Subgroups — C₁₃×#32910 #15719249

Order 3328.

1494 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	—	2	4	no	—
25	C₄×C₁₃×#41	—	2	4	no	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	—	2	1	no	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	—	2	1	no	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#464	—	2	4	no	—
37	C₁₃×#463	—	2	4	no	—
38	C₁₃×#452	—	2	4	no	—
39	C₁₃×#449	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#388	—	2	1	no	—
56	C₁₃×#386	—	2	1	no	—
57	C₁₃×#386	—	2	1	no	—
58	C₁₃×#382	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	C₁₃×#336	C₂²	1	1	yes	characteristic
64	C₁₃×#336	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	D₄	1	4	yes	—
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	—	2	1	no	—
79	C₂³×C₄×C₁₃	—	2	1	no	—
80	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×Q₁₆	—	2	2	no	—
84	C₂×C₁₃×Q₁₆	—	2	2	no	—
85	C₂×C₁₃×Q₁₆	—	2	2	no	—
86	C₂×C₁₃×SD₁₆	—	2	2	no	—
87	C₂×C₁₃×SD₁₆	—	2	2	no	—
88	C₂×C₁₃×SD₁₆	—	2	2	no	—
89	C₂×C₁₃×SD₁₆	—	2	2	no	—
90	C₂×C₁₃×SD₁₆	—	2	2	no	—
91	C₂×C₁₃×SD₁₆	—	2	2	no	—
92	C₂×C₁₃×D₈	—	2	2	no	—
93	C₂×C₁₃×D₈	—	2	2	no	—
94	C₂×C₁₃×D₈	—	2	2	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×C₂²⋊Q₈	—	2	2	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
109	C₄×D₄×C₁₃	—	2	8	no	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
115	C₁₃×#117	—	2	8	no	—
116	C₁₃×#117	—	2	2	no	—
117	C₁₃×#117	—	2	2	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₁₃	—	2	8	no	—
135	C₂×C₄²×C₁₃	—	2	1	no	—
136	C₂×C₄²×C₁₃	—	2	1	no	—
137	C₂×C₄²×C₁₃	—	2	1	no	—
138	C₂×C₄²×C₁₃	—	2	2	no	—
139	C₂×C₄²×C₁₃	—	2	2	no	—
140	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊C₈	—	2	2	no	—
145	C₁₃×C₄⋊C₈	—	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×#102	—	2	2	no	—
151	C₁₃×#102	—	2	2	no	—
152	C₁₃×#102	—	2	2	no	—
153	C₁₃×#102	—	2	2	no	—
154	C₁₃×C₂²⋊C₈	—	2	2	no	—
155	C₁₃×C₂²⋊C₈	—	2	2	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	#32910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₃	—	2	1	no	—
162	C₂⁴×C₁₃	—	2	1	no	—
163	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₁₃×#41	—	2	8	no	—
165	C₁₃×#41	—	2	8	no	—
166	C₁₃×#41	—	2	8	no	—
167	C₁₃×#41	—	2	8	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	—	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	1	no	—
177	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
179	C₂×Q₈×C₁₃	#41	1	2	yes	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂×D₄×C₁₃	—	4	2	no	—
195	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₃	#41	1	2	yes	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	4	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	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	4	1	no	—
217	C₂²×C₄×C₁₃	—	4	1	no	—
218	C₂²×C₄×C₁₃	—	4	1	no	—
219	C₂²×C₄×C₁₃	—	4	2	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	#41	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₁₃×Q₁₆	—	4	4	no	—
232	C₁₃×SD₁₆	—	4	4	no	—
233	C₁₃×SD₁₆	—	4	4	no	—
234	C₁₃×D₈	—	4	4	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	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	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	4	2	no	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	4	2	no	—
262	C₁₃×C₂²⋊C₄	—	4	2	no	—
263	C₁₃×C₂²⋊C₄	—	4	2	no	—
264	C₁₃×C₂²⋊C₄	—	4	2	no	—
265	C₁₃×C₂²⋊C₄	—	4	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₄²×C₁₃	—	2	4	no	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	2	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	—	2	2	no	—
272	C₄²×C₁₃	—	2	1	no	—
273	C₄²×C₁₃	—	2	1	no	—
274	C₄²×C₁₃	C₂×D₄	1	2	yes	—
275	C₄²×C₁₃	C₂×D₄	1	2	yes	—
276	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#449	C₂×C₁₃	1	1	yes	characteristic
281	#2850	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	2	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	—	4	1	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	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	#121	1	2	yes	—
312	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	4	1	no	—
317	Q₈×C₁₃	—	4	1	no	—
318	Q₈×C₁₃	—	4	1	no	—
319	Q₈×C₁₃	—	4	1	no	—
320	Q₈×C₁₃	#121	1	4	yes	—
321	D₄×C₁₃	—	2	16	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	1	no	—
326	D₄×C₁₃	—	4	1	no	—
327	D₄×C₁₃	—	4	1	no	—
328	D₄×C₁₃	—	4	1	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	#121	1	4	yes	—
331	C₂×C₄×C₁₃	—	2	16	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	4	4	no	—
353	C₂×C₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	4	4	no	—
355	C₂×C₄×C₁₃	—	4	8	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	#120	1	2	yes	—
370	C₂×C₄×C₁₃	#120	1	2	yes	—
371	C₂×C₄×C₁₃	#121	1	2	yes	—
372	C₂×C₄×C₁₃	#135	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
379	C₈×C₁₃	—	4	1	no	—
380	C₈×C₁₃	—	4	1	no	—
381	C₈×C₁₃	—	4	1	no	—
382	C₈×C₁₃	—	4	1	no	—
383	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
391	C₄×#41	—	2	4	no	—
392	C₄×#41	—	2	4	no	—
393	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×C₄×D₄	—	2	1	no	—
396	C₂×C₄×D₄	—	2	1	no	—
397	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#117	—	2	1	no	—
400	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
401	C₂²×C₄²	—	2	1	no	—
402	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
403	#464	—	2	4	no	—
404	#463	—	2	4	no	—
405	#452	—	2	4	no	—
406	#449	—	2	4	no	—
407	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₈	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×#103	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
419	#391	C₂²×C₁₃	1	1	yes	characteristic
420	#390	C₂²×C₁₃	1	1	yes	characteristic
421	#388	—	2	1	no	—
422	#388	—	2	1	no	—
423	#386	—	2	1	no	—
424	#386	—	2	1	no	—
425	#382	C₂²×C₁₃	1	1	yes	characteristic
426	#340	C₂²×C₁₃	1	1	yes	characteristic
427	#340	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	4	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	4	1	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	1	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	1	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	1	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	8	1	no	—
447	C₂²×C₁₃	—	8	1	no	—
448	C₂²×C₁₃	—	8	1	no	—
449	C₂²×C₁₃	—	8	1	no	—
450	C₂²×C₁₃	—	8	1	no	—
451	C₂²×C₁₃	—	8	1	no	—
452	C₂²×C₁₃	—	8	1	no	—
453	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
454	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
455	C₂²×C₁₃	#525	1	1	yes	characteristic
456	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
457	C₂²×C₁₃	#575	1	1	yes	characteristic
458	C₂²×C₁₃	#575	1	1	yes	characteristic
459	C₂²×C₁₃	#575	1	1	yes	characteristic
460	C₄×C₁₃	—	2	2	no	—
461	C₄×C₁₃	—	2	4	no	—
462	C₄×C₁₃	—	2	2	no	—
463	C₄×C₁₃	—	2	2	no	—
464	C₄×C₁₃	—	2	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	8	1	no	—
469	C₄×C₁₃	—	8	1	no	—
470	C₄×C₁₃	—	8	1	no	—
471	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
472	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
473	C₄×C₁₃	#525	1	1	yes	characteristic
474	C₄×C₁₃	#525	1	1	yes	characteristic
475	C₂×#41	—	2	2	no	—
476	C₂×#41	—	2	2	no	—
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	2	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	D₄×C₁₃	1	4	yes	—
481	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
491	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×Q₁₆	—	2	2	no	—
494	C₂×Q₁₆	—	2	2	no	—
495	C₂×Q₁₆	—	2	2	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×SD₁₆	—	2	2	no	—
500	C₂×SD₁₆	—	2	2	no	—
501	C₂×SD₁₆	—	2	2	no	—
502	C₂×D₈	—	2	2	no	—
503	C₂×D₈	—	2	2	no	—
504	C₂×D₈	—	2	2	no	—
505	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
525	#117	—	2	8	no	—
526	#117	—	2	2	no	—
527	#117	—	2	2	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	C₂³×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₄²	—	2	8	no	—
545	C₂×C₄²	—	2	1	no	—
546	C₂×C₄²	—	2	1	no	—
547	C₂×C₄²	—	2	1	no	—
548	C₂×C₄²	—	2	2	no	—
549	C₂×C₄²	—	2	2	no	—
550	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	C₄⋊C₈	—	2	2	no	—
555	C₄⋊C₈	—	2	2	no	—
556	#103	—	2	2	no	—
557	#103	—	2	2	no	—
558	#103	—	2	2	no	—
559	#103	—	2	2	no	—
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	2	2	no	—
563	#102	—	2	2	no	—
564	C₂²⋊C₈	—	2	2	no	—
565	C₂²⋊C₈	—	2	2	no	—
566	#95	—	2	1	no	—
567	#95	—	2	1	no	—
568	#95	—	2	1	no	—
569	#95	—	2	1	no	—
570	C₂×C₁₃	—	4	2	no	—
571	C₂×C₁₃	—	4	4	no	—
572	C₂×C₁₃	—	16	1	no	—
573	C₂×C₁₃	#2847	1	1	yes	characteristic
574	C₂×C₁₃	#3002	1	1	yes	characteristic
575	C₂×C₁₃	#3005	1	1	yes	characteristic
576	C₂×C₁₃	#3035	1	1	yes	characteristic
577	C₂×C₁₃	#3040	1	1	yes	characteristic
578	C₂×C₁₃	#3102	1	1	yes	characteristic
579	C₂×C₁₃	#3111	1	1	yes	characteristic
580	C₂⁴	—	2	1	no	—
581	C₂⁴	—	2	1	no	—
582	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
583	#41	—	2	8	no	—
584	#41	—	2	8	no	—
585	#41	—	2	8	no	—
586	#41	—	2	8	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	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	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
598	C₂×Q₈	C₁₃×#41	1	2	yes	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₂×D₄	C₁₃×#41	1	2	yes	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	4	1	no	—
636	C₂²×C₄	—	4	1	no	—
637	C₂²×C₄	—	4	1	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	—	4	2	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₁₃×#41	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	4	4	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	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	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	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	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	C₂²⋊C₄	—	4	2	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	1	no	—
692	C₄²	—	2	1	no	—
693	C₄²	C₂×D₄×C₁₃	1	2	yes	—
694	C₄²	C₂×D₄×C₁₃	1	2	yes	—
695	C₁₃	#32910	1	1	yes	characteristic, direct product factor, Sylow
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	C₁₃×#121	1	2	yes	—
717	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	1	no	—
722	Q₈	—	4	1	no	—
723	Q₈	—	4	1	no	—
724	Q₈	—	4	1	no	—
725	Q₈	C₁₃×#121	1	4	yes	—
726	D₄	—	2	16	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	8	4	no	—
735	D₄	C₁₃×#121	1	4	yes	—
736	C₂×C₄	—	2	16	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	4	4	no	—
758	C₂×C₄	—	4	8	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	8	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	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	C₁₃×#120	1	2	yes	—
775	C₂×C₄	C₁₃×#120	1	2	yes	—
776	C₂×C₄	C₁₃×#121	1	2	yes	—
777	C₂×C₄	C₁₃×#135	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
782	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
783	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₈	—	4	1	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	4	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
810	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
811	C₂²	C₁₃×#525	1	1	yes	characteristic
812	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
813	C₂²	C₁₃×#575	1	1	yes	characteristic
814	C₂²	C₁₃×#575	1	1	yes	characteristic
815	C₂²	C₁₃×#575	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	8	1	no	—
825	C₄	—	8	1	no	—
826	C₄	—	8	1	no	—
827	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
828	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
829	C₄	C₁₃×#525	1	1	yes	characteristic
830	C₄	C₁₃×#525	1	1	yes	characteristic
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	16	1	no	—
834	C₂	C₁₃×#2847	1	1	yes	characteristic
835	C₂	C₁₃×#3002	1	1	yes	characteristic
836	C₂	C₁₃×#3005	1	1	yes	characteristic
837	C₂	C₁₃×#3035	1	1	yes	characteristic
838	C₂	C₁₃×#3040	1	1	yes	characteristic
839	C₂	C₁₃×#3102	1	1	yes	characteristic
840	C₂	C₁₃×#3111	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#464	C₂	semidirect
3. C₂×C₁₃×#463	C₂	semidirect
4. C₂×C₁₃×#452	C₂	semidirect
6. C₁₃×#2850	C₂	semidirect
7. C₁₃×#1880	C₂	semidirect
8. C₁₃×#1879	C₂	semidirect
9. C₁₃×#1878	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₁₃×#1875	C₂	semidirect
12. C₁₃×#1873	C₂	semidirect
13. C₁₃×#1805	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₁₃×#1797	C₂	semidirect
108. C₄×Q₈×C₁₃	D₄	semidirect
114. C₄×D₄×C₁₃	D₄	semidirect
160. #32910	C₁₃	direct (N × H)
276. C₂×C₄×#41	C₂×C₁₃	semidirect
277. C₂×#464	C₂×C₁₃	semidirect
278. C₂×#463	C₂×C₁₃	semidirect
279. C₂×#452	C₂×C₁₃	semidirect
281. #2850	C₂×C₁₃	semidirect
282. #1880	C₂×C₁₃	semidirect
283. #1879	C₂×C₁₃	semidirect
284. #1878	C₂×C₁₃	semidirect
285. #1877	C₂×C₁₃	semidirect
286. #1875	C₂×C₁₃	semidirect
287. #1873	C₂×C₁₃	semidirect
288. #1805	C₂×C₁₃	semidirect
289. #1804	C₂×C₁₃	semidirect
290. #1797	C₂×C₁₃	semidirect
518. C₄×Q₈	D₄×C₁₃	semidirect
524. C₄×D₄	D₄×C₁₃	semidirect
695. C₁₃	#32910	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×#41	2
C₂×C₁₃×#464	2
C₂×C₁₃×#463	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₁₃×#2850	2
C₁₃×#1880	2
C₁₃×#1879	2
C₁₃×#1878	2
C₁₃×#1877	2
C₁₃×#1875	2
C₁₃×#1873	2
C₁₃×#1805	2
C₁₃×#1804	2
C₁₃×#1797	2
#32910	13

Subgroups — C13×#32910 #15719249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32910 #15719249