Subgroups — C₁₃×#25908 #15712247

Order 3328.

1320 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1993	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1874	C₂	1	2	yes	maximal
8	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#489	—	2	8	no	—
23	C₂×C₁₃×#103	C₂²	1	4	yes	—
24	C₂×C₁₃×#102	C₂²	1	4	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	C₂²	1	2	yes	—
27	C₁₃×#391	C₂²	1	1	yes	characteristic
28	C₁₃×#390	C₂²	1	1	yes	characteristic
29	C₁₃×#388	—	2	1	no	—
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#386	—	2	1	no	—
32	C₁₃×#386	—	2	1	no	—
33	C₁₃×#382	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#340	C₂²	1	4	yes	—
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	8	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	4	4	no	—
41	C₂²×Q₈×C₁₃	—	4	4	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
50	C₁₃×C₄⋊Q₈	—	2	8	no	—
51	C₁₃×C₄⋊Q₈	—	2	8	no	—
52	C₁₃×C₄⋊Q₈	—	2	8	no	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	8	yes	complemented
55	C₁₃×#124	—	2	4	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×#121	—	2	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	4	no	—
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#103	—	2	8	no	—
79	C₁₃×#102	—	2	8	no	—
80	C₁₃×C₂²⋊C₈	—	2	4	no	—
81	C₁₃×#97	—	2	4	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	#25908	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	1	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	2	8	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	4	32	no	—
95	C₂×Q₈×C₁₃	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	4	4	no	—
97	C₂×Q₈×C₁₃	—	4	4	no	—
98	C₂×Q₈×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	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	8	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	4	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₁₃	—	2	4	no	—
128	C₂×C₈×C₁₃	—	2	4	no	—
129	C₂×C₈×C₁₃	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
138	C₁₃×C₂²⋊C₄	—	4	2	no	—
139	C₁₃×C₂²⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#489	C₂×C₁₃	1	2	yes	complemented
150	#2850	C₂×C₁₃	1	1	yes	characteristic
151	#2024	C₂×C₁₃	1	2	yes	complemented
152	#2023	C₂×C₁₃	1	2	yes	complemented
153	#1993	C₂×C₁₃	1	2	yes	complemented
154	#1874	C₂×C₁₃	1	2	yes	—
155	#1872	C₂×C₁₃	1	2	yes	complemented
156	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	#124	1	2	yes	—
169	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
170	C₂³×C₁₃	#137	1	2	yes	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₃	—	4	16	no	—
173	Q₈×C₁₃	—	4	16	no	—
174	Q₈×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	4	16	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	#120	1	2	yes	—
204	C₂×C₄×C₁₃	#120	1	2	yes	—
205	C₂×C₄×C₁₃	#124	1	2	yes	—
206	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
207	C₂×C₄×C₁₃	#137	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
211	C₈×C₁₃	—	4	4	no	—
212	C₂³×Q₈	—	2	1	no	—
213	C₂×C₄⋊Q₈	—	2	8	no	—
214	C₂×C₄⋊Q₈	—	2	1	no	—
215	C₂×C₄⋊Q₈	—	2	1	no	—
216	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
218	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	—	2	1	no	—
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
224	#489	—	2	8	no	—
225	C₂×#103	C₂²×C₁₃	1	4	yes	—
226	C₂×#102	C₂²×C₁₃	1	4	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#97	C₂²×C₁₃	1	2	yes	—
229	#391	C₂²×C₁₃	1	1	yes	characteristic
230	#390	C₂²×C₁₃	1	1	yes	characteristic
231	#388	—	2	1	no	—
232	#388	—	2	1	no	—
233	#386	—	2	1	no	—
234	#386	—	2	1	no	—
235	#382	C₂²×C₁₃	1	1	yes	characteristic
236	#340	C₂²×C₁₃	1	4	yes	—
237	#340	C₂²×C₁₃	1	4	yes	—
238	#336	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	8	1	no	—
246	C₂²×C₁₃	—	8	1	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	—	8	1	no	—
252	C₂²×C₁₃	#489	1	4	yes	complemented
253	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
255	C₂²×C₁₃	#536	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
259	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	2	2	no	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	4	8	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	1	no	—
269	C₄×C₁₃	#548	1	4	yes	—
270	C₂²×Q₈	—	2	8	no	—
271	C₂²×Q₈	—	2	2	no	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	4	4	no	—
274	C₂²×Q₈	—	4	4	no	—
275	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
283	C₄⋊Q₈	—	2	8	no	—
284	C₄⋊Q₈	—	2	8	no	—
285	C₄⋊Q₈	—	2	8	no	—
286	C₄⋊Q₈	—	2	4	no	—
287	C₄⋊Q₈	D₄×C₁₃	1	8	yes	complemented
288	#124	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	#121	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	8	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	4	no	—
307	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	#103	—	2	8	no	—
312	#102	—	2	8	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	#97	—	2	4	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	C₂×C₁₃	—	2	4	no	—
320	C₂×C₁₃	—	16	1	no	—
321	C₂×C₁₃	#2436	1	1	yes	characteristic
322	C₂×C₁₃	#3003	1	1	yes	characteristic
323	C₂×C₁₃	#3004	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
325	C₂×C₁₃	#3141	1	1	yes	characteristic
326	C₂×C₁₃	#3238	1	1	yes	characteristic
327	C₂×C₁₃	#3239	1	1	yes	characteristic
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×Q₈	—	2	8	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	32	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₁₃×#41	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	C₂×D₄×C₁₃	1	4	yes	—
389	C₁₃	#25908	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	C₁₃×#124	1	2	yes	—
402	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
403	C₂³	C₁₃×#137	1	2	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
405	Q₈	—	4	16	no	—
406	Q₈	—	4	16	no	—
407	Q₈	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	8	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	C₁₃×#120	1	2	yes	—
437	C₂×C₄	C₁₃×#120	1	2	yes	—
438	C₂×C₄	C₁₃×#124	1	2	yes	—
439	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
440	C₂×C₄	C₁₃×#137	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
442	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
443	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
444	C₈	—	4	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	C₁₃×#489	1	4	yes	complemented
459	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
460	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
461	C₂²	C₁₃×#536	1	1	yes	characteristic
462	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
465	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	8	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	1	no	—
475	C₄	C₁₃×#548	1	4	yes	—
476	C₂	—	2	4	no	—
477	C₂	—	16	1	no	—
478	C₂	C₁₃×#2436	1	1	yes	characteristic
479	C₂	C₁₃×#3003	1	1	yes	characteristic
480	C₂	C₁₃×#3004	1	1	yes	characteristic
481	C₂	C₂×C₁₃×#489	1	1	yes	characteristic
482	C₂	C₁₃×#3141	1	1	yes	characteristic
483	C₂	C₁₃×#3238	1	1	yes	characteristic
484	C₂	C₁₃×#3239	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
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
2. C₂×C₁₃×#489	C₂	semidirect
4. C₁₃×#2024	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
6. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1872	C₂	semidirect
9. C₁₃×#1749	C₂	semidirect
54. C₁₃×C₄⋊Q₈	D₄	semidirect
86. #25908	C₁₃	direct (N × H)
148. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
149. C₂×#489	C₂×C₁₃	semidirect
151. #2024	C₂×C₁₃	semidirect
152. #2023	C₂×C₁₃	semidirect
153. #1993	C₂×C₁₃	semidirect
155. #1872	C₂×C₁₃	semidirect
156. #1749	C₂×C₁₃	semidirect
252. C₂²×C₁₃	#489	semidirect
287. C₄⋊Q₈	D₄×C₁₃	semidirect
389. C₁₃	#25908	direct (N × H)
458. C₂²	C₁₃×#489	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#489	2
C₁₃×#2850	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1993	2
C₁₃×#1874	2
C₁₃×#1872	2
C₁₃×#1749	2
#25908	13

Subgroups — C13×#25908 #15712247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25908 #15712247