Subgroups — C₁₃×#24774 #15711113

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#472	—	2	4	no	—
27	C₁₃×#471	—	2	4	no	—
28	C₁₃×#464	—	2	1	no	—
29	C₁₃×#464	—	2	1	no	—
30	C₁₃×#463	—	2	1	no	—
31	C₁₃×#463	—	2	1	no	—
32	C₁₃×#463	—	2	1	no	—
33	C₁₃×#463	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#463	—	2	1	no	—
36	C₁₃×#442	—	2	1	no	—
37	C₁₃×#440	—	2	1	no	—
38	C₄×C₁₃×SD₁₆	—	2	1	no	—
39	C₄×C₁₃×D₈	—	2	1	no	—
40	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#424	—	2	1	no	—
44	C₁₃×#424	—	2	1	no	—
45	C₁₃×#424	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	1	yes	characteristic
47	C₁₃×#423	—	2	1	no	—
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₁₃×#423	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₁₃×#419	C₂²	1	1	yes	characteristic
53	C₁₃×#418	C₂²	1	1	yes	characteristic
54	C₁₃×#418	C₂²	1	1	yes	characteristic
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#341	C₂²	1	1	yes	characteristic
68	C₁₃×#341	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₁₃×#137	—	2	2	no	—
75	C₁₃×#137	—	2	2	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
79	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	—
80	C₂×C₁₃×Q₁₆	—	2	1	no	—
81	C₂×C₁₃×SD₁₆	—	2	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	2	no	—
85	C₂×C₁₃×SD₁₆	—	2	1	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×SD₁₆	—	4	1	no	—
88	C₂×C₁₃×D₈	—	2	1	no	—
89	C₂×C₁₃×D₈	—	2	1	no	—
90	C₂×C₁₃×D₈	—	2	2	no	—
91	C₂×C₁₃×D₈	—	2	1	no	—
92	C₂×C₁₃×D₈	—	2	1	no	—
93	C₂×C₁₃×D₈	—	4	1	no	—
94	C₁₃×#131	—	2	2	no	—
95	C₁₃×#131	—	2	2	no	—
96	C₁₃×#131	—	4	1	no	—
97	C₁₃×#131	—	4	1	no	—
98	C₂×C₁₃×M₁₆	—	2	1	no	—
99	C₂×C₁₃×M₁₆	—	2	1	no	—
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	—	2	1	no	—
107	C₂²×C₈×C₁₃	—	2	1	no	—
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#124	—	2	1	no	—
112	C₁₃×#124	—	2	1	no	—
113	C₁₃×#124	—	2	1	no	—
114	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
116	C₄×D₄×C₁₃	—	2	1	no	—
117	C₄×D₄×C₁₃	—	2	1	no	—
118	C₄×D₄×C₁₃	—	2	1	no	—
119	C₄×D₄×C₁₃	—	2	1	no	—
120	C₄×D₄×C₁₃	—	2	1	no	—
121	C₄×D₄×C₁₃	—	2	1	no	—
122	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
123	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
124	C₁₃×#117	—	2	1	no	—
125	C₁₃×#117	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#108	—	2	2	no	—
133	C₁₃×#108	—	2	2	no	—
134	C₁₃×#107	—	2	1	no	—
135	C₁₃×#106	—	2	1	no	—
136	C₁₃×C₄⋊C₈	—	2	1	no	—
137	C₁₃×C₄⋊C₈	—	2	1	no	—
138	C₁₃×C₄⋊C₈	—	2	1	no	—
139	C₁₃×C₄⋊C₈	—	2	1	no	—
140	C₁₃×C₄⋊C₈	—	2	1	no	—
141	C₁₃×C₄⋊C₈	—	2	1	no	—
142	C₁₃×C₄⋊C₈	—	2	1	no	—
143	C₁₃×C₄⋊C₈	—	2	1	no	—
144	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
145	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
146	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
147	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#103	—	2	1	no	—
152	C₁₃×#103	—	2	1	no	—
153	C₁₃×#102	—	2	1	no	—
154	C₁₃×#102	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#102	—	2	1	no	—
159	C₁₃×#102	—	2	1	no	—
160	C₁₃×#101	—	2	2	no	—
161	C₁₃×#101	—	4	1	no	—
162	C₁₃×#100	—	2	2	no	—
163	C₁₃×#100	—	2	2	no	—
164	C₁₃×#100	—	2	2	no	—
165	C₁₃×#100	—	4	1	no	—
166	C₁₃×#97	—	2	1	no	—
167	C₄×C₈×C₁₃	—	2	1	no	—
168	#24774	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	—	2	1	no	—
170	C₂⁴×C₁₃	—	2	1	no	—
171	C₁₃×#41	—	2	1	no	—
172	C₁₃×#41	—	2	1	no	—
173	C₁₃×#41	C₂×D₄	1	2	yes	—
174	C₁₃×#41	#41	1	2	yes	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	—	4	1	no	—
203	C₂²×C₄×C₁₃	—	8	2	no	—
204	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×Q₁₆	—	4	2	no	—
208	C₁₃×SD₁₆	—	2	4	no	—
209	C₁₃×SD₁₆	—	4	2	no	—
210	C₁₃×SD₁₆	—	4	2	no	—
211	C₁₃×SD₁₆	—	4	2	no	—
212	C₁₃×SD₁₆	—	4	2	no	—
213	C₁₃×D₈	—	2	4	no	—
214	C₁₃×D₈	—	4	2	no	—
215	C₁₃×D₈	—	4	2	no	—
216	C₁₃×D₈	—	4	2	no	—
217	C₁₃×M₁₆	—	2	1	no	—
218	C₁₃×M₁₆	—	2	1	no	—
219	C₁₃×M₁₆	—	2	1	no	—
220	C₁₃×M₁₆	—	2	1	no	—
221	C₁₃×M₁₆	—	2	1	no	—
222	C₁₃×M₁₆	—	2	1	no	—
223	C₁₃×M₁₆	—	2	1	no	—
224	C₁₃×M₁₆	—	2	1	no	—
225	C₁₃×M₁₆	—	2	1	no	—
226	C₁₃×M₁₆	—	2	1	no	—
227	C₁₃×M₁₆	—	2	1	no	—
228	C₁₃×M₁₆	—	4	2	no	—
229	C₁₃×M₁₆	—	4	2	no	—
230	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	4	2	no	—
242	C₂×C₈×C₁₃	—	4	2	no	—
243	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	2	1	no	—
255	C₁₃×C₂²⋊C₄	—	2	1	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	1	no	—
258	C₁₃×C₂²⋊C₄	—	4	1	no	—
259	C₁₃×C₂²⋊C₄	—	4	1	no	—
260	C₁₃×C₂²⋊C₄	—	4	1	no	—
261	C₁₃×C₂²⋊C₄	—	4	1	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂×#472	C₂×C₁₃	1	1	yes	characteristic
270	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#3040	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2045	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂³×C₁₃	—	2	1	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	8	1	no	—
292	C₂³×C₁₃	—	8	1	no	—
293	C₂³×C₁₃	—	8	1	no	—
294	C₂³×C₁₃	—	8	1	no	—
295	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
296	Q₈×C₁₃	—	2	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	—	4	1	no	—
300	Q₈×C₁₃	—	4	1	no	—
301	Q₈×C₁₃	#121	1	2	yes	—
302	D₄×C₁₃	—	2	2	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	2	2	no	—
305	D₄×C₁₃	—	2	1	no	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	#121	1	2	yes	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	2	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	8	1	no	—
327	C₂×C₄×C₁₃	—	8	2	no	—
328	C₂×C₄×C₁₃	—	8	2	no	—
329	C₂×C₄×C₁₃	—	8	1	no	—
330	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
331	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
332	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
333	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
340	C₈×C₁₃	—	2	2	no	—
341	C₈×C₁₃	—	2	1	no	—
342	C₈×C₁₃	—	2	1	no	—
343	C₈×C₁₃	—	2	1	no	—
344	C₈×C₁₃	—	2	1	no	—
345	C₈×C₁₃	—	4	1	no	—
346	C₈×C₁₃	—	4	1	no	—
347	C₈×C₁₃	—	4	1	no	—
348	C₈×C₁₃	—	4	1	no	—
349	C₈×C₁₃	—	4	1	no	—
350	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
358	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
360	#472	—	2	4	no	—
361	#471	—	2	4	no	—
362	#464	—	2	1	no	—
363	#464	—	2	1	no	—
364	#463	—	2	1	no	—
365	#463	—	2	1	no	—
366	#463	—	2	1	no	—
367	#463	—	2	1	no	—
368	#463	—	2	1	no	—
369	#463	—	2	1	no	—
370	#442	—	2	1	no	—
371	#440	—	2	1	no	—
372	C₄×SD₁₆	—	2	1	no	—
373	C₄×D₈	—	2	1	no	—
374	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
376	#428	C₂²×C₁₃	1	1	yes	characteristic
377	#424	—	2	1	no	—
378	#424	—	2	1	no	—
379	#424	C₂²×C₁₃	1	1	yes	characteristic
380	#424	C₂²×C₁₃	1	1	yes	characteristic
381	#423	—	2	1	no	—
382	#423	C₂²×C₁₃	1	1	yes	characteristic
383	#423	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₈	—	2	1	no	—
385	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
386	#419	C₂²×C₁₃	1	1	yes	characteristic
387	#418	C₂²×C₁₃	1	1	yes	characteristic
388	#418	C₂²×C₁₃	1	1	yes	characteristic
389	#417	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
398	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
399	#343	C₂²×C₁₃	1	1	yes	characteristic
400	#343	C₂²×C₁₃	1	1	yes	characteristic
401	#341	C₂²×C₁₃	1	1	yes	characteristic
402	#341	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×C₁₃	—	2	1	no	—
404	C₂²×C₁₃	—	2	1	no	—
405	C₂²×C₁₃	—	2	2	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	4	1	no	—
408	C₂²×C₁₃	—	4	2	no	—
409	C₂²×C₁₃	—	8	2	no	—
410	C₂²×C₁₃	—	8	2	no	—
411	C₂²×C₁₃	—	8	1	no	—
412	C₂²×C₁₃	—	8	1	no	—
413	C₂²×C₁₃	—	8	1	no	—
414	C₂²×C₁₃	—	8	1	no	—
415	C₂²×C₁₃	—	8	1	no	—
416	C₂²×C₁₃	—	16	1	no	—
417	C₂²×C₁₃	—	16	1	no	—
418	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
419	C₂²×C₁₃	#547	1	1	yes	characteristic
420	C₂²×C₁₃	#553	1	1	yes	characteristic
421	C₄×C₁₃	—	2	2	no	—
422	C₄×C₁₃	—	2	1	no	—
423	C₄×C₁₃	—	2	1	no	—
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	4	1	no	—
427	C₄×C₁₃	—	4	1	no	—
428	C₄×C₁₃	—	8	1	no	—
429	C₄×C₁₃	—	8	1	no	—
430	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
431	C₄×C₁₃	#537	1	1	yes	characteristic
432	C₄×C₁₃	D₄²	1	1	yes	characteristic
433	C₄×C₁₃	#548	1	1	yes	characteristic
434	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
435	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	#137	—	2	2	no	—
440	#137	—	2	2	no	—
441	AGL(1,ℤ/8)	—	2	2	no	—
442	AGL(1,ℤ/8)	—	2	2	no	—
443	AGL(1,ℤ/8)	—	2	2	no	—
444	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	—
445	C₂×Q₁₆	—	2	1	no	—
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×SD₁₆	—	2	1	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×SD₁₆	—	2	1	no	—
451	C₂×SD₁₆	—	2	1	no	—
452	C₂×SD₁₆	—	4	1	no	—
453	C₂×D₈	—	2	1	no	—
454	C₂×D₈	—	2	2	no	—
455	C₂×D₈	—	2	1	no	—
456	C₂×D₈	—	2	1	no	—
457	C₂×D₈	—	2	1	no	—
458	C₂×D₈	—	4	1	no	—
459	#131	—	2	2	no	—
460	#131	—	2	2	no	—
461	#131	—	4	1	no	—
462	#131	—	4	1	no	—
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	—	2	1	no	—
465	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×C₈	—	2	1	no	—
472	C₂²×C₈	—	2	1	no	—
473	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
475	#124	—	2	1	no	—
476	#124	—	2	1	no	—
477	#124	—	2	1	no	—
478	#124	—	2	1	no	—
479	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
480	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
488	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
489	#117	—	2	1	no	—
490	#117	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
497	#108	—	2	2	no	—
498	#108	—	2	2	no	—
499	#107	—	2	1	no	—
500	#106	—	2	1	no	—
501	C₄⋊C₈	—	2	1	no	—
502	C₄⋊C₈	—	2	1	no	—
503	C₄⋊C₈	—	2	1	no	—
504	C₄⋊C₈	—	2	1	no	—
505	C₄⋊C₈	—	2	1	no	—
506	C₄⋊C₈	—	2	1	no	—
507	C₄⋊C₈	—	2	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
510	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
511	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
512	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
513	#103	—	2	1	no	—
514	#103	—	2	1	no	—
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#102	—	2	1	no	—
519	#102	—	2	1	no	—
520	#102	—	2	1	no	—
521	#102	—	2	1	no	—
522	#102	—	2	1	no	—
523	#102	—	2	1	no	—
524	#102	—	2	1	no	—
525	#101	—	2	2	no	—
526	#101	—	4	1	no	—
527	#100	—	2	2	no	—
528	#100	—	2	2	no	—
529	#100	—	2	2	no	—
530	#100	—	4	1	no	—
531	#97	—	2	1	no	—
532	C₄×C₈	—	2	1	no	—
533	C₂×C₁₃	—	2	1	no	—
534	C₂×C₁₃	—	2	1	no	—
535	C₂×C₁₃	—	4	2	no	—
536	C₂×C₁₃	—	8	2	no	—
537	C₂×C₁₃	—	16	1	no	—
538	C₂×C₁₃	#2416	1	1	yes	characteristic
539	C₂×C₁₃	#3067	1	1	yes	characteristic
540	C₂×C₁₃	#3068	1	1	yes	characteristic
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	#41	—	2	1	no	—
544	#41	—	2	1	no	—
545	#41	C₂×D₄×C₁₃	1	2	yes	—
546	#41	C₁₃×#41	1	2	yes	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
567	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	4	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
577	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
579	Q₁₆	—	4	2	no	—
580	SD₁₆	—	2	4	no	—
581	SD₁₆	—	4	2	no	—
582	SD₁₆	—	4	2	no	—
583	SD₁₆	—	4	2	no	—
584	SD₁₆	—	4	2	no	—
585	D₈	—	2	4	no	—
586	D₈	—	4	2	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	2	no	—
589	M₁₆	—	2	1	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	1	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	—	2	1	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	2	1	no	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	1	no	—
600	M₁₆	—	4	2	no	—
601	M₁₆	—	4	2	no	—
602	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	4	2	no	—
614	C₂×C₈	—	4	2	no	—
615	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	4	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	4	1	no	—
633	C₂²⋊C₄	—	4	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₁₃	#24774	1	1	yes	characteristic, direct product factor, Sylow
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	—	8	1	no	—
651	C₂³	—	8	1	no	—
652	C₂³	—	8	1	no	—
653	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
654	Q₈	—	2	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	C₁₃×#121	1	2	yes	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	2	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	C₁₃×#121	1	2	yes	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	—	8	1	no	—
688	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
689	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
690	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
691	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
696	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₈	—	2	1	no	—
702	C₈	—	2	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	8	2	no	—
715	C₂²	—	8	2	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	16	1	no	—
722	C₂²	—	16	1	no	—
723	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
724	C₂²	C₁₃×#547	1	1	yes	characteristic
725	C₂²	C₁₃×#553	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	8	1	no	—
734	C₄	—	8	1	no	—
735	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
736	C₄	C₁₃×#537	1	1	yes	characteristic
737	C₄	D₄²×C₁₃	1	1	yes	characteristic
738	C₄	C₁₃×#548	1	1	yes	characteristic
739	C₂	—	2	1	no	—
740	C₂	—	2	1	no	—
741	C₂	—	4	2	no	—
742	C₂	—	8	2	no	—
743	C₂	—	16	1	no	—
744	C₂	C₁₃×#2416	1	1	yes	characteristic
745	C₂	C₁₃×#3067	1	1	yes	characteristic
746	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#471	C₂	semidirect
3. C₁₃×#3040	C₂	semidirect
4. C₂×C₁₃×#463	C₂	semidirect
5. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
6. C₁₃×#2906	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#2046	C₂	semidirect
10. C₁₃×#2045	C₂	semidirect
11. C₁₃×#1967	C₂	semidirect
12. C₁₃×#1950	C₂	semidirect
13. C₁₃×#1908	C₂	semidirect
14. C₁₃×#1907	C₂	semidirect
15. C₁₃×#1800	C₂	semidirect
168. #24774	C₁₃	direct (N × H)
270. C₂×#471	C₂×C₁₃	semidirect
271. #3040	C₂×C₁₃	semidirect
272. C₂×#463	C₂×C₁₃	semidirect
273. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
274. #2906	C₂×C₁₃	semidirect
275. #2064	C₂×C₁₃	semidirect
276. #2063	C₂×C₁₃	semidirect
277. #2046	C₂×C₁₃	semidirect
278. #2045	C₂×C₁₃	semidirect
279. #1967	C₂×C₁₃	semidirect
280. #1950	C₂×C₁₃	semidirect
281. #1908	C₂×C₁₃	semidirect
282. #1907	C₂×C₁₃	semidirect
283. #1800	C₂×C₁₃	semidirect
641. C₁₃	#24774	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×#472	2
C₂×C₁₃×#471	2
C₁₃×#3040	2
C₂×C₁₃×#463	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2906	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2046	2
C₁₃×#2045	2
C₁₃×#1967	2
C₁₃×#1950	2
C₁₃×#1908	2
C₁₃×#1907	2
C₁₃×#1800	2
#24774	13

Subgroups — C13×#24774 #15711113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24774 #15711113