Subgroups — C₁₃×#24044 #15710383

Order 3328.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	—	2	1	no	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	D₄²×C₁₃	—	2	4	no	—
21	D₄²×C₁₃	—	2	4	no	—
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#120	—	2	1	no	—
27	C₂×C₁₃×#120	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#482	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#418	—	2	4	no	—
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#397	—	2	1	no	—
51	C₁₃×#394	—	2	1	no	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#387	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	—	2	1	no	—
64	C₂⁵×C₁₃	—	2	1	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	8	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	2	no	—
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	2	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	4	1	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	—	4	1	no	—
82	C₂²×D₄×C₁₃	—	4	1	no	—
83	C₂²×D₄×C₁₃	—	4	4	no	—
84	C₂²×D₄×C₁₃	—	4	4	no	—
85	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	D₄	1	4	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	—	2	1	no	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	—	2	2	no	—
94	C₂×C₁₃×M₁₆	—	4	1	no	—
95	C₂×C₁₃×M₁₆	—	4	1	no	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#127	—	2	2	no	—
101	C₁₃×#127	—	2	2	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	D₄	1	4	yes	—
107	C₁₃×#120	—	2	8	no	—
108	C₁₃×#120	—	2	8	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₁₃×#117	—	2	2	no	—
114	C₁₃×#117	—	2	2	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	—	2	1	no	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×#107	—	2	2	no	—
135	C₁₃×#106	—	2	2	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	2	2	no	—
143	C₁₃×#102	—	2	2	no	—
144	C₁₃×#102	—	4	1	no	—
145	C₁₃×#102	—	4	1	no	—
146	C₁₃×#102	—	4	1	no	—
147	C₁₃×#102	—	4	1	no	—
148	C₁₃×C₂²⋊C₈	—	2	2	no	—
149	C₁₃×C₂²⋊C₈	—	4	1	no	—
150	C₁₃×C₂²⋊C₈	—	4	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	C₁₃×#95	—	2	1	no	—
155	C₁₃×#95	—	2	1	no	—
156	#24044	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	—	2	1	no	—
158	C₂⁴×C₁₃	—	2	4	no	—
159	C₂⁴×C₁₃	—	2	1	no	—
160	C₂⁴×C₁₃	—	2	1	no	—
161	C₂⁴×C₁₃	—	2	4	no	—
162	C₂⁴×C₁₃	—	4	2	no	—
163	C₂⁴×C₁₃	—	4	2	no	—
164	C₂⁴×C₁₃	—	4	2	no	—
165	C₂⁴×C₁₃	—	4	2	no	—
166	C₂⁴×C₁₃	—	4	2	no	—
167	C₂⁴×C₁₃	—	4	2	no	—
168	C₂⁴×C₁₃	—	4	2	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	—	8	1	no	—
171	C₂⁴×C₁₃	—	8	1	no	—
172	C₂⁴×C₁₃	—	8	1	no	—
173	C₂⁴×C₁₃	—	8	1	no	—
174	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	2	no	—
178	C₂×D₄×C₁₃	—	2	8	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	4	4	no	—
200	C₂×D₄×C₁₃	—	4	4	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	4	2	no	—
203	C₂×D₄×C₁₃	—	4	2	no	—
204	C₂×D₄×C₁₃	—	4	2	no	—
205	C₂×D₄×C₁₃	—	4	2	no	—
206	C₂×D₄×C₁₃	—	4	2	no	—
207	C₂×D₄×C₁₃	—	4	4	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	32	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	8	1	no	—
218	C₂×D₄×C₁₃	—	8	1	no	—
219	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₁₃	#41	1	2	yes	—
223	C₂×D₄×C₁₃	#41	1	2	yes	—
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	4	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₁₃×M₁₆	—	4	4	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	—	2	1	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	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	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	8	1	no	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	8	1	no	—
283	C₁₃×C₂²⋊C₄	—	8	1	no	—
284	C₄²×C₁₃	—	2	1	no	—
285	C₄²×C₁₃	—	2	1	no	—
286	C₄²×C₁₃	—	4	2	no	—
287	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
288	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#2485	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#1895	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#1870	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	2	2	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	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	1	no	—
316	C₂³×C₁₃	—	2	1	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	4	8	no	—
320	C₂³×C₁₃	—	4	8	no	—
321	C₂³×C₁₃	—	4	8	no	—
322	C₂³×C₁₃	—	4	8	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	—	4	1	no	—
326	C₂³×C₁₃	—	4	1	no	—
327	C₂³×C₁₃	—	4	1	no	—
328	C₂³×C₁₃	—	4	1	no	—
329	C₂³×C₁₃	—	4	1	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	—	4	1	no	—
332	C₂³×C₁₃	—	4	1	no	—
333	C₂³×C₁₃	—	4	1	no	—
334	C₂³×C₁₃	—	4	1	no	—
335	C₂³×C₁₃	—	4	1	no	—
336	C₂³×C₁₃	—	4	1	no	—
337	C₂³×C₁₃	—	4	1	no	—
338	C₂³×C₁₃	—	4	1	no	—
339	C₂³×C₁₃	—	8	4	no	—
340	C₂³×C₁₃	—	8	4	no	—
341	C₂³×C₁₃	—	8	4	no	—
342	C₂³×C₁₃	—	8	4	no	—
343	C₂³×C₁₃	—	8	4	no	—
344	C₂³×C₁₃	—	8	4	no	—
345	C₂³×C₁₃	—	8	4	no	—
346	C₂³×C₁₃	—	8	4	no	—
347	C₂³×C₁₃	—	8	4	no	—
348	C₂³×C₁₃	—	8	4	no	—
349	C₂³×C₁₃	#120	1	2	yes	—
350	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
351	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	D₄×C₁₃	—	2	8	no	—
353	D₄×C₁₃	—	2	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	4	8	no	—
361	D₄×C₁₃	—	4	8	no	—
362	D₄×C₁₃	—	4	8	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	8	no	—
365	D₄×C₁₃	—	4	1	no	—
366	D₄×C₁₃	—	4	1	no	—
367	D₄×C₁₃	—	4	1	no	—
368	D₄×C₁₃	—	4	1	no	—
369	D₄×C₁₃	—	8	4	no	—
370	D₄×C₁₃	#123	1	4	yes	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	4	8	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	1	no	—
403	C₂×C₄×C₁₃	—	4	1	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	#120	1	2	yes	—
406	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
411	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
413	C₈×C₁₃	—	4	1	no	—
414	C₈×C₁₃	—	4	1	no	—
415	C₈×C₁₃	—	4	1	no	—
416	C₈×C₁₃	—	4	1	no	—
417	C₂³×D₄	—	2	1	no	—
418	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	D₄²	—	2	4	no	—
422	D₄²	—	2	4	no	—
423	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#121	—	2	1	no	—
425	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#120	—	2	1	no	—
428	C₂×#120	—	2	1	no	—
429	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#482	—	2	4	no	—
433	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#418	—	2	4	no	—
436	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#397	—	2	1	no	—
452	#394	—	2	1	no	—
453	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#388	—	2	1	no	—
456	#387	—	2	1	no	—
457	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	C₂²×C₁₃	—	2	2	no	—
465	C₂²×C₁₃	—	2	4	no	—
466	C₂²×C₁₃	—	2	2	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	2	no	—
469	C₂²×C₁₃	—	2	2	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	4	1	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	1	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	1	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	1	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	1	no	—
480	C₂²×C₁₃	—	4	1	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	1	no	—
483	C₂²×C₁₃	—	4	1	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	2	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	8	16	no	—
492	C₂²×C₁₃	—	8	16	no	—
493	C₂²×C₁₃	—	8	1	no	—
494	C₂²×C₁₃	—	8	1	no	—
495	C₂²×C₁₃	—	8	1	no	—
496	C₂²×C₁₃	—	8	1	no	—
497	C₂²×C₁₃	—	8	1	no	—
498	C₂²×C₁₃	—	8	1	no	—
499	C₂²×C₁₃	—	8	1	no	—
500	C₂²×C₁₃	—	8	1	no	—
501	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
502	C₂²×C₁₃	#546	1	1	yes	characteristic
503	C₂²×C₁₃	#546	1	1	yes	characteristic
504	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
505	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₂²×C₁₃	#576	1	1	yes	characteristic
507	C₂²×C₁₃	#577	1	1	yes	characteristic
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	2	no	—
510	C₄×C₁₃	—	4	1	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	8	1	no	—
514	C₄×C₁₃	—	8	1	no	—
515	C₄×C₁₃	—	8	1	no	—
516	C₄×C₁₃	—	8	1	no	—
517	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
518	C₄×C₁₃	#534	1	1	yes	characteristic
519	C₄×C₁₃	#546	1	1	yes	characteristic
520	C₄×C₁₃	#546	1	1	yes	characteristic
521	C₂⁵	—	2	1	no	—
522	C₂⁵	—	2	1	no	—
523	C₂²×D₄	—	2	2	no	—
524	C₂²×D₄	—	2	2	no	—
525	C₂²×D₄	—	2	8	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	—	2	2	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	2	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	—	4	1	no	—
538	C₂²×D₄	—	4	1	no	—
539	C₂²×D₄	—	4	1	no	—
540	C₂²×D₄	—	4	1	no	—
541	C₂²×D₄	—	4	4	no	—
542	C₂²×D₄	—	4	4	no	—
543	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
544	C₂²×D₄	D₄×C₁₃	1	4	yes	—
545	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂³×C₄	—	2	1	no	—
549	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×M₁₆	—	2	2	no	—
552	C₂×M₁₆	—	4	1	no	—
553	C₂×M₁₆	—	4	1	no	—
554	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
558	#127	—	2	2	no	—
559	#127	—	2	2	no	—
560	#121	—	2	8	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	#121	D₄×C₁₃	1	4	yes	—
565	#120	—	2	8	no	—
566	#120	—	2	8	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
590	C₂×C₄²	—	2	1	no	—
591	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
592	#107	—	2	2	no	—
593	#106	—	2	2	no	—
594	#102	—	2	2	no	—
595	#102	—	2	2	no	—
596	#102	—	2	2	no	—
597	#102	—	2	2	no	—
598	#102	—	2	2	no	—
599	#102	—	2	2	no	—
600	#102	—	2	2	no	—
601	#102	—	2	2	no	—
602	#102	—	4	1	no	—
603	#102	—	4	1	no	—
604	#102	—	4	1	no	—
605	#102	—	4	1	no	—
606	C₂²⋊C₈	—	2	2	no	—
607	C₂²⋊C₈	—	4	1	no	—
608	C₂²⋊C₈	—	4	1	no	—
609	#95	—	2	1	no	—
610	#95	—	2	1	no	—
611	#95	—	2	1	no	—
612	#95	—	2	1	no	—
613	#95	—	2	1	no	—
614	C₂×C₁₃	—	4	2	no	—
615	C₂×C₁₃	—	4	2	no	—
616	C₂×C₁₃	—	4	4	no	—
617	C₂×C₁₃	—	8	2	no	—
618	C₂×C₁₃	—	8	2	no	—
619	C₂×C₁₃	#2405	1	1	yes	characteristic
620	C₂×C₁₃	#3003	1	1	yes	characteristic
621	C₂×C₁₃	#3012	1	1	yes	characteristic
622	C₂×C₁₃	#3310	1	1	yes	characteristic
623	C₂×C₁₃	#3318	1	1	yes	characteristic
624	C₂×C₁₃	#3324	1	1	yes	characteristic
625	C₂×C₁₃	#3325	1	1	yes	characteristic
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	4	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	2	1	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	4	2	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	4	2	no	—
637	C₂⁴	—	4	2	no	—
638	C₂⁴	—	4	2	no	—
639	C₂⁴	—	8	1	no	—
640	C₂⁴	—	8	1	no	—
641	C₂⁴	—	8	1	no	—
642	C₂⁴	—	8	1	no	—
643	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	—	4	32	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	8	1	no	—
687	C₂×D₄	—	8	1	no	—
688	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂×D₄	C₁₃×#41	1	2	yes	—
692	C₂×D₄	C₁₃×#41	1	2	yes	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	M₁₆	—	4	4	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	8	1	no	—
743	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	8	1	no	—
752	C₂²⋊C₄	—	8	1	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	4	2	no	—
756	C₁₃	#24044	1	1	yes	characteristic, direct product factor, Sylow
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	8	no	—
776	C₂³	—	4	8	no	—
777	C₂³	—	4	8	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	1	no	—
787	C₂³	—	4	1	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	8	4	no	—
795	C₂³	—	8	4	no	—
796	C₂³	—	8	4	no	—
797	C₂³	—	8	4	no	—
798	C₂³	—	8	4	no	—
799	C₂³	—	8	4	no	—
800	C₂³	—	8	4	no	—
801	C₂³	—	8	4	no	—
802	C₂³	—	8	4	no	—
803	C₂³	—	8	4	no	—
804	C₂³	C₁₃×#120	1	2	yes	—
805	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
806	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	D₄	—	2	8	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	8	no	—
818	D₄	—	4	8	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	4	1	no	—
824	D₄	—	8	4	no	—
825	D₄	C₁₃×#123	1	4	yes	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	C₁₃×#120	1	2	yes	—
861	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
862	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
864	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
865	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
866	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
867	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
868	C₈	—	4	1	no	—
869	C₈	—	4	1	no	—
870	C₈	—	4	1	no	—
871	C₈	—	4	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	8	16	no	—
900	C₂²	—	8	16	no	—
901	C₂²	—	8	1	no	—
902	C₂²	—	8	1	no	—
903	C₂²	—	8	1	no	—
904	C₂²	—	8	1	no	—
905	C₂²	—	8	1	no	—
906	C₂²	—	8	1	no	—
907	C₂²	—	8	1	no	—
908	C₂²	—	8	1	no	—
909	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
910	C₂²	C₁₃×#546	1	1	yes	characteristic
911	C₂²	C₁₃×#546	1	1	yes	characteristic
912	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
913	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
914	C₂²	C₁₃×#576	1	1	yes	characteristic
915	C₂²	C₁₃×#577	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	8	1	no	—
922	C₄	—	8	1	no	—
923	C₄	—	8	1	no	—
924	C₄	—	8	1	no	—
925	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
926	C₄	C₁₃×#534	1	1	yes	characteristic
927	C₄	C₁₃×#546	1	1	yes	characteristic
928	C₄	C₁₃×#546	1	1	yes	characteristic
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₁₃×#2405	1	1	yes	characteristic
935	C₂	C₁₃×#3003	1	1	yes	characteristic
936	C₂	C₁₃×#3012	1	1	yes	characteristic
937	C₂	C₁₃×#3310	1	1	yes	characteristic
938	C₂	C₁₃×#3318	1	1	yes	characteristic
939	C₂	C₁₃×#3324	1	1	yes	characteristic
940	C₂	C₁₃×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×D₄²×C₁₃	C₂
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×#482	C₂	semidirect
3. C₂×C₁₃×#418	C₂	semidirect
4. C₁₃×#2485	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#2041	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1895	C₂	semidirect
10. C₁₃×#1870	C₂	semidirect
11. C₁₃×#1864	C₂	semidirect
12. C₁₃×#1862	C₂	semidirect
13. C₁₃×#1786	C₂	semidirect
14. C₁₃×#1786	C₂	semidirect
15. C₁₃×#1786	C₂	semidirect
19. C₂²×C₁₃×M₁₆	C₂²	semidirect
30. C₂×C₁₃×#117	C₂²	semidirect
32. C₂×C₁₃×#107	C₂²	semidirect
33. C₂×C₁₃×#106	C₂²	semidirect
39. C₂×C₁₃×#102	C₂²	semidirect
40. C₂×C₁₃×#102	C₂²	semidirect
41. C₂×C₁₃×#102	C₂²	semidirect
42. C₂×C₁₃×#102	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×#102	C₂²	semidirect
46. C₂×C₁₃×#102	C₂²	semidirect
47. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
48. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
49. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
53. C₁₃×#389	C₂²	semidirect
56. C₁₃×#380	C₂²	semidirect
57. C₁₃×#380	C₂²	semidirect
58. C₁₃×#380	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#336	C₂²	semidirect
62. C₁₃×#336	C₂²	semidirect
156. #24044	C₁₃	direct (N × H)
288. C₂×#482	C₂×C₁₃	semidirect
289. C₂×#418	C₂×C₁₃	semidirect
290. #2485	C₂×C₁₃	semidirect
291. #2041	C₂×C₁₃	semidirect
292. #2041	C₂×C₁₃	semidirect
293. #2034	C₂×C₁₃	semidirect
294. #2033	C₂×C₁₃	semidirect
295. #1895	C₂×C₁₃	semidirect
296. #1870	C₂×C₁₃	semidirect
297. #1864	C₂×C₁₃	semidirect
298. #1862	C₂×C₁₃	semidirect
299. #1786	C₂×C₁₃	semidirect
300. #1786	C₂×C₁₃	semidirect
301. #1786	C₂×C₁₃	semidirect
420. C₂²×M₁₆	C₂²×C₁₃	semidirect
431. C₂×#117	C₂²×C₁₃	semidirect
433. C₂×#107	C₂²×C₁₃	semidirect
434. C₂×#106	C₂²×C₁₃	semidirect
440. C₂×#102	C₂²×C₁₃	semidirect
441. C₂×#102	C₂²×C₁₃	semidirect
442. C₂×#102	C₂²×C₁₃	semidirect
443. C₂×#102	C₂²×C₁₃	semidirect
444. C₂×#102	C₂²×C₁₃	semidirect
445. C₂×#102	C₂²×C₁₃	semidirect
446. C₂×#102	C₂²×C₁₃	semidirect
447. C₂×#102	C₂²×C₁₃	semidirect
448. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
449. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
450. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
453. #389	C₂²×C₁₃	semidirect
454. #389	C₂²×C₁₃	semidirect
457. #380	C₂²×C₁₃	semidirect
458. #380	C₂²×C₁₃	semidirect
459. #380	C₂²×C₁₃	semidirect
460. #340	C₂²×C₁₃	semidirect
461. #340	C₂²×C₁₃	semidirect
462. #336	C₂²×C₁₃	semidirect
463. #336	C₂²×C₁₃	semidirect
756. C₁₃	#24044	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×D₄²×C₁₃	2
C₂×C₁₃×#482	2
C₂×C₁₃×#418	2
C₁₃×#2485	2
C₁₃×#2041	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1895	2
C₁₃×#1870	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1786	2
#24044	13

Subgroups — C13×#24044 #15710383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24044 #15710383