Subgroups — C₁₃×#34518 #15720857

Order 3328.

2464 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#560	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2358	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
20	C₁₃×#560	C₄	1	16	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₁₃×#120	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#390	C₂²	1	2	yes	—
43	C₁₃×#390	C₂²	1	2	yes	—
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	2	yes	—
46	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#390	C₂²	1	2	yes	complemented
48	C₁₃×#389	C₂²	1	2	yes	complemented
49	C₁₃×#389	C₂²	1	2	yes	complemented
50	C₁₃×#389	C₂²	1	2	yes	complemented
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
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	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	complemented
61	C₁₃×#388	C₂²	1	2	yes	complemented
62	C₁₃×#388	C₂²	1	2	yes	complemented
63	C₁₃×#387	C₂²	1	2	yes	complemented
64	C₁₃×#387	C₂²	1	2	yes	complemented
65	C₁₃×#387	C₂²	1	2	yes	complemented
66	C₁₃×#387	C₂²	1	2	yes	complemented
67	C₁₃×#387	C₂²	1	2	yes	complemented
68	C₁₃×#387	C₂²	1	2	yes	complemented
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#386	C₂²	1	1	yes	characteristic
71	C₁₃×#386	C₂²	1	2	yes	—
72	C₁₃×#386	C₂²	1	2	yes	—
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#386	C₂²	1	1	yes	characteristic
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	complemented
80	C₁₃×#386	C₂²	1	2	yes	complemented
81	C₁₃×#386	C₂²	1	2	yes	complemented
82	C₁₃×#385	C₂²	1	1	yes	characteristic
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#385	C₂²	1	2	yes	complemented
89	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#381	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#381	C₂²	1	2	yes	complemented
92	C₁₃×#380	C₂²	1	2	yes	complemented
93	C₁₃×#379	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×#127	C₂×C₄	1	8	yes	complemented
127	C₁₃×#126	C₂×C₄	1	16	yes	complemented
128	C₁₃×#123	C₂×C₄	1	8	yes	complemented
129	C₁₃×#123	C₂×C₄	1	16	yes	complemented
130	C₁₃×#121	C₂×C₄	1	16	yes	complemented
131	C₁₃×#121	C₂×C₄	1	16	yes	complemented
132	C₁₃×#121	C₂×C₄	1	16	yes	complemented
133	C₁₃×#120	C₂×C₄	1	16	yes	complemented
134	C₁₃×#120	C₂×C₄	1	8	yes	complemented
135	C₄×D₄×C₁₃	—	4	4	no	—
136	C₄×D₄×C₁₃	—	4	2	no	—
137	C₄×D₄×C₁₃	—	4	2	no	—
138	C₄×D₄×C₁₃	—	4	4	no	—
139	C₄×D₄×C₁₃	—	4	4	no	—
140	C₄×D₄×C₁₃	—	4	4	no	—
141	C₄×D₄×C₁₃	—	4	4	no	—
142	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	—	4	2	no	—
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	#34518	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	4	1	no	—
217	C₂⁴×C₁₃	—	4	2	no	—
218	C₂⁴×C₁₃	—	4	2	no	—
219	C₂⁴×C₁₃	—	4	1	no	—
220	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
221	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
222	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
224	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂×D₄×C₁₃	—	4	2	no	—
226	C₂×D₄×C₁₃	—	4	1	no	—
227	C₂×D₄×C₁₃	—	4	1	no	—
228	C₂×D₄×C₁₃	—	4	2	no	—
229	C₂×D₄×C₁₃	—	4	2	no	—
230	C₂×D₄×C₁₃	—	4	2	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	1	no	—
235	C₂×D₄×C₁₃	—	4	1	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	2	no	—
239	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
241	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
242	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
243	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
244	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
245	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	—	4	2	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	—	4	1	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	1	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	—	4	2	no	—
270	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
271	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	4	2	no	—
291	C₁₃×C₄⋊C₄	—	4	2	no	—
292	C₁₃×C₄⋊C₄	—	4	2	no	—
293	C₁₃×C₄⋊C₄	—	4	2	no	—
294	C₁₃×C₄⋊C₄	—	4	2	no	—
295	C₁₃×C₄⋊C₄	—	4	1	no	—
296	C₁₃×C₄⋊C₄	—	4	1	no	—
297	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
298	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	2	no	—
308	C₁₃×C₂²⋊C₄	—	4	2	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	1	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	1	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	1	no	—
315	C₁₃×C₂²⋊C₄	—	4	1	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
323	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
324	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
325	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
326	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	4	2	no	—
330	C₄²×C₁₃	—	4	2	no	—
331	C₄²×C₁₃	—	4	2	no	—
332	C₄²×C₁₃	—	4	1	no	—
333	C₄²×C₁₃	—	4	2	no	—
334	C₄²×C₁₃	—	4	2	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
338	C₂×#560	C₂×C₁₃	1	1	yes	characteristic
339	#2377	C₂×C₁₃	1	2	yes	complemented
340	#2376	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2374	C₂×C₁₃	1	2	yes	complemented
342	#2373	C₂×C₁₃	1	2	yes	complemented
343	#2366	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2361	C₂×C₁₃	1	2	yes	complemented
345	#2361	C₂×C₁₃	1	2	yes	complemented
346	#2358	C₂×C₁₃	1	2	yes	complemented
347	#2358	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#2334	C₂×C₁₃	1	2	yes	complemented
349	#2333	C₂×C₁₃	1	2	yes	complemented
350	#2333	C₂×C₁₃	1	2	yes	complemented
351	#2328	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2322	C₂×C₁₃	1	2	yes	complemented
353	#2321	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2321	C₂×C₁₃	1	2	yes	complemented
355	C₄×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₄×#121	C₂×C₁₃	1	2	yes	complemented
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	1	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	4	8	no	—
378	C₂³×C₁₃	—	4	4	no	—
379	C₂³×C₁₃	—	8	2	no	—
380	C₂³×C₁₃	—	8	2	no	—
381	C₂³×C₁₃	—	8	4	no	—
382	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
383	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
384	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
385	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
386	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
387	D₄×C₁₃	—	4	8	no	—
388	D₄×C₁₃	—	4	8	no	—
389	D₄×C₁₃	—	4	8	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	8	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	8	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	8	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	4	4	no	—
432	C₂×C₄×C₁₃	—	8	2	no	—
433	C₂×C₄×C₁₃	—	8	4	no	—
434	C₂×C₄×C₁₃	—	8	4	no	—
435	C₂×C₄×C₁₃	—	8	4	no	—
436	C₂×C₄×C₁₃	—	8	2	no	—
437	C₂×C₄×C₁₃	—	8	4	no	—
438	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
440	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
441	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
442	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
443	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
444	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
445	#560	C₄×C₁₃	1	16	yes	complemented
446	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#126	C₂²×C₁₃	1	2	yes	—
448	C₂×#123	C₂²×C₁₃	1	2	yes	—
449	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#121	C₂²×C₁₃	1	2	yes	—
451	C₂×#121	C₂²×C₁₃	1	2	yes	—
452	C₂×#121	C₂²×C₁₃	1	2	yes	—
453	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#120	C₂²×C₁₃	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
458	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
459	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
460	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
462	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
463	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#390	C₂²×C₁₃	1	2	yes	—
467	#390	C₂²×C₁₃	1	2	yes	—
468	#390	C₂²×C₁₃	1	2	yes	—
469	#390	C₂²×C₁₃	1	1	yes	characteristic
470	#390	C₂²×C₁₃	1	2	yes	—
471	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#390	C₂²×C₁₃	1	2	yes	complemented
473	#389	C₂²×C₁₃	1	2	yes	complemented
474	#389	C₂²×C₁₃	1	2	yes	complemented
475	#389	C₂²×C₁₃	1	2	yes	complemented
476	#388	C₂²×C₁₃	1	2	yes	—
477	#388	C₂²×C₁₃	1	2	yes	—
478	#388	C₂²×C₁₃	1	2	yes	—
479	#388	C₂²×C₁₃	1	2	yes	—
480	#388	C₂²×C₁₃	1	2	yes	—
481	#388	C₂²×C₁₃	1	2	yes	—
482	#388	C₂²×C₁₃	1	2	yes	—
483	#388	C₂²×C₁₃	1	2	yes	—
484	#388	C₂²×C₁₃	1	2	yes	—
485	#388	C₂²×C₁₃	1	2	yes	complemented
486	#388	C₂²×C₁₃	1	2	yes	complemented
487	#388	C₂²×C₁₃	1	2	yes	complemented
488	#387	C₂²×C₁₃	1	2	yes	complemented
489	#387	C₂²×C₁₃	1	2	yes	complemented
490	#387	C₂²×C₁₃	1	2	yes	complemented
491	#387	C₂²×C₁₃	1	2	yes	complemented
492	#387	C₂²×C₁₃	1	2	yes	complemented
493	#387	C₂²×C₁₃	1	2	yes	complemented
494	#386	C₂²×C₁₃	1	2	yes	—
495	#386	C₂²×C₁₃	1	2	yes	—
496	#386	C₂²×C₁₃	1	2	yes	—
497	#386	C₂²×C₁₃	1	2	yes	—
498	#386	C₂²×C₁₃	1	1	yes	characteristic
499	#386	C₂²×C₁₃	1	2	yes	—
500	#386	C₂²×C₁₃	1	2	yes	—
501	#386	C₂²×C₁₃	1	2	yes	—
502	#386	C₂²×C₁₃	1	2	yes	—
503	#386	C₂²×C₁₃	1	1	yes	characteristic
504	#386	C₂²×C₁₃	1	2	yes	complemented
505	#386	C₂²×C₁₃	1	2	yes	complemented
506	#386	C₂²×C₁₃	1	2	yes	complemented
507	#385	C₂²×C₁₃	1	1	yes	characteristic
508	#385	C₂²×C₁₃	1	2	yes	—
509	#385	C₂²×C₁₃	1	2	yes	—
510	#385	C₂²×C₁₃	1	2	yes	—
511	#385	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	complemented
513	#385	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#381	C₂²×C₁₃	1	2	yes	complemented
516	#381	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#380	C₂²×C₁₃	1	2	yes	complemented
518	#379	C₂²×C₁₃	1	1	yes	characteristic
519	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
523	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
524	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
525	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
527	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
528	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
529	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
531	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
532	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	2	4	no	—
535	C₂²×C₁₃	—	2	4	no	—
536	C₂²×C₁₃	—	2	4	no	—
537	C₂²×C₁₃	—	2	4	no	—
538	C₂²×C₁₃	—	2	4	no	—
539	C₂²×C₁₃	—	2	4	no	—
540	C₂²×C₁₃	—	2	4	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	4	1	no	—
544	C₂²×C₁₃	—	4	1	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	1	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	4	1	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	8	8	no	—
558	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
559	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
561	C₂²×C₁₃	#585	1	2	yes	—
562	C₂²×C₁₃	#585	1	1	yes	characteristic
563	C₄×C₁₃	—	2	4	no	—
564	C₄×C₁₃	—	2	4	no	—
565	C₄×C₁₃	—	2	4	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	4	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	4	no	—
570	C₄×C₁₃	—	4	1	no	—
571	C₄×C₁₃	—	4	1	no	—
572	C₄×C₁₃	—	4	1	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
580	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
581	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
582	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
586	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
588	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
593	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
594	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
595	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
596	#127	C₂×C₄×C₁₃	1	8	yes	complemented
597	#126	C₂×C₄×C₁₃	1	16	yes	complemented
598	#123	C₂×C₄×C₁₃	1	16	yes	complemented
599	#123	C₂×C₄×C₁₃	1	8	yes	complemented
600	#121	C₂×C₄×C₁₃	1	16	yes	complemented
601	#121	C₂×C₄×C₁₃	1	16	yes	complemented
602	#121	C₂×C₄×C₁₃	1	16	yes	complemented
603	#120	C₂×C₄×C₁₃	1	8	yes	complemented
604	#120	C₂×C₄×C₁₃	1	16	yes	complemented
605	C₄×D₄	—	4	4	no	—
606	C₄×D₄	—	4	2	no	—
607	C₄×D₄	—	4	2	no	—
608	C₄×D₄	—	4	4	no	—
609	C₄×D₄	—	4	4	no	—
610	C₄×D₄	—	4	4	no	—
611	C₄×D₄	—	4	4	no	—
612	C₂×C₄⋊C₄	—	4	4	no	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	—	4	4	no	—
627	C₂×C₂²⋊C₄	—	4	2	no	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄²	—	4	2	no	—
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
658	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
666	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	C₂×C₁₃	—	4	2	no	—
686	C₂×C₁₃	—	4	4	no	—
687	C₂×C₁₃	—	4	2	no	—
688	C₂×C₁₃	—	4	4	no	—
689	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂×C₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
691	C₂×C₁₃	#3533	1	1	yes	characteristic
692	C₂×C₁₃	#3537	1	1	yes	characteristic
693	C₂×C₁₃	#3562	1	2	yes	—
694	C₂⁴	—	4	1	no	—
695	C₂⁴	—	4	2	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	—	4	1	no	—
698	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
699	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
701	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
702	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
718	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
720	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
722	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
723	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	1	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
749	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	1	no	—
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	—	4	2	no	—
774	C₄⋊C₄	—	4	2	no	—
775	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
776	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
777	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	1	no	—
787	C₂²⋊C₄	—	4	1	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	1	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	1	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
799	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
800	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
801	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
802	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
803	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	4	2	no	—
808	C₄²	—	4	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	1	no	—
815	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
816	C₁₃	#34518	1	1	yes	characteristic, direct product factor, Sylow
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	4	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	4	no	—
842	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
843	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
844	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
845	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
846	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	8	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	8	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	4	no	—
894	C₂×C₄	—	8	4	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
900	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
901	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
902	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
903	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
904	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	2	4	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	8	8	no	—
930	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
931	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
932	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
933	C₂²	C₁₃×#585	1	2	yes	—
934	C₂²	C₁₃×#585	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	4	no	—
954	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
955	C₂	C₄×C₁₃×H(5,𝔽₂)	1	2	yes	—
956	C₂	C₁₃×#3533	1	1	yes	characteristic
957	C₂	C₁₃×#3537	1	1	yes	characteristic
958	C₂	C₁₃×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#560	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×#2377	C₂	semidirect
3. C₁₃×#2376	C₂	semidirect
4. C₁₃×#2374	C₂	semidirect
5. C₁₃×#2373	C₂	semidirect
6. C₁₃×#2366	C₂	semidirect
7. C₁₃×#2361	C₂	semidirect
8. C₁₃×#2361	C₂	semidirect
9. C₁₃×#2358	C₂	semidirect
10. C₁₃×#2358	C₂	semidirect
11. C₁₃×#2334	C₂	semidirect
12. C₁₃×#2333	C₂	semidirect
13. C₁₃×#2333	C₂	semidirect
14. C₁₃×#2328	C₂	semidirect
15. C₁₃×#2322	C₂	semidirect
16. C₁₃×#2321	C₂	semidirect
17. C₁₃×#2321	C₂	semidirect
18. C₄×C₁₃×#123	C₂	semidirect
19. C₄×C₁₃×#121	C₂	semidirect
20. C₁₃×#560	C₄	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
40. C₂²×C₄²×C₁₃	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#389	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
60. C₁₃×#388	C₂²	semidirect
61. C₁₃×#388	C₂²	semidirect
62. C₁₃×#388	C₂²	semidirect
63. C₁₃×#387	C₂²	semidirect
64. C₁₃×#387	C₂²	semidirect
65. C₁₃×#387	C₂²	semidirect
66. C₁₃×#387	C₂²	semidirect
67. C₁₃×#387	C₂²	semidirect
68. C₁₃×#387	C₂²	semidirect
79. C₁₃×#386	C₂²	semidirect
80. C₁₃×#386	C₂²	semidirect
81. C₁₃×#386	C₂²	semidirect
87. C₁₃×#385	C₂²	semidirect
88. C₁₃×#385	C₂²	semidirect
89. C₁₃×#382	C₂²	semidirect
90. C₁₃×#381	C₂²	semidirect
91. C₁₃×#381	C₂²	semidirect
92. C₁₃×#380	C₂²	semidirect
94. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
95. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
96. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
97. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
103. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
104. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
105. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
106. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
107. C₁₃×#376	C₂²	semidirect
126. C₁₃×#127	C₂×C₄	semidirect
127. C₁₃×#126	C₂×C₄	semidirect
128. C₁₃×#123	C₂×C₄	semidirect
129. C₁₃×#123	C₂×C₄	semidirect
130. C₁₃×#121	C₂×C₄	semidirect
131. C₁₃×#121	C₂×C₄	semidirect
132. C₁₃×#121	C₂×C₄	semidirect
133. C₁₃×#120	C₂×C₄	semidirect
134. C₁₃×#120	C₂×C₄	semidirect
215. #34518	C₁₃	direct (N × H)
339. #2377	C₂×C₁₃	semidirect
340. #2376	C₂×C₁₃	semidirect
341. #2374	C₂×C₁₃	semidirect
342. #2373	C₂×C₁₃	semidirect
343. #2366	C₂×C₁₃	semidirect
344. #2361	C₂×C₁₃	semidirect
345. #2361	C₂×C₁₃	semidirect
346. #2358	C₂×C₁₃	semidirect
347. #2358	C₂×C₁₃	semidirect
348. #2334	C₂×C₁₃	semidirect
349. #2333	C₂×C₁₃	semidirect
350. #2333	C₂×C₁₃	semidirect
351. #2328	C₂×C₁₃	semidirect
352. #2322	C₂×C₁₃	semidirect
353. #2321	C₂×C₁₃	semidirect
354. #2321	C₂×C₁₃	semidirect
355. C₄×#123	C₂×C₁₃	semidirect
356. C₄×#121	C₂×C₁₃	semidirect
445. #560	C₄×C₁₃	semidirect
460. C₂×C₄×D₄	C₂²×C₁₃	semidirect
461. C₂×C₄×D₄	C₂²×C₁₃	semidirect
462. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
465. C₂²×C₄²	C₂²×C₁₃	semidirect
471. #390	C₂²×C₁₃	semidirect
472. #390	C₂²×C₁₃	semidirect
473. #389	C₂²×C₁₃	semidirect
474. #389	C₂²×C₁₃	semidirect
475. #389	C₂²×C₁₃	semidirect
485. #388	C₂²×C₁₃	semidirect
486. #388	C₂²×C₁₃	semidirect
487. #388	C₂²×C₁₃	semidirect
488. #387	C₂²×C₁₃	semidirect
489. #387	C₂²×C₁₃	semidirect
490. #387	C₂²×C₁₃	semidirect
491. #387	C₂²×C₁₃	semidirect
492. #387	C₂²×C₁₃	semidirect
493. #387	C₂²×C₁₃	semidirect
504. #386	C₂²×C₁₃	semidirect
505. #386	C₂²×C₁₃	semidirect
506. #386	C₂²×C₁₃	semidirect
512. #385	C₂²×C₁₃	semidirect
513. #385	C₂²×C₁₃	semidirect
514. #382	C₂²×C₁₃	semidirect
515. #381	C₂²×C₁₃	semidirect
516. #381	C₂²×C₁₃	semidirect
517. #380	C₂²×C₁₃	semidirect
519. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
520. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
521. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
522. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
528. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
529. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
530. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
531. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
532. #376	C₂²×C₁₃	semidirect
596. #127	C₂×C₄×C₁₃	semidirect
597. #126	C₂×C₄×C₁₃	semidirect
598. #123	C₂×C₄×C₁₃	semidirect
599. #123	C₂×C₄×C₁₃	semidirect
600. #121	C₂×C₄×C₁₃	semidirect
601. #121	C₂×C₄×C₁₃	semidirect
602. #121	C₂×C₄×C₁₃	semidirect
603. #120	C₂×C₄×C₁₃	semidirect
604. #120	C₂×C₄×C₁₃	semidirect
816. C₁₃	#34518	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×#560	2
C₁₃×#2377	2
C₁₃×#2376	2
C₁₃×#2374	2
C₁₃×#2373	2
C₁₃×#2366	2
C₁₃×#2361	2
C₁₃×#2358	2
C₁₃×#2334	2
C₁₃×#2333	2
C₁₃×#2328	2
C₁₃×#2322	2
C₁₃×#2321	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
#34518	13

Subgroups — C13×#34518 #15720857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34518 #15720857