Subgroups — C₁₃×#25156 #15711495

Order 3328.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×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×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
28	C₁₃×#461	—	2	4	no	—
29	C₁₃×#450	—	2	4	no	—
30	C₁₃×#450	—	2	4	no	—
31	C₄×C₁₃×SD₁₆	—	2	4	no	—
32	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#398	—	2	1	no	—
47	C₁₃×#396	—	2	1	no	—
48	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#389	—	2	1	no	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#386	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#379	—	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	2	no	—
70	C₂²×D₄×C₁₃	—	2	1	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	—	2	1	no	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	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	—	2	2	no	—
85	C₂×C₁₃×SD₁₆	—	2	2	no	—
86	C₂×C₁₃×SD₁₆	—	2	2	no	—
87	C₂×C₁₃×SD₁₆	—	4	1	no	—
88	C₂×C₁₃×SD₁₆	—	4	1	no	—
89	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	4	1	no	—
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	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	4	1	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	4	1	no	—
105	C₄×D₄×C₁₃	—	4	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	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	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×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	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
126	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	—	2	1	no	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₁₃×#106	—	2	2	no	—
132	C₁₃×#106	—	4	1	no	—
133	C₁₃×C₄⋊C₈	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	4	1	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	D₄	1	4	yes	—
142	C₁₃×C₂²⋊C₈	—	2	2	no	—
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₄×C₈×C₁₃	—	2	2	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	D₄	1	1	yes	characteristic
150	C₁₃×#95	D₄	1	1	yes	characteristic
151	#25156	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	—	2	4	no	—
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	—	4	2	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	—	4	2	no	—
158	C₂⁴×C₁₃	—	4	2	no	—
159	C₂⁴×C₁₃	—	8	1	no	—
160	C₂⁴×C₁₃	—	8	1	no	—
161	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
173	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₁₃	—	2	4	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	—	4	2	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	—	4	4	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₃	#41	1	2	yes	—
192	C₂×D₄×C₁₃	#41	1	2	yes	—
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	—	4	2	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	—	8	1	no	—
210	C₂²×C₄×C₁₃	—	8	1	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
217	C₁₃×SD₁₆	—	2	8	no	—
218	C₁₃×SD₁₆	—	4	4	no	—
219	C₁₃×SD₁₆	—	4	4	no	—
220	C₁₃×SD₁₆	—	4	4	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	—	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	C₂×D₄	1	2	yes	—
232	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	4	2	no	—
241	C₁₃×C₄⋊C₄	—	4	2	no	—
242	C₁₃×C₄⋊C₄	—	4	2	no	—
243	C₁₃×C₄⋊C₄	—	4	2	no	—
244	C₁₃×C₄⋊C₄	—	4	2	no	—
245	C₁₃×C₄⋊C₄	—	4	2	no	—
246	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
247	C₁₃×C₂²⋊C₄	—	4	1	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	C₁₃×C₂²⋊C₄	—	4	2	no	—
255	C₁₃×C₂²⋊C₄	—	8	1	no	—
256	C₁₃×C₂²⋊C₄	—	8	1	no	—
257	C₁₃×C₂²⋊C₄	SD₁₆	1	4	yes	complemented
258	C₄²×C₁₃	—	2	1	no	—
259	C₄²×C₁₃	—	2	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	4	2	no	—
263	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
265	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
266	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2429	C₂×C₁₃	1	1	yes	characteristic, complemented
268	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
269	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1968	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1923	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	4	8	no	—
289	C₂³×C₁₃	—	4	8	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	—	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	—	8	4	no	—
301	C₂³×C₁₃	—	8	4	no	—
302	C₂³×C₁₃	—	8	4	no	—
303	C₂³×C₁₃	—	8	4	no	—
304	C₂³×C₁₃	—	8	4	no	—
305	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
306	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	4	1	no	—
310	Q₈×C₁₃	—	4	1	no	—
311	Q₈×C₁₃	—	4	1	no	—
312	Q₈×C₁₃	—	4	1	no	—
313	Q₈×C₁₃	—	4	1	no	—
314	Q₈×C₁₃	—	4	1	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	2	2	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	4	8	no	—
321	D₄×C₁₃	—	4	1	no	—
322	D₄×C₁₃	—	4	1	no	—
323	D₄×C₁₃	#121	1	4	yes	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	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	2	no	—
332	C₂×C₄×C₁₃	—	2	2	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	—	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	—	8	4	no	—
360	C₂×C₄×C₁₃	—	8	4	no	—
361	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
362	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
369	C₈×C₁₃	—	2	2	no	—
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	—	4	1	no	—
372	C₈×C₁₃	—	4	1	no	—
373	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	—	2	1	no	—
385	#461	—	2	4	no	—
386	#450	—	2	4	no	—
387	#450	—	2	4	no	—
388	C₄×SD₁₆	—	2	4	no	—
389	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
390	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
392	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
395	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#398	—	2	1	no	—
404	#396	—	2	1	no	—
405	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	#390	C₂²×C₁₃	1	1	yes	characteristic
407	#390	C₂²×C₁₃	1	1	yes	characteristic
408	#389	—	2	1	no	—
409	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	#388	—	2	1	no	—
411	#386	—	2	1	no	—
412	#386	—	2	1	no	—
413	#380	C₂²×C₁₃	1	1	yes	characteristic
414	#379	—	2	1	no	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	4	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	1	no	—
428	C₂²×C₁₃	—	4	1	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	1	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	8	16	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	#525	1	1	yes	characteristic
443	C₂²×C₁₃	D₄²	1	1	yes	characteristic
444	C₂²×C₁₃	D₄²	1	1	yes	characteristic
445	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
446	C₂²×C₁₃	#575	1	1	yes	characteristic
447	C₂²×C₁₃	#577	1	1	yes	characteristic
448	C₂²×C₁₃	#577	1	1	yes	characteristic
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	4	1	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	—	4	1	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	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	C₂×#121	1	1	yes	characteristic
461	C₄×C₁₃	#538	1	1	yes	characteristic
462	C₄×C₁₃	#546	1	1	yes	characteristic
463	C₄×C₁₃	#546	1	1	yes	characteristic
464	C₂⁵	—	2	1	no	—
465	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	4	1	no	—
473	C₂²×D₄	—	4	1	no	—
474	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×SD₁₆	—	2	2	no	—
481	C₂×SD₁₆	—	2	2	no	—
482	C₂×SD₁₆	—	2	2	no	—
483	C₂×SD₁₆	—	2	2	no	—
484	C₂×SD₁₆	—	2	2	no	—
485	C₂×SD₁₆	—	2	2	no	—
486	C₂×SD₁₆	—	2	2	no	—
487	C₂×SD₁₆	—	2	2	no	—
488	C₂×SD₁₆	—	4	1	no	—
489	C₂×SD₁₆	—	4	1	no	—
490	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
491	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	4	1	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	4	1	no	—
500	C₂²⋊Q₈	—	4	1	no	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	4	1	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	4	1	no	—
506	C₄×D₄	—	4	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	4	4	no	—
527	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
532	#106	—	2	2	no	—
533	#106	—	4	1	no	—
534	C₄⋊C₈	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#103	—	2	2	no	—
538	#103	—	4	1	no	—
539	#102	—	2	2	no	—
540	#102	—	2	2	no	—
541	#102	—	2	2	no	—
542	#102	D₄×C₁₃	1	4	yes	—
543	C₂²⋊C₈	—	2	2	no	—
544	C₂²⋊C₈	—	2	2	no	—
545	C₄×C₈	—	2	2	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	—	2	1	no	—
550	#95	D₄×C₁₃	1	1	yes	characteristic
551	#95	D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₁₃	—	4	2	no	—
553	C₂×C₁₃	—	4	4	no	—
554	C₂×C₁₃	—	8	2	no	—
555	C₂×C₁₃	#2424	1	1	yes	characteristic
556	C₂×C₁₃	#3101	1	1	yes	characteristic
557	C₂×C₁₃	#3123	1	1	yes	characteristic
558	C₂×C₁₃	#3267	1	1	yes	characteristic
559	C₂×C₁₃	#3275	1	1	yes	characteristic
560	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
561	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
562	C₂⁴	—	2	1	no	—
563	C₂⁴	—	2	4	no	—
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	4	2	no	—
566	C₂⁴	—	4	2	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	8	1	no	—
570	C₂⁴	—	8	1	no	—
571	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
584	C₂×D₄	—	2	4	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	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
600	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₂×D₄	C₁₃×#41	1	2	yes	—
602	C₂×D₄	C₁₃×#41	1	2	yes	—
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	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	8	1	no	—
620	C₂²×C₄	—	8	1	no	—
621	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	SD₁₆	—	2	8	no	—
628	SD₁₆	—	4	4	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	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	C₂×D₄×C₁₃	1	2	yes	—
642	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
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	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₂²⋊C₄	—	4	1	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	—	8	1	no	—
666	C₂²⋊C₄	—	8	1	no	—
667	C₂²⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	4	2	no	—
673	C₁₃	#25156	1	1	yes	characteristic, direct product factor, Sylow
674	C₂³	—	2	1	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	8	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
702	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	8	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	C₁₃×#121	1	4	yes	—
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	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	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	—	2	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	—	8	4	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
758	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
762	C₂×C₄	C₂×C₁₃×#41	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	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	16	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	8	1	no	—
791	C₂²	C₁₃×#525	1	1	yes	characteristic
792	C₂²	D₄²×C₁₃	1	1	yes	characteristic
793	C₂²	D₄²×C₁₃	1	1	yes	characteristic
794	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
795	C₂²	C₁₃×#575	1	1	yes	characteristic
796	C₂²	C₁₃×#577	1	1	yes	characteristic
797	C₂²	C₁₃×#577	1	1	yes	characteristic
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	—	8	1	no	—
808	C₄	—	8	1	no	—
809	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
810	C₄	C₁₃×#538	1	1	yes	characteristic
811	C₄	C₁₃×#546	1	1	yes	characteristic
812	C₄	C₁₃×#546	1	1	yes	characteristic
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₁₃×#2424	1	1	yes	characteristic
817	C₂	C₁₃×#3101	1	1	yes	characteristic
818	C₂	C₁₃×#3123	1	1	yes	characteristic
819	C₂	C₁₃×#3267	1	1	yes	characteristic
820	C₂	C₁₃×#3275	1	1	yes	characteristic
821	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
822	C₂	D₄×C₁₃×SD₁₆	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×#461	C₂	semidirect
4. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#2429	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2035	C₂	semidirect
10. C₁₃×#2013	C₂	semidirect
11. C₁₃×#1968	C₂	semidirect
12. C₁₃×#1923	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1877	C₂	semidirect
15. C₁₃×#1864	C₂	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₁₃×#106	C₂²	semidirect
33. C₂×C₁₃×#106	C₂²	semidirect
34. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
37. C₂×C₁₃×#103	C₂²	semidirect
38. C₂×C₁₃×#103	C₂²	semidirect
45. C₂×C₄×C₈×C₁₃	C₂²	semidirect
48. C₁₃×#391	C₂²	semidirect
52. C₁₃×#389	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#336	C₂²	semidirect
62. C₁₃×#336	C₂²	semidirect
151. #25156	C₁₃	direct (N × H)
257. C₁₃×C₂²⋊C₄	SD₁₆	semidirect
263. C₂×#461	C₂×C₁₃	semidirect
266. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
267. #2429	C₂×C₁₃	semidirect
269. #2065	C₂×C₁₃	semidirect
270. #2035	C₂×C₁₃	semidirect
271. #2035	C₂×C₁₃	semidirect
272. #2013	C₂×C₁₃	semidirect
273. #1968	C₂×C₁₃	semidirect
274. #1923	C₂×C₁₃	semidirect
275. #1880	C₂×C₁₃	semidirect
276. #1877	C₂×C₁₃	semidirect
277. #1864	C₂×C₁₃	semidirect
378. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
381. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
389. C₂×#106	C₂²×C₁₃	semidirect
390. C₂×#106	C₂²×C₁₃	semidirect
391. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
392. C₂×#103	C₂²×C₁₃	semidirect
393. C₂×#103	C₂²×C₁₃	semidirect
394. C₂×#103	C₂²×C₁₃	semidirect
395. C₂×#103	C₂²×C₁₃	semidirect
402. C₂×C₄×C₈	C₂²×C₁₃	semidirect
405. #391	C₂²×C₁₃	semidirect
409. #389	C₂²×C₁₃	semidirect
416. #340	C₂²×C₁₃	semidirect
417. #340	C₂²×C₁₃	semidirect
418. #336	C₂²×C₁₃	semidirect
419. #336	C₂²×C₁₃	semidirect
667. C₂²⋊C₄	C₁₃×SD₁₆	semidirect
673. C₁₃	#25156	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×C₁₃×#461	2
C₂×C₁₃×#450	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2429	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2065	2
C₁₃×#2035	2
C₁₃×#2013	2
C₁₃×#1968	2
C₁₃×#1923	2
C₁₃×#1880	2
C₁₃×#1877	2
C₁₃×#1864	2
#25156	13

Subgroups — C13×#25156 #15711495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25156 #15711495