Subgroups — C₁₃×#25016 #15711355

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#484	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2076	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₁₃×#484	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#396	—	2	2	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₁₃×#380	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₂²⋊Q₈	—	2	4	no	—
50	C₁₃×C₂²⋊Q₈	—	4	2	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	4	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	4	no	—
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×#107	—	4	2	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	D₄	1	4	yes	complemented
85	C₁₃×C₂²⋊C₈	—	2	4	no	—
86	C₁₃×C₂²⋊C₈	—	2	4	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	#25016	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	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	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	8	2	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	4	4	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	8	1	no	—
146	C₁₃×C₄⋊C₄	—	8	1	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₁₃×C₂²⋊C₄	—	8	2	no	—
152	C₄²×C₁₃	—	4	2	no	—
153	C₄²×C₁₃	—	4	2	no	—
154	C₄²×C₁₃	#41	1	2	yes	—
155	C₄²×C₁₃	#41	1	2	yes	—
156	C₂×#484	C₂×C₁₃	1	2	yes	complemented
157	#2538	C₂×C₁₃	1	1	yes	characteristic
158	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
159	#2076	C₂×C₁₃	1	2	yes	complemented
160	#2036	C₂×C₁₃	1	2	yes	complemented
161	#1954	C₂×C₁₃	1	1	yes	characteristic
162	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1852	C₂×C₁₃	1	2	yes	complemented
164	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
174	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	4	1	no	—
178	Q₈×C₁₃	—	4	1	no	—
179	D₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	8	8	no	—
208	C₂×C₄×C₁₃	#123	1	2	yes	—
209	C₂×C₄×C₁₃	#123	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
211	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
226	#484	—	2	8	no	—
227	C₂×#107	C₂²×C₁₃	1	2	yes	—
228	C₂×#107	C₂²×C₁₃	1	2	yes	—
229	C₂×#107	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
237	#396	—	2	2	no	—
238	#390	—	2	1	no	—
239	#389	—	2	1	no	—
240	#389	—	2	1	no	—
241	#385	—	2	2	no	—
242	#384	C₂²×C₁₃	1	1	yes	characteristic
243	#384	C₂²×C₁₃	1	1	yes	characteristic
244	#380	C₂²×C₁₃	1	2	yes	—
245	#380	C₂²×C₁₃	1	2	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	#340	C₂²×C₁₃	1	2	yes	—
248	#340	C₂²×C₁₃	1	1	yes	characteristic
249	#340	C₂²×C₁₃	1	2	yes	—
250	#340	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	2	4	no	—
253	C₂²×C₁₃	—	2	4	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
259	C₂²×C₁₃	D₄²	1	1	yes	characteristic
260	C₂²×C₁₃	#547	1	1	yes	characteristic
261	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₁₃	#576	1	1	yes	characteristic
264	C₂²×C₁₃	#578	1	1	yes	characteristic
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	8	1	no	—
270	C₄×C₁₃	—	8	1	no	—
271	C₄×C₁₃	—	8	2	no	—
272	C₄×C₁₃	—	8	2	no	—
273	C₄×C₁₃	#484	1	4	yes	complemented
274	C₄×C₁₃	#532	1	1	yes	characteristic
275	C₄×C₁₃	#542	1	1	yes	characteristic
276	C₄×C₁₃	#547	1	1	yes	characteristic
277	C₄×C₁₃	#553	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	4	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	4	4	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
314	#107	—	2	4	no	—
315	#107	—	2	4	no	—
316	#107	—	4	2	no	—
317	C₄⋊C₈	—	2	2	no	—
318	#103	—	2	4	no	—
319	#103	—	2	2	no	—
320	#103	D₄×C₁₃	1	4	yes	complemented
321	C₂²⋊C₈	—	2	4	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	C₂×C₁₃	—	4	4	no	—
328	C₂×C₁₃	#2422	1	1	yes	characteristic
329	C₂×C₁₃	C₂×#484	1	1	yes	characteristic
330	C₂×C₁₃	#3098	1	1	yes	characteristic
331	C₂×C₁₃	#3274	1	1	yes	characteristic
332	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
333	C₂×C₁₃	#3338	1	1	yes	characteristic
334	C₂×C₁₃	#3353	1	1	yes	characteristic
335	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	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	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	8	2	no	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
372	C₂×C₈	C₁₃×#41	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	8	1	no	—
389	C₄⋊C₄	—	8	1	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	4	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	C₁₃×#41	1	2	yes	—
398	C₄²	C₁₃×#41	1	2	yes	—
399	C₁₃	#25016	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
407	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	1	no	—
412	D₄	—	2	8	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	8	8	no	—
441	C₂×C₄	C₁₃×#123	1	2	yes	—
442	C₂×C₄	C₁₃×#123	1	2	yes	—
443	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
444	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
449	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
462	C₂²	D₄²×C₁₃	1	1	yes	characteristic
463	C₂²	C₁₃×#547	1	1	yes	characteristic
464	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
465	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂²	C₁₃×#576	1	1	yes	characteristic
467	C₂²	C₁₃×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	C₁₃×#484	1	4	yes	complemented
477	C₄	C₁₃×#532	1	1	yes	characteristic
478	C₄	C₁₃×#542	1	1	yes	characteristic
479	C₄	C₁₃×#547	1	1	yes	characteristic
480	C₄	C₁₃×#553	1	1	yes	characteristic
481	C₂	—	4	4	no	—
482	C₂	C₁₃×#2422	1	1	yes	characteristic
483	C₂	C₂×C₁₃×#484	1	1	yes	characteristic
484	C₂	C₁₃×#3098	1	1	yes	characteristic
485	C₂	C₁₃×#3274	1	1	yes	characteristic
486	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
487	C₂	C₁₃×#3338	1	1	yes	characteristic
488	C₂	C₁₃×#3353	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#484	C₂	semidirect
4. C₁₃×#2076	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
7. C₁₃×#1947	C₂	semidirect
8. C₁₃×#1852	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
10. C₁₃×#1803	C₂	semidirect
11. C₄×C₁₃×#103	C₂	semidirect
84. C₁₃×#103	D₄	semidirect
91. #25016	C₁₃	direct (N × H)
156. C₂×#484	C₂×C₁₃	semidirect
159. #2076	C₂×C₁₃	semidirect
160. #2036	C₂×C₁₃	semidirect
162. #1947	C₂×C₁₃	semidirect
163. #1852	C₂×C₁₃	semidirect
164. #1845	C₂×C₁₃	semidirect
165. #1803	C₂×C₁₃	semidirect
166. C₄×#103	C₂×C₁₃	semidirect
273. C₄×C₁₃	#484	semidirect
320. #103	D₄×C₁₃	semidirect
399. C₁₃	#25016	direct (N × H)
476. C₄	C₁₃×#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#484	2
C₁₃×#2538	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2076	2
C₁₃×#2036	2
C₁₃×#1954	2
C₁₃×#1947	2
C₁₃×#1852	2
C₁₃×#1845	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#25016	13

Subgroups — C13×#25016 #15711355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25016 #15711355