Subgroups — C₁₃×#25130 #15711469

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2416	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₃×#468	—	2	4	no	—
29	C₁₃×#448	—	2	4	no	—
30	C₁₃×#435	—	2	4	no	—
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	—	2	4	no	—
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
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×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
46	C₁₃×#396	—	2	1	no	—
47	C₁₃×#395	—	2	1	no	—
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#393	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#385	—	2	1	no	—
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	—	2	2	no	—
67	C₂²×Q₈×C₁₃	—	2	2	no	—
68	C₂²×Q₈×C₁₃	—	4	1	no	—
69	C₂²×Q₈×C₁₃	—	4	1	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	—	2	2	no	—
88	C₂×C₁₃×M₁₆	—	4	1	no	—
89	C₂²×C₈×C₁₃	—	2	2	no	—
90	C₂²×C₈×C₁₃	—	2	2	no	—
91	C₂²×C₈×C₁₃	—	4	1	no	—
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	4	1	no	—
99	C₁₃×C₂²⋊Q₈	—	4	1	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	4	1	no	—
104	C₁₃×#121	—	4	4	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#107	—	2	2	no	—
131	C₁₃×#107	—	4	1	no	—
132	C₁₃×C₄⋊C₈	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	D₄	1	4	yes	complemented
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	4	1	no	—
141	C₁₃×C₂²⋊C₈	—	2	2	no	—
142	C₁₃×C₂²⋊C₈	D₄	1	4	yes	complemented
143	C₁₃×#97	—	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	—	2	1	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	#25130	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	8	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
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	—	4	2	no	—
167	C₂×Q₈×C₁₃	—	4	2	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂×Q₈×C₁₃	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	4	4	no	—
171	C₂×Q₈×C₁₃	—	4	2	no	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₁₃	#41	1	2	yes	—
174	C₂×D₄×C₁₃	—	2	2	no	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	2	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	—	4	2	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	8	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	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	—	4	2	no	—
207	C₂²×C₄×C₁₃	—	4	2	no	—
208	C₂²×C₄×C₁₃	—	4	2	no	—
209	C₂²×C₄×C₁₃	—	4	2	no	—
210	C₂²×C₄×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	—	8	1	no	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₁₃	#41	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₁₃×SD₁₆	—	4	4	no	—
220	C₁₃×SD₁₆	—	4	4	no	—
221	C₁₃×M₁₆	—	4	4	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	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	4	4	no	—
232	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
233	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	—	4	2	no	—
247	C₁₃×C₄⋊C₄	—	4	2	no	—
248	C₁₃×C₄⋊C₄	—	4	2	no	—
249	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	4	2	no	—
254	C₁₃×C₂²⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	4	2	no	—
256	C₁₃×C₂²⋊C₄	—	4	2	no	—
257	C₁₃×C₂²⋊C₄	—	4	2	no	—
258	C₁₃×C₂²⋊C₄	—	4	2	no	—
259	C₁₃×C₂²⋊C₄	—	8	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
265	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2416	C₂×C₁₃	1	1	yes	characteristic
267	#2409	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1935	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	—	2	1	no	—
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	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	—	4	1	no	—
295	C₂³×C₁₃	#121	1	2	yes	—
296	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
297	C₂³×C₁₃	#137	1	2	yes	—
298	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₁₃	—	2	2	no	—
300	Q₈×C₁₃	—	2	2	no	—
301	Q₈×C₁₃	—	2	2	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	4	8	no	—
304	Q₈×C₁₃	—	4	1	no	—
305	Q₈×C₁₃	—	4	1	no	—
306	Q₈×C₁₃	—	4	1	no	—
307	Q₈×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	4	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	—	8	4	no	—
314	D₄×C₁₃	—	8	4	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	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	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	4	8	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
357	C₂×C₄×C₁₃	#121	1	2	yes	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
362	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	—	2	2	no	—
366	C₈×C₁₃	—	2	2	no	—
367	C₈×C₁₃	—	4	1	no	—
368	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
372	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#121	—	2	1	no	—
376	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	#468	—	2	4	no	—
381	#448	—	2	4	no	—
382	#435	—	2	4	no	—
383	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#103	—	2	4	no	—
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#103	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×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
398	#396	—	2	1	no	—
399	#395	—	2	1	no	—
400	#394	—	2	1	no	—
401	#393	—	2	1	no	—
402	#391	C₂²×C₁₃	1	1	yes	characteristic
403	#391	C₂²×C₁₃	1	1	yes	characteristic
404	#390	C₂²×C₁₃	1	1	yes	characteristic
405	#389	C₂²×C₁₃	1	1	yes	characteristic
406	#386	—	2	1	no	—
407	#386	—	2	1	no	—
408	#385	—	2	1	no	—
409	#380	C₂²×C₁₃	1	1	yes	characteristic
410	#380	C₂²×C₁₃	1	1	yes	characteristic
411	#340	C₂²×C₁₃	1	1	yes	characteristic
412	#340	C₂²×C₁₃	1	1	yes	characteristic
413	#340	C₂²×C₁₃	1	1	yes	characteristic
414	#340	C₂²×C₁₃	1	1	yes	characteristic
415	C₂²×C₁₃	—	2	2	no	—
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	—	4	1	no	—
422	C₂²×C₁₃	—	4	1	no	—
423	C₂²×C₁₃	—	4	1	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	1	no	—
427	C₂²×C₁₃	—	4	1	no	—
428	C₂²×C₁₃	—	8	1	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	#468	1	4	yes	complemented
436	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
437	C₂²×C₁₃	D₄²	1	1	yes	characteristic
438	C₂²×C₁₃	#546	1	1	yes	characteristic
439	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
441	C₂²×C₁₃	#577	1	1	yes	characteristic
442	C₂²×C₁₃	#578	1	1	yes	characteristic
443	C₄×C₁₃	—	2	2	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	1	no	—
449	C₄×C₁₃	—	4	1	no	—
450	C₄×C₁₃	—	8	1	no	—
451	C₄×C₁₃	—	8	1	no	—
452	C₄×C₁₃	—	8	1	no	—
453	C₄×C₁₃	—	8	1	no	—
454	C₄×C₁₃	#525	1	1	yes	characteristic
455	C₄×C₁₃	#538	1	1	yes	characteristic
456	C₄×C₁₃	D₄²	1	1	yes	characteristic
457	C₄×C₁₃	#546	1	1	yes	characteristic
458	C₂²×Q₈	—	2	1	no	—
459	C₂²×Q₈	—	2	2	no	—
460	C₂²×Q₈	—	2	2	no	—
461	C₂²×Q₈	—	2	2	no	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×Q₈	—	4	1	no	—
464	C₂²×Q₈	—	4	1	no	—
465	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂×SD₁₆	—	2	2	no	—
476	C₂×SD₁₆	—	2	2	no	—
477	C₂×SD₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×SD₁₆	—	4	1	no	—
480	C₂×SD₁₆	—	4	1	no	—
481	C₂×M₁₆	—	2	2	no	—
482	C₂×M₁₆	—	2	2	no	—
483	C₂×M₁₆	—	4	1	no	—
484	C₂²×C₈	—	2	2	no	—
485	C₂²×C₈	—	2	2	no	—
486	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	4	1	no	—
494	C₂²⋊Q₈	—	4	1	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	4	1	no	—
499	#121	—	4	4	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
507	C₂×C₄⋊C₄	—	4	1	no	—
508	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
522	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
525	#107	—	2	2	no	—
526	#107	—	4	1	no	—
527	C₄⋊C₈	—	2	2	no	—
528	#103	—	2	2	no	—
529	#103	—	2	2	no	—
530	#103	—	2	2	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	D₄×C₁₃	1	4	yes	complemented
534	#102	—	2	2	no	—
535	#102	—	4	1	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	D₄×C₁₃	1	4	yes	complemented
538	#97	—	2	2	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	C₂×C₁₃	—	2	4	no	—
547	C₂×C₁₃	—	8	1	no	—
548	C₂×C₁₃	—	16	1	no	—
549	C₂×C₁₃	#2424	1	1	yes	characteristic
550	C₂×C₁₃	C₂×#468	1	1	yes	characteristic
551	C₂×C₁₃	#3063	1	1	yes	characteristic
552	C₂×C₁₃	#3265	1	1	yes	characteristic
553	C₂×C₁₃	#3270	1	1	yes	characteristic
554	C₂×C₁₃	#3308	1	1	yes	characteristic
555	C₂×C₁₃	#3320	1	1	yes	characteristic
556	C₂⁴	—	2	1	no	—
557	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	8	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	—	4	4	no	—
574	C₂×Q₈	—	4	4	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
577	C₂×Q₈	C₁₃×#41	1	2	yes	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	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	—	4	2	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	8	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
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	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	—	4	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	8	1	no	—
616	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
621	C₂²×C₄	C₁₃×#41	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	SD₁₆	—	4	4	no	—
624	SD₁₆	—	4	4	no	—
625	M₁₆	—	4	4	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	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	4	4	no	—
636	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
637	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
638	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₁₃	#25130	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	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	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	C₁₃×#121	1	2	yes	—
686	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
687	C₂³	C₁₃×#137	1	2	yes	—
688	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	4	8	no	—
694	Q₈	—	4	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	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	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	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	—	8	4	no	—
747	C₂×C₄	C₁₃×#121	1	2	yes	—
748	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
751	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
752	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
754	C₈	—	2	2	no	—
755	C₈	—	2	2	no	—
756	C₈	—	2	2	no	—
757	C₈	—	4	1	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	C₁₃×#468	1	4	yes	complemented
779	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
780	C₂²	D₄²×C₁₃	1	1	yes	characteristic
781	C₂²	C₁₃×#546	1	1	yes	characteristic
782	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
783	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
784	C₂²	C₁₃×#577	1	1	yes	characteristic
785	C₂²	C₁₃×#578	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	—	8	1	no	—
797	C₄	C₁₃×#525	1	1	yes	characteristic
798	C₄	C₁₃×#538	1	1	yes	characteristic
799	C₄	D₄²×C₁₃	1	1	yes	characteristic
800	C₄	C₁₃×#546	1	1	yes	characteristic
801	C₂	—	2	4	no	—
802	C₂	—	8	1	no	—
803	C₂	—	16	1	no	—
804	C₂	C₁₃×#2424	1	1	yes	characteristic
805	C₂	C₂×C₁₃×#468	1	1	yes	characteristic
806	C₂	C₁₃×#3063	1	1	yes	characteristic
807	C₂	C₁₃×#3265	1	1	yes	characteristic
808	C₂	C₁₃×#3270	1	1	yes	characteristic
809	C₂	C₁₃×#3308	1	1	yes	characteristic
810	C₂	C₁₃×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2416	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
1. C₂×C₁₃×#468	C₂	semidirect
2. C₂×C₁₃×#448	C₂	semidirect
3. C₂×C₁₃×#435	C₂	semidirect
4. C₂²×C₁₃×#103	C₂	semidirect
6. C₁₃×#2409	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2036	C₂	semidirect
10. C₁₃×#2000	C₂	semidirect
11. C₁₃×#1973	C₂	semidirect
12. C₁₃×#1935	C₂	semidirect
13. C₁₃×#1894	C₂	semidirect
14. C₁₃×#1893	C₂	semidirect
15. C₁₃×#1852	C₂	semidirect
138. C₁₃×#103	D₄	semidirect
142. C₁₃×C₂²⋊C₈	D₄	semidirect
151. #25130	C₁₃	direct (N × H)
262. C₂×#468	C₂×C₁₃	semidirect
263. C₂×#448	C₂×C₁₃	semidirect
264. C₂×#435	C₂×C₁₃	semidirect
265. C₂²×#103	C₂×C₁₃	semidirect
267. #2409	C₂×C₁₃	semidirect
268. #2068	C₂×C₁₃	semidirect
269. #2055	C₂×C₁₃	semidirect
270. #2036	C₂×C₁₃	semidirect
271. #2000	C₂×C₁₃	semidirect
272. #1973	C₂×C₁₃	semidirect
273. #1935	C₂×C₁₃	semidirect
274. #1894	C₂×C₁₃	semidirect
275. #1893	C₂×C₁₃	semidirect
276. #1852	C₂×C₁₃	semidirect
435. C₂²×C₁₃	#468	semidirect
533. #103	D₄×C₁₃	semidirect
537. C₂²⋊C₈	D₄×C₁₃	semidirect
666. C₁₃	#25130	direct (N × H)
778. C₂²	C₁₃×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#468	2
C₂×C₁₃×#448	2
C₂×C₁₃×#435	2
C₂²×C₁₃×#103	2
C₁₃×#2416	2
C₁₃×#2409	2
C₁₃×#2068	2
C₁₃×#2055	2
C₁₃×#2036	2
C₁₃×#2000	2
C₁₃×#1973	2
C₁₃×#1935	2
C₁₃×#1894	2
C₁₃×#1893	2
C₁₃×#1852	2
#25130	13

Subgroups — C13×#25130 #15711469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25130 #15711469