Subgroups — C₁₃×#26463 #15712802

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 474 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	2	yes	maximal, complemented
2	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#478	—	2	8	no	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#398	—	2	2	no	—
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#127	—	2	2	no	—
50	C₁₃×#127	Q₈	1	4	yes	—
51	C₁₃×#125	—	2	4	no	—
52	C₁₃×#125	—	4	2	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₄×D₄×C₁₃	—	4	2	no	—
55	C₄×D₄×C₁₃	—	4	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#106	—	2	2	no	—
77	C₁₃×#106	D₄	1	4	yes	complemented
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#102	—	4	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	D₄	1	2	yes	—
89	#26463	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	8	1	no	—
101	C₂×D₄×C₁₃	—	8	1	no	—
102	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	8	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	8	1	no	—
138	C₁₃×C₄⋊C₄	—	8	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
141	C₁₃×C₄⋊C₄	#41	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
150	C₄²×C₁₃	#41	1	2	yes	—
151	C₂×#478	C₂×C₁₃	1	2	yes	complemented
152	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2366	C₂×C₁₃	1	1	yes	characteristic
154	#2065	C₂×C₁₃	1	2	yes	complemented
155	#2025	C₂×C₁₃	1	2	yes	complemented
156	#1982	C₂×C₁₃	1	1	yes	characteristic
157	#1957	C₂×C₁₃	1	1	yes	characteristic
158	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1862	C₂×C₁₃	1	2	yes	complemented
161	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	8	no	—
175	D₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	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	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	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	—	8	8	no	—
200	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
202	C₂×C₄×C₁₃	#135	1	2	yes	—
203	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#125	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
217	#478	—	2	8	no	—
218	C₂×#107	C₂²×C₁₃	1	2	yes	—
219	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#102	C₂²×C₁₃	1	2	yes	—
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
228	#398	—	2	2	no	—
229	#390	—	2	1	no	—
230	#390	C₂²×C₁₃	1	2	yes	—
231	#389	—	2	1	no	—
232	#389	C₂²×C₁₃	1	2	yes	—
233	#386	—	2	2	no	—
234	#384	—	2	1	no	—
235	#384	C₂²×C₁₃	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	1	yes	characteristic
242	#336	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²×C₁₃	D₄²	1	1	yes	characteristic
252	C₂²×C₁₃	#548	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂²×C₁₃	#576	1	1	yes	characteristic
256	C₂²×C₁₃	#577	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	#478	1	4	yes	complemented
266	C₄×C₁₃	#532	1	1	yes	characteristic
267	C₄×C₁₃	#542	1	1	yes	characteristic
268	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
269	C₄×C₁₃	#554	1	1	yes	characteristic
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
273	C₂³×C₄	—	2	2	no	—
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	#127	—	2	2	no	—
278	#127	Q₈×C₁₃	1	4	yes	—
279	#125	—	2	4	no	—
280	#125	—	4	2	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	4	2	no	—
283	C₄×D₄	—	4	4	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	#106	—	2	2	no	—
305	#106	D₄×C₁₃	1	4	yes	complemented
306	C₄⋊C₈	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	#102	—	4	2	no	—
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	#95	D₄×C₁₃	1	2	yes	—
317	C₂×C₁₃	—	8	4	no	—
318	C₂×C₁₃	#2452	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
320	C₂×C₁₃	#3081	1	1	yes	characteristic
321	C₂×C₁₃	#3274	1	1	yes	characteristic
322	C₂×C₁₃	#3284	1	1	yes	characteristic
323	C₂×C₁₃	#3361	1	1	yes	characteristic
324	C₂×C₁₃	#3368	1	1	yes	characteristic
325	C₂⁴	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	8	1	no	—
336	C₂×D₄	—	8	1	no	—
337	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	8	1	no	—
373	C₄⋊C₄	—	8	2	no	—
374	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
376	C₄⋊C₄	C₁₃×#41	1	2	yes	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	8	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
385	C₄²	C₁₃×#41	1	2	yes	—
386	C₁₃	#26463	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	8	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
426	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
427	C₂×C₄	C₁₃×#135	1	2	yes	—
428	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
446	C₂²	D₄²×C₁₃	1	1	yes	characteristic
447	C₂²	C₁₃×#548	1	1	yes	characteristic
448	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
449	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
450	C₂²	C₁₃×#576	1	1	yes	characteristic
451	C₂²	C₁₃×#577	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	1	no	—
460	C₄	C₁₃×#478	1	4	yes	complemented
461	C₄	C₁₃×#532	1	1	yes	characteristic
462	C₄	C₁₃×#542	1	1	yes	characteristic
463	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
464	C₄	C₁₃×#554	1	1	yes	characteristic
465	C₂	—	8	4	no	—
466	C₂	C₁₃×#2452	1	1	yes	characteristic
467	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
468	C₂	C₁₃×#3081	1	1	yes	characteristic
469	C₂	C₁₃×#3274	1	1	yes	characteristic
470	C₂	C₁₃×#3284	1	1	yes	characteristic
471	C₂	C₁₃×#3361	1	1	yes	characteristic
472	C₂	C₁₃×#3368	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#478	C₂	semidirect
2. C₁₃×#2552	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
77. C₁₃×#106	D₄	semidirect
89. #26463	C₁₃	direct (N × H)
151. C₂×#478	C₂×C₁₃	semidirect
152. #2552	C₂×C₁₃	semidirect
154. #2065	C₂×C₁₃	semidirect
155. #2025	C₂×C₁₃	semidirect
158. #1947	C₂×C₁₃	semidirect
159. #1939	C₂×C₁₃	semidirect
160. #1862	C₂×C₁₃	semidirect
161. C₄×#106	C₂×C₁₃	semidirect
265. C₄×C₁₃	#478	semidirect
305. #106	D₄×C₁₃	semidirect
386. C₁₃	#26463	direct (N × H)
460. C₄	C₁₃×#478	semidirect

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×#2552	2
C₁₃×#2366	2
C₁₃×#2065	2
C₁₃×#2025	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1862	2
C₄×C₁₃×#106	2
#26463	13

Subgroups — C13×#26463 #15712802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26463 #15712802