Subgroups — C₁₃×#26851 #15713190

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2003	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₃×#544	C₂²	1	1	yes	characteristic
18	C₁₃×#536	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#518	C₂²	1	1	yes	characteristic
22	C₁₃×#491	—	2	1	no	—
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#487	—	2	1	no	—
26	C₁₃×#485	—	2	1	no	—
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#484	—	2	1	no	—
29	C₁₃×#483	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#476	—	2	1	no	—
33	C₁₃×#474	—	2	1	no	—
34	C₁₃×#442	—	2	1	no	—
35	C₁₃×#440	—	2	1	no	—
36	C₄×C₁₃×SD₁₆	—	2	1	no	—
37	C₄×C₁₃×D₈	—	2	1	no	—
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₁₃×#419	C₂²	1	1	yes	characteristic
46	C₁₃×#419	C₂²	1	1	yes	characteristic
47	C₁₃×#418	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#416	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₁₃×#382	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#125	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×#124	—	2	2	no	—
87	C₁₃×#124	—	2	2	no	—
88	C₁₃×#123	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	4	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	4	1	no	—
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	C₂³	1	1	yes	characteristic
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#108	—	2	2	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	D₄	1	1	yes	characteristic
114	C₁₃×#107	D₄	1	1	yes	characteristic
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	D₄	1	1	yes	characteristic
119	C₁₃×#106	D₄	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	—	2	1	no	—
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×#104	—	2	2	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	D₄	1	1	yes	characteristic
133	C₁₃×#103	D₄	1	1	yes	characteristic
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	2	1	no	—
137	C₁₃×#102	—	2	1	no	—
138	C₁₃×#102	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	D₄	1	1	yes	characteristic
142	C₁₃×#102	D₄	1	1	yes	characteristic
143	C₁₃×#101	—	2	2	no	—
144	C₁₃×#100	—	2	2	no	—
145	C₁₃×C₂²⋊C₈	—	2	1	no	—
146	C₁₃×C₂²⋊C₈	—	2	1	no	—
147	C₁₃×#97	—	2	1	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₄×C₈×C₁₃	—	2	1	no	—
150	C₄×C₈×C₁₃	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	2	no	—
152	C₁₃×#95	—	4	1	no	—
153	#26851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	4	1	no	—
166	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₁₃	#41	1	2	yes	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	4	1	no	—
181	C₂²×C₄×C₁₃	—	4	1	no	—
182	C₂²×C₄×C₁₃	—	4	1	no	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×SD₁₆	—	2	4	no	—
185	C₁₃×D₈	—	2	4	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	—	2	1	no	—
191	C₁₃×M₁₆	—	2	1	no	—
192	C₁₃×M₁₆	—	2	1	no	—
193	C₁₃×M₁₆	#41	1	2	yes	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	4	1	no	—
213	C₁₃×C₄⋊C₄	—	4	1	no	—
214	C₁₃×C₄⋊C₄	—	4	1	no	—
215	C₁₃×C₄⋊C₄	—	4	1	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₄	—	2	1	no	—
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₁₃×C₂²⋊C₄	—	4	1	no	—
226	C₁₃×C₂²⋊C₄	—	4	1	no	—
227	C₁₃×C₂²⋊C₄	—	4	4	no	—
228	C₁₃×C₂²⋊C₄	—	4	1	no	—
229	C₁₃×C₂²⋊C₄	—	4	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	4	1	no	—
236	C₄²×C₁₃	#41	1	2	yes	—
237	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2946	C₂×C₁₃	1	1	yes	characteristic
241	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2051	C₂×C₁₃	1	1	yes	characteristic
244	#2003	C₂×C₁₃	1	1	yes	characteristic
245	#1958	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1937	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1885	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	8	1	no	—
257	C₂³×C₁₃	—	8	1	no	—
258	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
259	Q₈×C₁₃	—	2	1	no	—
260	Q₈×C₁₃	—	2	1	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	1	no	—
263	Q₈×C₁₃	—	4	1	no	—
264	Q₈×C₁₃	—	4	1	no	—
265	Q₈×C₁₃	—	16	1	no	—
266	D₄×C₁₃	—	2	1	no	—
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	2	1	no	—
269	D₄×C₁₃	—	2	2	no	—
270	D₄×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	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	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	2	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	—	8	1	no	—
292	C₂×C₄×C₁₃	—	8	1	no	—
293	C₂×C₄×C₁₃	—	16	1	no	—
294	C₂×C₄×C₁₃	—	16	1	no	—
295	C₂×C₄×C₁₃	—	16	1	no	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
302	C₈×C₁₃	—	2	2	no	—
303	C₈×C₁₃	—	2	1	no	—
304	C₈×C₁₃	—	2	1	no	—
305	C₈×C₁₃	—	2	1	no	—
306	C₈×C₁₃	—	2	1	no	—
307	C₈×C₁₃	—	4	1	no	—
308	C₈×C₁₃	—	4	1	no	—
309	C₈×C₁₃	—	4	1	no	—
310	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
311	#544	C₂²×C₁₃	1	1	yes	characteristic
312	#536	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
314	#520	C₂²×C₁₃	1	1	yes	characteristic
315	#518	C₂²×C₁₃	1	1	yes	characteristic
316	#491	—	2	1	no	—
317	#489	—	2	1	no	—
318	#488	—	2	1	no	—
319	#487	—	2	1	no	—
320	#485	—	2	1	no	—
321	#485	—	2	1	no	—
322	#484	—	2	1	no	—
323	#483	—	2	1	no	—
324	#478	—	2	1	no	—
325	#478	—	2	1	no	—
326	#476	—	2	1	no	—
327	#474	—	2	1	no	—
328	#442	—	2	1	no	—
329	#440	—	2	1	no	—
330	C₄×SD₁₆	—	2	1	no	—
331	C₄×D₈	—	2	1	no	—
332	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
333	#428	C₂²×C₁₃	1	1	yes	characteristic
334	#428	C₂²×C₁₃	1	1	yes	characteristic
335	#428	C₂²×C₁₃	1	1	yes	characteristic
336	#427	C₂²×C₁₃	1	1	yes	characteristic
337	#424	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
339	#419	C₂²×C₁₃	1	1	yes	characteristic
340	#419	C₂²×C₁₃	1	1	yes	characteristic
341	#418	C₂²×C₁₃	1	1	yes	characteristic
342	#417	C₂²×C₁₃	1	1	yes	characteristic
343	#416	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
350	#408	C₂²×C₁₃	1	1	yes	characteristic
351	#405	C₂²×C₁₃	1	1	yes	characteristic
352	#405	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
354	#382	C₂²×C₁₃	1	1	yes	characteristic
355	#343	C₂²×C₁₃	1	1	yes	characteristic
356	#343	C₂²×C₁₃	1	1	yes	characteristic
357	#341	C₂²×C₁₃	1	1	yes	characteristic
358	#339	C₂²×C₁₃	1	1	yes	characteristic
359	#339	C₂²×C₁₃	1	1	yes	characteristic
360	#339	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×C₁₃	—	2	1	no	—
362	C₂²×C₁₃	—	2	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	8	2	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	16	1	no	—
371	C₂²×C₁₃	#542	1	1	yes	characteristic
372	C₂²×C₁₃	D₄²	1	1	yes	characteristic
373	C₂²×C₁₃	#551	1	1	yes	characteristic
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	4	1	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	8	1	no	—
383	C₄×C₁₃	—	8	1	no	—
384	C₄×C₁₃	—	8	1	no	—
385	C₄×C₁₃	#525	1	1	yes	characteristic
386	C₄×C₁₃	#532	1	1	yes	characteristic
387	C₄×C₁₃	#547	1	1	yes	characteristic
388	C₄×C₁₃	#548	1	1	yes	characteristic
389	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	AGL(1,ℤ/8)	—	2	2	no	—
393	AGL(1,ℤ/8)	—	2	2	no	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₄⋊Q₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	1	no	—
404	C₄⋊Q₈	—	2	1	no	—
405	#125	—	2	1	no	—
406	#125	—	2	1	no	—
407	#124	—	2	1	no	—
408	#124	—	2	2	no	—
409	#124	—	2	2	no	—
410	#123	—	4	1	no	—
411	C₂²⋊Q₈	—	2	1	no	—
412	C₂²⋊Q₈	—	2	1	no	—
413	C₂²⋊Q₈	—	4	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	4	1	no	—
421	#117	—	2	1	no	—
422	#117	C₂³×C₁₃	1	1	yes	characteristic
423	#117	C₂³×C₁₃	1	1	yes	characteristic
424	#117	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	—	4	1	no	—
429	C₂×C₂²⋊C₄	—	4	1	no	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	#108	—	2	2	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#107	—	2	1	no	—
435	#107	D₄×C₁₃	1	1	yes	characteristic
436	#107	D₄×C₁₃	1	1	yes	characteristic
437	#106	—	2	1	no	—
438	#106	—	2	1	no	—
439	#106	—	2	1	no	—
440	#106	D₄×C₁₃	1	1	yes	characteristic
441	#106	D₄×C₁₃	1	1	yes	characteristic
442	C₄⋊C₈	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	#104	—	2	2	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	—	2	1	no	—
450	#103	—	2	1	no	—
451	#103	—	2	1	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	D₄×C₁₃	1	1	yes	characteristic
455	#103	D₄×C₁₃	1	1	yes	characteristic
456	#102	—	2	1	no	—
457	#102	—	2	1	no	—
458	#102	—	2	1	no	—
459	#102	—	2	1	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	D₄×C₁₃	1	1	yes	characteristic
464	#102	D₄×C₁₃	1	1	yes	characteristic
465	#101	—	2	2	no	—
466	#100	—	2	2	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	C₂²⋊C₈	—	2	1	no	—
469	#97	—	2	1	no	—
470	#97	—	2	1	no	—
471	C₄×C₈	—	2	1	no	—
472	C₄×C₈	—	2	1	no	—
473	C₄×C₈	—	2	2	no	—
474	#95	—	4	1	no	—
475	C₂×C₁₃	—	2	1	no	—
476	C₂×C₁₃	—	2	1	no	—
477	C₂×C₁₃	—	8	1	no	—
478	C₂×C₁₃	—	8	2	no	—
479	C₂×C₁₃	#2461	1	1	yes	characteristic
480	C₂×C₁₃	#3290	1	1	yes	characteristic
481	C₂×C₁₃	#3290	1	1	yes	characteristic
482	C₂⁴	—	2	1	no	—
483	#41	—	2	1	no	—
484	#41	—	2	1	no	—
485	#41	—	2	1	no	—
486	#41	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×D₄	C₁₃×#41	1	2	yes	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
512	SD₁₆	—	2	4	no	—
513	D₈	—	2	4	no	—
514	M₁₆	—	2	1	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	C₁₃×#41	1	2	yes	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	4	1	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	4	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	4	1	no	—
564	C₄²	C₁₃×#41	1	2	yes	—
565	C₁₃	#26851	1	1	yes	characteristic, direct product factor, Sylow
566	C₂³	—	2	1	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	8	1	no	—
571	C₂³	—	8	1	no	—
572	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
573	Q₈	—	2	1	no	—
574	Q₈	—	2	1	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	—	16	1	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	1	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	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	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	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	—	8	1	no	—
606	C₂×C₄	—	8	1	no	—
607	C₂×C₄	—	16	1	no	—
608	C₂×C₄	—	16	1	no	—
609	C₂×C₄	—	16	1	no	—
610	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
613	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
614	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
615	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	1	no	—
618	C₈	—	2	1	no	—
619	C₈	—	2	1	no	—
620	C₈	—	2	1	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	16	1	no	—
634	C₂²	C₁₃×#542	1	1	yes	characteristic
635	C₂²	D₄²×C₁₃	1	1	yes	characteristic
636	C₂²	C₁₃×#551	1	1	yes	characteristic
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	C₁₃×#525	1	1	yes	characteristic
649	C₄	C₁₃×#532	1	1	yes	characteristic
650	C₄	C₁₃×#547	1	1	yes	characteristic
651	C₄	C₁₃×#548	1	1	yes	characteristic
652	C₂	—	2	1	no	—
653	C₂	—	2	1	no	—
654	C₂	—	8	1	no	—
655	C₂	—	8	2	no	—
656	C₂	C₁₃×#2461	1	1	yes	characteristic
657	C₂	C₁₃×#3290	1	1	yes	characteristic
658	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3137	C₂	semidirect
2. C₁₃×#3097	C₂	semidirect
3. C₁₃×#3081	C₂	semidirect
5. C₁₃×#2064	C₂	semidirect
6. C₁₃×#2061	C₂	semidirect
9. C₁₃×#1958	C₂	semidirect
10. C₁₃×#1937	C₂	semidirect
11. C₁₃×#1931	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1885	C₂	semidirect
14. C₁₃×#1860	C₂	semidirect
15. C₁₃×#1772	C₂	semidirect
153. #26851	C₁₃	direct (N × H)
237. #3137	C₂×C₁₃	semidirect
238. #3097	C₂×C₁₃	semidirect
239. #3081	C₂×C₁₃	semidirect
241. #2064	C₂×C₁₃	semidirect
242. #2061	C₂×C₁₃	semidirect
245. #1958	C₂×C₁₃	semidirect
246. #1937	C₂×C₁₃	semidirect
247. #1931	C₂×C₁₃	semidirect
248. #1930	C₂×C₁₃	semidirect
249. #1885	C₂×C₁₃	semidirect
250. #1860	C₂×C₁₃	semidirect
251. #1772	C₂×C₁₃	semidirect
565. C₁₃	#26851	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3137	2
C₁₃×#3097	2
C₁₃×#3081	2
C₁₃×#2946	2
C₁₃×#2064	2
C₁₃×#2061	2
C₁₃×#2051	2
C₁₃×#2003	2
C₁₃×#1958	2
C₁₃×#1937	2
C₁₃×#1931	2
C₁₃×#1930	2
C₁₃×#1885	2
C₁₃×#1860	2
C₁₃×#1772	2
#26851	13

Subgroups — C13×#26851 #15713190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26851 #15713190