Subgroups — C₁₃×#24453 #15710792

Order 3328.

1404 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2415	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₃	—	2	4	no	—
23	D₄×Q₈×C₁₃	—	2	4	no	—
24	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#470	—	2	4	no	—
37	C₁₃×#451	—	2	4	no	—
38	C₁₃×#451	—	2	4	no	—
39	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
40	C₁₃×#419	—	2	4	no	—
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₁₃×#397	—	2	1	no	—
55	C₁₃×#394	—	2	1	no	—
56	C₁₃×#391	C₂²	1	1	yes	characteristic
57	C₁₃×#389	—	2	1	no	—
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#388	—	2	1	no	—
60	C₁₃×#380	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₁₃×#336	C₂²	1	1	yes	characteristic
64	C₁₃×#336	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	—	2	2	no	—
67	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₂²×Q₈×C₁₃	—	2	2	no	—
70	C₂²×Q₈×C₁₃	—	2	2	no	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₂²×Q₈×C₁₃	—	2	2	no	—
73	C₂²×Q₈×C₁₃	—	2	2	no	—
74	C₂²×Q₈×C₁₃	—	4	1	no	—
75	C₂²×Q₈×C₁₃	—	4	1	no	—
76	C₂²×Q₈×C₁₃	—	4	1	no	—
77	C₂²×Q₈×C₁₃	—	4	1	no	—
78	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×Q₁₆	—	2	2	no	—
89	C₂×C₁₃×Q₁₆	—	2	2	no	—
90	C₂×C₁₃×Q₁₆	—	2	2	no	—
91	C₂×C₁₃×Q₁₆	—	2	2	no	—
92	C₂×C₁₃×Q₁₆	—	2	2	no	—
93	C₂×C₁₃×Q₁₆	—	2	2	no	—
94	C₂×C₁₃×Q₁₆	—	4	1	no	—
95	C₂×C₁₃×Q₁₆	—	4	1	no	—
96	C₂×C₁₃×Q₁₆	—	4	1	no	—
97	C₂×C₁₃×M₁₆	—	2	2	no	—
98	C₂×C₁₃×M₁₆	—	2	2	no	—
99	C₂×C₁₃×M₁₆	—	4	1	no	—
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	—	2	8	no	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	8	no	—
108	C₁₃×C₂²⋊Q₈	—	2	8	no	—
109	C₁₃×C₂²⋊Q₈	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	4	1	no	—
116	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
117	C₄×Q₈×C₁₃	—	2	2	no	—
118	C₄×Q₈×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	—	2	8	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₁₃×#117	—	2	2	no	—
123	C₁₃×#117	—	4	1	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
144	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	—	2	1	no	—
146	C₂×C₄²×C₁₃	—	2	1	no	—
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#106	—	2	2	no	—
149	C₁₃×#103	—	2	2	no	—
150	C₁₃×#103	—	2	2	no	—
151	C₁₃×#103	—	2	2	no	—
152	C₁₃×#103	—	2	2	no	—
153	C₁₃×#103	—	2	2	no	—
154	C₁₃×#103	—	2	2	no	—
155	C₁₃×#103	—	2	2	no	—
156	C₁₃×#103	—	2	2	no	—
157	C₁₃×#103	—	4	1	no	—
158	C₁₃×#103	D₄	1	4	yes	complemented
159	C₁₃×C₂²⋊C₈	—	2	2	no	—
160	C₁₃×C₂²⋊C₈	—	2	2	no	—
161	C₁₃×C₂²⋊C₈	—	4	1	no	—
162	C₁₃×#95	—	2	1	no	—
163	C₁₃×#95	—	2	1	no	—
164	C₁₃×#95	—	2	1	no	—
165	C₁₃×#95	—	2	1	no	—
166	#24453	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₁₃	—	2	4	no	—
170	C₂×Q₈×C₁₃	—	2	4	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	8	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	4	2	no	—
192	C₂×Q₈×C₁₃	—	4	2	no	—
193	C₂×Q₈×C₁₃	—	4	2	no	—
194	C₂×Q₈×C₁₃	—	4	2	no	—
195	C₂×Q₈×C₁₃	—	4	4	no	—
196	C₂×Q₈×C₁₃	—	4	4	no	—
197	C₂×Q₈×C₁₃	—	4	4	no	—
198	C₂×Q₈×C₁₃	—	4	4	no	—
199	C₂×Q₈×C₁₃	—	4	4	no	—
200	C₂×Q₈×C₁₃	—	4	4	no	—
201	C₂×Q₈×C₁₃	—	4	4	no	—
202	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₁₃	#41	1	2	yes	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₁₃×Q₁₆	—	4	4	no	—
242	C₁₃×Q₁₆	—	4	4	no	—
243	C₁₃×Q₁₆	—	4	4	no	—
244	C₁₃×M₁₆	—	4	4	no	—
245	C₂×C₈×C₁₃	—	2	1	no	—
246	C₂×C₈×C₁₃	—	2	1	no	—
247	C₂×C₈×C₁₃	—	2	1	no	—
248	C₂×C₈×C₁₃	—	2	1	no	—
249	C₂×C₈×C₁₃	—	2	1	no	—
250	C₂×C₈×C₁₃	—	2	1	no	—
251	C₂×C₈×C₁₃	—	2	1	no	—
252	C₂×C₈×C₁₃	—	2	1	no	—
253	C₂×C₈×C₁₃	—	2	1	no	—
254	C₂×C₈×C₁₃	—	2	1	no	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	2	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
273	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	1	no	—
284	C₄²×C₁₃	—	2	1	no	—
285	C₄²×C₁₃	—	4	2	no	—
286	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
287	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#2415	C₂×C₁₃	1	1	yes	characteristic
292	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#2001	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#1870	C₂×C₁₃	1	1	yes	characteristic
299	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂³×C₁₃	—	2	1	no	—
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	2	1	no	—
304	C₂³×C₁₃	—	2	1	no	—
305	C₂³×C₁₃	—	2	1	no	—
306	C₂³×C₁₃	—	2	1	no	—
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	#120	1	2	yes	—
314	C₂³×C₁₃	#137	1	2	yes	—
315	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₁₃	—	2	2	no	—
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	2	no	—
323	Q₈×C₁₃	—	4	8	no	—
324	Q₈×C₁₃	—	4	8	no	—
325	Q₈×C₁₃	—	4	1	no	—
326	Q₈×C₁₃	—	4	1	no	—
327	Q₈×C₁₃	—	4	1	no	—
328	Q₈×C₁₃	—	4	1	no	—
329	Q₈×C₁₃	—	4	1	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	Q₈×C₁₃	—	4	1	no	—
332	Q₈×C₁₃	—	4	1	no	—
333	Q₈×C₁₃	#121	1	4	yes	—
334	D₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	1	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	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	4	8	no	—
357	C₂×C₄×C₁₃	—	4	8	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	#120	1	2	yes	—
380	C₂×C₄×C₁₃	#137	1	2	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
386	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	4	1	no	—
389	C₈×C₁₃	—	4	1	no	—
390	C₈×C₁₃	—	4	1	no	—
391	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
397	D₄×Q₈	—	2	4	no	—
398	D₄×Q₈	—	2	4	no	—
399	C₂×C₄⋊Q₈	—	2	1	no	—
400	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	—	2	1	no	—
402	C₂×C₂²⋊Q₈	—	2	1	no	—
403	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₄×D₄	—	2	1	no	—
409	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
411	#470	—	2	4	no	—
412	#451	—	2	4	no	—
413	#451	—	2	4	no	—
414	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
415	#419	—	2	4	no	—
416	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
429	#397	—	2	1	no	—
430	#394	—	2	1	no	—
431	#391	C₂²×C₁₃	1	1	yes	characteristic
432	#389	—	2	1	no	—
433	#389	C₂²×C₁₃	1	1	yes	characteristic
434	#388	—	2	1	no	—
435	#380	C₂²×C₁₃	1	1	yes	characteristic
436	#340	C₂²×C₁₃	1	1	yes	characteristic
437	#340	C₂²×C₁₃	1	1	yes	characteristic
438	#336	C₂²×C₁₃	1	1	yes	characteristic
439	#336	C₂²×C₁₃	1	1	yes	characteristic
440	C₂²×C₁₃	—	2	2	no	—
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	2	2	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	4	1	no	—
447	C₂²×C₁₃	—	4	1	no	—
448	C₂²×C₁₃	—	4	1	no	—
449	C₂²×C₁₃	—	4	1	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
455	C₂²×C₁₃	D₄²	1	1	yes	characteristic
456	C₂²×C₁₃	#546	1	1	yes	characteristic
457	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
458	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
459	C₂²×C₁₃	#578	1	1	yes	characteristic
460	C₂²×C₁₃	#578	1	1	yes	characteristic
461	C₄×C₁₃	—	2	2	no	—
462	C₄×C₁₃	—	2	4	no	—
463	C₄×C₁₃	—	2	2	no	—
464	C₄×C₁₃	—	4	1	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	8	1	no	—
471	C₄×C₁₃	—	8	1	no	—
472	C₄×C₁₃	—	8	1	no	—
473	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
474	C₄×C₁₃	#534	1	1	yes	characteristic
475	C₄×C₁₃	D₄²	1	1	yes	characteristic
476	C₄×C₁₃	#546	1	1	yes	characteristic
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	—	2	1	no	—
480	C₂²×Q₈	—	2	1	no	—
481	C₂²×Q₈	—	2	2	no	—
482	C₂²×Q₈	—	2	2	no	—
483	C₂²×Q₈	—	2	2	no	—
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	4	1	no	—
487	C₂²×Q₈	—	4	1	no	—
488	C₂²×Q₈	—	4	1	no	—
489	C₂²×Q₈	—	4	1	no	—
490	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
491	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	—	2	1	no	—
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×Q₁₆	—	2	2	no	—
501	C₂×Q₁₆	—	2	2	no	—
502	C₂×Q₁₆	—	2	2	no	—
503	C₂×Q₁₆	—	2	2	no	—
504	C₂×Q₁₆	—	2	2	no	—
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	4	1	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×M₁₆	—	2	2	no	—
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	4	1	no	—
512	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊Q₈	—	2	8	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	8	no	—
520	C₂²⋊Q₈	—	2	8	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	4	1	no	—
528	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×D₄	—	2	8	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	4	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₄⋊C₄	—	2	1	no	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	#106	—	2	2	no	—
561	#103	—	2	2	no	—
562	#103	—	2	2	no	—
563	#103	—	2	2	no	—
564	#103	—	2	2	no	—
565	#103	—	2	2	no	—
566	#103	—	2	2	no	—
567	#103	—	2	2	no	—
568	#103	—	2	2	no	—
569	#103	—	4	1	no	—
570	#103	D₄×C₁₃	1	4	yes	complemented
571	C₂²⋊C₈	—	2	2	no	—
572	C₂²⋊C₈	—	2	2	no	—
573	C₂²⋊C₈	—	4	1	no	—
574	#95	—	2	1	no	—
575	#95	—	2	1	no	—
576	#95	—	2	1	no	—
577	#95	—	2	1	no	—
578	C₂×C₁₃	—	4	2	no	—
579	C₂×C₁₃	—	4	2	no	—
580	C₂×C₁₃	#2410	1	1	yes	characteristic
581	C₂×C₁₃	#3004	1	1	yes	characteristic
582	C₂×C₁₃	#3011	1	1	yes	characteristic
583	C₂×C₁₃	#3270	1	1	yes	characteristic
584	C₂×C₁₃	#3276	1	1	yes	characteristic
585	C₂×C₁₃	#3312	1	1	yes	characteristic
586	C₂×C₁₃	#3328	1	1	yes	characteristic
587	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	8	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	4	no	—
616	C₂×Q₈	—	4	4	no	—
617	C₂×Q₈	—	4	4	no	—
618	C₂×Q₈	—	4	4	no	—
619	C₂×Q₈	—	4	4	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	—	4	4	no	—
622	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
623	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
624	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
625	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
626	C₂×Q₈	C₁₃×#41	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	Q₁₆	—	4	4	no	—
662	Q₁₆	—	4	4	no	—
663	Q₁₆	—	4	4	no	—
664	M₁₆	—	4	4	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	4	2	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
693	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	4	2	no	—
699	C₂²⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₄²	—	2	4	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	4	2	no	—
706	C₁₃	#24453	1	1	yes	characteristic, direct product factor, Sylow
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	C₁₃×#120	1	2	yes	—
720	C₂³	C₁₃×#137	1	2	yes	—
721	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	2	no	—
726	Q₈	—	2	2	no	—
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	4	8	no	—
730	Q₈	—	4	8	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	Q₈	—	4	1	no	—
735	Q₈	—	4	1	no	—
736	Q₈	—	4	1	no	—
737	Q₈	—	4	1	no	—
738	Q₈	—	4	1	no	—
739	Q₈	C₁₃×#121	1	4	yes	—
740	D₄	—	2	8	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	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	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	C₁₃×#120	1	2	yes	—
786	C₂×C₄	C₁₃×#137	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
790	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
791	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
793	C₈	—	2	2	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₈	—	4	1	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
812	C₂²	D₄²×C₁₃	1	1	yes	characteristic
813	C₂²	C₁₃×#546	1	1	yes	characteristic
814	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
815	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
816	C₂²	C₁₃×#578	1	1	yes	characteristic
817	C₂²	C₁₃×#578	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	2	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
831	C₄	C₁₃×#534	1	1	yes	characteristic
832	C₄	D₄²×C₁₃	1	1	yes	characteristic
833	C₄	C₁₃×#546	1	1	yes	characteristic
834	C₂	—	4	2	no	—
835	C₂	—	4	2	no	—
836	C₂	C₁₃×#2410	1	1	yes	characteristic
837	C₂	C₁₃×#3004	1	1	yes	characteristic
838	C₂	C₁₃×#3011	1	1	yes	characteristic
839	C₂	C₁₃×#3270	1	1	yes	characteristic
840	C₂	C₁₃×#3276	1	1	yes	characteristic
841	C₂	C₁₃×#3312	1	1	yes	characteristic
842	C₂	C₁₃×#3328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#470	C₂	semidirect
3. C₂×C₁₃×#451	C₂	semidirect
4. C₂×C₁₃×#451	C₂	semidirect
5. C₂×C₁₃×#419	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2016	C₂	semidirect
10. C₁₃×#2001	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
12. C₁₃×#1873	C₂	semidirect
14. C₁₃×#1865	C₂	semidirect
15. C₁₃×#1787	C₂	semidirect
158. C₁₃×#103	D₄	semidirect
166. #24453	C₁₃	direct (N × H)
287. C₂×#470	C₂×C₁₃	semidirect
288. C₂×#451	C₂×C₁₃	semidirect
289. C₂×#451	C₂×C₁₃	semidirect
290. C₂×#419	C₂×C₁₃	semidirect
292. #2043	C₂×C₁₃	semidirect
293. #2035	C₂×C₁₃	semidirect
294. #2016	C₂×C₁₃	semidirect
295. #2001	C₂×C₁₃	semidirect
296. #1878	C₂×C₁₃	semidirect
297. #1873	C₂×C₁₃	semidirect
299. #1865	C₂×C₁₃	semidirect
300. #1787	C₂×C₁₃	semidirect
570. #103	D₄×C₁₃	semidirect
706. C₁₃	#24453	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#470	2
C₂×C₁₃×#451	2
C₂×C₁₃×#419	2
C₁₃×#2415	2
C₁₃×#2043	2
C₁₃×#2035	2
C₁₃×#2016	2
C₁₃×#2001	2
C₁₃×#1878	2
C₁₃×#1873	2
C₁₃×#1870	2
C₁₃×#1865	2
C₁₃×#1787	2
#24453	13

Subgroups — C13×#24453 #15710792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24453 #15710792