Subgroups — C₁₃×#26472 #15712811

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 678 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, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#478	—	2	4	no	—
23	C₁₃×#476	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
40	C₁₃×#398	—	2	1	no	—
41	C₁₃×#395	—	2	1	no	—
42	C₁₃×#391	—	2	1	no	—
43	C₁₃×#390	—	2	1	no	—
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	—	2	1	no	—
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#386	—	2	1	no	—
50	C₁₃×#386	—	2	1	no	—
51	C₁₃×#382	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×C₄⋊C₄	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×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	—	4	1	no	—
74	C₁₃×#127	—	2	2	no	—
75	C₁₃×#127	Q₈	1	4	yes	complemented
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	—	4	1	no	—
78	C₄×D₄×C₁₃	—	2	2	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	4	1	no	—
81	C₄×D₄×C₁₃	—	4	1	no	—
82	C₄×D₄×C₁₃	—	4	4	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#107	—	2	2	no	—
109	C₁₃×#106	—	2	2	no	—
110	C₁₃×#106	D₄	1	4	yes	complemented
111	C₁₃×C₄⋊C₈	—	2	2	no	—
112	C₁₃×C₄⋊C₈	—	2	2	no	—
113	C₁₃×C₄⋊C₈	—	2	2	no	—
114	C₁₃×#102	—	2	2	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	2	no	—
117	C₁₃×#102	—	2	2	no	—
118	C₁₃×#102	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	4	1	no	—
121	C₁₃×#102	—	4	1	no	—
122	C₁₃×#97	—	2	2	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	D₄	1	1	yes	characteristic
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	#26472	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	4	2	no	—
135	C₂×Q₈×C₁₃	—	4	2	no	—
136	C₂×Q₈×C₁₃	—	8	1	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	4	2	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	8	1	no	—
152	C₂×D₄×C₁₃	—	8	1	no	—
153	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
154	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	8	1	no	—
166	C₂²×C₄×C₁₃	—	8	1	no	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	2	no	—
201	C₁₃×C₄⋊C₄	—	8	1	no	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
204	C₁₃×C₄⋊C₄	#41	1	2	yes	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	8	1	no	—
210	C₁₃×C₂²⋊C₄	—	8	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	4	2	no	—
216	C₄²×C₁₃	—	8	1	no	—
217	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
218	C₄²×C₁₃	#41	1	2	yes	—
219	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2550	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2366	C₂×C₁₃	1	1	yes	characteristic
223	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1982	C₂×C₁₃	1	1	yes	characteristic
228	#1961	C₂×C₁₃	1	1	yes	characteristic
229	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1776	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	1	no	—
242	C₂³×C₁₃	—	4	1	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	Q₈×C₁₃	—	8	4	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	2	2	no	—
253	D₄×C₁₃	—	2	2	no	—
254	D₄×C₁₃	—	4	8	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	4	1	no	—
257	D₄×C₁₃	—	4	1	no	—
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	8	4	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	8	4	no	—
294	C₂×C₄×C₁₃	—	8	4	no	—
295	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
296	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
297	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
304	C₈×C₁₃	—	2	2	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₈×C₁₃	—	4	1	no	—
307	C₈×C₁₃	—	4	1	no	—
308	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄×D₄	—	2	1	no	—
312	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
314	#478	—	2	4	no	—
315	#476	—	2	4	no	—
316	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
332	#398	—	2	1	no	—
333	#395	—	2	1	no	—
334	#391	—	2	1	no	—
335	#390	—	2	1	no	—
336	#390	C₂²×C₁₃	1	1	yes	characteristic
337	#390	C₂²×C₁₃	1	1	yes	characteristic
338	#389	—	2	1	no	—
339	#389	C₂²×C₁₃	1	1	yes	characteristic
340	#389	C₂²×C₁₃	1	1	yes	characteristic
341	#386	—	2	1	no	—
342	#386	—	2	1	no	—
343	#382	C₂²×C₁₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
347	#340	C₂²×C₁₃	1	1	yes	characteristic
348	#340	C₂²×C₁₃	1	1	yes	characteristic
349	#340	C₂²×C₁₃	1	1	yes	characteristic
350	#340	C₂²×C₁₃	1	1	yes	characteristic
351	#336	C₂²×C₁₃	1	1	yes	characteristic
352	#336	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	4	2	no	—
355	C₂²×C₁₃	—	4	2	no	—
356	C₂²×C₁₃	—	4	2	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	8	1	no	—
360	C₂²×C₁₃	—	8	1	no	—
361	C₂²×C₁₃	—	8	1	no	—
362	C₂²×C₁₃	—	8	1	no	—
363	C₂²×C₁₃	—	8	1	no	—
364	C₂²×C₁₃	—	8	1	no	—
365	C₂²×C₁₃	—	8	1	no	—
366	C₂²×C₁₃	—	8	1	no	—
367	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂²×C₁₃	D₄²	1	1	yes	characteristic
369	C₂²×C₁₃	#548	1	1	yes	characteristic
370	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
371	C₂²×C₁₃	#575	1	1	yes	characteristic
372	C₂²×C₁₃	#576	1	1	yes	characteristic
373	C₂²×C₁₃	#577	1	1	yes	characteristic
374	C₄×C₁₃	—	2	2	no	—
375	C₄×C₁₃	—	2	2	no	—
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	4	2	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	4	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	8	1	no	—
384	C₄×C₁₃	—	8	1	no	—
385	C₄×C₁₃	—	8	1	no	—
386	C₄×C₁₃	#532	1	1	yes	characteristic
387	C₄×C₁₃	#542	1	1	yes	characteristic
388	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
389	C₄×C₁₃	#554	1	1	yes	characteristic
390	C₂²×Q₈	—	2	1	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₄⋊Q₈	—	2	2	no	—
402	C₄⋊Q₈	—	4	1	no	—
403	#127	—	2	2	no	—
404	#127	Q₈×C₁₃	1	4	yes	complemented
405	#125	—	2	2	no	—
406	#125	—	4	1	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	4	1	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	4	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
436	#107	—	2	2	no	—
437	#107	—	2	2	no	—
438	#106	—	2	2	no	—
439	#106	D₄×C₁₃	1	4	yes	complemented
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	4	1	no	—
450	#102	—	4	1	no	—
451	#97	—	2	2	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	D₄×C₁₃	1	1	yes	characteristic
459	#95	D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₁₃	—	8	2	no	—
461	C₂×C₁₃	—	8	2	no	—
462	C₂×C₁₃	#2452	1	1	yes	characteristic
463	C₂×C₁₃	#3077	1	1	yes	characteristic
464	C₂×C₁₃	#3081	1	1	yes	characteristic
465	C₂×C₁₃	#3265	1	1	yes	characteristic
466	C₂×C₁₃	#3268	1	1	yes	characteristic
467	C₂×C₁₃	#3366	1	1	yes	characteristic
468	C₂×C₁₃	#3371	1	1	yes	characteristic
469	C₂⁴	—	2	1	no	—
470	C₂⁴	—	2	1	no	—
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	8	1	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	—	8	1	no	—
490	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
491	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	8	1	no	—
539	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
540	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
541	C₄⋊C₄	C₁₃×#41	1	2	yes	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	8	1	no	—
547	C₂²⋊C₄	—	8	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	4	2	no	—
553	C₄²	—	8	1	no	—
554	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
555	C₄²	C₁₃×#41	1	2	yes	—
556	C₁₃	#26472	1	1	yes	characteristic, direct product factor, Sylow
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
572	Q₈	—	8	4	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	—	4	8	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	8	4	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	—	8	4	no	—
618	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
619	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
620	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
624	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
625	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
627	C₈	—	2	2	no	—
628	C₈	—	4	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
646	C₂²	D₄²×C₁₃	1	1	yes	characteristic
647	C₂²	C₁₃×#548	1	1	yes	characteristic
648	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
649	C₂²	C₁₃×#575	1	1	yes	characteristic
650	C₂²	C₁₃×#576	1	1	yes	characteristic
651	C₂²	C₁₃×#577	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	C₁₃×#532	1	1	yes	characteristic
665	C₄	C₁₃×#542	1	1	yes	characteristic
666	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
667	C₄	C₁₃×#554	1	1	yes	characteristic
668	C₂	—	8	2	no	—
669	C₂	—	8	2	no	—
670	C₂	C₁₃×#2452	1	1	yes	characteristic
671	C₂	C₁₃×#3077	1	1	yes	characteristic
672	C₂	C₁₃×#3081	1	1	yes	characteristic
673	C₂	C₁₃×#3265	1	1	yes	characteristic
674	C₂	C₁₃×#3268	1	1	yes	characteristic
675	C₂	C₁₃×#3366	1	1	yes	characteristic
676	C₂	C₁₃×#3371	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. C₂×C₁₃×#476	C₂	semidirect
3. C₁₃×#2550	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2025	C₂	semidirect
8. C₁₃×#2023	C₂	semidirect
11. C₁₃×#1949	C₂	semidirect
12. C₁₃×#1940	C₂	semidirect
13. C₁₃×#1864	C₂	semidirect
14. C₁₃×#1862	C₂	semidirect
15. C₁₃×#1776	C₂	semidirect
75. C₁₃×#127	Q₈	semidirect
110. C₁₃×#106	D₄	semidirect
131. #26472	C₁₃	direct (N × H)
219. C₂×#478	C₂×C₁₃	semidirect
220. C₂×#476	C₂×C₁₃	semidirect
221. #2550	C₂×C₁₃	semidirect
223. #2067	C₂×C₁₃	semidirect
224. #2067	C₂×C₁₃	semidirect
225. #2025	C₂×C₁₃	semidirect
226. #2023	C₂×C₁₃	semidirect
229. #1949	C₂×C₁₃	semidirect
230. #1940	C₂×C₁₃	semidirect
231. #1864	C₂×C₁₃	semidirect
232. #1862	C₂×C₁₃	semidirect
233. #1776	C₂×C₁₃	semidirect
404. #127	Q₈×C₁₃	semidirect
439. #106	D₄×C₁₃	semidirect
556. C₁₃	#26472	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
C₂×C₁₃×#476	2
C₁₃×#2550	2
C₁₃×#2366	2
C₁₃×#2067	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#1982	2
C₁₃×#1961	2
C₁₃×#1949	2
C₁₃×#1940	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1776	2
#26472	13

Subgroups — C13×#26472 #15712811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26472 #15712811