Subgroups — C₁₃×#32709 #15719048

Order 3328.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2847	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1779	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#120	—	2	1	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×#386	—	2	1	no	—
41	C₁₃×#386	—	2	1	no	—
42	C₁₃×#386	—	2	1	no	—
43	C₁₃×#385	—	2	1	no	—
44	C₁₃×#385	—	2	1	no	—
45	C₁₃×#385	—	2	1	no	—
46	C₁₃×#380	C₂²	1	1	yes	characteristic
47	C₁₃×#380	C₂²	1	1	yes	characteristic
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₁₃×#379	—	2	1	no	—
53	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	4	1	no	—
66	C₂³×C₄×C₁₃	—	4	1	no	—
67	C₂³×C₄×C₁₃	—	4	1	no	—
68	C₂³×C₄×C₁₃	—	4	1	no	—
69	C₂³×C₄×C₁₃	—	4	1	no	—
70	C₂³×C₄×C₁₃	—	4	1	no	—
71	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×SD₁₆	—	4	1	no	—
78	C₂×C₁₃×SD₁₆	—	4	1	no	—
79	C₂×C₁₃×SD₁₆	—	4	1	no	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₂²⋊Q₈	—	4	1	no	—
85	C₁₃×C₂²⋊Q₈	—	4	1	no	—
86	C₁₃×C₂²⋊Q₈	—	4	1	no	—
87	C₁₃×C₂²⋊Q₈	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×#121	—	4	1	no	—
91	C₁₃×#121	—	4	1	no	—
92	C₁₃×#121	—	4	1	no	—
93	C₁₃×#121	—	4	1	no	—
94	C₁₃×#121	—	4	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₁₃×#120	—	4	4	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₁₃×#107	—	4	1	no	—
119	C₁₃×#107	—	4	1	no	—
120	C₁₃×#106	—	4	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#103	—	4	1	no	—
123	C₁₃×#103	—	4	1	no	—
124	C₁₃×#102	—	4	1	no	—
125	C₁₃×#102	—	4	1	no	—
126	C₁₃×#102	—	4	1	no	—
127	C₁₃×C₂²⋊C₈	—	4	1	no	—
128	C₁₃×C₂²⋊C₈	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	4	1	no	—
130	C₁₃×C₂²⋊C₈	—	4	1	no	—
131	C₁₃×C₂²⋊C₈	—	4	1	no	—
132	C₁₃×C₂²⋊C₈	—	4	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	#32709	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₂⁴×C₁₃	—	2	2	no	—
142	C₂⁴×C₁₃	—	2	2	no	—
143	C₂⁴×C₁₃	—	2	1	no	—
144	C₂⁴×C₁₃	—	4	1	no	—
145	C₂⁴×C₁₃	—	4	1	no	—
146	C₂⁴×C₁₃	—	4	1	no	—
147	C₂⁴×C₁₃	—	4	1	no	—
148	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	4	2	no	—
164	C₂×D₄×C₁₃	—	4	2	no	—
165	C₂×D₄×C₁₃	—	4	2	no	—
166	C₂×D₄×C₁₃	—	4	2	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	2	no	—
170	C₂×D₄×C₁₃	—	4	2	no	—
171	C₂×D₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	1	no	—
188	C₂²×C₄×C₁₃	—	2	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	—	4	1	no	—
198	C₂²×C₄×C₁₃	—	4	1	no	—
199	C₂²×C₄×C₁₃	—	4	1	no	—
200	C₂²×C₄×C₁₃	—	4	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	—	4	1	no	—
203	C₂²×C₄×C₁₃	—	4	1	no	—
204	C₂²×C₄×C₁₃	—	4	1	no	—
205	C₂²×C₄×C₁₃	—	4	1	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	4	no	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₁₃×SD₁₆	—	4	4	no	—
215	C₂×C₈×C₁₃	—	2	1	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	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	4	2	no	—
240	C₁₃×C₄⋊C₄	—	4	2	no	—
241	C₁₃×C₄⋊C₄	—	4	2	no	—
242	C₁₃×C₂²⋊C₄	—	4	2	no	—
243	C₁₃×C₂²⋊C₄	—	4	2	no	—
244	C₁₃×C₂²⋊C₄	—	4	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	—	4	2	no	—
251	C₁₃×C₂²⋊C₄	—	4	2	no	—
252	C₁₃×C₂²⋊C₄	—	4	2	no	—
253	C₁₃×C₂²⋊C₄	—	4	2	no	—
254	#2848	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2847	C₂×C₁₃	1	1	yes	characteristic
256	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2076	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2075	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1779	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	1	no	—
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	2	1	no	—
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	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	—	4	4	no	—
288	C₂³×C₁₃	—	4	4	no	—
289	C₂³×C₁₃	—	4	4	no	—
290	C₂³×C₁₃	—	4	4	no	—
291	C₂³×C₁₃	—	4	4	no	—
292	C₂³×C₁₃	—	4	4	no	—
293	C₂³×C₁₃	—	4	4	no	—
294	C₂³×C₁₃	—	4	1	no	—
295	C₂³×C₁₃	—	4	1	no	—
296	C₂³×C₁₃	—	4	1	no	—
297	C₂³×C₁₃	—	4	1	no	—
298	C₂³×C₁₃	—	4	1	no	—
299	C₂³×C₁₃	—	4	1	no	—
300	C₂³×C₁₃	—	4	1	no	—
301	C₂³×C₁₃	#135	1	2	yes	—
302	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
303	C₂³×C₁₃	#137	1	2	yes	—
304	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₁₃	—	4	1	no	—
306	Q₈×C₁₃	—	4	1	no	—
307	Q₈×C₁₃	—	4	1	no	—
308	Q₈×C₁₃	—	4	1	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	D₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	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	—	4	4	no	—
326	C₂×C₄×C₁₃	—	4	4	no	—
327	C₂×C₄×C₁₃	—	4	4	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	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	—	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	H(5,𝔽₂)	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	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
367	C₈×C₁₃	—	4	1	no	—
368	C₈×C₁₃	—	4	1	no	—
369	C₈×C₁₃	—	4	1	no	—
370	C₈×C₁₃	—	4	1	no	—
371	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#120	—	2	1	no	—
380	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
395	#386	—	2	1	no	—
396	#386	—	2	1	no	—
397	#386	—	2	1	no	—
398	#385	—	2	1	no	—
399	#385	—	2	1	no	—
400	#385	—	2	1	no	—
401	#380	C₂²×C₁₃	1	1	yes	characteristic
402	#380	C₂²×C₁₃	1	1	yes	characteristic
403	#380	C₂²×C₁₃	1	1	yes	characteristic
404	#380	C₂²×C₁₃	1	1	yes	characteristic
405	#380	C₂²×C₁₃	1	1	yes	characteristic
406	#380	C₂²×C₁₃	1	1	yes	characteristic
407	#379	—	2	1	no	—
408	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂²×C₁₃	—	2	2	no	—
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	—	2	2	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	4	16	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	—	4	1	no	—
429	C₂²×C₁₃	—	4	1	no	—
430	C₂²×C₁₃	—	4	1	no	—
431	C₂²×C₁₃	—	4	1	no	—
432	C₂²×C₁₃	—	4	1	no	—
433	C₂²×C₁₃	—	4	1	no	—
434	C₂²×C₁₃	—	4	1	no	—
435	C₂²×C₁₃	—	4	1	no	—
436	C₂²×C₁₃	—	8	1	no	—
437	C₂²×C₁₃	—	8	1	no	—
438	C₂²×C₁₃	—	8	1	no	—
439	C₂²×C₁₃	—	8	1	no	—
440	C₂²×C₁₃	—	8	1	no	—
441	C₂²×C₁₃	—	8	1	no	—
442	C₂²×C₁₃	—	8	1	no	—
443	C₂²×C₁₃	#534	1	1	yes	characteristic
444	C₂²×C₁₃	#534	1	1	yes	characteristic
445	C₂²×C₁₃	#534	1	1	yes	characteristic
446	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
447	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
449	C₂²×C₁₃	#575	1	1	yes	characteristic
450	C₄×C₁₃	—	4	1	no	—
451	C₄×C₁₃	—	4	1	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	—	8	1	no	—
457	C₄×C₁₃	—	8	1	no	—
458	C₄×C₁₃	—	8	1	no	—
459	C₄×C₁₃	—	8	1	no	—
460	C₄×C₁₃	#560	1	1	yes	characteristic
461	C₄×C₁₃	#560	1	1	yes	characteristic
462	C₄×C₁₃	#560	1	1	yes	characteristic
463	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
464	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	—	4	1	no	—
471	C₂³×C₄	—	4	1	no	—
472	C₂³×C₄	—	4	1	no	—
473	C₂³×C₄	—	4	1	no	—
474	C₂³×C₄	—	4	1	no	—
475	C₂³×C₄	—	4	1	no	—
476	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
478	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×SD₁₆	—	4	1	no	—
483	C₂×SD₁₆	—	4	1	no	—
484	C₂×SD₁₆	—	4	1	no	—
485	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
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⋊Q₈	—	4	1	no	—
490	C₂²⋊Q₈	—	4	1	no	—
491	C₂²⋊Q₈	—	4	1	no	—
492	C₂²⋊Q₈	—	4	1	no	—
493	C₂²⋊Q₈	—	4	1	no	—
494	C₂²⋊Q₈	—	4	1	no	—
495	#121	—	4	1	no	—
496	#121	—	4	1	no	—
497	#121	—	4	1	no	—
498	#121	—	4	1	no	—
499	#121	—	4	1	no	—
500	#121	—	4	1	no	—
501	#120	—	4	4	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	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	#107	—	4	1	no	—
524	#107	—	4	1	no	—
525	#106	—	4	1	no	—
526	#103	—	4	1	no	—
527	#103	—	4	1	no	—
528	#103	—	4	1	no	—
529	#102	—	4	1	no	—
530	#102	—	4	1	no	—
531	#102	—	4	1	no	—
532	C₂²⋊C₈	—	4	1	no	—
533	C₂²⋊C₈	—	4	1	no	—
534	C₂²⋊C₈	—	4	1	no	—
535	C₂²⋊C₈	—	4	1	no	—
536	C₂²⋊C₈	—	4	1	no	—
537	C₂²⋊C₈	—	4	1	no	—
538	#95	—	2	1	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	C₂×C₁₃	—	4	2	no	—
545	C₂×C₁₃	—	4	2	no	—
546	C₂×C₁₃	—	4	2	no	—
547	C₂×C₁₃	—	16	1	no	—
548	C₂×C₁₃	#2812	1	1	yes	characteristic
549	C₂×C₁₃	#3188	1	1	yes	characteristic
550	C₂×C₁₃	#3190	1	1	yes	characteristic
551	C₂×C₁₃	#3191	1	1	yes	characteristic
552	C₂×C₁₃	#3193	1	1	yes	characteristic
553	C₂×C₁₃	#3194	1	1	yes	characteristic
554	C₂×C₁₃	#3196	1	1	yes	characteristic
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	4	1	no	—
560	C₂⁴	—	4	1	no	—
561	C₂⁴	—	4	1	no	—
562	C₂⁴	—	4	1	no	—
563	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	4	2	no	—
583	C₂×D₄	—	4	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	—	4	2	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	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	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	4	1	no	—
618	C₂²×C₄	—	4	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
629	SD₁₆	—	4	4	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	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	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	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊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	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₁₃	#32709	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	4	4	no	—
689	C₂³	—	4	4	no	—
690	C₂³	—	4	4	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	C₁₃×#135	1	2	yes	—
703	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
704	C₂³	C₁₃×#137	1	2	yes	—
705	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	D₄	—	4	1	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	1	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	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	4	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	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	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	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
764	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
766	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₈	—	4	1	no	—
771	C₈	—	4	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	16	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	C₁₃×#534	1	1	yes	characteristic
802	C₂²	C₁₃×#534	1	1	yes	characteristic
803	C₂²	C₁₃×#534	1	1	yes	characteristic
804	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
805	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
806	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
807	C₂²	C₁₃×#575	1	1	yes	characteristic
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	8	1	no	—
812	C₄	—	8	1	no	—
813	C₄	—	8	1	no	—
814	C₄	—	8	1	no	—
815	C₄	—	8	1	no	—
816	C₄	—	8	1	no	—
817	C₄	—	8	1	no	—
818	C₄	C₁₃×#560	1	1	yes	characteristic
819	C₄	C₁₃×#560	1	1	yes	characteristic
820	C₄	C₁₃×#560	1	1	yes	characteristic
821	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
822	C₂	—	4	2	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	2	no	—
825	C₂	—	16	1	no	—
826	C₂	C₁₃×#2812	1	1	yes	characteristic
827	C₂	C₁₃×#3188	1	1	yes	characteristic
828	C₂	C₁₃×#3190	1	1	yes	characteristic
829	C₂	C₁₃×#3191	1	1	yes	characteristic
830	C₂	C₁₃×#3193	1	1	yes	characteristic
831	C₂	C₁₃×#3194	1	1	yes	characteristic
832	C₂	C₁₃×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2848	C₂	semidirect
3. C₁₃×#2077	C₂	semidirect
4. C₁₃×#2076	C₂	semidirect
5. C₁₃×#2075	C₂	semidirect
6. C₁₃×#2036	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2034	C₂	semidirect
10. C₁₃×#2033	C₂	semidirect
11. C₁₃×#2033	C₂	semidirect
12. C₁₃×#2000	C₂	semidirect
13. C₁₃×#2000	C₂	semidirect
14. C₁₃×#2000	C₂	semidirect
15. C₁₃×#1779	C₂	semidirect
17. C₂²×C₁₃×SD₁₆	C₂²	semidirect
25. C₂×C₁₃×#107	C₂²	semidirect
26. C₂×C₁₃×#107	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
28. C₂×C₁₃×#103	C₂²	semidirect
29. C₂×C₁₃×#103	C₂²	semidirect
30. C₂×C₁₃×#103	C₂²	semidirect
31. C₂×C₁₃×#102	C₂²	semidirect
32. C₂×C₁₃×#102	C₂²	semidirect
33. C₂×C₁₃×#102	C₂²	semidirect
53. C₁₃×#340	C₂²	semidirect
54. C₁₃×#340	C₂²	semidirect
55. C₁₃×#340	C₂²	semidirect
56. C₁₃×#340	C₂²	semidirect
57. C₁₃×#340	C₂²	semidirect
58. C₁₃×#340	C₂²	semidirect
139. #32709	C₁₃	direct (N × H)
254. #2848	C₂×C₁₃	semidirect
256. #2077	C₂×C₁₃	semidirect
257. #2076	C₂×C₁₃	semidirect
258. #2075	C₂×C₁₃	semidirect
259. #2036	C₂×C₁₃	semidirect
260. #2036	C₂×C₁₃	semidirect
261. #2035	C₂×C₁₃	semidirect
262. #2034	C₂×C₁₃	semidirect
263. #2033	C₂×C₁₃	semidirect
264. #2033	C₂×C₁₃	semidirect
265. #2000	C₂×C₁₃	semidirect
266. #2000	C₂×C₁₃	semidirect
267. #2000	C₂×C₁₃	semidirect
268. #1779	C₂×C₁₃	semidirect
372. C₂²×SD₁₆	C₂²×C₁₃	semidirect
380. C₂×#107	C₂²×C₁₃	semidirect
381. C₂×#107	C₂²×C₁₃	semidirect
382. C₂×#106	C₂²×C₁₃	semidirect
383. C₂×#103	C₂²×C₁₃	semidirect
384. C₂×#103	C₂²×C₁₃	semidirect
385. C₂×#103	C₂²×C₁₃	semidirect
386. C₂×#102	C₂²×C₁₃	semidirect
387. C₂×#102	C₂²×C₁₃	semidirect
388. C₂×#102	C₂²×C₁₃	semidirect
408. #340	C₂²×C₁₃	semidirect
409. #340	C₂²×C₁₃	semidirect
410. #340	C₂²×C₁₃	semidirect
411. #340	C₂²×C₁₃	semidirect
412. #340	C₂²×C₁₃	semidirect
413. #340	C₂²×C₁₃	semidirect
669. C₁₃	#32709	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2848	2
C₁₃×#2847	2
C₁₃×#2077	2
C₁₃×#2076	2
C₁₃×#2075	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#2000	2
C₁₃×#1779	2
#32709	13

Subgroups — C13×#32709 #15719048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32709 #15719048