Subgroups — C₁₃×#22122 #15708461

Order 3328.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#478	C₄	1	8	yes	complemented
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#389	—	2	1	no	—
34	C₁₃×#389	—	2	1	no	—
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	2	1	no	—
40	C₁₃×#388	—	2	1	no	—
41	C₁₃×#387	—	2	1	no	—
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#384	C₂²	1	1	yes	characteristic
44	C₁₃×#381	—	2	1	no	—
45	C₁₃×#380	—	2	1	no	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₁₃×#376	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	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×#336	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	C₂×C₄	1	4	yes	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	C₂×C₄	1	4	yes	—
97	C₁₃×#106	—	4	1	no	—
98	C₁₃×#106	—	4	1	no	—
99	C₁₃×#106	C₂×C₄	1	4	yes	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
102	C₁₃×#102	—	4	1	no	—
103	C₁₃×#102	—	4	1	no	—
104	C₁₃×#102	C₂×C₄	1	4	yes	—
105	C₁₃×#102	C₂×C₄	1	4	yes	—
106	C₁₃×#97	—	4	1	no	—
107	C₄×C₈×C₁₃	—	4	1	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	D₄	1	1	yes	characteristic
116	C₁₃×#95	D₄	1	1	yes	characteristic
117	C₁₃×#95	D₄	1	1	yes	characteristic
118	C₁₃×#95	D₄	1	1	yes	characteristic
119	#22122	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	8	1	no	—
136	C₂²×C₄×C₁₃	—	8	1	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	8	1	no	—
170	C₁₃×C₄⋊C₄	—	8	1	no	—
171	C₁₃×C₄⋊C₄	—	8	1	no	—
172	C₁₃×C₄⋊C₄	—	8	1	no	—
173	C₁₃×C₄⋊C₄	—	8	1	no	—
174	C₁₃×C₄⋊C₄	—	8	1	no	—
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
178	C₁₃×C₂²⋊C₄	—	2	4	no	—
179	C₁₃×C₂²⋊C₄	—	8	1	no	—
180	C₁₃×C₂²⋊C₄	—	8	1	no	—
181	C₁₃×C₂²⋊C₄	—	8	1	no	—
182	C₁₃×C₂²⋊C₄	—	8	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	8	1	no	—
188	C₄²×C₁₃	—	8	1	no	—
189	C₄²×C₁₃	—	8	1	no	—
190	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
191	C₄²×C₁₃	#41	1	2	yes	—
192	C₂×#478	C₂×C₁₃	1	1	yes	characteristic
193	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2319	C₂×C₁₃	1	1	yes	characteristic
195	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1936	C₂×C₁₃	1	1	yes	characteristic
200	#1934	C₂×C₁₃	1	1	yes	characteristic
201	#1926	C₂×C₁₃	1	1	yes	characteristic
202	#1926	C₂×C₁₃	1	1	yes	characteristic
203	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1802	C₂×C₁₃	1	1	yes	characteristic
206	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	4	1	no	—
218	D₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	8	4	no	—
257	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
265	C₈×C₁₃	—	2	2	no	—
266	C₈×C₁₃	—	2	2	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
271	#478	C₄×C₁₃	1	8	yes	complemented
272	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
284	#390	C₂²×C₁₃	1	1	yes	characteristic
285	#390	C₂²×C₁₃	1	1	yes	characteristic
286	#389	—	2	1	no	—
287	#389	—	2	1	no	—
288	#389	C₂²×C₁₃	1	1	yes	characteristic
289	#389	C₂²×C₁₃	1	1	yes	characteristic
290	#389	C₂²×C₁₃	1	1	yes	characteristic
291	#389	C₂²×C₁₃	1	1	yes	characteristic
292	#388	—	2	1	no	—
293	#388	—	2	1	no	—
294	#387	—	2	1	no	—
295	#387	—	2	1	no	—
296	#384	C₂²×C₁₃	1	1	yes	characteristic
297	#381	—	2	1	no	—
298	#380	—	2	1	no	—
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	#376	C₂²×C₁₃	1	1	yes	characteristic
303	#340	C₂²×C₁₃	1	1	yes	characteristic
304	#340	C₂²×C₁₃	1	1	yes	characteristic
305	#340	C₂²×C₁₃	1	1	yes	characteristic
306	#340	C₂²×C₁₃	1	1	yes	characteristic
307	#340	C₂²×C₁₃	1	1	yes	characteristic
308	#340	C₂²×C₁₃	1	1	yes	characteristic
309	#340	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#336	C₂²×C₁₃	1	1	yes	characteristic
312	#336	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	8	1	no	—
317	C₂²×C₁₃	—	8	1	no	—
318	C₂²×C₁₃	—	8	1	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
321	C₂²×C₁₃	#536	1	1	yes	characteristic
322	C₂²×C₁₃	#537	1	1	yes	characteristic
323	C₂²×C₁₃	#576	1	1	yes	characteristic
324	C₂²×C₁₃	#577	1	1	yes	characteristic
325	C₂²×C₁₃	#577	1	1	yes	characteristic
326	C₂²×C₁₃	#577	1	1	yes	characteristic
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	#519	1	1	yes	characteristic
341	C₄×C₁₃	#520	1	1	yes	characteristic
342	C₄×C₁₃	#541	1	1	yes	characteristic
343	C₄×C₁₃	#542	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
350	#125	—	2	2	no	—
351	#125	C₂×C₄×C₁₃	1	4	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	#107	C₂×C₄×C₁₃	1	4	yes	—
381	#106	—	4	1	no	—
382	#106	—	4	1	no	—
383	#106	C₂×C₄×C₁₃	1	4	yes	—
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
386	#102	—	4	1	no	—
387	#102	—	4	1	no	—
388	#102	C₂×C₄×C₁₃	1	4	yes	—
389	#102	C₂×C₄×C₁₃	1	4	yes	—
390	#97	—	4	1	no	—
391	C₄×C₈	—	4	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	D₄×C₁₃	1	1	yes	characteristic
400	#95	D₄×C₁₃	1	1	yes	characteristic
401	#95	D₄×C₁₃	1	1	yes	characteristic
402	#95	D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₁₃	—	8	2	no	—
404	C₂×C₁₃	#2323	1	1	yes	characteristic
405	C₂×C₁₃	#2946	1	1	yes	characteristic
406	C₂×C₁₃	#2952	1	1	yes	characteristic
407	C₂×C₁₃	#3241	1	1	yes	characteristic
408	C₂×C₁₃	#3244	1	1	yes	characteristic
409	C₂×C₁₃	#3257	1	1	yes	characteristic
410	C₂×C₁₃	#3260	1	1	yes	characteristic
411	C₂⁴	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	8	1	no	—
427	C₂²×C₄	—	8	1	no	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
446	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	8	1	no	—
461	C₄⋊C₄	—	8	1	no	—
462	C₄⋊C₄	—	8	1	no	—
463	C₄⋊C₄	—	8	1	no	—
464	C₄⋊C₄	—	8	1	no	—
465	C₄⋊C₄	—	8	1	no	—
466	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
467	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
468	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	8	1	no	—
471	C₂²⋊C₄	—	8	1	no	—
472	C₂²⋊C₄	—	8	1	no	—
473	C₂²⋊C₄	—	8	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	8	1	no	—
479	C₄²	—	8	1	no	—
480	C₄²	—	8	1	no	—
481	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
482	C₄²	C₁₃×#41	1	2	yes	—
483	C₁₃	#22122	1	1	yes	characteristic, direct product factor, Sylow
484	C₂³	—	2	2	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
535	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
536	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
537	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
538	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
540	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
554	C₂²	C₁₃×#536	1	1	yes	characteristic
555	C₂²	C₁₃×#537	1	1	yes	characteristic
556	C₂²	C₁₃×#576	1	1	yes	characteristic
557	C₂²	C₁₃×#577	1	1	yes	characteristic
558	C₂²	C₁₃×#577	1	1	yes	characteristic
559	C₂²	C₁₃×#577	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₁₃×#519	1	1	yes	characteristic
574	C₄	C₁₃×#520	1	1	yes	characteristic
575	C₄	C₁₃×#541	1	1	yes	characteristic
576	C₄	C₁₃×#542	1	1	yes	characteristic
577	C₂	—	8	2	no	—
578	C₂	C₁₃×#2323	1	1	yes	characteristic
579	C₂	C₁₃×#2946	1	1	yes	characteristic
580	C₂	C₁₃×#2952	1	1	yes	characteristic
581	C₂	C₁₃×#3241	1	1	yes	characteristic
582	C₂	C₁₃×#3244	1	1	yes	characteristic
583	C₂	C₁₃×#3257	1	1	yes	characteristic
584	C₂	C₁₃×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2330	C₂	semidirect
4. C₁₃×#1989	C₂	semidirect
5. C₁₃×#1948	C₂	semidirect
6. C₁₃×#1943	C₂	semidirect
7. C₁₃×#1941	C₂	semidirect
12. C₁₃×#1920	C₂	semidirect
13. C₁₃×#1918	C₂	semidirect
15. C₁₃×#1768	C₂	semidirect
18. C₁₃×#478	C₄	semidirect
119. #22122	C₁₃	direct (N × H)
193. #2330	C₂×C₁₃	semidirect
195. #1989	C₂×C₁₃	semidirect
196. #1948	C₂×C₁₃	semidirect
197. #1943	C₂×C₁₃	semidirect
198. #1941	C₂×C₁₃	semidirect
203. #1920	C₂×C₁₃	semidirect
204. #1918	C₂×C₁₃	semidirect
206. #1768	C₂×C₁₃	semidirect
271. #478	C₄×C₁₃	semidirect
483. C₁₃	#22122	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×#478	2
C₁₃×#2330	2
C₁₃×#2319	2
C₁₃×#1989	2
C₁₃×#1948	2
C₁₃×#1943	2
C₁₃×#1941	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1920	2
C₁₃×#1918	2
C₁₃×#1802	2
C₁₃×#1768	2
#22122	13

Subgroups — C13×#22122 #15708461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22122 #15708461