Subgroups — C₁₃×#24446 #15710785

Order 3328.

1458 conjugacy classes of subgroups.

The subgroup lattice has 878 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
2	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
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×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	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×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₁₃×#547	—	2	4	no	—
23	C₁₃×#547	—	2	4	no	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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×#121	—	2	1	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#470	—	2	4	no	—
37	C₁₃×#452	—	2	4	no	—
38	C₁₃×#452	—	2	4	no	—
39	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
40	C₁₃×#417	—	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×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	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×#398	—	2	1	no	—
55	C₁₃×#396	—	2	1	no	—
56	C₁₃×#391	C₂²	1	1	yes	characteristic
57	C₁₃×#389	C₂²	1	1	yes	characteristic
58	C₁₃×#386	—	2	1	no	—
59	C₁₃×#380	—	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	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	2	2	no	—
72	C₂×C₁₃×#41	—	4	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	—	4	1	no	—
75	C₂×C₁₃×#41	—	4	1	no	—
76	C₂×C₁₃×#41	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	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
94	C₂×C₁₃×Q₁₆	—	4	1	no	—
95	C₂×C₁₃×Q₁₆	—	4	1	no	—
96	C₂×C₁₃×SD₁₆	—	2	2	no	—
97	C₂×C₁₃×SD₁₆	—	2	2	no	—
98	C₂×C₁₃×SD₁₆	—	2	2	no	—
99	C₂×C₁₃×M₁₆	—	2	2	no	—
100	C₂×C₁₃×M₁₆	—	2	2	no	—
101	C₂×C₁₃×M₁₆	—	4	1	no	—
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×#123	—	2	8	no	—
109	C₁₃×#123	—	2	8	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	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	4	1	no	—
117	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
118	C₁₃×#121	—	2	8	no	—
119	C₄×D₄×C₁₃	—	2	2	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	8	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	2	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	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	—	4	1	no	—
156	C₁₃×#102	—	2	2	no	—
157	C₁₃×#102	—	2	2	no	—
158	C₁₃×#102	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	#24446	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	1	no	—
168	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₁₃×#41	—	2	8	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	4	4	no	—
174	C₁₃×#41	—	4	4	no	—
175	C₁₃×#41	—	4	4	no	—
176	C₁₃×#41	—	4	4	no	—
177	C₁₃×#41	—	4	4	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	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
195	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	4	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	4	1	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	2	no	—
208	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₁₃	#41	1	2	yes	—
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	4	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	—	2	1	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	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	8	1	no	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₁₃×Q₁₆	—	4	4	no	—
248	C₁₃×Q₁₆	—	4	4	no	—
249	C₁₃×SD₁₆	—	4	4	no	—
250	C₁₃×M₁₆	—	4	4	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	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	4	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	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	8	1	no	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	4	2	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	—	8	1	no	—
288	C₄²×C₁₃	—	2	1	no	—
289	C₄²×C₁₃	—	2	1	no	—
290	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
291	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#2417	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2001	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#1870	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	1	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	1	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	1	no	—
318	C₂³×C₁₃	—	2	1	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	#120	1	2	yes	—
326	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	4	1	no	—
332	Q₈×C₁₃	—	4	1	no	—
333	Q₈×C₁₃	—	4	1	no	—
334	Q₈×C₁₃	—	4	1	no	—
335	Q₈×C₁₃	—	4	1	no	—
336	Q₈×C₁₃	—	4	1	no	—
337	Q₈×C₁₃	—	4	1	no	—
338	Q₈×C₁₃	—	4	1	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	4	4	no	—
343	D₄×C₁₃	—	4	8	no	—
344	D₄×C₁₃	—	4	8	no	—
345	D₄×C₁₃	#121	1	4	yes	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	4	8	no	—
365	C₂×C₄×C₁₃	—	4	8	no	—
366	C₂×C₄×C₁₃	—	4	8	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	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	8	4	no	—
389	C₂×C₄×C₁₃	#120	1	2	yes	—
390	C₂×C₄×C₁₃	#137	1	2	yes	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
395	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
396	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
397	C₈×C₁₃	—	2	2	no	—
398	C₈×C₁₃	—	4	1	no	—
399	C₈×C₁₃	—	4	1	no	—
400	C₈×C₁₃	—	4	1	no	—
401	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
404	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
407	#547	—	2	4	no	—
408	#547	—	2	4	no	—
409	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#123	—	2	1	no	—
411	C₂×#123	—	2	1	no	—
412	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#121	—	2	1	no	—
417	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	—	2	1	no	—
420	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
421	#470	—	2	4	no	—
422	#452	—	2	4	no	—
423	#452	—	2	4	no	—
424	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
425	#417	—	2	4	no	—
426	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
439	#398	—	2	1	no	—
440	#396	—	2	1	no	—
441	#391	C₂²×C₁₃	1	1	yes	characteristic
442	#389	C₂²×C₁₃	1	1	yes	characteristic
443	#386	—	2	1	no	—
444	#380	—	2	1	no	—
445	#380	C₂²×C₁₃	1	1	yes	characteristic
446	#340	C₂²×C₁₃	1	1	yes	characteristic
447	#340	C₂²×C₁₃	1	1	yes	characteristic
448	#336	C₂²×C₁₃	1	1	yes	characteristic
449	#336	C₂²×C₁₃	1	1	yes	characteristic
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	2	no	—
453	C₂²×C₁₃	—	2	2	no	—
454	C₂²×C₁₃	—	4	1	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	4	1	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
472	C₂²×C₁₃	D₄²	1	1	yes	characteristic
473	C₂²×C₁₃	#546	1	1	yes	characteristic
474	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
475	C₂²×C₁₃	#575	1	1	yes	characteristic
476	C₂²×C₁₃	#577	1	1	yes	characteristic
477	C₂²×C₁₃	#578	1	1	yes	characteristic
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	2	2	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	2	no	—
484	C₄×C₁₃	—	4	2	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	8	1	no	—
487	C₄×C₁₃	—	8	1	no	—
488	C₄×C₁₃	—	8	1	no	—
489	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
490	C₄×C₁₃	#534	1	1	yes	characteristic
491	C₄×C₁₃	D₄²	1	1	yes	characteristic
492	C₄×C₁₃	#546	1	1	yes	characteristic
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	4	1	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	—	4	1	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	D₄×C₁₃	1	4	yes	—
505	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×Q₁₆	—	2	2	no	—
519	C₂×Q₁₆	—	2	2	no	—
520	C₂×Q₁₆	—	2	2	no	—
521	C₂×Q₁₆	—	4	1	no	—
522	C₂×Q₁₆	—	4	1	no	—
523	C₂×Q₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×M₁₆	—	2	2	no	—
528	C₂×M₁₆	—	2	2	no	—
529	C₂×M₁₆	—	4	1	no	—
530	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₄⋊Q₈	—	2	2	no	—
535	C₄⋊Q₈	—	2	2	no	—
536	#123	—	2	8	no	—
537	#123	—	2	8	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	4	1	no	—
545	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
546	#121	—	2	8	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	8	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	2	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	4	1	no	—
562	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	#106	—	2	2	no	—
577	#103	—	2	2	no	—
578	#103	—	2	2	no	—
579	#103	—	2	2	no	—
580	#103	—	2	2	no	—
581	#103	—	2	2	no	—
582	#103	—	2	2	no	—
583	#103	—	4	1	no	—
584	#102	—	2	2	no	—
585	#102	—	2	2	no	—
586	#102	D₄×C₁₃	1	4	yes	complemented
587	C₂²⋊C₈	—	2	2	no	—
588	C₂²⋊C₈	—	2	2	no	—
589	C₂²⋊C₈	—	4	1	no	—
590	#95	—	2	1	no	—
591	#95	—	2	1	no	—
592	#95	—	2	1	no	—
593	#95	—	2	1	no	—
594	C₂×C₁₃	—	4	2	no	—
595	C₂×C₁₃	—	4	4	no	—
596	C₂×C₁₃	—	8	1	no	—
597	C₂×C₁₃	#2410	1	1	yes	characteristic
598	C₂×C₁₃	#3007	1	1	yes	characteristic
599	C₂×C₁₃	#3013	1	1	yes	characteristic
600	C₂×C₁₃	#3267	1	1	yes	characteristic
601	C₂×C₁₃	#3276	1	1	yes	characteristic
602	C₂×C₁₃	#3315	1	1	yes	characteristic
603	C₂×C₁₃	#3331	1	1	yes	characteristic
604	C₂⁴	—	2	1	no	—
605	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
607	#41	—	2	8	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	4	no	—
614	#41	—	4	4	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
632	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	4	1	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂×D₄	C₁₃×#41	1	2	yes	—
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	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	8	1	no	—
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	Q₁₆	—	4	4	no	—
685	Q₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	M₁₆	—	4	4	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	8	1	no	—
715	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	8	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₁₃	#24446	1	1	yes	characteristic, direct product factor, Sylow
728	C₂³	—	2	2	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	C₁₃×#120	1	2	yes	—
749	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	1	no	—
757	Q₈	—	4	1	no	—
758	Q₈	—	4	1	no	—
759	Q₈	—	4	1	no	—
760	Q₈	—	4	1	no	—
761	Q₈	—	4	1	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	8	no	—
768	D₄	C₁₃×#121	1	4	yes	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	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	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	4	8	no	—
788	C₂×C₄	—	4	8	no	—
789	C₂×C₄	—	4	8	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	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	C₁₃×#120	1	2	yes	—
813	C₂×C₄	C₁₃×#137	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
818	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
819	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	4	1	no	—
822	C₈	—	4	1	no	—
823	C₈	—	4	1	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
846	C₂²	D₄²×C₁₃	1	1	yes	characteristic
847	C₂²	C₁₃×#546	1	1	yes	characteristic
848	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
849	C₂²	C₁₃×#575	1	1	yes	characteristic
850	C₂²	C₁₃×#577	1	1	yes	characteristic
851	C₂²	C₁₃×#578	1	1	yes	characteristic
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	8	1	no	—
861	C₄	—	8	1	no	—
862	C₄	—	8	1	no	—
863	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
864	C₄	C₁₃×#534	1	1	yes	characteristic
865	C₄	D₄²×C₁₃	1	1	yes	characteristic
866	C₄	C₁₃×#546	1	1	yes	characteristic
867	C₂	—	4	2	no	—
868	C₂	—	4	4	no	—
869	C₂	—	8	1	no	—
870	C₂	C₁₃×#2410	1	1	yes	characteristic
871	C₂	C₁₃×#3007	1	1	yes	characteristic
872	C₂	C₁₃×#3013	1	1	yes	characteristic
873	C₂	C₁₃×#3267	1	1	yes	characteristic
874	C₂	C₁₃×#3276	1	1	yes	characteristic
875	C₂	C₁₃×#3315	1	1	yes	characteristic
876	C₂	C₁₃×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#547	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×#470	C₂	semidirect
3. C₂×C₁₃×#452	C₂	semidirect
4. C₂×C₁₃×#452	C₂	semidirect
5. C₂×C₁₃×#417	C₂	semidirect
6. C₁₃×#2417	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2016	C₂	semidirect
10. C₁₃×#2001	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1870	C₂	semidirect
14. C₁₃×#1864	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
158. C₁₃×#102	D₄	semidirect
166. #24446	C₁₃	direct (N × H)
291. C₂×#470	C₂×C₁₃	semidirect
292. C₂×#452	C₂×C₁₃	semidirect
293. C₂×#452	C₂×C₁₃	semidirect
294. C₂×#417	C₂×C₁₃	semidirect
295. #2417	C₂×C₁₃	semidirect
296. #2043	C₂×C₁₃	semidirect
297. #2035	C₂×C₁₃	semidirect
298. #2016	C₂×C₁₃	semidirect
299. #2001	C₂×C₁₃	semidirect
300. #1877	C₂×C₁₃	semidirect
301. #1872	C₂×C₁₃	semidirect
302. #1870	C₂×C₁₃	semidirect
303. #1864	C₂×C₁₃	semidirect
304. #1788	C₂×C₁₃	semidirect
586. #102	D₄×C₁₃	semidirect
727. C₁₃	#24446	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×#470	2
C₂×C₁₃×#452	2
C₂×C₁₃×#417	2
C₁₃×#2417	2
C₁₃×#2043	2
C₁₃×#2035	2
C₁₃×#2016	2
C₁₃×#2001	2
C₁₃×#1877	2
C₁₃×#1872	2
C₁₃×#1870	2
C₁₃×#1864	2
C₁₃×#1788	2
#24446	13

Subgroups — C13×#24446 #15710785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24446 #15710785