Subgroups — C₁₃×#26798 #15713137

Order 3328.

880 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₁₃×#482	—	2	4	no	—
23	C₁₃×#478	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#397	—	2	1	no	—
40	C₁₃×#394	—	2	1	no	—
41	C₁₃×#390	—	2	1	no	—
42	C₁₃×#390	—	2	1	no	—
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#386	—	2	1	no	—
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×D₈	—	2	2	no	—
68	C₂×C₁₃×D₈	—	2	2	no	—
69	C₂×C₁₃×D₈	—	4	1	no	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	—	4	1	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	4	1	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	4	1	no	—
82	C₁₃×#117	—	2	2	no	—
83	C₁₃×#117	—	4	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#107	—	2	2	no	—
112	C₁₃×#107	—	4	1	no	—
113	C₁₃×#107	D₄	1	4	yes	complemented
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×#102	—	2	2	no	—
118	C₁₃×#102	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×C₂²⋊C₈	—	2	2	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₄×C₈×C₁₃	—	2	2	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	#26798	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	4	2	no	—
149	C₂×D₄×C₁₃	—	4	2	no	—
150	C₂×D₄×C₁₃	—	8	1	no	—
151	C₂×D₄×C₁₃	—	8	1	no	—
152	C₂×D₄×C₁₃	—	8	1	no	—
153	C₂×D₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	8	1	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×D₈	—	4	4	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₁₃	#41	1	2	yes	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	8	1	no	—
200	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₄⋊C₄	#41	1	2	yes	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	—	8	1	no	—
212	C₁₃×C₂²⋊C₄	—	8	1	no	—
213	C₁₃×C₂²⋊C₄	—	8	1	no	—
214	C₁₃×C₂²⋊C₄	—	8	1	no	—
215	C₁₃×C₂²⋊C₄	—	8	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	2	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	4	2	no	—
221	C₄²×C₁₃	—	8	1	no	—
222	C₄²×C₁₃	—	8	1	no	—
223	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2490	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1999	C₂×C₁₃	1	1	yes	characteristic
231	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1923	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	D₄×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	1	no	—
265	D₄×C₁₃	—	4	1	no	—
266	D₄×C₁₃	—	4	1	no	—
267	D₄×C₁₃	—	4	1	no	—
268	D₄×C₁₃	—	8	4	no	—
269	D₄×C₁₃	—	8	4	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	8	4	no	—
307	C₂×C₄×C₁₃	#135	1	2	yes	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
314	C₈×C₁₃	—	2	2	no	—
315	C₈×C₁₃	—	2	2	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
324	#482	—	2	4	no	—
325	#478	—	2	4	no	—
326	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
341	#397	—	2	1	no	—
342	#394	—	2	1	no	—
343	#390	—	2	1	no	—
344	#390	—	2	1	no	—
345	#390	C₂²×C₁₃	1	1	yes	characteristic
346	#390	C₂²×C₁₃	1	1	yes	characteristic
347	#390	C₂²×C₁₃	1	1	yes	characteristic
348	#389	C₂²×C₁₃	1	1	yes	characteristic
349	#388	—	2	1	no	—
350	#388	—	2	1	no	—
351	#386	—	2	1	no	—
352	#380	C₂²×C₁₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
354	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	—	2	1	no	—
356	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#340	C₂²×C₁₃	1	1	yes	characteristic
360	#340	C₂²×C₁₃	1	1	yes	characteristic
361	#336	C₂²×C₁₃	1	1	yes	characteristic
362	#336	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	2	no	—
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	1	no	—
373	C₂²×C₁₃	—	8	1	no	—
374	C₂²×C₁₃	—	8	1	no	—
375	C₂²×C₁₃	—	8	1	no	—
376	C₂²×C₁₃	—	8	1	no	—
377	C₂²×C₁₃	—	8	1	no	—
378	C₂²×C₁₃	—	8	1	no	—
379	C₂²×C₁₃	—	8	1	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	8	1	no	—
384	C₂²×C₁₃	#525	1	1	yes	characteristic
385	C₂²×C₁₃	D₄²	1	1	yes	characteristic
386	C₂²×C₁₃	#547	1	1	yes	characteristic
387	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
388	C₂²×C₁₃	#575	1	1	yes	characteristic
389	C₂²×C₁₃	#576	1	1	yes	characteristic
390	C₂²×C₁₃	#576	1	1	yes	characteristic
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	4	1	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	4	1	no	—
396	C₄×C₁₃	—	4	2	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	8	1	no	—
400	C₄×C₁₃	—	8	1	no	—
401	C₄×C₁₃	—	8	1	no	—
402	C₄×C₁₃	#532	1	1	yes	characteristic
403	C₄×C₁₃	#542	1	1	yes	characteristic
404	C₄×C₁₃	#548	1	1	yes	characteristic
405	C₄×C₁₃	#551	1	1	yes	characteristic
406	C₂²×D₄	—	2	1	no	—
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂³×C₄	—	2	1	no	—
411	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×D₈	—	2	2	no	—
413	C₂×D₈	—	2	2	no	—
414	C₂×D₈	—	4	1	no	—
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	#125	—	2	2	no	—
420	#125	—	4	1	no	—
421	#121	—	2	2	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#121	—	4	1	no	—
425	C₄×D₄	—	2	2	no	—
426	C₄×D₄	—	4	1	no	—
427	#117	—	2	2	no	—
428	#117	—	4	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
456	#107	—	2	2	no	—
457	#107	—	4	1	no	—
458	#107	D₄×C₁₃	1	4	yes	complemented
459	#106	—	2	2	no	—
460	#106	—	2	2	no	—
461	C₄⋊C₈	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	C₄×C₈	—	2	2	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	D₄×C₁₃	1	1	yes	characteristic
476	#95	D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₁₃	—	8	1	no	—
478	C₂×C₁₃	—	8	2	no	—
479	C₂×C₁₃	—	16	1	no	—
480	C₂×C₁₃	#2461	1	1	yes	characteristic
481	C₂×C₁₃	#3102	1	1	yes	characteristic
482	C₂×C₁₃	#3122	1	1	yes	characteristic
483	C₂×C₁₃	#3273	1	1	yes	characteristic
484	C₂×C₁₃	#3287	1	1	yes	characteristic
485	C₂×C₁₃	#3339	1	1	yes	characteristic
486	C₂×C₁₃	#3347	1	1	yes	characteristic
487	C₂⁴	—	2	1	no	—
488	C₂⁴	—	2	1	no	—
489	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	8	1	no	—
505	C₂×D₄	—	8	1	no	—
506	C₂×D₄	—	8	1	no	—
507	C₂×D₄	C₁₃×#41	1	2	yes	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	D₈	—	4	4	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
541	C₂×C₈	C₁₃×#41	1	2	yes	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	8	1	no	—
554	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
556	C₄⋊C₄	C₁₃×#41	1	2	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	4	1	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	8	1	no	—
566	C₂²⋊C₄	—	8	1	no	—
567	C₂²⋊C₄	—	8	1	no	—
568	C₂²⋊C₄	—	8	1	no	—
569	C₂²⋊C₄	—	8	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	4	2	no	—
575	C₄²	—	8	1	no	—
576	C₄²	—	8	1	no	—
577	C₁₃	#26798	1	1	yes	characteristic, direct product factor, Sylow
578	C₂³	—	2	2	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	8	4	no	—
609	D₄	—	8	4	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₁₃×#135	1	2	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
650	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
651	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
652	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	C₁₃×#525	1	1	yes	characteristic
680	C₂²	D₄²×C₁₃	1	1	yes	characteristic
681	C₂²	C₁₃×#547	1	1	yes	characteristic
682	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
683	C₂²	C₁₃×#575	1	1	yes	characteristic
684	C₂²	C₁₃×#576	1	1	yes	characteristic
685	C₂²	C₁₃×#576	1	1	yes	characteristic
686	C₄	—	2	2	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	C₁₃×#532	1	1	yes	characteristic
698	C₄	C₁₃×#542	1	1	yes	characteristic
699	C₄	C₁₃×#548	1	1	yes	characteristic
700	C₄	C₁₃×#551	1	1	yes	characteristic
701	C₂	—	8	1	no	—
702	C₂	—	8	2	no	—
703	C₂	—	16	1	no	—
704	C₂	C₁₃×#2461	1	1	yes	characteristic
705	C₂	C₁₃×#3102	1	1	yes	characteristic
706	C₂	C₁₃×#3122	1	1	yes	characteristic
707	C₂	C₁₃×#3273	1	1	yes	characteristic
708	C₂	C₁₃×#3287	1	1	yes	characteristic
709	C₂	C₁₃×#3339	1	1	yes	characteristic
710	C₂	C₁₃×#3347	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#1999	C₂
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×#482	C₂	semidirect
2. C₂×C₁₃×#478	C₂	semidirect
3. C₁₃×#2490	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2059	C₂	semidirect
7. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1970	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1926	C₂	semidirect
12. C₁₃×#1923	C₂	semidirect
13. C₁₃×#1879	C₂	semidirect
14. C₁₃×#1854	C₂	semidirect
15. C₄×C₁₃×#107	C₂	semidirect
113. C₁₃×#107	D₄	semidirect
132. #26798	C₁₃	direct (N × H)
223. C₂×#482	C₂×C₁₃	semidirect
224. C₂×#478	C₂×C₁₃	semidirect
225. #2490	C₂×C₁₃	semidirect
226. #2363	C₂×C₁₃	semidirect
227. #2067	C₂×C₁₃	semidirect
228. #2059	C₂×C₁₃	semidirect
229. #2033	C₂×C₁₃	semidirect
231. #1970	C₂×C₁₃	semidirect
232. #1926	C₂×C₁₃	semidirect
233. #1926	C₂×C₁₃	semidirect
234. #1923	C₂×C₁₃	semidirect
235. #1879	C₂×C₁₃	semidirect
236. #1854	C₂×C₁₃	semidirect
237. C₄×#107	C₂×C₁₃	semidirect
458. #107	D₄×C₁₃	semidirect
577. C₁₃	#26798	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×#482	2
C₂×C₁₃×#478	2
C₁₃×#2490	2
C₁₃×#2363	2
C₁₃×#2067	2
C₁₃×#2059	2
C₁₃×#2033	2
C₁₃×#1999	2
C₁₃×#1970	2
C₁₃×#1926	2
C₁₃×#1923	2
C₁₃×#1879	2
C₁₃×#1854	2
C₄×C₁₃×#107	2
#26798	13

Subgroups — C13×#26798 #15713137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26798 #15713137