Subgroups — C₁₃×#23972 #15710311

Order 3328.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
21	C₁₃×#547	—	2	4	no	—
22	C₁₃×#547	—	2	4	no	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#123	—	2	1	no	—
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#449	—	2	4	no	—
36	C₁₃×#417	—	2	4	no	—
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×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#392	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#386	—	2	1	no	—
53	C₁₃×#385	—	2	1	no	—
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	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	C₂×C₁₃×#41	—	2	8	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂×C₁₃×#41	—	4	1	no	—
70	C₂×C₁₃×#41	—	4	4	no	—
71	C₂×C₁₃×#41	—	4	4	no	—
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	no	—
78	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×SD₁₆	—	2	2	no	—
88	C₂×C₁₃×SD₁₆	—	2	2	no	—
89	C₂×C₁₃×SD₁₆	—	4	1	no	—
90	C₂×C₁₃×D₈	—	2	2	no	—
91	C₂×C₁₃×D₈	—	2	2	no	—
92	C₂×C₁₃×D₈	—	4	1	no	—
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×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	—	2	2	no	—
102	C₁₃×#123	—	2	8	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×C₂²⋊Q₈	—	2	8	no	—
105	C₁₃×C₂²⋊Q₈	—	2	2	no	—
106	C₁₃×C₂²⋊Q₈	—	4	1	no	—
107	C₁₃×#121	—	2	2	no	—
108	C₁₃×#121	—	2	2	no	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	4	1	no	—
112	C₁₃×#121	D₄	1	4	yes	complemented
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×#103	—	2	2	no	—
143	C₁₃×#103	—	2	2	no	—
144	C₁₃×#103	—	2	2	no	—
145	C₁₃×#102	—	2	2	no	—
146	C₁₃×#102	—	2	2	no	—
147	C₁₃×#102	—	2	2	no	—
148	C₁₃×#102	—	4	1	no	—
149	C₁₃×#102	—	4	1	no	—
150	C₁₃×C₂²⋊C₈	—	2	2	no	—
151	C₁₃×C₂²⋊C₈	—	4	1	no	—
152	C₁₃×C₂²⋊C₈	—	4	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	C₁₃×#95	—	2	1	no	—
155	C₁₃×#95	—	2	1	no	—
156	#23972	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	—	2	1	no	—
158	C₂⁴×C₁₃	—	2	1	no	—
159	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₁₃×#41	—	2	8	no	—
162	C₁₃×#41	—	4	4	no	—
163	C₁₃×#41	—	4	4	no	—
164	C₁₃×#41	—	4	4	no	—
165	C₁₃×#41	—	4	32	no	—
166	C₂×Q₈×C₁₃	—	2	4	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	—	4	2	no	—
173	C₂×Q₈×C₁₃	—	4	2	no	—
174	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	2	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂×D₄×C₁₃	—	4	2	no	—
195	C₂×D₄×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	2	no	—
198	C₂×D₄×C₁₃	—	4	2	no	—
199	C₂×D₄×C₁₃	—	8	1	no	—
200	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₁₃	#41	1	2	yes	complemented
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	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	4	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	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	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	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	2	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×SD₁₆	—	4	4	no	—
238	C₁₃×D₈	—	4	4	no	—
239	C₁₃×M₁₆	—	4	4	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	2	1	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	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	2	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₁₃×C₂²⋊C₄	—	4	2	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	8	1	no	—
276	C₁₃×C₂²⋊C₄	—	8	1	no	—
277	C₄²×C₁₃	—	2	1	no	—
278	C₄²×C₁₃	—	2	1	no	—
279	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2407	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1999	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1895	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1874	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#1870	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#1824	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	1	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	1	no	—
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	2	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	4	1	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	#120	1	2	yes	—
321	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
322	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
323	Q₈×C₁₃	—	2	2	no	—
324	Q₈×C₁₃	—	2	2	no	—
325	Q₈×C₁₃	—	4	8	no	—
326	Q₈×C₁₃	—	4	1	no	—
327	Q₈×C₁₃	—	4	1	no	—
328	D₄×C₁₃	—	2	8	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	2	2	no	—
331	D₄×C₁₃	—	2	2	no	—
332	D₄×C₁₃	—	2	2	no	—
333	D₄×C₁₃	—	4	8	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	1	no	—
337	D₄×C₁₃	—	4	1	no	—
338	D₄×C₁₃	—	4	1	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	8	4	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	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	1	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	4	8	no	—
360	C₂×C₄×C₁₃	—	4	8	no	—
361	C₂×C₄×C₁₃	—	4	8	no	—
362	C₂×C₄×C₁₃	—	4	8	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	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	#120	1	2	yes	—
382	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
387	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
389	C₈×C₁₃	—	4	1	no	—
390	C₈×C₁₃	—	4	1	no	—
391	C₈×C₁₃	—	4	1	no	—
392	C₈×C₁₃	—	4	1	no	—
393	C₂²×#41	—	2	1	no	—
394	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
398	#547	—	2	4	no	—
399	#547	—	2	4	no	—
400	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#123	—	2	1	no	—
402	C₂×#123	—	2	1	no	—
403	C₂×C₂²⋊Q₈	—	2	1	no	—
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	#449	—	2	4	no	—
413	#417	—	2	4	no	—
414	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
425	#394	—	2	1	no	—
426	#392	—	2	1	no	—
427	#391	C₂²×C₁₃	1	1	yes	characteristic
428	#390	C₂²×C₁₃	1	1	yes	characteristic
429	#386	—	2	1	no	—
430	#385	—	2	1	no	—
431	#380	C₂²×C₁₃	1	1	yes	characteristic
432	#340	C₂²×C₁₃	1	1	yes	characteristic
433	#340	C₂²×C₁₃	1	1	yes	characteristic
434	#340	C₂²×C₁₃	1	1	yes	characteristic
435	#340	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	—	4	2	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	8	1	no	—
461	C₂²×C₁₃	—	8	1	no	—
462	C₂²×C₁₃	—	8	1	no	—
463	C₂²×C₁₃	—	8	1	no	—
464	C₂²×C₁₃	—	8	1	no	—
465	C₂²×C₁₃	—	8	1	no	—
466	C₂²×C₁₃	—	8	1	no	—
467	C₂²×C₁₃	—	8	1	no	—
468	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
469	C₂²×C₁₃	#546	1	1	yes	characteristic
470	C₂²×C₁₃	#546	1	1	yes	characteristic
471	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂²×C₁₃	#577	1	1	yes	characteristic
474	C₂²×C₁₃	#578	1	1	yes	characteristic
475	C₄×C₁₃	—	2	2	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	4	1	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	1	no	—
483	C₄×C₁₃	—	8	1	no	—
484	C₄×C₁₃	—	8	1	no	—
485	C₄×C₁₃	#525	1	1	yes	characteristic
486	C₄×C₁₃	#535	1	1	yes	characteristic
487	C₄×C₁₃	#546	1	1	yes	characteristic
488	C₄×C₁₃	#546	1	1	yes	characteristic
489	C₂×#41	—	2	8	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	4	1	no	—
495	C₂×#41	—	4	1	no	—
496	C₂×#41	—	4	4	no	—
497	C₂×#41	—	4	4	no	—
498	C₂²×Q₈	—	2	1	no	—
499	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
505	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×D₈	—	2	2	no	—
517	C₂×D₈	—	2	2	no	—
518	C₂×D₈	—	4	1	no	—
519	C₂×M₁₆	—	2	2	no	—
520	C₂×M₁₆	—	4	1	no	—
521	C₂×M₁₆	—	4	1	no	—
522	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	#123	—	2	8	no	—
529	#123	—	2	8	no	—
530	C₂²⋊Q₈	—	2	8	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	4	1	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	—	4	1	no	—
538	#121	D₄×C₁₃	1	4	yes	complemented
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	complemented
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
566	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
568	#103	—	2	2	no	—
569	#103	—	2	2	no	—
570	#103	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	4	1	no	—
575	#102	—	4	1	no	—
576	C₂²⋊C₈	—	2	2	no	—
577	C₂²⋊C₈	—	4	1	no	—
578	C₂²⋊C₈	—	4	1	no	—
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	C₂×C₁₃	—	4	2	no	—
583	C₂×C₁₃	—	4	2	no	—
584	C₂×C₁₃	—	8	2	no	—
585	C₂×C₁₃	—	8	2	no	—
586	C₂×C₁₃	#2404	1	1	yes	characteristic
587	C₂×C₁₃	#3003	1	1	yes	characteristic
588	C₂×C₁₃	#3013	1	1	yes	characteristic
589	C₂×C₁₃	#3306	1	1	yes	characteristic
590	C₂×C₁₃	#3308	1	1	yes	characteristic
591	C₂×C₁₃	#3330	1	1	yes	characteristic
592	C₂×C₁₃	#3332	1	1	yes	characteristic
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	1	no	—
595	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
597	#41	—	2	8	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	4	no	—
601	#41	—	4	32	no	—
602	C₂×Q₈	—	2	4	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	—	4	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	8	1	no	—
636	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₂×D₄	C₁₃×#41	1	2	yes	complemented
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	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	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	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	4	2	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	SD₁₆	—	4	4	no	—
674	D₈	—	4	4	no	—
675	M₁₆	—	4	4	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	8	1	no	—
712	C₂²⋊C₄	—	8	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	1	no	—
715	C₁₃	#23972	1	1	yes	characteristic, direct product factor, Sylow
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	C₁₃×#120	1	2	yes	—
743	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
744	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	Q₈	—	2	2	no	—
746	Q₈	—	2	2	no	—
747	Q₈	—	4	8	no	—
748	Q₈	—	4	1	no	—
749	Q₈	—	4	1	no	—
750	D₄	—	2	8	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	4	8	no	—
756	D₄	—	4	8	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	1	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	8	4	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	4	8	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	C₁₃×#120	1	2	yes	—
804	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
808	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
809	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
810	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
811	C₈	—	4	1	no	—
812	C₈	—	4	1	no	—
813	C₈	—	4	1	no	—
814	C₈	—	4	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	8	1	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	—	8	1	no	—
840	C₂²	—	8	1	no	—
841	C₂²	—	8	1	no	—
842	C₂²	—	8	1	no	—
843	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
844	C₂²	C₁₃×#546	1	1	yes	characteristic
845	C₂²	C₁₃×#546	1	1	yes	characteristic
846	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
847	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
848	C₂²	C₁₃×#577	1	1	yes	characteristic
849	C₂²	C₁₃×#578	1	1	yes	characteristic
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	8	1	no	—
859	C₄	—	8	1	no	—
860	C₄	C₁₃×#525	1	1	yes	characteristic
861	C₄	C₁₃×#535	1	1	yes	characteristic
862	C₄	C₁₃×#546	1	1	yes	characteristic
863	C₄	C₁₃×#546	1	1	yes	characteristic
864	C₂	—	4	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	2	no	—
868	C₂	C₁₃×#2404	1	1	yes	characteristic
869	C₂	C₁₃×#3003	1	1	yes	characteristic
870	C₂	C₁₃×#3013	1	1	yes	characteristic
871	C₂	C₁₃×#3306	1	1	yes	characteristic
872	C₂	C₁₃×#3308	1	1	yes	characteristic
873	C₂	C₁₃×#3330	1	1	yes	characteristic
874	C₂	C₁₃×#3332	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₂×C₁₃×#547	C₂	semidirect
2. C₂×C₁₃×#449	C₂	semidirect
3. C₂×C₁₃×#417	C₂	semidirect
4. C₁₃×#2407	C₂	semidirect
5. C₁₃×#2024	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#2000	C₂	semidirect
8. C₁₃×#1999	C₂	semidirect
9. C₁₃×#1895	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1874	C₂	semidirect
13. C₁₃×#1872	C₂	semidirect
14. C₁₃×#1870	C₂	semidirect
15. C₁₃×#1824	C₂	semidirect
112. C₁₃×#121	D₄	semidirect
125. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
156. #23972	C₁₃	direct (N × H)
174. C₂×Q₈×C₁₃	#41	semidirect
201. C₂×D₄×C₁₃	#41	semidirect
279. C₂×#547	C₂×C₁₃	semidirect
280. C₂×#449	C₂×C₁₃	semidirect
281. C₂×#417	C₂×C₁₃	semidirect
282. #2407	C₂×C₁₃	semidirect
283. #2024	C₂×C₁₃	semidirect
284. #2023	C₂×C₁₃	semidirect
285. #2000	C₂×C₁₃	semidirect
286. #1999	C₂×C₁₃	semidirect
287. #1895	C₂×C₁₃	semidirect
288. #1879	C₂×C₁₃	semidirect
289. #1877	C₂×C₁₃	semidirect
290. #1874	C₂×C₁₃	semidirect
291. #1872	C₂×C₁₃	semidirect
292. #1870	C₂×C₁₃	semidirect
293. #1824	C₂×C₁₃	semidirect
538. #121	D₄×C₁₃	semidirect
551. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
610. C₂×Q₈	C₁₃×#41	semidirect
637. C₂×D₄	C₁₃×#41	semidirect
715. C₁₃	#23972	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×C₁₃×#547	2
C₂×C₁₃×#449	2
C₂×C₁₃×#417	2
C₁₃×#2407	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#2000	2
C₁₃×#1999	2
C₁₃×#1895	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1874	2
C₁₃×#1872	2
C₁₃×#1870	2
C₁₃×#1824	2
#23972	13

Subgroups — C13×#23972 #15710311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23972 #15710311