Subgroups — C₁₃×#24608 #15710947

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2087	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1944	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#123	—	2	1	no	—
13	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#480	—	2	4	no	—
19	C₁₃×#432	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#388	—	2	1	no	—
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#386	—	2	1	no	—
39	C₁₃×#380	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#95	—	2	1	no	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#123	—	4	4	no	—
55	C₁₃×#121	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	2	no	—
80	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	—	2	4	no	—
85	C₁₃×#106	—	2	4	no	—
86	C₁₃×C₄⋊C₈	—	2	4	no	—
87	C₁₃×#102	—	2	4	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₁₃×C₂²⋊C₈	D₄	1	4	yes	—
91	C₁₃×#97	—	2	4	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	#24608	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	1	no	—
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	4	4	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	#41	1	4	yes	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	2	1	no	—
166	C₂×#480	C₂×C₁₃	1	1	yes	characteristic
167	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2854	C₂×C₁₃	1	1	yes	characteristic
169	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2087	C₂×C₁₃	1	2	yes	complemented
171	#2065	C₂×C₁₃	1	2	yes	complemented
172	#1944	C₂×C₁₃	1	2	yes	complemented
173	#1936	C₂×C₁₃	1	2	yes	complemented
174	#1874	C₂×C₁₃	1	1	yes	characteristic
175	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	#121	1	2	yes	—
189	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
190	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	2	no	—
194	D₄×C₁₃	—	8	4	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	8	4	no	—
229	C₂×C₄×C₁₃	#121	1	2	yes	—
230	C₂×C₄×C₁₃	#137	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
235	C₈×C₁₃	—	2	4	no	—
236	C₈×C₁₃	—	4	2	no	—
237	C₂×#123	—	2	1	no	—
238	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	—	2	1	no	—
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
243	#480	—	2	4	no	—
244	#432	—	2	4	no	—
245	C₂×#107	C₂²×C₁₃	1	2	yes	—
246	C₂×#106	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#97	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	1	yes	characteristic
254	#390	C₂²×C₁₃	1	1	yes	characteristic
255	#389	—	2	1	no	—
256	#389	—	2	1	no	—
257	#389	C₂²×C₁₃	1	2	yes	—
258	#389	C₂²×C₁₃	1	1	yes	characteristic
259	#389	C₂²×C₁₃	1	1	yes	characteristic
260	#389	C₂²×C₁₃	1	2	yes	—
261	#388	—	2	1	no	—
262	#388	—	2	1	no	—
263	#386	—	2	1	no	—
264	#380	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#95	—	2	1	no	—
266	#340	C₂²×C₁₃	1	2	yes	—
267	#340	C₂²×C₁₃	1	2	yes	—
268	#340	C₂²×C₁₃	1	2	yes	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	—	8	1	no	—
281	C₂²×C₁₃	—	8	1	no	—
282	C₂²×C₁₃	—	8	1	no	—
283	C₂²×C₁₃	#469	1	4	yes	—
284	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
285	C₂²×C₁₃	#525	1	1	yes	characteristic
286	C₂²×C₁₃	#536	1	1	yes	characteristic
287	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
290	C₂²×C₁₃	#575	1	1	yes	characteristic
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	4	1	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	—	8	1	no	—
299	C₄×C₁₃	—	8	2	no	—
300	C₄×C₁₃	—	8	1	no	—
301	C₄×C₁₃	#547	1	2	yes	—
302	C₄×C₁₃	#552	1	2	yes	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
312	#123	—	4	4	no	—
313	#121	—	2	2	no	—
314	#121	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	4	4	no	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	#107	—	2	4	no	—
343	#106	—	2	4	no	—
344	C₄⋊C₈	—	2	4	no	—
345	#102	—	2	4	no	—
346	#102	—	2	4	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	D₄×C₁₃	1	4	yes	—
349	#97	—	2	4	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	C₂×C₁₃	—	2	4	no	—
356	C₂×C₁₃	—	16	1	no	—
357	C₂×C₁₃	#2413	1	1	yes	characteristic
358	C₂×C₁₃	C₂×#469	1	1	yes	characteristic
359	C₂×C₁₃	#3056	1	1	yes	characteristic
360	C₂×C₁₃	#3112	1	1	yes	characteristic
361	C₂×C₁₃	#3114	1	1	yes	characteristic
362	C₂×C₁₃	#3234	1	1	yes	characteristic
363	C₂×C₁₃	#3238	1	1	yes	characteristic
364	C₂⁴	—	2	1	no	—
365	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₁₃×#41	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	C₁₃×#41	1	4	yes	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₁₃	#24608	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	C₁₃×#121	1	2	yes	—
445	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
446	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
447	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	8	4	no	—
485	C₂×C₄	C₁₃×#121	1	2	yes	—
486	C₂×C₄	C₁₃×#137	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
489	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
490	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
491	C₈	—	2	4	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	C₁₃×#469	1	4	yes	—
507	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
508	C₂²	C₁₃×#525	1	1	yes	characteristic
509	C₂²	C₁₃×#536	1	1	yes	characteristic
510	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
511	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
512	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
513	C₂²	C₁₃×#575	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	4	no	—
520	C₄	—	8	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	1	no	—
524	C₄	C₁₃×#547	1	2	yes	—
525	C₄	C₁₃×#552	1	2	yes	—
526	C₂	—	2	4	no	—
527	C₂	—	16	1	no	—
528	C₂	C₁₃×#2413	1	1	yes	characteristic
529	C₂	C₂×C₁₃×#469	1	1	yes	characteristic
530	C₂	C₁₃×#3056	1	1	yes	characteristic
531	C₂	C₁₃×#3112	1	1	yes	characteristic
532	C₂	C₁₃×#3114	1	1	yes	characteristic
533	C₂	C₁₃×#3234	1	1	yes	characteristic
534	C₂	C₁₃×#3238	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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
2. C₂×C₁₃×#432	C₂	semidirect
4. C₂×C₁₃×#389	C₂	semidirect
5. C₁₃×#2087	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1944	C₂	semidirect
8. C₁₃×#1936	C₂	semidirect
10. C₁₃×#1853	C₂	semidirect
11. C₁₃×#1823	C₂	semidirect
97. #24608	C₁₃	direct (N × H)
167. C₂×#432	C₂×C₁₃	semidirect
169. C₂×#389	C₂×C₁₃	semidirect
170. #2087	C₂×C₁₃	semidirect
171. #2065	C₂×C₁₃	semidirect
172. #1944	C₂×C₁₃	semidirect
173. #1936	C₂×C₁₃	semidirect
175. #1853	C₂×C₁₃	semidirect
176. #1823	C₂×C₁₃	semidirect
432. C₁₃	#24608	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×#480	2
C₂×C₁₃×#432	2
C₁₃×#2854	2
C₂×C₁₃×#389	2
C₁₃×#2087	2
C₁₃×#2065	2
C₁₃×#1944	2
C₁₃×#1936	2
C₁₃×#1874	2
C₁₃×#1853	2
C₁₃×#1823	2
#24608	13

Subgroups — C13×#24608 #15710947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24608 #15710947