Subgroups — C₁₃×#34961 #15721300

Order 3328.

1954 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2585	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2573	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2556	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2553	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2466	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2463	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2460	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2455	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2392	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₃×#126	C₂²	1	2	yes	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
33	C₁₃×#400	C₂²	1	1	yes	characteristic
34	C₁₃×#400	C₂²	1	2	yes	—
35	C₁₃×#399	C₂²	1	1	yes	characteristic
36	C₁₃×#399	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	1	yes	characteristic
40	C₁₃×#397	C₂²	1	1	yes	characteristic
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#396	C₂²	1	2	yes	—
45	C₁₃×#396	C₂²	1	2	yes	—
46	C₁₃×#395	C₂²	1	1	yes	characteristic
47	C₁₃×#394	C₂²	1	1	yes	characteristic
48	C₁₃×#394	C₂²	1	2	yes	—
49	C₁₃×#394	C₂²	1	2	yes	—
50	C₁₃×#394	C₂²	1	2	yes	—
51	C₁₃×#393	C₂²	1	1	yes	characteristic
52	C₁₃×#392	C₂²	1	1	yes	characteristic
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	2	yes	—
69	C₁₃×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#385	C₂²	1	1	yes	characteristic
77	C₁₃×#385	C₂²	1	1	yes	characteristic
78	C₁₃×#385	C₂²	1	1	yes	characteristic
79	C₁₃×#385	C₂²	1	1	yes	characteristic
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#383	C₂²	1	2	yes	—
84	C₁₃×#382	C₂²	1	2	yes	—
85	C₁₃×#381	C₂²	1	2	yes	—
86	C₁₃×#380	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
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	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
106	C₄³×C₁₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#126	—	2	8	no	—
117	C₁₃×#125	—	2	8	no	—
118	C₁₃×#123	—	2	8	no	—
119	C₁₃×C₂²⋊Q₈	—	2	8	no	—
120	C₄×Q₈×C₁₃	—	4	2	no	—
121	C₄×D₄×C₁₃	—	2	8	no	—
122	C₄×D₄×C₁₃	—	2	8	no	—
123	C₄×D₄×C₁₃	—	2	8	no	—
124	C₄×D₄×C₁₃	—	4	2	no	—
125	C₁₃×#117	—	2	4	no	—
126	C₁₃×#117	—	4	2	no	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	—	4	2	no	—
166	C₂×C₄²×C₁₃	—	4	4	no	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	1	yes	characteristic
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
206	C₁₃×#95	C₂³	1	1	yes	characteristic
207	#34961	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
209	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂×Q₈×C₁₃	—	2	4	no	—
211	C₂×Q₈×C₁₃	—	4	1	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	4	1	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	4	1	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	#41	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	4	1	no	—
266	C₁₃×C₄⋊C₄	—	4	1	no	—
267	C₁₃×C₄⋊C₄	—	4	1	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	1	no	—
270	C₁₃×C₄⋊C₄	#41	1	8	yes	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	4	1	no	—
285	C₁₃×C₂²⋊C₄	—	4	1	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
288	C₄²×C₁₃	—	2	4	no	—
289	C₄²×C₁₃	—	2	4	no	—
290	C₄²×C₁₃	—	2	4	no	—
291	C₄²×C₁₃	—	2	4	no	—
292	C₄²×C₁₃	—	2	4	no	—
293	C₄²×C₁₃	—	2	4	no	—
294	C₄²×C₁₃	—	2	4	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	—	4	2	no	—
300	C₄²×C₁₃	—	4	2	no	—
301	C₄²×C₁₃	—	4	2	no	—
302	#2585	C₂×C₁₃	1	2	yes	complemented
303	#2573	C₂×C₁₃	1	2	yes	complemented
304	#2556	C₂×C₁₃	1	2	yes	complemented
305	#2553	C₂×C₁₃	1	2	yes	complemented
306	#2523	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2517	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#2466	C₂×C₁₃	1	2	yes	complemented
309	#2463	C₂×C₁₃	1	1	yes	characteristic
310	#2460	C₂×C₁₃	1	2	yes	complemented
311	#2455	C₂×C₁₃	1	1	yes	characteristic
312	#2396	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2395	C₂×C₁₃	1	2	yes	complemented
314	#2392	C₂×C₁₃	1	1	yes	characteristic
315	C₄×#125	C₂×C₁₃	1	2	yes	complemented
316	C₄×#126	C₂×C₁₃	1	2	yes	complemented
317	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
318	C₄×#123	C₂×C₁₃	1	2	yes	complemented
319	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
320	C₄²×D₄	C₂×C₁₃	1	2	yes	complemented
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	2	1	no	—
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	1	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	C₂×#41	1	2	yes	—
332	C₂³×C₁₃	C₂×#41	1	4	yes	—
333	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
334	Q₈×C₁₃	—	4	4	no	—
335	D₄×C₁₃	—	2	16	no	—
336	D₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	8	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	4	4	no	—
378	C₂×C₄×C₁₃	—	4	8	no	—
379	C₂×C₄×C₁₃	—	4	8	no	—
380	C₂×C₄×C₁₃	—	4	8	no	—
381	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
382	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
383	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
384	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
385	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
386	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
387	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
388	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
389	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
390	C₂×#126	C₂²×C₁₃	1	2	yes	—
391	C₂×#125	C₂²×C₁₃	1	2	yes	—
392	C₂×#123	C₂²×C₁₃	1	2	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
394	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
403	#400	C₂²×C₁₃	1	1	yes	characteristic
404	#400	C₂²×C₁₃	1	2	yes	—
405	#399	C₂²×C₁₃	1	2	yes	—
406	#399	C₂²×C₁₃	1	1	yes	characteristic
407	#398	C₂²×C₁₃	1	1	yes	characteristic
408	#398	C₂²×C₁₃	1	2	yes	—
409	#398	C₂²×C₁₃	1	2	yes	—
410	#397	C₂²×C₁₃	1	2	yes	—
411	#397	C₂²×C₁₃	1	1	yes	characteristic
412	#397	C₂²×C₁₃	1	2	yes	—
413	#397	C₂²×C₁₃	1	2	yes	—
414	#396	C₂²×C₁₃	1	2	yes	—
415	#396	C₂²×C₁₃	1	2	yes	—
416	#395	C₂²×C₁₃	1	1	yes	characteristic
417	#394	C₂²×C₁₃	1	2	yes	—
418	#394	C₂²×C₁₃	1	1	yes	characteristic
419	#394	C₂²×C₁₃	1	2	yes	—
420	#394	C₂²×C₁₃	1	2	yes	—
421	#393	C₂²×C₁₃	1	1	yes	characteristic
422	#392	C₂²×C₁₃	1	1	yes	characteristic
423	#391	C₂²×C₁₃	1	2	yes	—
424	#389	C₂²×C₁₃	1	2	yes	—
425	#389	C₂²×C₁₃	1	2	yes	—
426	#389	C₂²×C₁₃	1	2	yes	—
427	#389	C₂²×C₁₃	1	2	yes	—
428	#389	C₂²×C₁₃	1	2	yes	—
429	#388	C₂²×C₁₃	1	2	yes	—
430	#388	C₂²×C₁₃	1	2	yes	—
431	#388	C₂²×C₁₃	1	2	yes	—
432	#388	C₂²×C₁₃	1	2	yes	—
433	#388	C₂²×C₁₃	1	2	yes	—
434	#387	C₂²×C₁₃	1	2	yes	—
435	#387	C₂²×C₁₃	1	2	yes	—
436	#387	C₂²×C₁₃	1	2	yes	—
437	#387	C₂²×C₁₃	1	2	yes	—
438	#387	C₂²×C₁₃	1	2	yes	—
439	#387	C₂²×C₁₃	1	2	yes	—
440	#387	C₂²×C₁₃	1	2	yes	—
441	#387	C₂²×C₁₃	1	2	yes	—
442	#387	C₂²×C₁₃	1	2	yes	—
443	#387	C₂²×C₁₃	1	2	yes	—
444	#387	C₂²×C₁₃	1	2	yes	—
445	#386	C₂²×C₁₃	1	2	yes	—
446	#385	C₂²×C₁₃	1	2	yes	—
447	#385	C₂²×C₁₃	1	1	yes	characteristic
448	#385	C₂²×C₁₃	1	1	yes	characteristic
449	#385	C₂²×C₁₃	1	2	yes	—
450	#385	C₂²×C₁₃	1	1	yes	characteristic
451	#385	C₂²×C₁₃	1	1	yes	characteristic
452	#385	C₂²×C₁₃	1	2	yes	—
453	#383	C₂²×C₁₃	1	2	yes	—
454	#382	C₂²×C₁₃	1	2	yes	—
455	#381	C₂²×C₁₃	1	2	yes	—
456	#380	C₂²×C₁₃	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
476	C₄³	C₂²×C₁₃	1	2	yes	—
477	C₂²×C₁₃	—	2	4	no	—
478	C₂²×C₁₃	—	2	4	no	—
479	C₂²×C₁₃	—	2	2	no	—
480	C₂²×C₁₃	—	2	4	no	—
481	C₂²×C₁₃	—	2	4	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	4	1	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	2	no	—
489	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₁₃	C₂²×#41	1	2	yes	—
491	C₂²×C₁₃	C₂²×#41	1	2	yes	—
492	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₄×C₁₃	—	2	4	no	—
495	C₄×C₁₃	—	2	2	no	—
496	C₄×C₁₃	—	2	4	no	—
497	C₄×C₁₃	—	2	4	no	—
498	C₄×C₁₃	—	2	4	no	—
499	C₄×C₁₃	—	2	4	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	1	no	—
505	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	1	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	#539	1	4	yes	—
511	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
513	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
519	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
520	#126	—	2	8	no	—
521	#125	—	2	8	no	—
522	#123	—	2	8	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₄×Q₈	—	4	2	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	4	2	no	—
529	#117	—	2	4	no	—
530	#117	—	4	2	no	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄²	—	4	2	no	—
570	C₂×C₄²	—	4	4	no	—
571	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
583	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	2	yes	—
595	#95	C₂³×C₁₃	1	2	yes	—
596	#95	C₂³×C₁₃	1	2	yes	—
597	#95	C₂³×C₁₃	1	2	yes	—
598	#95	C₂³×C₁₃	1	2	yes	—
599	#95	C₂³×C₁₃	1	2	yes	—
600	#95	C₂³×C₁₃	1	1	yes	characteristic
601	#95	C₂³×C₁₃	1	2	yes	—
602	#95	C₂³×C₁₃	1	2	yes	—
603	#95	C₂³×C₁₃	1	1	yes	characteristic
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	2	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	1	yes	characteristic
610	#95	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₁₃	—	4	2	no	—
612	C₂×C₁₃	—	4	4	no	—
613	C₂×C₁₃	#3444	1	2	yes	—
614	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
615	C₂×C₁₃	#3481	1	1	yes	characteristic
616	C₂×C₁₃	#3481	1	1	yes	characteristic
617	C₂×C₁₃	#3482	1	2	yes	—
618	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
619	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	4	1	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	4	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	4	1	no	—
639	C₂²×C₄	—	4	1	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₁₃×#41	1	4	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	C₁₃×#41	1	8	yes	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	4	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	2	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	4	no	—
709	C₄²	—	4	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₁₃	#34961	1	1	yes	characteristic, direct product factor, Sylow
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	C₂×C₁₃×#41	1	2	yes	—
724	C₂³	C₂×C₁₃×#41	1	4	yes	—
725	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
726	Q₈	—	4	4	no	—
727	D₄	—	2	16	no	—
728	D₄	—	4	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	8	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
774	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
775	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
776	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
777	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
778	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
779	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
780	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
781	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
795	C₂²	C₂²×C₁₃×#41	1	2	yes	—
796	C₂²	C₂²×C₁₃×#41	1	2	yes	—
797	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
799	C₄	—	2	4	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	4	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	2	no	—
815	C₄	C₁₃×#539	1	4	yes	—
816	C₂	—	4	2	no	—
817	C₂	—	4	4	no	—
818	C₂	C₁₃×#3444	1	2	yes	—
819	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
820	C₂	C₁₃×#3481	1	1	yes	characteristic
821	C₂	C₁₃×#3481	1	1	yes	characteristic
822	C₂	C₁₃×#3482	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#392	C₂²
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×#2585	C₂	semidirect
2. C₁₃×#2573	C₂	semidirect
3. C₁₃×#2556	C₂	semidirect
4. C₁₃×#2553	C₂	semidirect
5. C₁₃×#2523	C₂	semidirect
6. C₁₃×#2517	C₂	semidirect
7. C₁₃×#2466	C₂	semidirect
9. C₁₃×#2460	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
14. C₄×C₁₃×#125	C₂	semidirect
15. C₄×C₁₃×#126	C₂	semidirect
16. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₁₃×#123	C₂	semidirect
18. C₁₃×#2296	C₂	semidirect
19. C₄²×D₄×C₁₃	C₂	semidirect
207. #34961	C₁₃	direct (N × H)
302. #2585	C₂×C₁₃	semidirect
303. #2573	C₂×C₁₃	semidirect
304. #2556	C₂×C₁₃	semidirect
305. #2553	C₂×C₁₃	semidirect
306. #2523	C₂×C₁₃	semidirect
307. #2517	C₂×C₁₃	semidirect
308. #2466	C₂×C₁₃	semidirect
310. #2460	C₂×C₁₃	semidirect
312. #2396	C₂×C₁₃	semidirect
313. #2395	C₂×C₁₃	semidirect
315. C₄×#125	C₂×C₁₃	semidirect
316. C₄×#126	C₂×C₁₃	semidirect
317. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
318. C₄×#123	C₂×C₁₃	semidirect
319. #2296	C₂×C₁₃	semidirect
320. C₄²×D₄	C₂×C₁₃	semidirect
712. C₁₃	#34961	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×#2585	2
C₁₃×#2573	2
C₁₃×#2556	2
C₁₃×#2553	2
C₁₃×#2523	2
C₁₃×#2517	2
C₁₃×#2466	2
C₁₃×#2463	2
C₁₃×#2460	2
C₁₃×#2455	2
C₁₃×#2396	2
C₁₃×#2395	2
C₁₃×#2392	2
C₄×C₁₃×#125	2
C₄×C₁₃×#126	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₁₃×#2296	2
C₄²×D₄×C₁₃	2
#34961	13

Subgroups — C13×#34961 #15721300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34961 #15721300