Subgroups — C₁₃×#24770 #15711109

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 598 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	2	yes	maximal, complemented
2	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2045	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1907	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#472	—	2	8	no	—
20	C₁₃×#460	—	2	1	no	—
21	C₁₃×#460	—	2	1	no	—
22	C₁₃×#459	—	2	1	no	—
23	C₁₃×#459	—	2	1	no	—
24	C₁₃×#459	—	2	1	no	—
25	C₁₃×#459	—	2	1	no	—
26	C₁₃×#459	—	2	2	no	—
27	C₁₃×#442	—	2	1	no	—
28	C₁₃×#440	—	2	1	no	—
29	C₄×C₁₃×SD₁₆	—	2	1	no	—
30	C₄×C₁₃×D₈	—	2	1	no	—
31	C₂×C₁₃×#108	C₂²	1	2	yes	—
32	C₁₃×#428	C₂²	1	1	yes	characteristic
33	C₁₃×#424	—	2	2	no	—
34	C₁₃×#424	C₂²	1	2	yes	—
35	C₁₃×#423	—	2	1	no	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×#418	C₂²	1	2	yes	—
41	C₁₃×#418	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	2	yes	—
44	C₂×C₁₃×#100	C₂²	1	2	yes	—
45	C₂×C₁₃×#100	C₂²	1	2	yes	—
46	C₂×C₁₃×#100	C₂²	1	2	yes	—
47	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#341	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
57	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
59	C₁₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×D₈	—	2	1	no	—
63	C₂×C₁₃×D₈	—	2	2	no	—
64	C₂×C₁₃×D₈	—	2	4	no	—
65	C₂×C₁₃×D₈	—	2	2	no	—
66	C₂×C₁₃×D₈	—	2	2	no	—
67	C₂×C₁₃×D₈	—	4	2	no	—
68	C₁₃×#131	—	2	4	no	—
69	C₁₃×#131	—	4	2	no	—
70	C₂×C₁₃×M₁₆	—	2	2	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	—	2	2	no	—
76	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#127	—	2	1	no	—
78	C₁₃×#127	—	2	1	no	—
79	C₁₃×#127	—	2	1	no	—
80	C₁₃×#127	—	2	1	no	—
81	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₁₃	—	2	1	no	—
84	C₄×D₄×C₁₃	—	2	1	no	—
85	C₄×D₄×C₁₃	—	2	1	no	—
86	C₄×D₄×C₁₃	—	2	1	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
91	C₁₃×#117	—	2	1	no	—
92	C₁₃×#117	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#108	—	2	4	no	—
98	C₁₃×#107	—	2	1	no	—
99	C₁₃×#106	—	2	1	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
109	C₁₃×#103	—	2	1	no	—
110	C₁₃×#102	—	2	1	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#102	—	2	1	no	—
114	C₁₃×#102	—	2	1	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	2	no	—
117	C₁₃×#100	—	2	4	no	—
118	C₁₃×#100	—	2	4	no	—
119	C₁₃×#100	—	4	2	no	—
120	C₁₃×#97	—	2	1	no	—
121	C₄×C₈×C₁₃	—	2	1	no	—
122	#24770	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	1	no	—
124	C₂⁴×C₁₃	—	2	2	no	—
125	C₁₃×#41	—	2	1	no	—
126	C₁₃×#41	—	2	1	no	—
127	C₁₃×#41	C₂×D₄	1	2	yes	—
128	C₁₃×#41	#41	1	2	yes	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	4	1	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂×D₄×C₁₃	—	4	1	no	—
145	C₂×D₄×C₁₃	—	4	1	no	—
146	C₂×D₄×C₁₃	—	8	2	no	—
147	C₂×D₄×C₁₃	—	8	2	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	4	1	no	—
155	C₂²×C₄×C₁₃	—	4	1	no	—
156	C₂²×C₄×C₁₃	—	8	2	no	—
157	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×SD₁₆	—	2	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×D₈	—	2	4	no	—
163	C₁₃×D₈	—	4	4	no	—
164	C₁₃×D₈	—	4	4	no	—
165	C₁₃×D₈	—	4	4	no	—
166	C₁₃×M₁₆	—	2	1	no	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	2	1	no	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	1	no	—
173	C₁₃×M₁₆	—	4	4	no	—
174	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	2	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	4	4	no	—
182	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₁₃×C₂²⋊C₄	—	4	1	no	—
194	C₁₃×C₂²⋊C₄	—	4	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂×#472	C₂×C₁₃	1	2	yes	complemented
203	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2063	C₂×C₁₃	1	2	yes	complemented
208	#2045	C₂×C₁₃	1	2	yes	complemented
209	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1907	C₂×C₁₃	1	2	yes	complemented
212	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	8	1	no	—
221	C₂³×C₁₃	—	8	1	no	—
222	C₂³×C₁₃	—	8	2	no	—
223	C₂³×C₁₃	—	8	2	no	—
224	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	#121	1	2	yes	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	1	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	4	1	no	—
234	D₄×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	8	2	no	—
239	D₄×C₁₃	—	8	2	no	—
240	D₄×C₁₃	—	8	2	no	—
241	D₄×C₁₃	—	8	2	no	—
242	D₄×C₁₃	#121	1	2	yes	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	8	1	no	—
253	C₂×C₄×C₁₃	—	8	2	no	—
254	C₂×C₄×C₁₃	—	8	2	no	—
255	C₂×C₄×C₁₃	—	8	1	no	—
256	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
266	C₈×C₁₃	—	2	2	no	—
267	C₈×C₁₃	—	2	2	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	4	2	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	2	no	—
272	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
273	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
275	C₂×#131	C₂²×C₁₃	1	2	yes	—
276	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
277	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	#472	—	2	8	no	—
280	#460	—	2	1	no	—
281	#460	—	2	1	no	—
282	#459	—	2	1	no	—
283	#459	—	2	1	no	—
284	#459	—	2	1	no	—
285	#459	—	2	1	no	—
286	#459	—	2	2	no	—
287	#442	—	2	1	no	—
288	#440	—	2	1	no	—
289	C₄×SD₁₆	—	2	1	no	—
290	C₄×D₈	—	2	1	no	—
291	C₂×#108	C₂²×C₁₃	1	2	yes	—
292	#428	C₂²×C₁₃	1	1	yes	characteristic
293	#424	—	2	2	no	—
294	#424	C₂²×C₁₃	1	2	yes	—
295	#423	—	2	1	no	—
296	#423	C₂²×C₁₃	1	1	yes	characteristic
297	#423	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₈	—	2	1	no	—
299	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
300	#418	C₂²×C₁₃	1	2	yes	—
301	#418	C₂²×C₁₃	1	1	yes	characteristic
302	#417	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#102	C₂²×C₁₃	1	2	yes	—
304	C₂×#100	C₂²×C₁₃	1	2	yes	—
305	C₂×#100	C₂²×C₁₃	1	2	yes	—
306	C₂×#100	C₂²×C₁₃	1	2	yes	—
307	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	#343	C₂²×C₁₃	1	2	yes	—
309	#341	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	4	1	no	—
314	C₂²×C₁₃	—	4	1	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	8	2	no	—
317	C₂²×C₁₃	—	8	2	no	—
318	C₂²×C₁₃	—	8	1	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	2	no	—
321	C₂²×C₁₃	—	8	2	no	—
322	C₂²×C₁₃	—	8	2	no	—
323	C₂²×C₁₃	—	16	2	no	—
324	C₂²×C₁₃	—	16	2	no	—
325	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
326	C₂²×C₁₃	#547	1	1	yes	characteristic
327	C₂²×C₁₃	#553	1	1	yes	characteristic
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	#472	1	2	yes	complemented
336	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
337	C₄×C₁₃	#537	1	1	yes	characteristic
338	C₄×C₁₃	D₄²	1	1	yes	characteristic
339	C₄×C₁₃	#548	1	1	yes	characteristic
340	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
344	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	AGL(1,ℤ/8)	—	2	2	no	—
347	AGL(1,ℤ/8)	—	2	4	no	—
348	AGL(1,ℤ/8)	—	2	4	no	—
349	AGL(1,ℤ/8)	D₄×C₁₃	1	4	yes	complemented
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×D₈	—	2	1	no	—
353	C₂×D₈	—	2	4	no	—
354	C₂×D₈	—	2	2	no	—
355	C₂×D₈	—	2	2	no	—
356	C₂×D₈	—	2	2	no	—
357	C₂×D₈	—	4	2	no	—
358	#131	—	2	4	no	—
359	#131	—	4	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
362	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
363	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×C₈	—	2	2	no	—
366	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
367	#127	—	2	1	no	—
368	#127	—	2	1	no	—
369	#127	—	2	1	no	—
370	#127	—	2	1	no	—
371	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
372	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
380	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
381	#117	—	2	1	no	—
382	#117	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	#108	—	2	4	no	—
388	#107	—	2	1	no	—
389	#106	—	2	1	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	2	2	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
399	#103	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#100	—	2	4	no	—
408	#100	—	2	4	no	—
409	#100	—	4	2	no	—
410	#97	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₂×C₁₃	—	2	1	no	—
413	C₂×C₁₃	—	2	1	no	—
414	C₂×C₁₃	—	4	2	no	—
415	C₂×C₁₃	—	8	2	no	—
416	C₂×C₁₃	—	16	2	no	—
417	C₂×C₁₃	#2416	1	1	yes	characteristic
418	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
419	C₂×C₁₃	#3068	1	1	yes	characteristic
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	2	2	no	—
422	#41	—	2	1	no	—
423	#41	—	2	1	no	—
424	#41	C₂×D₄×C₁₃	1	2	yes	—
425	#41	C₁₃×#41	1	2	yes	—
426	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	8	2	no	—
444	C₂×D₄	—	8	2	no	—
445	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	8	2	no	—
454	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
455	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	SD₁₆	—	2	4	no	—
458	SD₁₆	—	4	4	no	—
459	D₈	—	2	4	no	—
460	D₈	—	4	4	no	—
461	D₈	—	4	4	no	—
462	D₈	—	4	4	no	—
463	M₁₆	—	2	1	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	1	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	4	4	no	—
471	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	4	no	—
479	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
480	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₁₃	#24770	1	1	yes	characteristic, direct product factor, Sylow
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	8	1	no	—
508	C₂³	—	8	1	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	2	no	—
511	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
512	Q₈	—	2	1	no	—
513	Q₈	C₁₃×#121	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	2	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	C₁₃×#121	1	2	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
544	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
545	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
546	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
551	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	4	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	2	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	16	2	no	—
573	C₂²	—	16	2	no	—
574	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
575	C₂²	C₁₃×#547	1	1	yes	characteristic
576	C₂²	C₁₃×#553	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	8	1	no	—
584	C₄	C₁₃×#472	1	2	yes	complemented
585	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
586	C₄	C₁₃×#537	1	1	yes	characteristic
587	C₄	D₄²×C₁₃	1	1	yes	characteristic
588	C₄	C₁₃×#548	1	1	yes	characteristic
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	4	2	no	—
592	C₂	—	8	2	no	—
593	C₂	—	16	2	no	—
594	C₂	C₁₃×#2416	1	1	yes	characteristic
595	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
596	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₂×C₁₃×#472	C₂	semidirect
2. C₁₃×#3038	C₂	semidirect
3. C₂×C₁₃×#459	C₂	semidirect
4. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
5. C₁₃×#2906	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2045	C₂	semidirect
8. C₁₃×#1965	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1907	C₂	semidirect
11. C₁₃×#1800	C₂	semidirect
59. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
122. #24770	C₁₃	direct (N × H)
202. C₂×#472	C₂×C₁₃	semidirect
203. #3038	C₂×C₁₃	semidirect
204. C₂×#459	C₂×C₁₃	semidirect
205. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
206. #2906	C₂×C₁₃	semidirect
207. #2063	C₂×C₁₃	semidirect
208. #2045	C₂×C₁₃	semidirect
209. #1965	C₂×C₁₃	semidirect
210. #1950	C₂×C₁₃	semidirect
211. #1907	C₂×C₁₃	semidirect
212. #1800	C₂×C₁₃	semidirect
335. C₄×C₁₃	#472	semidirect
349. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
499. C₁₃	#24770	direct (N × H)
584. C₄	C₁₃×#472	semidirect

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
C₁₃×#3038	2
C₂×C₁₃×#459	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2906	2
C₁₃×#2063	2
C₁₃×#2045	2
C₁₃×#1965	2
C₁₃×#1950	2
C₁₃×#1907	2
C₁₃×#1800	2
#24770	13

Subgroups — C13×#24770 #15711109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24770 #15711109