Subgroups — C₁₃×#24145 #15710484

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2003	C₂	1	2	yes	maximal
7	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1888	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1857	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#556	—	2	1	no	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#552	—	2	2	no	—
19	C₁₃×#541	—	2	2	no	—
20	C₁₃×#536	C₂²	1	2	yes	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	—	2	1	no	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	C₂²	1	2	yes	—
26	C₁₃×#519	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#478	—	2	2	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#474	—	2	1	no	—
32	C₁₃×#442	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×SD₁₆	—	2	1	no	—
35	C₄×C₁₃×D₈	—	2	1	no	—
36	C₁₃×#428	C₂²	1	2	yes	—
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	2	yes	—
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×#101	C₂²	1	2	yes	—
44	C₂×C₁₃×#101	C₂²	1	2	yes	—
45	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
46	C₁₃×#397	—	2	2	no	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#380	—	2	2	no	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₁₃×#339	C₂²	1	2	yes	—
51	C₁₃×#339	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	1	no	—
60	C₂×C₁₃×D₈	—	2	1	no	—
61	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#126	—	2	4	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	—	2	2	no	—
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	D₄	1	2	yes	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	—	4	2	no	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₁₃×#117	—	2	4	no	—
109	C₁₃×#117	—	2	1	no	—
110	C₁₃×#117	C₂³	1	1	yes	characteristic
111	C₁₃×#117	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²×C₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	—	2	1	no	—
122	C₁₃×#107	—	2	2	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×#106	—	2	2	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×#104	—	4	2	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	2	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#101	—	2	4	no	—
135	C₁₃×#101	—	4	2	no	—
136	C₁₃×#97	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	4	no	—
140	#24145	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₁₃×#41	—	2	1	no	—
143	C₁₃×#41	—	2	1	no	—
144	C₁₃×#41	—	2	1	no	—
145	C₁₃×#41	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	2	2	no	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₃	#41	1	2	yes	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	—	4	1	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×SD₁₆	—	2	4	no	—
176	C₁₃×D₈	—	2	4	no	—
177	C₁₃×M₁₆	—	2	1	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	—	2	1	no	—
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	#41	1	2	yes	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	4	2	no	—
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₁₃×C₂²⋊C₄	—	2	1	no	—
213	C₁₃×C₂²⋊C₄	—	4	8	no	—
214	C₁₃×C₂²⋊C₄	—	4	1	no	—
215	C₁₃×C₂²⋊C₄	—	4	1	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	—	2	4	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	2	no	—
222	C₄²×C₁₃	—	2	2	no	—
223	C₄²×C₁₃	—	2	2	no	—
224	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
228	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
231	#2547	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2038	C₂×C₁₃	1	2	yes	complemented
233	#2003	C₂×C₁₃	1	2	yes	—
234	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1888	C₂×C₁₃	1	2	yes	complemented
237	#1857	C₂×C₁₃	1	2	yes	complemented
238	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	4	2	no	—
242	C₂³×C₁₃	—	4	2	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₁₃	—	2	1	no	—
247	Q₈×C₁₃	—	2	1	no	—
248	Q₈×C₁₃	—	4	2	no	—
249	Q₈×C₁₃	—	4	2	no	—
250	Q₈×C₁₃	—	4	2	no	—
251	Q₈×C₁₃	—	4	2	no	—
252	Q₈×C₁₃	—	4	2	no	—
253	Q₈×C₁₃	—	4	2	no	—
254	D₄×C₁₃	—	2	1	no	—
255	D₄×C₁₃	—	2	2	no	—
256	D₄×C₁₃	—	2	1	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	4	1	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	8	2	no	—
282	C₂×C₄×C₁₃	—	8	2	no	—
283	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
284	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
285	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₈×C₁₃	—	4	2	no	—
296	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
297	#557	—	2	1	no	—
298	#557	—	2	1	no	—
299	#556	—	2	1	no	—
300	#556	—	2	1	no	—
301	#552	—	2	2	no	—
302	#552	—	2	2	no	—
303	#541	—	2	2	no	—
304	#536	C₂²×C₁₃	1	2	yes	—
305	#533	—	2	1	no	—
306	#533	—	2	1	no	—
307	#533	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#124	C₂²×C₁₃	1	2	yes	—
310	#519	C₂²×C₁₃	1	2	yes	—
311	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
313	#478	—	2	2	no	—
314	#476	—	2	1	no	—
315	#474	—	2	1	no	—
316	#442	—	2	1	no	—
317	#440	—	2	1	no	—
318	C₄×SD₁₆	—	2	1	no	—
319	C₄×D₈	—	2	1	no	—
320	#428	C₂²×C₁₃	1	2	yes	—
321	#428	C₂²×C₁₃	1	1	yes	characteristic
322	#423	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#104	C₂²×C₁₃	1	2	yes	—
324	#418	C₂²×C₁₃	1	2	yes	—
325	#418	C₂²×C₁₃	1	1	yes	characteristic
326	#417	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#101	C₂²×C₁₃	1	2	yes	—
328	C₂×#101	C₂²×C₁₃	1	2	yes	—
329	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
330	#397	—	2	2	no	—
331	#391	C₂²×C₁₃	1	2	yes	—
332	#380	—	2	2	no	—
333	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
334	#339	C₂²×C₁₃	1	2	yes	—
335	#339	C₂²×C₁₃	1	2	yes	—
336	#339	C₂²×C₁₃	1	2	yes	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	8	2	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
348	C₂²×C₁₃	#546	1	1	yes	characteristic
349	C₂²×C₁₃	#547	1	1	yes	characteristic
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	4	4	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	8	2	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	#454	1	2	yes	—
362	C₄×C₁₃	#525	1	1	yes	characteristic
363	C₄×C₁₃	#537	1	1	yes	characteristic
364	C₄×C₁₃	#548	1	1	yes	characteristic
365	C₄×C₁₃	#550	1	1	yes	characteristic
366	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
368	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	AGL(1,ℤ/8)	—	2	2	no	—
371	AGL(1,ℤ/8)	—	2	2	no	—
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
376	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	—	2	1	no	—
379	C₄⋊Q₈	—	2	1	no	—
380	C₄⋊Q₈	—	2	1	no	—
381	C₄⋊Q₈	—	2	1	no	—
382	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
383	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
384	#126	—	2	4	no	—
385	#126	—	2	4	no	—
386	#125	—	2	2	no	—
387	#125	—	2	2	no	—
388	#125	—	2	4	no	—
389	#125	—	2	4	no	—
390	#125	D₄×C₁₃	1	2	yes	—
391	#124	—	2	2	no	—
392	#124	—	2	4	no	—
393	#124	—	4	2	no	—
394	#123	—	2	4	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	2	1	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
410	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
418	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
419	#117	—	2	2	no	—
420	#117	—	2	2	no	—
421	#117	—	2	4	no	—
422	#117	—	2	1	no	—
423	#117	C₂³×C₁₃	1	1	yes	characteristic
424	#117	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
427	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
434	#107	—	2	1	no	—
435	#107	—	2	2	no	—
436	#106	—	2	1	no	—
437	#106	—	2	2	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	#104	—	4	2	no	—
441	#103	—	2	1	no	—
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	2	no	—
446	#102	—	2	2	no	—
447	#101	—	2	4	no	—
448	#101	—	4	2	no	—
449	#97	—	2	1	no	—
450	C₄×C₈	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	4	no	—
453	C₂×C₁₃	—	2	1	no	—
454	C₂×C₁₃	—	2	1	no	—
455	C₂×C₁₃	—	8	1	no	—
456	C₂×C₁₃	—	8	2	no	—
457	C₂×C₁₃	#2407	1	1	yes	characteristic
458	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
459	C₂×C₁₃	#3020	1	1	yes	characteristic
460	C₂⁴	—	2	1	no	—
461	#41	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂×D₄	C₁₃×#41	1	2	yes	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
494	SD₁₆	—	2	4	no	—
495	D₈	—	2	4	no	—
496	M₁₆	—	2	1	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	2	1	no	—
499	M₁₆	—	2	2	no	—
500	M₁₆	—	2	1	no	—
501	M₁₆	C₁₃×#41	1	2	yes	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	2	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	2	4	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	4	8	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	4	no	—
536	C₄²	—	2	4	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	2	2	no	—
543	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₁₃	#24145	1	1	yes	characteristic, direct product factor, Sylow
548	C₂³	—	2	1	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	Q₈	—	2	1	no	—
556	Q₈	—	2	1	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	4	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	Q₈	—	4	2	no	—
563	D₄	—	2	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	1	no	—
566	D₄	—	2	2	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
593	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
594	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
595	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
616	C₂²	C₁₃×#546	1	1	yes	characteristic
617	C₂²	C₁₃×#547	1	1	yes	characteristic
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	4	no	—
626	C₄	—	4	1	no	—
627	C₄	—	8	2	no	—
628	C₄	—	8	1	no	—
629	C₄	C₁₃×#454	1	2	yes	—
630	C₄	C₁₃×#525	1	1	yes	characteristic
631	C₄	C₁₃×#537	1	1	yes	characteristic
632	C₄	C₁₃×#548	1	1	yes	characteristic
633	C₄	C₁₃×#550	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	8	2	no	—
637	C₂	—	8	1	no	—
638	C₂	C₁₃×#2407	1	1	yes	characteristic
639	C₂	C₂×C₁₃×#454	1	1	yes	characteristic
640	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
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 ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
4. C₁₃×#2547	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
7. C₁₃×#1986	C₂	semidirect
8. C₁₃×#1966	C₂	semidirect
9. C₁₃×#1888	C₂	semidirect
10. C₁₃×#1857	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
140. #24145	C₁₃	direct (N × H)
228. #3509	C₂×C₁₃	semidirect
229. #3077	C₂×C₁₃	semidirect
231. #2547	C₂×C₁₃	semidirect
232. #2038	C₂×C₁₃	semidirect
234. #1986	C₂×C₁₃	semidirect
235. #1966	C₂×C₁₃	semidirect
236. #1888	C₂×C₁₃	semidirect
237. #1857	C₂×C₁₃	semidirect
238. #1806	C₂×C₁₃	semidirect
547. C₁₃	#24145	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×#3509	2
C₁₃×#3077	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2547	2
C₁₃×#2038	2
C₁₃×#2003	2
C₁₃×#1986	2
C₁₃×#1966	2
C₁₃×#1888	2
C₁₃×#1857	2
C₁₃×#1806	2
#24145	13

Subgroups — C13×#24145 #15710484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24145 #15710484