Subgroups — C₁₃×#24808 #15711147

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3069	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3068	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2916	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2070	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2069	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2049	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2048	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1903	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1902	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#575	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₁₃×#568	C₂²	1	1	yes	characteristic
23	C₁₃×#568	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
26	C₁₃×#473	—	2	2	no	—
27	C₁₃×#472	—	2	2	no	—
28	C₁₃×#471	—	2	2	no	—
29	C₁₃×#471	—	2	2	no	—
30	C₁₃×#471	—	2	2	no	—
31	C₁₃×#471	—	2	2	no	—
32	C₁₃×#471	—	2	2	no	—
33	C₁₃×#471	—	2	2	no	—
34	C₁₃×#444	—	2	2	no	—
35	C₁₃×#443	—	2	2	no	—
36	C₁₃×#430	—	2	2	no	—
37	C₁₃×#430	C₂²	1	1	yes	characteristic
38	C₁₃×#430	C₂²	1	1	yes	characteristic
39	C₁₃×#430	C₂²	1	1	yes	characteristic
40	C₁₃×#430	C₂²	1	1	yes	characteristic
41	C₁₃×#430	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#108	—	2	2	no	—
43	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
46	C₁₃×#421	C₂²	1	1	yes	characteristic
47	C₁₃×#421	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#413	C₂²	1	1	yes	characteristic
51	C₁₃×#413	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₁₃×#344	C₂²	1	1	yes	characteristic
60	C₁₃×#344	C₂²	1	1	yes	characteristic
61	C₁₃×#338	C₂²	1	1	yes	characteristic
62	C₁₃×#338	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#137	—	2	1	no	—
68	C₁₃×#137	—	2	2	no	—
69	C₁₃×#137	—	2	2	no	—
70	C₁₃×#137	—	2	2	no	—
71	C₁₃×#137	—	4	1	no	—
72	C₁₃×#137	D₄	1	2	yes	—
73	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
74	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
78	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
79	C₁₃×#135	—	2	2	no	—
80	C₂×C₁₃×Q₁₆	—	2	1	no	—
81	C₂×C₁₃×Q₁₆	—	2	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	1	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	—	2	1	no	—
88	C₂×C₁₃×SD₁₆	—	2	1	no	—
89	C₂×C₁₃×SD₁₆	—	2	1	no	—
90	C₂×C₁₃×SD₁₆	—	2	1	no	—
91	C₂×C₁₃×SD₁₆	—	2	1	no	—
92	C₂×C₁₃×D₈	—	2	1	no	—
93	C₂×C₁₃×D₈	—	2	1	no	—
94	C₁₃×#131	—	2	1	no	—
95	C₁₃×#131	—	2	1	no	—
96	C₁₃×#131	—	2	2	no	—
97	C₁₃×#131	—	2	2	no	—
98	C₁₃×#131	—	2	1	no	—
99	C₁₃×#131	—	2	1	no	—
100	C₁₃×#131	—	2	1	no	—
101	C₁₃×#131	—	2	1	no	—
102	C₁₃×#131	—	4	1	no	—
103	C₁₃×#131	—	4	1	no	—
104	C₁₃×#131	D₄	1	2	yes	—
105	C₁₃×#131	D₄	1	2	yes	—
106	C₂×C₁₃×M₁₆	—	2	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	—	2	2	no	—
109	C₂×C₁₃×M₁₆	—	2	2	no	—
110	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	—	2	1	no	—
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#117	C₂³	1	1	yes	characteristic
123	C₁₃×#108	—	2	2	no	—
124	C₁₃×#108	—	2	2	no	—
125	C₁₃×#108	—	2	2	no	—
126	C₁₃×#108	—	2	2	no	—
127	C₁₃×#108	—	2	2	no	—
128	C₁₃×#108	—	2	1	no	—
129	C₁₃×#108	—	2	1	no	—
130	C₁₃×#108	—	2	1	no	—
131	C₁₃×#108	—	2	1	no	—
132	C₁₃×#108	D₄	1	2	yes	—
133	C₁₃×#108	D₄	1	2	yes	—
134	C₁₃×#104	—	2	2	no	—
135	C₁₃×#104	—	2	2	no	—
136	C₁₃×#103	—	4	1	no	—
137	C₁₃×#102	—	4	1	no	—
138	C₁₃×#101	—	2	1	no	—
139	C₁₃×#101	—	2	1	no	—
140	C₁₃×#101	—	2	2	no	—
141	C₁₃×#101	—	2	2	no	—
142	C₁₃×#101	—	2	2	no	—
143	C₁₃×#100	—	2	1	no	—
144	C₁₃×#100	—	2	1	no	—
145	C₁₃×#100	—	2	2	no	—
146	C₁₃×#100	—	2	2	no	—
147	C₁₃×#100	—	2	2	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₄×C₈×C₁₃	—	2	1	no	—
150	#24808	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₁₃×#41	—	2	1	no	—
153	C₁₃×#41	—	2	1	no	—
154	C₁₃×#41	—	2	1	no	—
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	C₂×D₄	1	2	yes	—
159	C₁₃×#41	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
166	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
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	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×Q₁₆	—	2	2	no	—
183	C₁₃×Q₁₆	—	4	2	no	—
184	C₁₃×Q₁₆	—	4	2	no	—
185	C₁₃×SD₁₆	—	2	2	no	—
186	C₁₃×SD₁₆	—	2	2	no	—
187	C₁₃×SD₁₆	—	4	2	no	—
188	C₁₃×SD₁₆	—	4	2	no	—
189	C₁₃×SD₁₆	—	4	2	no	—
190	C₁₃×SD₁₆	—	4	2	no	—
191	C₁₃×SD₁₆	—	4	1	no	—
192	C₁₃×SD₁₆	—	4	1	no	—
193	C₁₃×SD₁₆	—	4	1	no	—
194	C₁₃×SD₁₆	—	4	1	no	—
195	C₁₃×D₈	—	2	2	no	—
196	C₁₃×D₈	—	4	2	no	—
197	C₁₃×D₈	—	4	2	no	—
198	C₁₃×M₁₆	—	2	1	no	—
199	C₁₃×M₁₆	—	2	1	no	—
200	C₁₃×M₁₆	—	2	1	no	—
201	C₁₃×M₁₆	—	2	1	no	—
202	C₁₃×M₁₆	—	2	2	no	—
203	C₁₃×M₁₆	—	2	2	no	—
204	C₁₃×M₁₆	—	2	1	no	—
205	C₁₃×M₁₆	—	2	1	no	—
206	C₁₃×M₁₆	—	2	1	no	—
207	C₁₃×M₁₆	—	2	1	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	2	1	no	—
211	C₁₃×M₁₆	—	2	1	no	—
212	C₁₃×M₁₆	—	2	1	no	—
213	C₁₃×M₁₆	—	2	1	no	—
214	C₁₃×M₁₆	—	4	2	no	—
215	C₁₃×M₁₆	—	4	2	no	—
216	C₁₃×M₁₆	—	4	1	no	—
217	C₁₃×M₁₆	—	4	1	no	—
218	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
219	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
220	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
221	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	2	no	—
227	C₂×C₈×C₁₃	—	2	2	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	4	2	no	—
234	C₂×C₈×C₁₃	—	4	2	no	—
235	C₂×C₈×C₁₃	—	4	1	no	—
236	C₂×C₈×C₁₃	—	4	1	no	—
237	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
242	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₄²×C₁₃	—	2	1	no	—
246	#3069	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#3068	C₂×C₁₃	1	1	yes	characteristic
248	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2955	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#2916	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2070	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2069	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2049	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2048	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1953	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1903	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1902	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	16	1	no	—
267	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
268	Q₈×C₁₃	—	2	1	no	—
269	Q₈×C₁₃	—	2	1	no	—
270	Q₈×C₁₃	—	2	1	no	—
271	Q₈×C₁₃	—	4	1	no	—
272	Q₈×C₁₃	—	4	1	no	—
273	Q₈×C₁₃	—	4	1	no	—
274	Q₈×C₁₃	—	4	1	no	—
275	Q₈×C₁₃	#121	1	2	yes	—
276	D₄×C₁₃	—	2	2	no	—
277	D₄×C₁₃	—	2	2	no	—
278	D₄×C₁₃	—	2	1	no	—
279	D₄×C₁₃	—	2	1	no	—
280	D₄×C₁₃	—	2	1	no	—
281	D₄×C₁₃	—	4	1	no	—
282	D₄×C₁₃	—	4	1	no	—
283	D₄×C₁₃	—	4	1	no	—
284	D₄×C₁₃	—	4	1	no	—
285	D₄×C₁₃	—	4	1	no	—
286	D₄×C₁₃	—	4	1	no	—
287	D₄×C₁₃	#121	1	2	yes	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
304	C₈×C₁₃	—	2	2	no	—
305	C₈×C₁₃	—	2	2	no	—
306	C₈×C₁₃	—	2	2	no	—
307	C₈×C₁₃	—	2	2	no	—
308	C₈×C₁₃	—	4	1	no	—
309	C₈×C₁₃	—	4	1	no	—
310	C₈×C₁₃	—	4	1	no	—
311	C₈×C₁₃	—	4	1	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	#121	1	1	yes	characteristic
314	C₈×C₁₃	#121	1	1	yes	characteristic
315	C₈×C₁₃	#121	1	1	yes	characteristic
316	C₈×C₁₃	#121	1	1	yes	characteristic
317	#575	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
323	#568	C₂²×C₁₃	1	1	yes	characteristic
324	#568	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
327	#473	—	2	2	no	—
328	#472	—	2	2	no	—
329	#471	—	2	2	no	—
330	#471	—	2	2	no	—
331	#471	—	2	2	no	—
332	#471	—	2	2	no	—
333	#471	—	2	2	no	—
334	#471	—	2	2	no	—
335	#444	—	2	2	no	—
336	#443	—	2	2	no	—
337	#430	—	2	2	no	—
338	#430	C₂²×C₁₃	1	1	yes	characteristic
339	#430	C₂²×C₁₃	1	1	yes	characteristic
340	#430	C₂²×C₁₃	1	1	yes	characteristic
341	#430	C₂²×C₁₃	1	1	yes	characteristic
342	#430	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#108	—	2	2	no	—
344	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
347	#421	C₂²×C₁₃	1	1	yes	characteristic
348	#421	C₂²×C₁₃	1	1	yes	characteristic
349	#419	C₂²×C₁₃	1	1	yes	characteristic
350	#418	C₂²×C₁₃	1	1	yes	characteristic
351	#413	C₂²×C₁₃	1	1	yes	characteristic
352	#413	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
359	#405	C₂²×C₁₃	1	1	yes	characteristic
360	#344	C₂²×C₁₃	1	1	yes	characteristic
361	#344	C₂²×C₁₃	1	1	yes	characteristic
362	#338	C₂²×C₁₃	1	1	yes	characteristic
363	#338	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₁₃	—	2	2	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	16	1	no	—
371	C₂²×C₁₃	—	16	1	no	—
372	C₂²×C₁₃	—	16	1	no	—
373	C₂²×C₁₃	#537	1	1	yes	characteristic
374	C₂²×C₁₃	#547	1	1	yes	characteristic
375	C₂²×C₁₃	#548	1	1	yes	characteristic
376	C₄×C₁₃	—	2	2	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	8	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
381	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
382	C₄×C₁₃	D₄²	1	1	yes	characteristic
383	C₄×C₁₃	#553	1	1	yes	characteristic
384	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
388	#137	—	2	1	no	—
389	#137	—	2	2	no	—
390	#137	—	2	2	no	—
391	#137	—	2	2	no	—
392	#137	—	4	1	no	—
393	#137	D₄×C₁₃	1	2	yes	—
394	AGL(1,ℤ/8)	—	2	1	no	—
395	AGL(1,ℤ/8)	—	2	2	no	—
396	AGL(1,ℤ/8)	—	2	2	no	—
397	AGL(1,ℤ/8)	—	2	2	no	—
398	AGL(1,ℤ/8)	—	4	1	no	—
399	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	—
400	#135	—	2	2	no	—
401	C₂×Q₁₆	—	2	1	no	—
402	C₂×Q₁₆	—	2	1	no	—
403	C₂×SD₁₆	—	2	1	no	—
404	C₂×SD₁₆	—	2	1	no	—
405	C₂×SD₁₆	—	2	1	no	—
406	C₂×SD₁₆	—	2	1	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×SD₁₆	—	2	1	no	—
409	C₂×SD₁₆	—	2	1	no	—
410	C₂×SD₁₆	—	2	1	no	—
411	C₂×SD₁₆	—	2	1	no	—
412	C₂×SD₁₆	—	2	1	no	—
413	C₂×D₈	—	2	1	no	—
414	C₂×D₈	—	2	1	no	—
415	#131	—	2	1	no	—
416	#131	—	2	1	no	—
417	#131	—	2	2	no	—
418	#131	—	2	2	no	—
419	#131	—	2	1	no	—
420	#131	—	2	1	no	—
421	#131	—	2	1	no	—
422	#131	—	2	1	no	—
423	#131	—	4	1	no	—
424	#131	—	4	1	no	—
425	#131	D₄×C₁₃	1	2	yes	—
426	#131	D₄×C₁₃	1	2	yes	—
427	C₂×M₁₆	—	2	1	no	—
428	C₂×M₁₆	—	2	1	no	—
429	C₂×M₁₆	—	2	2	no	—
430	C₂×M₁₆	—	2	2	no	—
431	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
440	C₂²×C₈	—	2	1	no	—
441	C₂²×C₈	—	2	1	no	—
442	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
443	#117	C₂³×C₁₃	1	1	yes	characteristic
444	#108	—	2	2	no	—
445	#108	—	2	2	no	—
446	#108	—	2	2	no	—
447	#108	—	2	2	no	—
448	#108	—	2	2	no	—
449	#108	—	2	1	no	—
450	#108	—	2	1	no	—
451	#108	—	2	1	no	—
452	#108	—	2	1	no	—
453	#108	D₄×C₁₃	1	2	yes	—
454	#108	D₄×C₁₃	1	2	yes	—
455	#104	—	2	2	no	—
456	#104	—	2	2	no	—
457	#103	—	4	1	no	—
458	#102	—	4	1	no	—
459	#101	—	2	1	no	—
460	#101	—	2	1	no	—
461	#101	—	2	2	no	—
462	#101	—	2	2	no	—
463	#101	—	2	2	no	—
464	#100	—	2	1	no	—
465	#100	—	2	1	no	—
466	#100	—	2	2	no	—
467	#100	—	2	2	no	—
468	#100	—	2	2	no	—
469	#97	—	2	1	no	—
470	C₄×C₈	—	2	1	no	—
471	C₂×C₁₃	—	2	1	no	—
472	C₂×C₁₃	—	2	1	no	—
473	C₂×C₁₃	—	2	1	no	—
474	C₂×C₁₃	—	4	2	no	—
475	C₂×C₁₃	—	8	1	no	—
476	C₂×C₁₃	—	16	1	no	—
477	C₂×C₁₃	#2416	1	1	yes	characteristic
478	C₂⁴	—	2	1	no	—
479	#41	—	2	1	no	—
480	#41	—	2	1	no	—
481	#41	—	2	1	no	—
482	#41	—	2	1	no	—
483	#41	—	2	1	no	—
484	#41	—	2	1	no	—
485	#41	C₂×D₄×C₁₃	1	2	yes	—
486	#41	C₂×D₄×C₁₃	1	2	yes	—
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	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂×Q₈	C₁₃×#41	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	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
509	Q₁₆	—	2	2	no	—
510	Q₁₆	—	4	2	no	—
511	Q₁₆	—	4	2	no	—
512	SD₁₆	—	2	2	no	—
513	SD₁₆	—	2	2	no	—
514	SD₁₆	—	4	2	no	—
515	SD₁₆	—	4	2	no	—
516	SD₁₆	—	4	2	no	—
517	SD₁₆	—	4	2	no	—
518	SD₁₆	—	4	1	no	—
519	SD₁₆	—	4	1	no	—
520	SD₁₆	—	4	1	no	—
521	SD₁₆	—	4	1	no	—
522	D₈	—	2	2	no	—
523	D₈	—	4	2	no	—
524	D₈	—	4	2	no	—
525	M₁₆	—	2	1	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	2	no	—
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	4	2	no	—
542	M₁₆	—	4	2	no	—
543	M₁₆	—	4	1	no	—
544	M₁₆	—	4	1	no	—
545	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
546	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
547	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
548	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	2	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	4	2	no	—
561	C₂×C₈	—	4	2	no	—
562	C₂×C₈	—	4	1	no	—
563	C₂×C₈	—	4	1	no	—
564	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
569	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
570	C₄⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₁₃	#24808	1	1	yes	characteristic, direct product factor, Sylow
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	16	1	no	—
580	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
581	Q₈	—	2	1	no	—
582	Q₈	—	2	1	no	—
583	Q₈	—	2	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	Q₈	C₁₃×#121	1	2	yes	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	1	no	—
592	D₄	—	2	1	no	—
593	D₄	—	2	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	C₁₃×#121	1	2	yes	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	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	C₂²×D₄×C₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
615	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
616	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
617	C₈	—	2	2	no	—
618	C₈	—	2	2	no	—
619	C₈	—	2	2	no	—
620	C₈	—	2	2	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₈	—	4	1	no	—
625	C₈	—	4	1	no	—
626	C₈	C₁₃×#121	1	1	yes	characteristic
627	C₈	C₁₃×#121	1	1	yes	characteristic
628	C₈	C₁₃×#121	1	1	yes	characteristic
629	C₈	C₁₃×#121	1	1	yes	characteristic
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	16	1	no	—
637	C₂²	—	16	1	no	—
638	C₂²	—	16	1	no	—
639	C₂²	C₁₃×#537	1	1	yes	characteristic
640	C₂²	C₁₃×#547	1	1	yes	characteristic
641	C₂²	C₁₃×#548	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
647	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
648	C₄	D₄²×C₁₃	1	1	yes	characteristic
649	C₄	C₁₃×#553	1	1	yes	characteristic
650	C₂	—	2	1	no	—
651	C₂	—	2	1	no	—
652	C₂	—	2	1	no	—
653	C₂	—	4	2	no	—
654	C₂	—	8	1	no	—
655	C₂	—	16	1	no	—
656	C₂	C₁₃×#2416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2416
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3068	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3069	C₂	semidirect
3. C₂×C₁₃×#471	C₂	semidirect
4. C₂×C₁₃×#471	C₂	semidirect
5. C₁₃×#2955	C₂	semidirect
6. C₁₃×#2916	C₂	semidirect
7. C₁₃×#2070	C₂	semidirect
8. C₁₃×#2069	C₂	semidirect
9. C₁₃×#2049	C₂	semidirect
10. C₁₃×#2048	C₂	semidirect
11. C₁₃×#1977	C₂	semidirect
12. C₁₃×#1953	C₂	semidirect
13. C₁₃×#1903	C₂	semidirect
14. C₁₃×#1902	C₂	semidirect
15. C₁₃×#1813	C₂	semidirect
150. #24808	C₁₃	direct (N × H)
246. #3069	C₂×C₁₃	semidirect
248. C₂×#471	C₂×C₁₃	semidirect
249. C₂×#471	C₂×C₁₃	semidirect
250. #2955	C₂×C₁₃	semidirect
251. #2916	C₂×C₁₃	semidirect
252. #2070	C₂×C₁₃	semidirect
253. #2069	C₂×C₁₃	semidirect
254. #2049	C₂×C₁₃	semidirect
255. #2048	C₂×C₁₃	semidirect
256. #1977	C₂×C₁₃	semidirect
257. #1953	C₂×C₁₃	semidirect
258. #1903	C₂×C₁₃	semidirect
259. #1902	C₂×C₁₃	semidirect
260. #1813	C₂×C₁₃	semidirect
573. C₁₃	#24808	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×#3069	2
C₁₃×#3068	2
C₂×C₁₃×#471	2
C₁₃×#2955	2
C₁₃×#2916	2
C₁₃×#2070	2
C₁₃×#2069	2
C₁₃×#2049	2
C₁₃×#2048	2
C₁₃×#1977	2
C₁₃×#1953	2
C₁₃×#1903	2
C₁₃×#1902	2
C₁₃×#1813	2
#24808	13

Subgroups — C13×#24808 #15711147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24808 #15711147