#95	C₂³	1	1	yes	characteristic
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	1	yes	characteristic
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
246	#34261	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂⁴×C₁₃	—	2	4	no	—
248	C₂⁴×C₁₃	—	2	4	no	—
249	C₂⁴×C₁₃	—	4	2	no	—
250	C₂⁴×C₁₃	—	4	2	no	—
251	C₂⁴×C₁₃	—	4	2	no	—
252	C₂⁴×C₁₃	—	4	2	no	—
253	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
254	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
256	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	32	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
263	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
265	C₂×D₄×C₁₃	#41	1	4	yes	—
266	C₂×D₄×C₁₃	#41	1	4	yes	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	4	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	—	4	2	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	—	4	2	no	—
283	C₂²×C₄×C₁₃	—	4	2	no	—
284	C₂²×C₄×C₁₃	—	4	2	no	—
285	C₂²×C₄×C₁₃	—	4	2	no	—
286	C₂²×C₄×C₁₃	—	4	2	no	—
287	C₂²×C₄×C₁₃	—	4	2	no	—
288	C₂²×C₄×C₁₃	—	4	2	no	—
289	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
290	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
291	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	4	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	4	2	no	—
322	C₁₃×C₄⋊C₄	—	4	2	no	—
323	C₁₃×C₄⋊C₄	—	4	1	no	—
324	C₁₃×C₄⋊C₄	—	4	1	no	—
325	C₁₃×C₄⋊C₄	—	4	2	no	—
326	C₁₃×C₄⋊C₄	—	4	2	no	—
327	C₁₃×C₄⋊C₄	—	4	2	no	—
328	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
330	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
331	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
332	C₁₃×C₂²⋊C₄	—	2	4	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	—	2	4	no	—
340	C₁₃×C₂²⋊C₄	—	4	2	no	—
341	C₁₃×C₂²⋊C₄	—	4	2	no	—
342	C₁₃×C₂²⋊C₄	—	4	2	no	—
343	C₁₃×C₂²⋊C₄	—	4	2	no	—
344	C₁₃×C₂²⋊C₄	—	4	1	no	—
345	C₁₃×C₂²⋊C₄	—	4	2	no	—
346	C₁₃×C₂²⋊C₄	—	4	1	no	—
347	C₁₃×C₂²⋊C₄	—	4	2	no	—
348	C₁₃×C₂²⋊C₄	—	4	2	no	—
349	C₁₃×C₂²⋊C₄	—	4	2	no	—
350	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
351	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
352	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
353	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
354	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
355	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
356	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	2	no	—
360	C₄²×C₁₃	—	2	2	no	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	2	4	no	—
363	C₄²×C₁₃	—	2	2	no	—
364	C₄²×C₁₃	—	4	2	no	—
365	C₄²×C₁₃	—	4	2	no	—
366	C₄²×C₁₃	—	4	1	no	—
367	C₄²×C₁₃	—	4	2	no	—
368	C₄²×C₁₃	—	4	1	no	—
369	C₄²×C₁₃	—	4	2	no	—
370	C₄²×C₁₃	—	4	2	no	—
371	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
372	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
373	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
374	C₂×#518	C₂×C₁₃	1	1	yes	characteristic
375	#2357	C₂×C₁₃	1	1	yes	characteristic, complemented
376	#2354	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#2353	C₂×C₁₃	1	2	yes	complemented
378	#2352	C₂×C₁₃	1	2	yes	complemented
379	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
380	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#2346	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#2342	C₂×C₁₃	1	2	yes	complemented
384	#2342	C₂×C₁₃	1	2	yes	complemented
385	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
386	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
387	#2319	C₂×C₁₃	1	1	yes	characteristic, complemented
388	#2318	C₂×C₁₃	1	2	yes	complemented
389	#2314	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#2312	C₂×C₁₃	1	2	yes	complemented
391	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#2290	C₂×C₁₃	1	2	yes	complemented
394	C₂×#388	C₂×C₁₃	1	2	yes	complemented
395	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	2	2	no	—
399	C₂³×C₁₃	—	2	2	no	—
400	C₂³×C₁₃	—	2	2	no	—
401	C₂³×C₁₃	—	2	1	no	—
402	C₂³×C₁₃	—	2	1	no	—
403	C₂³×C₁₃	—	2	2	no	—
404	C₂³×C₁₃	—	2	2	no	—
405	C₂³×C₁₃	—	2	2	no	—
406	C₂³×C₁₃	—	2	2	no	—
407	C₂³×C₁₃	—	2	1	no	—
408	C₂³×C₁₃	—	2	1	no	—
409	C₂³×C₁₃	—	2	2	no	—
410	C₂³×C₁₃	—	2	2	no	—
411	C₂³×C₁₃	—	2	1	no	—
412	C₂³×C₁₃	—	2	1	no	—
413	C₂³×C₁₃	—	2	16	no	—
414	C₂³×C₁₃	—	4	8	no	—
415	C₂³×C₁₃	—	4	8	no	—
416	C₂³×C₁₃	—	8	4	no	—
417	C₂³×C₁₃	—	8	4	no	—
418	C₂³×C₁₃	—	8	4	no	—
419	C₂³×C₁₃	—	8	4	no	—
420	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
421	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
422	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
423	C₂³×C₁₃	C₂×#41	1	4	yes	—
424	C₂³×C₁₃	C₂×#41	1	4	yes	—
425	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
426	D₄×C₁₃	—	2	16	no	—
427	D₄×C₁₃	—	2	8	no	—
428	D₄×C₁₃	#117	1	16	yes	complemented
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	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	2	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	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	8	no	—
448	C₂×C₄×C₁₃	—	2	1	no	—
449	C₂×C₄×C₁₃	—	2	1	no	—
450	C₂×C₄×C₁₃	—	2	1	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	1	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	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	1	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	1	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	1	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	2	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	4	8	no	—
479	C₂×C₄×C₁₃	—	4	8	no	—
480	C₂×C₄×C₁₃	—	4	8	no	—
481	C₂×C₄×C₁₃	—	4	8	no	—
482	C₂×C₄×C₁₃	—	4	8	no	—
483	C₂×C₄×C₁₃	—	4	8	no	—
484	C₂×C₄×C₁₃	—	8	4	no	—
485	C₂×C₄×C₁₃	—	8	4	no	—
486	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
487	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
488	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
490	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
492	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
493	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
494	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
495	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
496	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
497	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
498	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
499	#518	C₄×C₁₃	1	16	yes	complemented
500	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
507	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
509	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
510	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
511	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
512	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
513	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
514	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
515	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
516	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
517	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
518	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
519	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
520	#390	C₂²×C₁₃	1	1	yes	characteristic
521	#390	C₂²×C₁₃	1	1	yes	characteristic
522	#390	C₂²×C₁₃	1	1	yes	characteristic
523	#390	C₂²×C₁₃	1	1	yes	characteristic
524	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#388	C₂²×C₁₃	1	1	yes	characteristic
529	#388	C₂²×C₁₃	1	2	yes	—
530	#388	C₂²×C₁₃	1	2	yes	—
531	#388	C₂²×C₁₃	1	2	yes	—
532	#388	C₂²×C₁₃	1	2	yes	—
533	#388	C₂²×C₁₃	1	1	yes	characteristic
534	#388	C₂²×C₁₃	1	1	yes	characteristic
535	#388	C₂²×C₁₃	1	2	yes	—
536	#388	C₂²×C₁₃	1	2	yes	—
537	#388	C₂²×C₁₃	1	1	yes	characteristic
538	#388	C₂²×C₁₃	1	2	yes	complemented
539	#388	C₂²×C₁₃	1	2	yes	complemented
540	#388	C₂²×C₁₃	1	2	yes	complemented
541	#388	C₂²×C₁₃	1	2	yes	complemented
542	#388	C₂²×C₁₃	1	2	yes	complemented
543	#388	C₂²×C₁₃	1	2	yes	complemented
544	#388	C₂²×C₁₃	1	2	yes	complemented
545	#388	C₂²×C₁₃	1	2	yes	complemented
546	#387	C₂²×C₁₃	1	2	yes	complemented
547	#387	C₂²×C₁₃	1	2	yes	complemented
548	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
549	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
550	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
551	#387	C₂²×C₁₃	1	1	yes	characteristic, complemented
552	#386	C₂²×C₁₃	1	2	yes	—
553	#386	C₂²×C₁₃	1	2	yes	—
554	#386	C₂²×C₁₃	1	2	yes	—
555	#386	C₂²×C₁₃	1	2	yes	—
556	#385	C₂²×C₁₃	1	2	yes	complemented
557	#385	C₂²×C₁₃	1	2	yes	complemented
558	#385	C₂²×C₁₃	1	2	yes	complemented
559	#385	C₂²×C₁₃	1	2	yes	complemented
560	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	#383	C₂²×C₁₃	1	2	yes	complemented
562	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#382	C₂²×C₁₃	1	2	yes	complemented
564	#381	C₂²×C₁₃	1	2	yes	complemented
565	#381	C₂²×C₁₃	1	2	yes	complemented
566	#380	C₂²×C₁₃	1	1	yes	characteristic
567	#380	C₂²×C₁₃	1	1	yes	characteristic
568	#380	C₂²×C₁₃	1	2	yes	complemented
569	#380	C₂²×C₁₃	1	2	yes	complemented
570	#380	C₂²×C₁₃	1	2	yes	complemented
571	#380	C₂²×C₁₃	1	2	yes	complemented
572	#379	C₂²×C₁₃	1	2	yes	—
573	#379	C₂²×C₁₃	1	2	yes	—
574	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
575	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
577	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
579	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
583	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
585	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
586	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
587	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
588	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
589	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
590	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
591	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
592	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
593	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#376	C₂²×C₁₃	1	2	yes	complemented
595	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
596	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
597	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	C₂²×C₁₃	—	2	4	no	—
599	C₂²×C₁₃	—	2	4	no	—
600	C₂²×C₁₃	—	2	4	no	—
601	C₂²×C₁₃	—	2	4	no	—
602	C₂²×C₁₃	—	2	4	no	—
603	C₂²×C₁₃	—	2	4	no	—
604	C₂²×C₁₃	—	2	2	no	—
605	C₂²×C₁₃	—	2	4	no	—
606	C₂²×C₁₃	—	2	4	no	—
607	C₂²×C₁₃	—	2	4	no	—
608	C₂²×C₁₃	—	2	2	no	—
609	C₂²×C₁₃	—	2	2	no	—
610	C₂²×C₁₃	—	4	2	no	—
611	C₂²×C₁₃	—	4	1	no	—
612	C₂²×C₁₃	—	4	2	no	—
613	C₂²×C₁₃	—	4	1	no	—
614	C₂²×C₁₃	—	4	2	no	—
615	C₂²×C₁₃	—	4	1	no	—
616	C₂²×C₁₃	—	4	2	no	—
617	C₂²×C₁₃	—	4	1	no	—
618	C₂²×C₁₃	—	8	16	no	—
619	C₂²×C₁₃	C₂×#117	1	8	yes	—
620	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
621	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
622	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
623	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂²×C₁₃	#585	1	1	yes	characteristic
626	C₂²×C₁₃	#585	1	1	yes	characteristic
627	C₄×C₁₃	—	2	2	no	—
628	C₄×C₁₃	—	2	2	no	—
629	C₄×C₁₃	—	2	4	no	—
630	C₄×C₁₃	—	2	2	no	—
631	C₄×C₁₃	—	2	2	no	—
632	C₄×C₁₃	—	2	2	no	—
633	C₄×C₁₃	—	2	4	no	—
634	C₄×C₁₃	—	2	2	no	—
635	C₄×C₁₃	—	2	2	no	—
636	C₄×C₁₃	—	4	1	no	—
637	C₄×C₁₃	—	4	2	no	—
638	C₄×C₁₃	—	4	1	no	—
639	C₄×C₁₃	—	4	2	no	—
640	C₄×C₁₃	—	4	1	no	—
641	C₄×C₁₃	—	4	2	no	—
642	C₄×C₁₃	—	4	2	no	—
643	C₄×C₁₃	—	4	1	no	—
644	C₄×C₁₃	—	4	1	no	—
645	C₄×C₁₃	—	4	1	no	—
646	C₄×C₁₃	C₂×#117	1	4	yes	—
647	C₂⁵	C₂³×C₁₃	1	2	yes	—
648	C₂²×D₄	—	2	4	no	—
649	C₂²×D₄	—	2	4	no	—
650	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
651	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
652	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
655	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
656	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
658	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
659	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
660	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
661	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
662	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	—	2	4	no	—
664	C₄×D₄	—	2	4	no	—
665	C₄×D₄	—	2	4	no	—
666	C₄×D₄	—	2	4	no	—
667	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
668	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
669	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
670	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
671	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
672	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
673	#117	—	4	4	no	—
674	#117	—	4	4	no	—
675	#117	C₂×C₄×C₁₃	1	8	yes	complemented
676	#117	C₂×C₄×C₁₃	1	8	yes	complemented
677	C₂×C₄⋊C₄	—	4	4	no	—
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	—	4	4	no	—
697	C₂×C₂²⋊C₄	—	4	4	no	—
698	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
699	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
700	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₄²	—	4	4	no	—
726	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
728	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
734	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
740	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
742	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
743	#95	C₂³×C₁₃	1	1	yes	characteristic
744	#95	C₂³×C₁₃	1	1	yes	characteristic
745	#95	C₂³×C₁₃	1	2	yes	—
746	#95	C₂³×C₁₃	1	2	yes	—
747	#95	C₂³×C₁₃	1	2	yes	—
748	#95	C₂³×C₁₃	1	2	yes	—
749	#95	C₂³×C₁₃	1	2	yes	—
750	#95	C₂³×C₁₃	1	2	yes	—
751	#95	C₂³×C₁₃	1	1	yes	characteristic
752	#95	C₂³×C₁₃	1	1	yes	characteristic
753	#95	C₂³×C₁₃	1	1	yes	characteristic
754	#95	C₂³×C₁₃	1	1	yes	characteristic
755	#95	C₂³×C₁₃	1	2	yes	—
756	#95	C₂³×C₁₃	1	2	yes	—
757	#95	C₂³×C₁₃	1	1	yes	characteristic
758	#95	C₂³×C₁₃	1	1	yes	characteristic
759	#95	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
764	#95	C₂³×C₁₃	1	2	yes	—
765	#95	C₂³×C₁₃	1	2	yes	—
766	#95	C₂³×C₁₃	1	2	yes	—
767	#95	C₂³×C₁₃	1	1	yes	characteristic
768	#95	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×C₁₃	—	2	8	no	—
770	C₂×C₁₃	—	4	4	no	—
771	C₂×C₁₃	—	4	2	no	—
772	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
773	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
775	C₂×C₁₃	#3513	1	1	yes	characteristic
776	C₂×C₁₃	#3514	1	1	yes	characteristic
777	C₂×C₁₃	#3519	1	1	yes	characteristic
778	C₂×C₁₃	#3521	1	1	yes	characteristic
779	C₂⁴	—	2	4	no	—
780	C₂⁴	—	2	4	no	—
781	C₂⁴	—	4	2	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
786	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
788	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	32	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
795	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
796	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
797	C₂×D₄	C₁₃×#41	1	4	yes	—
798	C₂×D₄	C₁₃×#41	1	4	yes	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
822	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
823	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
824	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
825	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
826	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	1	no	—
858	C₄⋊C₄	—	4	1	no	—
859	C₄⋊C₄	—	4	2	no	—
860	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
861	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
862	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
863	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	1	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
883	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
889	C₄²	—	2	2	no	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	4	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	1	no	—
901	C₄²	—	4	2	no	—
902	C₄²	—	4	1	no	—
903	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
904	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
905	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
906	C₁₃	#34261	1	1	yes	characteristic, direct product factor, Sylow
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	16	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	4	8	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
931	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
932	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
933	C₂³	C₂×C₁₃×#41	1	4	yes	—
934	C₂³	C₂×C₁₃×#41	1	4	yes	—
935	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
936	D₄	—	2	16	no	—
937	D₄	—	2	8	no	—
938	D₄	C₁₃×#117	1	16	yes	complemented
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	8	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	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	—	8	4	no	—
996	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1001	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1002	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
1003	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
1004	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1005	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1006	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1007	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	C₂×C₁₃×#117	1	8	yes	—
1030	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1031	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1032	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1033	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂²	C₁₃×#585	1	1	yes	characteristic
1036	C₂²	C₁₃×#585	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	4	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	C₂×C₁₃×#117	1	4	yes	—
1057	C₂	—	2	8	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	4	no	—
1060	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
1061	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1062	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1063	C₂	C₁₃×#3513	1	1	yes	characteristic
1064	C₂	C₁₃×#3514	1	1	yes	characteristic
1065	C₂	C₁₃×#3519	1	1	yes	characteristic
1066	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	C₂³×D₄×C₁₃	C₂²
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×#2357	C₂	semidirect
3. C₁₃×#2354	C₂	semidirect
4. C₁₃×#2353	C₂	semidirect
5. C₁₃×#2352	C₂	semidirect
6. C₁₃×#2349	C₂	semidirect
7. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
8. C₁₃×#2347	C₂	semidirect
9. C₁₃×#2346	C₂	semidirect
10. C₁₃×#2342	C₂	semidirect
11. C₁₃×#2342	C₂	semidirect
14. C₁₃×#2319	C₂	semidirect
15. C₁₃×#2318	C₂	semidirect
16. C₁₃×#2314	C₂	semidirect
17. C₁₃×#2312	C₂	semidirect
18. C₁₃×#2298	C₂	semidirect
19. C₁₃×#2293	C₂	semidirect
20. C₁₃×#2290	C₂	semidirect
21. C₂×C₁₃×#388	C₂	semidirect
22. C₁₃×#2275	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
25. C₁₃×#518	C₄	semidirect
38. C₂×C₁₃×#117	C₂²	semidirect
39. C₂×C₁₃×#117	C₂²	semidirect
40. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₂²×C₄²×C₁₃	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
51. C₁₃×#389	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
53. C₁₃×#389	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#388	C₂²	semidirect
66. C₁₃×#388	C₂²	semidirect
67. C₁₃×#388	C₂²	semidirect
68. C₁₃×#388	C₂²	semidirect
69. C₁₃×#388	C₂²	semidirect
70. C₁₃×#388	C₂²	semidirect
71. C₁₃×#388	C₂²	semidirect
72. C₁₃×#387	C₂²	semidirect
73. C₁₃×#387	C₂²	semidirect
74. C₁₃×#387	C₂²	semidirect
75. C₁₃×#387	C₂²	semidirect
76. C₁₃×#387	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
82. C₁₃×#385	C₂²	semidirect
83. C₁₃×#385	C₂²	semidirect
84. C₁₃×#385	C₂²	semidirect
85. C₁₃×#385	C₂²	semidirect
86. C₁₃×#384	C₂²	semidirect
87. C₁₃×#383	C₂²	semidirect
88. C₁₃×#382	C₂²	semidirect
89. C₁₃×#382	C₂²	semidirect
90. C₁₃×#381	C₂²	semidirect
91. C₁₃×#381	C₂²	semidirect
94. C₁₃×#380	C₂²	semidirect
95. C₁₃×#380	C₂²	semidirect
96. C₁₃×#380	C₂²	semidirect
97. C₁₃×#380	C₂²	semidirect
100. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
101. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
102. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
103. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
104. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
105. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
106. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
107. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
108. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
111. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
112. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
113. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
114. C₄×C₁₃×C₂²⋊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. C₁₃×#376	C₂²	semidirect
120. C₁₃×#376	C₂²	semidirect
121. C₂×C₁₃×#95	C₂²	semidirect
122. C₂×C₁₃×#95	C₂²	semidirect
123. C₄³×C₁₃	C₂²	semidirect
146. C₄×D₄×C₁₃	C₂×C₄	semidirect
147. C₄×D₄×C₁₃	C₂×C₄	semidirect
148. C₄×D₄×C₁₃	C₂×C₄	semidirect
149. C₄×D₄×C₁₃	C₂×C₄	semidirect
152. C₁₃×#117	C₂×C₄	semidirect
153. C₁₃×#117	C₂×C₄	semidirect
175. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
176. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
246. #34261	C₁₃	direct (N × H)
375. #2357	C₂×C₁₃	semidirect
376. #2354	C₂×C₁₃	semidirect
377. #2353	C₂×C₁₃	semidirect
378. #2352	C₂×C₁₃	semidirect
379. #2349	C₂×C₁₃	semidirect
380. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
381. #2347	C₂×C₁₃	semidirect
382. #2346	C₂×C₁₃	semidirect
383. #2342	C₂×C₁₃	semidirect
384. #2342	C₂×C₁₃	semidirect
387. #2319	C₂×C₁₃	semidirect
388. #2318	C₂×C₁₃	semidirect
389. #2314	C₂×C₁₃	semidirect
390. #2312	C₂×C₁₃	semidirect
391. #2298	C₂×C₁₃	semidirect
392. #2293	C₂×C₁₃	semidirect
393. #2290	C₂×C₁₃	semidirect
394. C₂×#388	C₂×C₁₃	semidirect
395. #2275	C₂×C₁₃	semidirect
396. C₄²×D₄	C₂×C₁₃	semidirect
428. D₄×C₁₃	#117	semidirect
499. #518	C₄×C₁₃	semidirect
512. C₂×#117	C₂²×C₁₃	semidirect
513. C₂×#117	C₂²×C₁₃	semidirect
514. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
519. C₂²×C₄²	C₂²×C₁₃	semidirect
524. #389	C₂²×C₁₃	semidirect
525. #389	C₂²×C₁₃	semidirect
526. #389	C₂²×C₁₃	semidirect
527. #389	C₂²×C₁₃	semidirect
538. #388	C₂²×C₁₃	semidirect
539. #388	C₂²×C₁₃	semidirect
540. #388	C₂²×C₁₃	semidirect
541. #388	C₂²×C₁₃	semidirect
542. #388	C₂²×C₁₃	semidirect
543. #388	C₂²×C₁₃	semidirect
544. #388	C₂²×C₁₃	semidirect
545. #388	C₂²×C₁₃	semidirect
546. #387	C₂²×C₁₃	semidirect
547. #387	C₂²×C₁₃	semidirect
548. #387	C₂²×C₁₃	semidirect
549. #387	C₂²×C₁₃	semidirect
550. #387	C₂²×C₁₃	semidirect
551. #387	C₂²×C₁₃	semidirect
556. #385	C₂²×C₁₃	semidirect
557. #385	C₂²×C₁₃	semidirect
558. #385	C₂²×C₁₃	semidirect
559. #385	C₂²×C₁₃	semidirect
560. #384	C₂²×C₁₃	semidirect
561. #383	C₂²×C₁₃	semidirect
562. #382	C₂²×C₁₃	semidirect
563. #382	C₂²×C₁₃	semidirect
564. #381	C₂²×C₁₃	semidirect
565. #381	C₂²×C₁₃	semidirect
568. #380	C₂²×C₁₃	semidirect
569. #380	C₂²×C₁₃	semidirect
570. #380	C₂²×C₁₃	semidirect
571. #380	C₂²×C₁₃	semidirect
574. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
575. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
576. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
577. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
578. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
579. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
580. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
581. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
582. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
585. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
586. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
587. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
588. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
589. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
590. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
591. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
592. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
593. #376	C₂²×C₁₃	semidirect
594. #376	C₂²×C₁₃	semidirect
595. C₂×#95	C₂²×C₁₃	semidirect
596. C₂×#95	C₂²×C₁₃	semidirect
597. C₄³	C₂²×C₁₃	semidirect
669. C₄×D₄	C₂×C₄×C₁₃	semidirect
670. C₄×D₄	C₂×C₄×C₁₃	semidirect
671. C₄×D₄	C₂×C₄×C₁₃	semidirect
672. C₄×D₄	C₂×C₄×C₁₃	semidirect
675. #117	C₂×C₄×C₁₃	semidirect
676. #117	C₂×C₄×C₁₃	semidirect
698. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
699. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
906. C₁₃	#34261	direct (N × H)
938. D₄	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#518	2
C₁₃×#2357	2
C₁₃×#2354	2
C₁₃×#2353	2
C₁₃×#2352	2
C₁₃×#2349	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2347	2
C₁₃×#2346	2
C₁₃×#2342	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2319	2
C₁₃×#2318	2
C₁₃×#2314	2
C₁₃×#2312	2
C₁₃×#2298	2
C₁₃×#2293	2
C₁₃×#2290	2
C₂×C₁₃×#388	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34261	13

Subgroups — C13×#34261 #15720600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34261 #15720600