Subgroups — C₁₃×#24369 #15710708

Order 3328.

1388 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	—	2	4	no	—
19	C₂×C₁₃×#137	—	2	4	no	—
20	C₂×C₁₃×#137	—	2	4	no	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#464	—	2	4	no	—
34	C₁₃×#462	—	2	4	no	—
35	C₁₃×#451	—	2	4	no	—
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₃×#394	—	2	1	no	—
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#391	—	2	1	no	—
50	C₁₃×#391	—	2	1	no	—
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#391	C₂²	1	1	yes	characteristic
54	C₁₃×#390	C₂²	1	1	yes	characteristic
55	C₁₃×#385	—	2	1	no	—
56	C₁₃×#385	—	2	1	no	—
57	C₁₃×#380	—	2	1	no	—
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₄×C₁₃×C₂²⋊C₄	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	—	4	1	no	—
70	C₂×C₁₃×#41	—	4	1	no	—
71	C₂²×Q₈×C₁₃	—	2	1	no	—
72	C₂²×Q₈×C₁₃	—	2	2	no	—
73	C₂²×Q₈×C₁₃	—	2	2	no	—
74	C₂²×Q₈×C₁₃	—	2	2	no	—
75	C₂²×Q₈×C₁₃	—	4	1	no	—
76	C₂²×Q₈×C₁₃	—	4	1	no	—
77	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
87	C₁₃×#137	—	2	32	no	—
88	C₂×C₁₃×Q₁₆	—	2	2	no	—
89	C₂×C₁₃×Q₁₆	—	2	2	no	—
90	C₂×C₁₃×Q₁₆	—	2	2	no	—
91	C₂×C₁₃×Q₁₆	—	2	2	no	—
92	C₂×C₁₃×Q₁₆	—	2	2	no	—
93	C₂×C₁₃×Q₁₆	—	2	2	no	—
94	C₂×C₁₃×Q₁₆	—	2	2	no	—
95	C₂×C₁₃×Q₁₆	—	2	2	no	—
96	C₂×C₁₃×Q₁₆	—	2	2	no	—
97	C₂×C₁₃×Q₁₆	—	4	1	no	—
98	C₂×C₁₃×Q₁₆	—	4	1	no	—
99	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
100	C₂×C₁₃×SD₁₆	—	2	2	no	—
101	C₂×C₁₃×SD₁₆	—	2	2	no	—
102	C₂×C₁₃×SD₁₆	—	2	2	no	—
103	C₂×C₁₃×SD₁₆	—	2	2	no	—
104	C₂×C₁₃×SD₁₆	—	2	2	no	—
105	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
106	C₂×C₁₃×M₁₆	—	2	2	no	—
107	C₂×C₁₃×M₁₆	—	2	2	no	—
108	C₂×C₁₃×M₁₆	—	2	2	no	—
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	4	1	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	—	4	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	2	no	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₄×Q₈×C₁₃	—	2	2	no	—
120	C₄×Q₈×C₁₃	—	2	2	no	—
121	C₄×Q₈×C₁₃	—	4	1	no	—
122	C₄×Q₈×C₁₃	—	4	1	no	—
123	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	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	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	—	2	1	no	—
140	C₂×C₄²×C₁₃	—	2	1	no	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊C₈	—	2	2	no	—
144	C₁₃×C₄⋊C₈	—	2	2	no	—
145	C₁₃×#103	—	2	2	no	—
146	C₁₃×#103	—	2	2	no	—
147	C₁₃×#103	—	2	2	no	—
148	C₁₃×#103	—	2	2	no	—
149	C₁₃×#103	—	2	2	no	—
150	C₁₃×#103	—	4	1	no	—
151	C₁₃×#102	—	2	2	no	—
152	C₁₃×#102	—	4	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	2	no	—
154	C₁₃×#95	—	2	1	no	—
155	C₁₃×#95	—	2	1	no	—
156	C₁₃×#95	—	2	1	no	—
157	C₁₃×#95	—	2	1	no	—
158	C₁₃×#95	—	2	1	no	—
159	C₁₃×#95	—	2	1	no	—
160	C₁₃×#95	—	2	1	no	—
161	C₁₃×#95	D₄	1	1	yes	characteristic
162	C₁₃×#95	D₄	1	1	yes	characteristic
163	#24369	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₁₃×#41	—	2	8	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	2	4	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	8	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	4	2	no	—
192	C₂×Q₈×C₁₃	—	4	2	no	—
193	C₂×Q₈×C₁₃	—	4	4	no	—
194	C₂×Q₈×C₁₃	—	4	4	no	—
195	C₂×Q₈×C₁₃	—	4	4	no	—
196	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
198	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
199	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	4	2	no	—
207	C₂×D₄×C₁₃	—	4	2	no	—
208	C₂×D₄×C₁₃	—	4	2	no	—
209	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	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	—	2	1	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	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	#41	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×Q₁₆	—	2	8	no	—
236	C₁₃×Q₁₆	—	2	8	no	—
237	C₁₃×Q₁₆	—	4	4	no	—
238	C₁₃×Q₁₆	—	4	4	no	—
239	C₁₃×SD₁₆	—	2	8	no	—
240	C₁₃×SD₁₆	—	2	8	no	—
241	C₁₃×M₁₆	—	2	8	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	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
261	C₁₃×C₄⋊C₄	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	1	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	4	2	no	—
269	C₁₃×C₂²⋊C₄	—	4	2	no	—
270	C₁₃×C₂²⋊C₄	—	4	2	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₄²×C₁₃	—	2	1	no	—
274	C₄²×C₁₃	—	2	1	no	—
275	C₄²×C₁₃	—	2	1	no	—
276	C₄²×C₁₃	—	2	1	no	—
277	C₄²×C₁₃	—	4	2	no	—
278	C₄²×C₁₃	—	4	2	no	—
279	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic
280	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2432	C₂×C₁₃	1	1	yes	characteristic
284	Q₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#1788	C₂×C₁₃	1	1	yes	characteristic
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	2	no	—
301	C₂³×C₁₃	—	4	1	no	—
302	C₂³×C₁₃	—	4	1	no	—
303	C₂³×C₁₃	—	4	1	no	—
304	C₂³×C₁₃	—	4	1	no	—
305	C₂³×C₁₃	—	4	1	no	—
306	C₂³×C₁₃	—	4	1	no	—
307	C₂³×C₁₃	#121	1	2	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₁₃	—	2	2	no	—
310	Q₈×C₁₃	—	2	2	no	—
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	4	8	no	—
317	Q₈×C₁₃	—	4	1	no	—
318	Q₈×C₁₃	—	4	1	no	—
319	Q₈×C₁₃	—	4	1	no	—
320	Q₈×C₁₃	—	4	1	no	—
321	Q₈×C₁₃	—	4	1	no	—
322	Q₈×C₁₃	—	4	1	no	—
323	Q₈×C₁₃	—	4	1	no	—
324	Q₈×C₁₃	—	4	1	no	—
325	Q₈×C₁₃	#120	1	4	yes	—
326	D₄×C₁₃	—	2	2	no	—
327	D₄×C₁₃	—	2	2	no	—
328	D₄×C₁₃	—	4	8	no	—
329	D₄×C₁₃	—	4	1	no	—
330	D₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	2	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	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	4	8	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	#121	1	2	yes	—
372	C₂×C₄×C₁₃	#137	1	2	yes	complemented
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	—	4	1	no	—
382	C₈×C₁₃	—	4	1	no	—
383	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
384	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#137	—	2	4	no	—
386	C₂×#137	—	2	4	no	—
387	C₂×#137	—	2	4	no	—
388	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	#464	—	2	4	no	—
401	#462	—	2	4	no	—
402	#451	—	2	4	no	—
403	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
414	#394	—	2	1	no	—
415	#394	—	2	1	no	—
416	#391	—	2	1	no	—
417	#391	—	2	1	no	—
418	#391	C₂²×C₁₃	1	1	yes	characteristic
419	#391	C₂²×C₁₃	1	1	yes	characteristic
420	#391	C₂²×C₁₃	1	1	yes	characteristic
421	#390	C₂²×C₁₃	1	1	yes	characteristic
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#380	—	2	1	no	—
425	#380	C₂²×C₁₃	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	—	2	1	no	—
427	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
428	#340	C₂²×C₁₃	1	1	yes	characteristic
429	#340	C₂²×C₁₃	1	1	yes	characteristic
430	#336	C₂²×C₁₃	1	1	yes	characteristic
431	#336	C₂²×C₁₃	1	1	yes	characteristic
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	2	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	4	1	no	—
436	C₂²×C₁₃	—	4	1	no	—
437	C₂²×C₁₃	—	4	1	no	—
438	C₂²×C₁₃	—	4	1	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	8	1	no	—
443	C₂²×C₁₃	—	8	1	no	—
444	C₂²×C₁₃	—	8	1	no	—
445	C₂²×C₁₃	—	8	1	no	—
446	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
447	C₂²×C₁₃	D₄²	1	1	yes	characteristic
448	C₂²×C₁₃	D₄²	1	1	yes	characteristic
449	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
450	C₂²×C₁₃	#575	1	1	yes	characteristic
451	C₂²×C₁₃	#578	1	1	yes	characteristic
452	C₂²×C₁₃	#578	1	1	yes	characteristic
453	C₄×C₁₃	—	2	2	no	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	2	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	1	no	—
459	C₄×C₁₃	—	4	1	no	—
460	C₄×C₁₃	—	4	1	no	—
461	C₄×C₁₃	—	8	1	no	—
462	C₄×C₁₃	—	8	1	no	—
463	C₄×C₁₃	—	8	1	no	—
464	C₄×C₁₃	—	8	1	no	—
465	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
466	C₄×C₁₃	#534	1	1	yes	characteristic
467	C₄×C₁₃	#546	1	1	yes	characteristic
468	C₄×C₁₃	#546	1	1	yes	characteristic
469	C₂×#41	—	2	2	no	—
470	C₂×#41	—	2	2	no	—
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	4	1	no	—
474	C₂×#41	—	4	1	no	—
475	C₂²×Q₈	—	2	1	no	—
476	C₂²×Q₈	—	2	2	no	—
477	C₂²×Q₈	—	2	2	no	—
478	C₂²×Q₈	—	2	2	no	—
479	C₂²×Q₈	—	4	1	no	—
480	C₂²×Q₈	—	4	1	no	—
481	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
482	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
491	#137	—	2	32	no	—
492	C₂×Q₁₆	—	2	2	no	—
493	C₂×Q₁₆	—	2	2	no	—
494	C₂×Q₁₆	—	2	2	no	—
495	C₂×Q₁₆	—	2	2	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×Q₁₆	—	2	2	no	—
498	C₂×Q₁₆	—	2	2	no	—
499	C₂×Q₁₆	—	2	2	no	—
500	C₂×Q₁₆	—	2	2	no	—
501	C₂×Q₁₆	—	4	1	no	—
502	C₂×Q₁₆	—	4	1	no	—
503	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
510	C₂×M₁₆	—	2	2	no	—
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	2	2	no	—
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	4	1	no	—
519	#124	—	2	2	no	—
520	#124	—	4	1	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	4	1	no	—
526	C₄×Q₈	—	4	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
547	C₄⋊C₈	—	2	2	no	—
548	C₄⋊C₈	—	2	2	no	—
549	#103	—	2	2	no	—
550	#103	—	2	2	no	—
551	#103	—	2	2	no	—
552	#103	—	2	2	no	—
553	#103	—	2	2	no	—
554	#103	—	4	1	no	—
555	#102	—	2	2	no	—
556	#102	—	4	1	no	—
557	C₂²⋊C₈	—	2	2	no	—
558	#95	—	2	1	no	—
559	#95	—	2	1	no	—
560	#95	—	2	1	no	—
561	#95	—	2	1	no	—
562	#95	—	2	1	no	—
563	#95	—	2	1	no	—
564	#95	—	2	1	no	—
565	#95	D₄×C₁₃	1	1	yes	characteristic
566	#95	D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₁₃	—	4	2	no	—
568	C₂×C₁₃	—	8	2	no	—
569	C₂×C₁₃	#2410	1	1	yes	characteristic
570	C₂×C₁₃	#3037	1	1	yes	characteristic
571	C₂×C₁₃	#3044	1	1	yes	characteristic
572	C₂×C₁₃	#3269	1	1	yes	characteristic
573	C₂×C₁₃	#3270	1	1	yes	characteristic
574	C₂×C₁₃	#3276	1	1	yes	characteristic
575	C₂×C₁₃	#3277	1	1	yes	characteristic
576	C₂⁴	—	2	1	no	—
577	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
578	#41	—	2	8	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	8	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	—	4	4	no	—
606	C₂×Q₈	—	4	4	no	—
607	C₂×Q₈	—	4	4	no	—
608	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
609	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
610	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	4	2	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₁₃×#41	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
647	Q₁₆	—	2	8	no	—
648	Q₁₆	—	2	8	no	—
649	Q₁₆	—	4	4	no	—
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	2	8	no	—
652	SD₁₆	—	2	8	no	—
653	M₁₆	—	2	8	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
665	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	4	2	no	—
690	C₄²	—	4	2	no	—
691	C₁₃	#24369	1	1	yes	characteristic, direct product factor, Sylow
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	C₁₃×#121	1	2	yes	—
706	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	2	2	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	4	8	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	1	no	—
717	Q₈	—	4	1	no	—
718	Q₈	—	4	1	no	—
719	Q₈	—	4	1	no	—
720	Q₈	—	4	1	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	Q₈	C₁₃×#120	1	4	yes	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	C₁₃×#121	1	2	yes	—
770	C₂×C₄	C₁₃×#137	1	2	yes	complemented
771	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
775	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	4	1	no	—
780	C₈	—	4	1	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	8	1	no	—
792	C₂²	—	8	1	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
796	C₂²	D₄²×C₁₃	1	1	yes	characteristic
797	C₂²	D₄²×C₁₃	1	1	yes	characteristic
798	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
799	C₂²	C₁₃×#575	1	1	yes	characteristic
800	C₂²	C₁₃×#578	1	1	yes	characteristic
801	C₂²	C₁₃×#578	1	1	yes	characteristic
802	C₄	—	2	2	no	—
803	C₄	—	2	2	no	—
804	C₄	—	2	4	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	8	1	no	—
811	C₄	—	8	1	no	—
812	C₄	—	8	1	no	—
813	C₄	—	8	1	no	—
814	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
815	C₄	C₁₃×#534	1	1	yes	characteristic
816	C₄	C₁₃×#546	1	1	yes	characteristic
817	C₄	C₁₃×#546	1	1	yes	characteristic
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	C₁₃×#2410	1	1	yes	characteristic
821	C₂	C₁₃×#3037	1	1	yes	characteristic
822	C₂	C₁₃×#3044	1	1	yes	characteristic
823	C₂	C₁₃×#3269	1	1	yes	characteristic
824	C₂	C₁₃×#3270	1	1	yes	characteristic
825	C₂	C₁₃×#3276	1	1	yes	characteristic
826	C₂	C₁₃×#3277	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#464	C₂	semidirect
3. C₂×C₁₃×#462	C₂	semidirect
4. C₂×C₁₃×#451	C₂	semidirect
6. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2016	C₂	semidirect
10. C₁₃×#2015	C₂	semidirect
11. C₁₃×#1894	C₂	semidirect
12. C₁₃×#1880	C₂	semidirect
13. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1851	C₂	semidirect
163. #24369	C₁₃	direct (N × H)
280. C₂×#464	C₂×C₁₃	semidirect
281. C₂×#462	C₂×C₁₃	semidirect
282. C₂×#451	C₂×C₁₃	semidirect
284. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
285. #2056	C₂×C₁₃	semidirect
286. #2055	C₂×C₁₃	semidirect
287. #2016	C₂×C₁₃	semidirect
288. #2015	C₂×C₁₃	semidirect
289. #1894	C₂×C₁₃	semidirect
290. #1880	C₂×C₁₃	semidirect
291. #1878	C₂×C₁₃	semidirect
292. #1851	C₂×C₁₃	semidirect
372. C₂×C₄×C₁₃	#137	semidirect
691. C₁₃	#24369	direct (N × H)
770. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#137	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#451	2
C₁₃×#2432	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2056	2
C₁₃×#2055	2
C₁₃×#2016	2
C₁₃×#2015	2
C₁₃×#1894	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1851	2
C₁₃×#1788	2
#24369	13

Subgroups — C13×#24369 #15710708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24369 #15710708