Subgroups — C₁₃×#25084 #15711423

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2435	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#467	—	2	4	no	—
28	C₁₃×#464	—	2	4	no	—
29	C₁₃×#450	—	2	4	no	—
30	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#102	—	2	4	no	—
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#394	—	2	1	no	—
46	C₁₃×#394	—	2	1	no	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#389	—	2	1	no	—
51	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#387	—	2	1	no	—
53	C₁₃×#385	—	2	1	no	—
54	C₁₃×#379	—	2	1	no	—
55	C₁₃×#379	—	2	1	no	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	2	no	—
71	C₂²×D₄×C₁₃	—	4	1	no	—
72	C₂²×D₄×C₁₃	—	4	1	no	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×Q₁₆	—	2	2	no	—
78	C₂×C₁₃×Q₁₆	—	2	2	no	—
79	C₂×C₁₃×Q₁₆	—	4	1	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	2	2	no	—
84	C₂×C₁₃×SD₁₆	—	4	1	no	—
85	C₂×C₁₃×SD₁₆	—	4	1	no	—
86	C₂²×C₈×C₁₃	—	2	2	no	—
87	C₂²×C₈×C₁₃	—	2	2	no	—
88	C₂²×C₈×C₁₃	—	4	1	no	—
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	—	2	2	no	—
95	C₁₃×#124	—	4	1	no	—
96	C₁₃×#124	—	4	1	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	4	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#107	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×C₄⋊C₈	—	4	1	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	4	1	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	D₄	1	4	yes	—
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	D₄	1	1	yes	characteristic
149	C₁₃×#95	D₄	1	1	yes	characteristic
150	#25084	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	4	2	no	—
154	C₂⁴×C₁₃	—	4	2	no	—
155	C₂⁴×C₁₃	—	4	2	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	—	4	2	no	—
158	C₂⁴×C₁₃	—	8	1	no	—
159	C₂⁴×C₁₃	—	8	1	no	—
160	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	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	—	4	4	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₃	#41	1	2	yes	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	2	no	—
204	C₂²×C₄×C₁₃	—	8	1	no	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₁₃	#41	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₁₃×Q₁₆	—	4	4	no	—
214	C₁₃×SD₁₆	—	4	4	no	—
215	C₁₃×SD₁₆	—	4	4	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	4	4	no	—
228	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	4	2	no	—
237	C₁₃×C₄⋊C₄	—	4	2	no	—
238	C₁₃×C₄⋊C₄	—	4	2	no	—
239	C₁₃×C₄⋊C₄	—	8	1	no	—
240	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	2	no	—
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
245	C₁₃×C₂²⋊C₄	—	4	2	no	—
246	C₁₃×C₂²⋊C₄	—	4	2	no	—
247	C₁₃×C₂²⋊C₄	—	4	2	no	—
248	C₁₃×C₂²⋊C₄	—	4	2	no	—
249	C₁₃×C₂²⋊C₄	—	4	2	no	—
250	C₁₃×C₂²⋊C₄	—	8	1	no	—
251	C₁₃×C₂²⋊C₄	—	8	1	no	—
252	C₁₃×C₂²⋊C₄	—	8	1	no	—
253	C₁₃×C₂²⋊C₄	—	8	1	no	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	2	1	no	—
256	C₄²×C₁₃	—	2	1	no	—
257	C₄²×C₁₃	—	2	1	no	—
258	C₄²×C₁₃	—	4	2	no	—
259	C₄²×C₁₃	—	8	1	no	—
260	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
263	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic
264	#2435	C₂×C₁₃	1	1	yes	characteristic
265	#2360	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1983	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	4	8	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	—	4	1	no	—
294	C₂³×C₁₃	—	8	4	no	—
295	C₂³×C₁₃	—	8	4	no	—
296	C₂³×C₁₃	—	8	4	no	—
297	C₂³×C₁₃	—	8	4	no	—
298	C₂³×C₁₃	—	8	4	no	—
299	C₂³×C₁₃	—	8	4	no	—
300	C₂³×C₁₃	#121	1	2	yes	—
301	C₂³×C₁₃	#135	1	2	yes	—
302	C₂³×C₁₃	#137	1	2	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₁₃	—	2	2	no	—
305	Q₈×C₁₃	—	2	2	no	—
306	Q₈×C₁₃	—	4	1	no	—
307	Q₈×C₁₃	—	4	1	no	—
308	Q₈×C₁₃	—	4	1	no	—
309	Q₈×C₁₃	—	4	1	no	—
310	Q₈×C₁₃	—	4	1	no	—
311	Q₈×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	2	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	4	8	no	—
317	D₄×C₁₃	—	4	1	no	—
318	D₄×C₁₃	—	4	1	no	—
319	D₄×C₁₃	—	4	1	no	—
320	D₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	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	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	8	4	no	—
358	C₂×C₄×C₁₃	#121	1	2	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
363	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
365	C₈×C₁₃	—	2	2	no	—
366	C₈×C₁₃	—	4	1	no	—
367	C₈×C₁₃	—	4	1	no	—
368	C₈×C₁₃	—	4	1	no	—
369	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
373	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	#467	—	2	4	no	—
381	#464	—	2	4	no	—
382	#450	—	2	4	no	—
383	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	C₂×#102	—	2	4	no	—
391	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
398	#394	—	2	1	no	—
399	#394	—	2	1	no	—
400	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	#390	C₂²×C₁₃	1	1	yes	characteristic
402	#390	C₂²×C₁₃	1	1	yes	characteristic
403	#389	—	2	1	no	—
404	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#387	—	2	1	no	—
406	#385	—	2	1	no	—
407	#379	—	2	1	no	—
408	#379	—	2	1	no	—
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₄×C₂²⋊C₄	—	2	1	no	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	8	16	no	—
429	C₂²×C₁₃	—	8	1	no	—
430	C₂²×C₁₃	—	8	1	no	—
431	C₂²×C₁₃	—	8	1	no	—
432	C₂²×C₁₃	—	8	1	no	—
433	C₂²×C₁₃	—	8	1	no	—
434	C₂²×C₁₃	—	8	1	no	—
435	C₂²×C₁₃	—	8	1	no	—
436	C₂²×C₁₃	—	8	1	no	—
437	C₂²×C₁₃	#464	1	4	yes	complemented
438	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
439	C₂²×C₁₃	D₄²	1	1	yes	characteristic
440	C₂²×C₁₃	#546	1	1	yes	characteristic
441	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
442	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
443	C₂²×C₁₃	#576	1	1	yes	characteristic
444	C₂²×C₁₃	#577	1	1	yes	characteristic
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	1	no	—
448	C₄×C₁₃	—	4	1	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	1	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	1	no	—
453	C₄×C₁₃	—	8	1	no	—
454	C₄×C₁₃	—	8	1	no	—
455	C₄×C₁₃	—	8	1	no	—
456	C₄×C₁₃	#525	1	1	yes	characteristic
457	C₄×C₁₃	#538	1	1	yes	characteristic
458	C₄×C₁₃	D₄²	1	1	yes	characteristic
459	C₄×C₁₃	#546	1	1	yes	characteristic
460	C₂⁵	—	2	1	no	—
461	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	4	1	no	—
469	C₂²×D₄	—	4	1	no	—
470	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×Q₁₆	—	2	2	no	—
475	C₂×Q₁₆	—	2	2	no	—
476	C₂×Q₁₆	—	4	1	no	—
477	C₂×SD₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×SD₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	4	1	no	—
482	C₂×SD₁₆	—	4	1	no	—
483	C₂²×C₈	—	2	2	no	—
484	C₂²×C₈	—	2	2	no	—
485	C₂²×C₈	—	4	1	no	—
486	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
490	#124	—	2	2	no	—
491	#124	—	2	2	no	—
492	#124	—	4	1	no	—
493	#124	—	4	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	4	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	4	1	no	—
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
527	#107	—	2	2	no	—
528	C₄⋊C₈	—	2	2	no	—
529	C₄⋊C₈	—	4	1	no	—
530	#103	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	4	1	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	D₄×C₁₃	1	4	yes	—
540	C₂²⋊C₈	—	2	2	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	D₄×C₁₃	1	1	yes	characteristic
546	#95	D₄×C₁₃	1	1	yes	characteristic
547	C₂×C₁₃	—	2	4	no	—
548	C₂×C₁₃	—	8	2	no	—
549	C₂×C₁₃	—	8	2	no	—
550	C₂×C₁₃	#2424	1	1	yes	characteristic
551	C₂×C₁₃	C₂×#464	1	1	yes	characteristic
552	C₂×C₁₃	#3045	1	1	yes	characteristic
553	C₂×C₁₃	#3266	1	1	yes	characteristic
554	C₂×C₁₃	#3280	1	1	yes	characteristic
555	C₂×C₁₃	#3296	1	1	yes	characteristic
556	C₂×C₁₃	#3314	1	1	yes	characteristic
557	C₂⁴	—	2	1	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	4	2	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	—	4	2	no	—
562	C₂⁴	—	4	2	no	—
563	C₂⁴	—	4	2	no	—
564	C₂⁴	—	8	1	no	—
565	C₂⁴	—	8	1	no	—
566	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	4	4	no	—
591	C₂×D₄	—	4	4	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×D₄	C₁₃×#41	1	2	yes	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	8	1	no	—
611	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
617	C₂²×C₄	C₁₃×#41	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	Q₁₆	—	4	4	no	—
620	SD₁₆	—	4	4	no	—
621	SD₁₆	—	4	4	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	4	4	no	—
634	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	8	1	no	—
646	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	8	1	no	—
657	C₂²⋊C₄	—	8	1	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₂²⋊C₄	—	8	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	4	2	no	—
665	C₄²	—	8	1	no	—
666	C₁₃	#25084	1	1	yes	characteristic, direct product factor, Sylow
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	8	4	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	4	no	—
690	C₂³	—	8	4	no	—
691	C₂³	—	8	4	no	—
692	C₂³	C₁₃×#121	1	2	yes	—
693	C₂³	C₁₃×#135	1	2	yes	—
694	C₂³	C₁₃×#137	1	2	yes	—
695	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	4	1	no	—
699	Q₈	—	4	1	no	—
700	Q₈	—	4	1	no	—
701	Q₈	—	4	1	no	—
702	Q₈	—	4	1	no	—
703	Q₈	—	4	1	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	C₁₃×#121	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
754	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
755	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
756	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	4	1	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	8	16	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	C₁₃×#464	1	4	yes	complemented
783	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
784	C₂²	D₄²×C₁₃	1	1	yes	characteristic
785	C₂²	C₁₃×#546	1	1	yes	characteristic
786	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
787	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
788	C₂²	C₁₃×#576	1	1	yes	characteristic
789	C₂²	C₁₃×#577	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	2	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	C₁₃×#525	1	1	yes	characteristic
802	C₄	C₁₃×#538	1	1	yes	characteristic
803	C₄	D₄²×C₁₃	1	1	yes	characteristic
804	C₄	C₁₃×#546	1	1	yes	characteristic
805	C₂	—	2	4	no	—
806	C₂	—	8	2	no	—
807	C₂	—	8	2	no	—
808	C₂	C₁₃×#2424	1	1	yes	characteristic
809	C₂	C₂×C₁₃×#464	1	1	yes	characteristic
810	C₂	C₁₃×#3045	1	1	yes	characteristic
811	C₂	C₁₃×#3266	1	1	yes	characteristic
812	C₂	C₁₃×#3280	1	1	yes	characteristic
813	C₂	C₁₃×#3296	1	1	yes	characteristic
814	C₂	C₁₃×#3314	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	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
1. C₂×C₁₃×#467	C₂	semidirect
2. C₂×C₁₃×#464	C₂	semidirect
6. C₁₃×#2360	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2042	C₂	semidirect
10. C₁₃×#2015	C₂	semidirect
11. C₁₃×#1983	C₂	semidirect
12. C₁₃×#1925	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1872	C₂	semidirect
15. C₁₃×#1850	C₂	semidirect
17. C₂²×C₁₃×Q₁₆	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂×C₁₃×#107	C₂²	semidirect
31. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
32. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
33. C₂×C₁₃×#103	C₂²	semidirect
34. C₂×C₁₃×#103	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
47. C₁₃×#391	C₂²	semidirect
51. C₁₃×#389	C₂²	semidirect
56. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#336	C₂²	semidirect
62. C₁₃×#336	C₂²	semidirect
150. #25084	C₁₃	direct (N × H)
260. C₂×#467	C₂×C₁₃	semidirect
261. C₂×#464	C₂×C₁₃	semidirect
265. #2360	C₂×C₁₃	semidirect
266. #2067	C₂×C₁₃	semidirect
267. #2055	C₂×C₁₃	semidirect
268. #2042	C₂×C₁₃	semidirect
269. #2015	C₂×C₁₃	semidirect
270. #1983	C₂×C₁₃	semidirect
271. #1925	C₂×C₁₃	semidirect
272. #1880	C₂×C₁₃	semidirect
273. #1872	C₂×C₁₃	semidirect
274. #1850	C₂×C₁₃	semidirect
370. C₂²×Q₁₆	C₂²×C₁₃	semidirect
378. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
383. C₂×#107	C₂²×C₁₃	semidirect
384. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
385. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
386. C₂×#103	C₂²×C₁₃	semidirect
387. C₂×#103	C₂²×C₁₃	semidirect
388. C₂×#103	C₂²×C₁₃	semidirect
389. C₂×#103	C₂²×C₁₃	semidirect
400. #391	C₂²×C₁₃	semidirect
404. #389	C₂²×C₁₃	semidirect
409. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
412. #340	C₂²×C₁₃	semidirect
413. #340	C₂²×C₁₃	semidirect
414. #336	C₂²×C₁₃	semidirect
415. #336	C₂²×C₁₃	semidirect
437. C₂²×C₁₃	#464	semidirect
666. C₁₃	#25084	direct (N × H)
782. C₂²	C₁₃×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#467	2
C₂×C₁₃×#464	2
C₂×C₁₃×#450	2
C₂²×C₁₃×#102	2
C₁₃×#2435	2
C₁₃×#2360	2
C₁₃×#2067	2
C₁₃×#2055	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1983	2
C₁₃×#1925	2
C₁₃×#1880	2
C₁₃×#1872	2
C₁₃×#1850	2
#25084	13

Subgroups — C13×#25084 #15711423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25084 #15711423