Subgroups — C₁₃×#34970 #15721309

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2531	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2526	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2476	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2471	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2428	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#121	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	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	1	yes	characteristic
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	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#400	C₂²	1	2	yes	—
44	C₁₃×#399	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#397	C₂²	1	2	yes	—
50	C₁₃×#397	C₂²	1	2	yes	—
51	C₁₃×#396	C₂²	1	2	yes	—
52	C₁₃×#396	C₂²	1	2	yes	—
53	C₁₃×#394	C₂²	1	2	yes	—
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#394	C₂²	1	2	yes	—
56	C₁₃×#394	C₂²	1	2	yes	—
57	C₁₃×#394	C₂²	1	2	yes	—
58	C₁₃×#392	C₂²	1	2	yes	—
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#390	C₂²	1	1	yes	characteristic
62	C₁₃×#390	C₂²	1	2	yes	—
63	C₁₃×#390	C₂²	1	2	yes	—
64	C₁₃×#390	C₂²	1	1	yes	characteristic
65	C₁₃×#390	C₂²	1	1	yes	characteristic
66	C₁₃×#390	C₂²	1	2	yes	—
67	C₁₃×#390	C₂²	1	1	yes	characteristic
68	C₁₃×#389	C₂²	1	1	yes	characteristic
69	C₁₃×#389	C₂²	1	1	yes	characteristic
70	C₁₃×#389	C₂²	1	1	yes	characteristic
71	C₁₃×#389	C₂²	1	2	yes	—
72	C₁₃×#389	C₂²	1	1	yes	characteristic
73	C₁₃×#389	C₂²	1	1	yes	characteristic
74	C₁₃×#389	C₂²	1	1	yes	characteristic
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	—
78	C₁₃×#388	C₂²	1	2	yes	—
79	C₁₃×#388	C₂²	1	2	yes	—
80	C₁₃×#388	C₂²	1	2	yes	—
81	C₁₃×#388	C₂²	1	2	yes	—
82	C₁₃×#388	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#386	C₂²	1	2	yes	—
90	C₁₃×#386	C₂²	1	2	yes	—
91	C₁₃×#386	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#384	C₂²	1	1	yes	characteristic
94	C₁₃×#382	C₂²	1	1	yes	characteristic
95	C₁₃×#381	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	1	yes	characteristic
97	C₁₃×#380	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₁₃×#376	C₂²	1	1	yes	characteristic
120	C₁₃×#376	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#127	—	2	4	no	—
137	C₁₃×#125	—	2	4	no	—
138	C₁₃×#123	—	2	8	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	8	no	—
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	4	4	no	—
147	C₄×D₄×C₁₃	—	4	4	no	—
148	C₄×D₄×C₁₃	—	4	4	no	—
149	C₄×D₄×C₁₃	—	4	4	no	—
150	C₁₃×#117	—	2	4	no	—
151	C₁₃×#117	—	2	4	no	—
152	C₁₃×#117	—	4	4	no	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₁₃	—	2	4	no	—
198	C₂×C₄²×C₁₃	—	4	4	no	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	1	yes	characteristic
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	1	yes	characteristic
226	C₁₃×#95	C₂³	1	1	yes	characteristic
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	1	yes	characteristic
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	2	yes	—
240	C₁₃×#95	C₂³	1	2	yes	—
241	#34970	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
243	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂×D₄×C₁₃	—	4	2	no	—
262	C₂×D₄×C₁₃	#41	1	4	yes	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
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	2	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	4	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	2	4	no	—
282	C₂²×C₄×C₁₃	—	4	2	no	—
283	C₂²×C₄×C₁₃	—	4	2	no	—
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	4	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	4	no	—
313	C₁₃×C₄⋊C₄	—	2	4	no	—
314	C₁₃×C₄⋊C₄	—	2	4	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	4	2	no	—
317	C₁₃×C₄⋊C₄	—	4	2	no	—
318	C₁₃×C₄⋊C₄	—	4	2	no	—
319	C₁₃×C₄⋊C₄	—	4	2	no	—
320	C₁₃×C₄⋊C₄	—	4	2	no	—
321	C₁₃×C₄⋊C₄	—	4	2	no	—
322	C₁₃×C₄⋊C₄	#41	1	4	yes	—
323	C₁₃×C₄⋊C₄	#41	1	4	yes	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	4	no	—
337	C₁₃×C₂²⋊C₄	—	4	2	no	—
338	C₁₃×C₂²⋊C₄	—	4	2	no	—
339	C₁₃×C₂²⋊C₄	—	4	2	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	2	no	—
345	C₁₃×C₂²⋊C₄	—	4	2	no	—
346	C₁₃×C₂²⋊C₄	—	4	2	no	—
347	C₁₃×C₂²⋊C₄	#41	1	4	yes	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	—	2	2	no	—
351	C₄²×C₁₃	—	2	2	no	—
352	C₄²×C₁₃	—	2	2	no	—
353	C₄²×C₁₃	—	2	2	no	—
354	C₄²×C₁₃	—	2	2	no	—
355	C₄²×C₁₃	—	2	2	no	—
356	C₄²×C₁₃	—	2	2	no	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	2	no	—
360	C₄²×C₁₃	—	2	4	no	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	2	4	no	—
363	C₄²×C₁₃	—	2	2	no	—
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	4	2	no	—
366	C₄²×C₁₃	—	4	2	no	—
367	C₄²×C₁₃	#41	1	4	yes	—
368	#2531	C₂×C₁₃	1	2	yes	complemented
369	#2526	C₂×C₁₃	1	2	yes	complemented
370	#2513	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#2507	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#2497	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#2490	C₂×C₁₃	1	1	yes	characteristic, complemented
374	#2476	C₂×C₁₃	1	2	yes	complemented
375	#2471	C₂×C₁₃	1	2	yes	complemented
376	#2454	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#2445	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#2428	C₂×C₁₃	1	1	yes	characteristic
379	#2420	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#2395	C₂×C₁₃	1	2	yes	complemented
381	#2392	C₂×C₁₃	1	2	yes	complemented
382	C₄×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
383	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
384	C₄×#123	C₂×C₁₃	1	2	yes	complemented
385	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
386	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
387	C₄×#121	C₂×C₁₃	1	2	yes	complemented
388	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
389	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
390	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
391	C₂³×C₁₃	—	2	1	no	—
392	C₂³×C₁₃	—	2	2	no	—
393	C₂³×C₁₃	—	2	2	no	—
394	C₂³×C₁₃	—	2	2	no	—
395	C₂³×C₁₃	—	2	1	no	—
396	C₂³×C₁₃	—	2	1	no	—
397	C₂³×C₁₃	—	2	1	no	—
398	C₂³×C₁₃	—	2	2	no	—
399	C₂³×C₁₃	—	2	1	no	—
400	C₂³×C₁₃	—	2	2	no	—
401	C₂³×C₁₃	—	2	1	no	—
402	C₂³×C₁₃	—	2	2	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	2	no	—
408	C₂³×C₁₃	—	2	2	no	—
409	C₂³×C₁₃	—	2	2	no	—
410	C₂³×C₁₃	C₂×#41	1	4	yes	—
411	C₂³×C₁₃	C₂×#41	1	2	yes	—
412	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
413	D₄×C₁₃	—	2	8	no	—
414	D₄×C₁₃	—	4	8	no	—
415	D₄×C₁₃	—	4	8	no	—
416	D₄×C₁₃	—	4	8	no	—
417	D₄×C₁₃	—	4	8	no	—
418	D₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	2	8	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	1	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	1	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	2	1	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	1	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	4	8	no	—
468	C₂×C₄×C₁₃	—	4	8	no	—
469	C₂×C₄×C₁₃	—	4	4	no	—
470	C₂×C₄×C₁₃	—	4	4	no	—
471	C₂×C₄×C₁₃	—	4	8	no	—
472	C₂×C₄×C₁₃	—	4	8	no	—
473	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
474	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
475	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
476	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
477	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
478	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
479	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
480	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
481	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
482	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
484	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
485	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
486	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×#123	C₂²×C₁₃	1	2	yes	—
489	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×#121	C₂²×C₁₃	1	2	yes	—
491	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
500	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×#117	C₂²×C₁₃	1	2	yes	—
503	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
504	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
505	#400	C₂²×C₁₃	1	2	yes	—
506	#399	C₂²×C₁₃	1	2	yes	—
507	#398	C₂²×C₁₃	1	2	yes	—
508	#398	C₂²×C₁₃	1	2	yes	—
509	#397	C₂²×C₁₃	1	2	yes	—
510	#397	C₂²×C₁₃	1	2	yes	—
511	#397	C₂²×C₁₃	1	2	yes	—
512	#397	C₂²×C₁₃	1	2	yes	—
513	#396	C₂²×C₁₃	1	2	yes	—
514	#396	C₂²×C₁₃	1	2	yes	—
515	#394	C₂²×C₁₃	1	2	yes	—
516	#394	C₂²×C₁₃	1	2	yes	—
517	#394	C₂²×C₁₃	1	2	yes	—
518	#394	C₂²×C₁₃	1	2	yes	—
519	#394	C₂²×C₁₃	1	2	yes	—
520	#392	C₂²×C₁₃	1	2	yes	—
521	#390	C₂²×C₁₃	1	1	yes	characteristic
522	#390	C₂²×C₁₃	1	2	yes	—
523	#390	C₂²×C₁₃	1	2	yes	—
524	#390	C₂²×C₁₃	1	1	yes	characteristic
525	#390	C₂²×C₁₃	1	1	yes	characteristic
526	#390	C₂²×C₁₃	1	1	yes	characteristic
527	#390	C₂²×C₁₃	1	1	yes	characteristic
528	#390	C₂²×C₁₃	1	1	yes	characteristic
529	#390	C₂²×C₁₃	1	2	yes	—
530	#389	C₂²×C₁₃	1	1	yes	characteristic
531	#389	C₂²×C₁₃	1	1	yes	characteristic
532	#389	C₂²×C₁₃	1	1	yes	characteristic
533	#389	C₂²×C₁₃	1	1	yes	characteristic
534	#389	C₂²×C₁₃	1	1	yes	characteristic
535	#389	C₂²×C₁₃	1	1	yes	characteristic
536	#389	C₂²×C₁₃	1	2	yes	—
537	#388	C₂²×C₁₃	1	2	yes	—
538	#388	C₂²×C₁₃	1	2	yes	—
539	#388	C₂²×C₁₃	1	2	yes	—
540	#388	C₂²×C₁₃	1	2	yes	—
541	#388	C₂²×C₁₃	1	2	yes	—
542	#388	C₂²×C₁₃	1	2	yes	—
543	#388	C₂²×C₁₃	1	2	yes	—
544	#388	C₂²×C₁₃	1	2	yes	—
545	#387	C₂²×C₁₃	1	2	yes	—
546	#387	C₂²×C₁₃	1	2	yes	—
547	#387	C₂²×C₁₃	1	2	yes	—
548	#387	C₂²×C₁₃	1	2	yes	—
549	#386	C₂²×C₁₃	1	2	yes	—
550	#386	C₂²×C₁₃	1	2	yes	—
551	#386	C₂²×C₁₃	1	2	yes	—
552	#386	C₂²×C₁₃	1	2	yes	—
553	#386	C₂²×C₁₃	1	2	yes	—
554	#385	C₂²×C₁₃	1	2	yes	—
555	#384	C₂²×C₁₃	1	1	yes	characteristic
556	#382	C₂²×C₁₃	1	1	yes	characteristic
557	#381	C₂²×C₁₃	1	2	yes	—
558	#380	C₂²×C₁₃	1	1	yes	characteristic
559	#380	C₂²×C₁₃	1	2	yes	—
560	#380	C₂²×C₁₃	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
571	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
572	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
576	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
577	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
578	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
581	#376	C₂²×C₁₃	1	1	yes	characteristic
582	#376	C₂²×C₁₃	1	1	yes	characteristic
583	C₄³	C₂²×C₁₃	1	1	yes	characteristic
584	C₄³	C₂²×C₁₃	1	1	yes	characteristic
585	C₂²×C₁₃	—	2	4	no	—
586	C₂²×C₁₃	—	2	2	no	—
587	C₂²×C₁₃	—	2	4	no	—
588	C₂²×C₁₃	—	2	2	no	—
589	C₂²×C₁₃	—	2	4	no	—
590	C₂²×C₁₃	—	2	2	no	—
591	C₂²×C₁₃	—	4	1	no	—
592	C₂²×C₁₃	—	4	2	no	—
593	C₂²×C₁₃	—	4	2	no	—
594	C₂²×C₁₃	—	4	1	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	4	1	no	—
597	C₂²×C₁₃	—	4	1	no	—
598	C₂²×C₁₃	—	4	2	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	4	2	no	—
601	C₂²×C₁₃	—	4	2	no	—
602	C₂²×C₁₃	—	4	2	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	2	no	—
605	C₂²×C₁₃	—	4	2	no	—
606	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
607	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
608	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
609	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
610	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
611	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₄×C₁₃	—	2	2	no	—
614	C₄×C₁₃	—	2	2	no	—
615	C₄×C₁₃	—	2	2	no	—
616	C₄×C₁₃	—	2	2	no	—
617	C₄×C₁₃	—	2	4	no	—
618	C₄×C₁₃	—	2	2	no	—
619	C₄×C₁₃	—	2	2	no	—
620	C₄×C₁₃	—	4	1	no	—
621	C₄×C₁₃	—	4	1	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	—	4	2	no	—
624	C₄×C₁₃	—	4	1	no	—
625	C₄×C₁₃	—	4	1	no	—
626	C₄×C₁₃	—	4	2	no	—
627	C₄×C₁₃	—	4	2	no	—
628	C₄×C₁₃	—	4	1	no	—
629	C₄×C₁₃	—	4	1	no	—
630	C₄×C₁₃	—	4	2	no	—
631	C₄×C₁₃	#529	1	4	yes	—
632	C₄×C₁₃	#540	1	4	yes	—
633	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
635	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
636	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
637	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
638	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
641	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
643	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
645	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
646	#127	—	2	4	no	—
647	#125	—	2	4	no	—
648	#123	—	2	8	no	—
649	#121	—	2	4	no	—
650	#121	—	2	4	no	—
651	#121	—	2	8	no	—
652	C₄×D₄	—	2	4	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	4	no	—
655	C₄×D₄	—	2	4	no	—
656	C₄×D₄	—	4	4	no	—
657	C₄×D₄	—	4	4	no	—
658	C₄×D₄	—	4	4	no	—
659	C₄×D₄	—	4	4	no	—
660	#117	—	2	4	no	—
661	#117	—	2	4	no	—
662	#117	—	4	4	no	—
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
707	C₂×C₄²	—	2	4	no	—
708	C₂×C₄²	—	4	4	no	—
709	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
711	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
720	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
727	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
728	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
729	#95	C₂³×C₁₃	1	1	yes	characteristic
730	#95	C₂³×C₁₃	1	1	yes	characteristic
731	#95	C₂³×C₁₃	1	1	yes	characteristic
732	#95	C₂³×C₁₃	1	1	yes	characteristic
733	#95	C₂³×C₁₃	1	1	yes	characteristic
734	#95	C₂³×C₁₃	1	1	yes	characteristic
735	#95	C₂³×C₁₃	1	1	yes	characteristic
736	#95	C₂³×C₁₃	1	1	yes	characteristic
737	#95	C₂³×C₁₃	1	2	yes	—
738	#95	C₂³×C₁₃	1	2	yes	—
739	#95	C₂³×C₁₃	1	2	yes	—
740	#95	C₂³×C₁₃	1	2	yes	—
741	#95	C₂³×C₁₃	1	2	yes	—
742	#95	C₂³×C₁₃	1	2	yes	—
743	#95	C₂³×C₁₃	1	2	yes	—
744	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	4	4	no	—
752	C₂×C₁₃	—	4	2	no	—
753	C₂×C₁₃	—	8	2	no	—
754	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
755	C₂×C₁₃	#3444	1	1	yes	characteristic
756	C₂×C₁₃	C₂×#540	1	1	yes	characteristic
757	C₂×C₁₃	#3481	1	1	yes	characteristic
758	C₂×C₁₃	#3481	1	1	yes	characteristic
759	C₂×C₁₃	#3481	1	1	yes	characteristic
760	C₂×C₁₃	#3483	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
762	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	4	no	—
768	C₂×D₄	—	2	4	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	C₁₃×#41	1	4	yes	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	4	no	—
832	C₄⋊C₄	—	2	4	no	—
833	C₄⋊C₄	—	2	4	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	C₁₃×#41	1	4	yes	—
842	C₄⋊C₄	C₁₃×#41	1	4	yes	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	4	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	4	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	C₁₃×#41	1	4	yes	—
887	C₁₃	#34970	1	1	yes	characteristic, direct product factor, Sylow
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	C₂×C₁₃×#41	1	4	yes	—
908	C₂³	C₂×C₁₃×#41	1	2	yes	—
909	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
910	D₄	—	2	8	no	—
911	D₄	—	4	8	no	—
912	D₄	—	4	8	no	—
913	D₄	—	4	8	no	—
914	D₄	—	4	8	no	—
915	D₄	—	4	4	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	4	8	no	—
965	C₂×C₄	—	4	8	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	8	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
971	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
972	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
973	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
974	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
975	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
976	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
977	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
978	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
979	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
980	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
981	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
982	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
983	C₂²	—	2	4	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	4	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	4	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1005	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1006	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1007	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1008	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1009	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1010	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	4	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₁₃×#529	1	4	yes	—
1030	C₄	C₁₃×#540	1	4	yes	—
1031	C₂	—	4	4	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
1035	C₂	C₁₃×#3444	1	1	yes	characteristic
1036	C₂	C₂×C₁₃×#540	1	1	yes	characteristic
1037	C₂	C₁₃×#3481	1	1	yes	characteristic
1038	C₂	C₁₃×#3481	1	1	yes	characteristic
1039	C₂	C₁₃×#3481	1	1	yes	characteristic
1040	C₂	C₁₃×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2428	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#2531	C₂	semidirect
2. C₁₃×#2526	C₂	semidirect
3. C₁₃×#2513	C₂	semidirect
4. C₁₃×#2507	C₂	semidirect
5. C₁₃×#2497	C₂	semidirect
6. C₁₃×#2490	C₂	semidirect
7. C₁₃×#2476	C₂	semidirect
8. C₁₃×#2471	C₂	semidirect
9. C₁₃×#2454	C₂	semidirect
10. C₁₃×#2445	C₂	semidirect
12. C₁₃×#2420	C₂	semidirect
13. C₁₃×#2395	C₂	semidirect
14. C₁₃×#2392	C₂	semidirect
15. C₄×C₁₃×#127	C₂	semidirect
16. C₄×C₁₃×#125	C₂	semidirect
17. C₄×C₁₃×#123	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₄×C₁₃×#121	C₂	semidirect
20. C₄×C₁₃×#121	C₂	semidirect
21. C₁₃×#2293	C₂	semidirect
22. C₄²×D₄×C₁₃	C₂	semidirect
23. C₄×C₁₃×#117	C₂	semidirect
241. #34970	C₁₃	direct (N × H)
368. #2531	C₂×C₁₃	semidirect
369. #2526	C₂×C₁₃	semidirect
370. #2513	C₂×C₁₃	semidirect
371. #2507	C₂×C₁₃	semidirect
372. #2497	C₂×C₁₃	semidirect
373. #2490	C₂×C₁₃	semidirect
374. #2476	C₂×C₁₃	semidirect
375. #2471	C₂×C₁₃	semidirect
376. #2454	C₂×C₁₃	semidirect
377. #2445	C₂×C₁₃	semidirect
379. #2420	C₂×C₁₃	semidirect
380. #2395	C₂×C₁₃	semidirect
381. #2392	C₂×C₁₃	semidirect
382. C₄×#127	C₂×C₁₃	semidirect
383. C₄×#125	C₂×C₁₃	semidirect
384. C₄×#123	C₂×C₁₃	semidirect
385. C₄×#121	C₂×C₁₃	semidirect
386. C₄×#121	C₂×C₁₃	semidirect
387. C₄×#121	C₂×C₁₃	semidirect
388. #2293	C₂×C₁₃	semidirect
389. C₄²×D₄	C₂×C₁₃	semidirect
390. C₄×#117	C₂×C₁₃	semidirect
887. C₁₃	#34970	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2531	2
C₁₃×#2526	2
C₁₃×#2513	2
C₁₃×#2507	2
C₁₃×#2497	2
C₁₃×#2490	2
C₁₃×#2476	2
C₁₃×#2471	2
C₁₃×#2454	2
C₁₃×#2445	2
C₁₃×#2428	2
C₁₃×#2420	2
C₁₃×#2395	2
C₁₃×#2392	2
C₄×C₁₃×#127	2
C₄×C₁₃×#125	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2293	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
#34970	13

Subgroups — C13×#34970 #15721309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34970 #15721309