Subgroups — C₁₃×#24053 #15710392

Order 3328.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 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×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2485	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1787	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×M₁₆	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	—	2	4	no	—
20	D₄×Q₈×C₁₃	—	2	4	no	—
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₁₃×#485	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₁₃×#419	—	2	4	no	—
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#397	—	2	1	no	—
51	C₁₃×#394	—	2	1	no	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#387	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	2	no	—
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	—	2	1	no	—
66	C₂²×Q₈×C₁₃	—	2	1	no	—
67	C₂²×Q₈×C₁₃	—	2	2	no	—
68	C₂²×Q₈×C₁₃	—	2	2	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	—	4	1	no	—
73	C₂²×Q₈×C₁₃	—	4	1	no	—
74	C₂²×Q₈×C₁₃	—	4	1	no	—
75	C₂²×Q₈×C₁₃	—	4	1	no	—
76	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	—	4	1	no	—
87	C₂×C₁₃×M₁₆	—	4	1	no	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×C₄⋊Q₈	—	2	8	no	—
93	C₁₃×C₄⋊Q₈	—	2	2	no	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₂²⋊Q₈	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	8	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#107	—	2	2	no	—
133	C₁₃×#106	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	2	2	no	—
139	C₁₃×#103	—	2	2	no	—
140	C₁₃×#103	—	2	2	no	—
141	C₁₃×#103	—	2	2	no	—
142	C₁₃×#103	—	4	1	no	—
143	C₁₃×#103	—	4	1	no	—
144	C₁₃×#103	—	4	1	no	—
145	C₁₃×#103	—	4	1	no	—
146	C₁₃×C₂²⋊C₈	—	2	2	no	—
147	C₁₃×C₂²⋊C₈	—	4	1	no	—
148	C₁₃×C₂²⋊C₈	—	4	1	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	#24053	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₃	—	2	4	no	—
158	C₂×Q₈×C₁₃	—	2	4	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	8	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	4	2	no	—
174	C₂×Q₈×C₁₃	—	4	2	no	—
175	C₂×Q₈×C₁₃	—	4	2	no	—
176	C₂×Q₈×C₁₃	—	4	2	no	—
177	C₂×Q₈×C₁₃	—	4	4	no	—
178	C₂×Q₈×C₁₃	—	4	4	no	—
179	C₂×Q₈×C₁₃	—	4	4	no	—
180	C₂×Q₈×C₁₃	—	4	4	no	—
181	C₂×Q₈×C₁₃	—	4	4	no	—
182	C₂×Q₈×C₁₃	—	4	4	no	—
183	C₂×Q₈×C₁₃	—	4	4	no	—
184	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×Q₈×C₁₃	#41	1	2	yes	—
188	C₂×Q₈×C₁₃	#41	1	2	yes	—
189	C₂×D₄×C₁₃	—	2	2	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	4	2	no	—
213	C₂²×C₄×C₁₃	—	4	2	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	4	2	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×M₁₆	—	4	4	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	4	2	no	—
252	C₁₃×C₄⋊C₄	—	8	1	no	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	2	no	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	4	2	no	—
259	C₁₃×C₂²⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	8	1	no	—
261	C₁₃×C₂²⋊C₄	—	8	1	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	4	2	no	—
266	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
267	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2485	C₂×C₁₃	1	1	yes	characteristic
270	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1870	C₂×C₁₃	1	1	yes	characteristic
276	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	—	2	1	no	—
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	1	no	—
288	C₂³×C₁₃	—	2	1	no	—
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	#120	1	2	yes	—
294	C₂³×C₁₃	#137	1	2	yes	—
295	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₁₃	—	2	2	no	—
297	Q₈×C₁₃	—	2	2	no	—
298	Q₈×C₁₃	—	2	2	no	—
299	Q₈×C₁₃	—	2	2	no	—
300	Q₈×C₁₃	—	2	2	no	—
301	Q₈×C₁₃	—	2	2	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	4	8	no	—
304	Q₈×C₁₃	—	4	8	no	—
305	Q₈×C₁₃	—	4	1	no	—
306	Q₈×C₁₃	—	4	1	no	—
307	Q₈×C₁₃	—	4	1	no	—
308	Q₈×C₁₃	—	4	1	no	—
309	Q₈×C₁₃	#123	1	4	yes	—
310	D₄×C₁₃	—	2	8	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	4	8	no	—
332	C₂×C₄×C₁₃	—	4	8	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	#120	1	2	yes	—
356	C₂×C₄×C₁₃	#137	1	2	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₁₃	—	4	1	no	—
364	C₈×C₁₃	—	4	1	no	—
365	C₈×C₁₃	—	4	1	no	—
366	C₈×C₁₃	—	4	1	no	—
367	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	D₄×Q₈	—	2	4	no	—
371	D₄×Q₈	—	2	4	no	—
372	C₂×C₄⋊Q₈	—	2	1	no	—
373	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	—	2	1	no	—
375	C₂×C₂²⋊Q₈	—	2	1	no	—
376	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄×D₄	—	2	1	no	—
380	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
382	#485	—	2	4	no	—
383	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
385	#419	—	2	4	no	—
386	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	#397	—	2	1	no	—
402	#394	—	2	1	no	—
403	#389	C₂²×C₁₃	1	1	yes	characteristic
404	#389	C₂²×C₁₃	1	1	yes	characteristic
405	#388	—	2	1	no	—
406	#387	—	2	1	no	—
407	#380	C₂²×C₁₃	1	1	yes	characteristic
408	#380	C₂²×C₁₃	1	1	yes	characteristic
409	#380	C₂²×C₁₃	1	1	yes	characteristic
410	#340	C₂²×C₁₃	1	1	yes	characteristic
411	#340	C₂²×C₁₃	1	1	yes	characteristic
412	#336	C₂²×C₁₃	1	1	yes	characteristic
413	#336	C₂²×C₁₃	1	1	yes	characteristic
414	C₂²×C₁₃	—	2	2	no	—
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	4	1	no	—
421	C₂²×C₁₃	—	4	1	no	—
422	C₂²×C₁₃	—	4	1	no	—
423	C₂²×C₁₃	—	4	1	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	1	no	—
427	C₂²×C₁₃	—	4	1	no	—
428	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
429	C₂²×C₁₃	#546	1	1	yes	characteristic
430	C₂²×C₁₃	#546	1	1	yes	characteristic
431	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
432	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
433	C₂²×C₁₃	#577	1	1	yes	characteristic
434	C₂²×C₁₃	#578	1	1	yes	characteristic
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	4	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	4	1	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	1	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	8	1	no	—
444	C₄×C₁₃	—	8	1	no	—
445	C₄×C₁₃	—	8	1	no	—
446	C₄×C₁₃	—	8	1	no	—
447	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
448	C₄×C₁₃	#534	1	1	yes	characteristic
449	C₄×C₁₃	#546	1	1	yes	characteristic
450	C₄×C₁₃	#546	1	1	yes	characteristic
451	C₂²×Q₈	—	2	2	no	—
452	C₂²×Q₈	—	2	2	no	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	—	2	2	no	—
456	C₂²×Q₈	—	2	2	no	—
457	C₂²×Q₈	—	2	2	no	—
458	C₂²×Q₈	—	2	2	no	—
459	C₂²×Q₈	—	2	2	no	—
460	C₂²×Q₈	—	4	1	no	—
461	C₂²×Q₈	—	4	1	no	—
462	C₂²×Q₈	—	4	1	no	—
463	C₂²×Q₈	—	4	1	no	—
464	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
465	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂³×C₄	—	2	1	no	—
471	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×M₁₆	—	2	2	no	—
474	C₂×M₁₆	—	4	1	no	—
475	C₂×M₁₆	—	4	1	no	—
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	8	no	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	—	2	8	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	#117	—	2	2	no	—
495	#117	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	#107	—	2	2	no	—
521	#106	—	2	2	no	—
522	#103	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#103	—	4	1	no	—
531	#103	—	4	1	no	—
532	#103	—	4	1	no	—
533	#103	—	4	1	no	—
534	C₂²⋊C₈	—	2	2	no	—
535	C₂²⋊C₈	—	4	1	no	—
536	C₂²⋊C₈	—	4	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	C₂×C₁₃	—	4	2	no	—
543	C₂×C₁₃	—	4	2	no	—
544	C₂×C₁₃	#2405	1	1	yes	characteristic
545	C₂×C₁₃	#3004	1	1	yes	characteristic
546	C₂×C₁₃	#3013	1	1	yes	characteristic
547	C₂×C₁₃	#3312	1	1	yes	characteristic
548	C₂×C₁₃	#3320	1	1	yes	characteristic
549	C₂×C₁₃	#3328	1	1	yes	characteristic
550	C₂×C₁₃	#3329	1	1	yes	characteristic
551	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	8	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	4	2	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	2	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	—	4	4	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	4	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	—	4	4	no	—
580	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
581	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
582	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
583	C₂×Q₈	C₁₃×#41	1	2	yes	—
584	C₂×Q₈	C₁₃×#41	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	M₁₆	—	4	4	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	8	1	no	—
649	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	8	1	no	—
657	C₂²⋊C₄	—	8	1	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	4	2	no	—
662	C₁₃	#24053	1	1	yes	characteristic, direct product factor, Sylow
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	C₁₃×#120	1	2	yes	—
676	C₂³	C₁₃×#137	1	2	yes	—
677	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	4	8	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	C₁₃×#123	1	4	yes	—
692	D₄	—	2	8	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	C₁₃×#120	1	2	yes	—
738	C₂×C₄	C₁₃×#137	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
741	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
742	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
743	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
744	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
764	C₂²	C₁₃×#546	1	1	yes	characteristic
765	C₂²	C₁₃×#546	1	1	yes	characteristic
766	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
767	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
768	C₂²	C₁₃×#577	1	1	yes	characteristic
769	C₂²	C₁₃×#578	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	4	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	—	8	1	no	—
781	C₄	—	8	1	no	—
782	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
783	C₄	C₁₃×#534	1	1	yes	characteristic
784	C₄	C₁₃×#546	1	1	yes	characteristic
785	C₄	C₁₃×#546	1	1	yes	characteristic
786	C₂	—	4	2	no	—
787	C₂	—	4	2	no	—
788	C₂	C₁₃×#2405	1	1	yes	characteristic
789	C₂	C₁₃×#3004	1	1	yes	characteristic
790	C₂	C₁₃×#3013	1	1	yes	characteristic
791	C₂	C₁₃×#3312	1	1	yes	characteristic
792	C₂	C₁₃×#3320	1	1	yes	characteristic
793	C₂	C₁₃×#3328	1	1	yes	characteristic
794	C₂	C₁₃×#3329	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×#485	C₂	semidirect
3. C₂×C₁₃×#419	C₂	semidirect
5. C₁₃×#2043	C₂	semidirect
6. C₁₃×#2043	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#1894	C₂	semidirect
11. C₁₃×#1865	C₂	semidirect
12. C₁₃×#1863	C₂	semidirect
13. C₁₃×#1787	C₂	semidirect
14. C₁₃×#1787	C₂	semidirect
15. C₁₃×#1787	C₂	semidirect
154. #24053	C₁₃	direct (N × H)
267. C₂×#485	C₂×C₁₃	semidirect
268. C₂×#419	C₂×C₁₃	semidirect
270. #2043	C₂×C₁₃	semidirect
271. #2043	C₂×C₁₃	semidirect
272. #2036	C₂×C₁₃	semidirect
273. #2035	C₂×C₁₃	semidirect
274. #1894	C₂×C₁₃	semidirect
276. #1865	C₂×C₁₃	semidirect
277. #1863	C₂×C₁₃	semidirect
278. #1787	C₂×C₁₃	semidirect
279. #1787	C₂×C₁₃	semidirect
280. #1787	C₂×C₁₃	semidirect
662. C₁₃	#24053	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×#485	2
C₂×C₁₃×#419	2
C₁₃×#2485	2
C₁₃×#2043	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#1894	2
C₁₃×#1870	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1787	2
#24053	13

Subgroups — C13×#24053 #15710392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24053 #15710392