Subgroups — C₁₃×#24320 #15710659

Order 3328.

1092 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	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×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2060	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2027	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1883	C₂	1	2	yes	maximal
10	C₁₃×#1859	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	Q₈²×C₁₃	—	2	1	no	—
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#554	—	2	1	no	—
16	C₁₃×#554	—	2	2	no	—
17	D₄×Q₈×C₁₃	—	2	2	no	—
18	D₄×Q₈×C₁₃	—	2	1	no	—
19	C₁₃×#544	—	2	2	no	—
20	C₁₃×#544	C₂²	1	2	yes	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₁₃×#520	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	1	yes	characteristic
41	C₁₃×#418	C₂²	1	2	yes	—
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
44	C₁₃×#399	—	2	2	no	—
45	C₁₃×#390	C₂²	1	2	yes	—
46	C₁₃×#384	C₂²	1	2	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#343	C₂²	1	2	yes	—
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	—	2	2	no	—
55	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
59	C₁₃×AGL(1,ℤ/8)	Q₈	1	4	yes	complemented
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×D₈	—	2	1	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	—	2	4	no	—
68	C₁₃×C₄⋊Q₈	—	2	2	no	—
69	C₁₃×C₄⋊Q₈	—	2	2	no	—
70	C₁₃×C₄⋊Q₈	—	2	1	no	—
71	C₁₃×C₄⋊Q₈	—	2	1	no	—
72	C₁₃×C₄⋊Q₈	—	2	1	no	—
73	C₁₃×C₄⋊Q₈	—	2	1	no	—
74	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	D₄	1	2	yes	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	4	8	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	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	4	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	D₄	1	1	yes	characteristic
104	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	C₁₃×#117	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
113	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	—	2	4	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×#97	—	2	1	no	—
135	C₄×C₈×C₁₃	—	2	1	no	—
136	C₁₃×#95	—	2	1	no	—
137	#24320	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	—	2	1	no	—
139	C₁₃×#41	—	2	1	no	—
140	C₁₃×#41	—	2	1	no	—
141	C₁₃×#41	C₂×Q₈	1	2	yes	—
142	C₁₃×#41	#41	1	2	yes	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	4	4	no	—
149	C₂×Q₈×C₁₃	—	8	4	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	complemented
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×SD₁₆	—	2	4	no	—
173	C₁₃×D₈	—	2	4	no	—
174	C₁₃×M₁₆	—	2	1	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	1	no	—
177	C₁₃×M₁₆	—	2	1	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	C₂×Q₈	1	2	yes	complemented
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	4	8	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
204	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	8	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₁₃×C₂²⋊C₄	—	4	1	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	2	2	no	—
218	C₄²×C₁₃	—	2	2	no	—
219	C₄²×C₁₃	—	2	2	no	—
220	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
224	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
227	#2542	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2060	C₂×C₁₃	1	2	yes	complemented
229	#2027	C₂×C₁₃	1	2	yes	complemented
230	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1883	C₂×C₁₃	1	2	yes	—
233	#1859	C₂×C₁₃	1	2	yes	complemented
234	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	4	2	no	—
238	C₂³×C₁₃	—	4	2	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₁₃	—	2	1	no	—
243	Q₈×C₁₃	—	4	2	no	—
244	Q₈×C₁₃	—	4	4	no	—
245	Q₈×C₁₃	—	4	2	no	—
246	Q₈×C₁₃	—	8	2	no	—
247	Q₈×C₁₃	—	8	4	no	—
248	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	complemented
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	2	1	no	—
253	D₄×C₁₃	—	2	2	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	complemented
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	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	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	4	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	8	2	no	—
276	C₂×C₄×C₁₃	—	8	4	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
279	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
280	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
281	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₁₃	—	2	2	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	2	no	—
291	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
292	Q₈²	—	2	1	no	—
293	#557	—	2	1	no	—
294	#554	—	2	1	no	—
295	#554	—	2	2	no	—
296	D₄×Q₈	—	2	2	no	—
297	D₄×Q₈	—	2	1	no	—
298	#544	—	2	2	no	—
299	#544	C₂²×C₁₃	1	2	yes	—
300	#533	—	2	1	no	—
301	#533	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊Q₈	—	2	1	no	—
303	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₂²⋊Q₈	—	2	2	no	—
305	#520	C₂²×C₁₃	1	2	yes	—
306	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	#478	—	2	2	no	—
309	#476	—	2	1	no	—
310	#474	—	2	1	no	—
311	#442	—	2	1	no	—
312	#440	—	2	1	no	—
313	C₄×SD₁₆	—	2	1	no	—
314	C₄×D₈	—	2	1	no	—
315	#428	C₂²×C₁₃	1	2	yes	—
316	#428	C₂²×C₁₃	1	1	yes	characteristic
317	#423	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#104	C₂²×C₁₃	1	2	yes	—
319	#418	C₂²×C₁₃	1	2	yes	—
320	#418	C₂²×C₁₃	1	1	yes	characteristic
321	#417	C₂²×C₁₃	1	1	yes	characteristic
322	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
323	#399	—	2	2	no	—
324	#390	C₂²×C₁₃	1	2	yes	—
325	#384	C₂²×C₁₃	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	#343	C₂²×C₁₃	1	2	yes	—
328	#343	C₂²×C₁₃	1	2	yes	—
329	#339	C₂²×C₁₃	1	2	yes	—
330	#339	C₂²×C₁₃	1	2	yes	—
331	#339	C₂²×C₁₃	1	2	yes	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	8	2	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
343	C₂²×C₁₃	#548	1	1	yes	characteristic
344	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	4	4	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	4	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	#453	1	2	yes	—
357	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄×C₁₃	#536	1	1	yes	characteristic
359	C₄×C₁₃	#548	1	1	yes	characteristic
360	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
361	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×Q₈	—	2	2	no	—
363	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂³×C₄	—	2	1	no	—
366	AGL(1,ℤ/8)	—	2	2	no	—
367	AGL(1,ℤ/8)	Q₈×C₁₃	1	4	yes	complemented
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×D₈	—	2	1	no	—
370	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
372	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	2	4	no	—
376	C₄⋊Q₈	—	2	2	no	—
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	#125	—	2	4	no	—
385	#125	—	2	2	no	—
386	#125	—	2	2	no	—
387	#125	D₄×C₁₃	1	2	yes	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	4	no	—
391	C₂²⋊Q₈	—	2	4	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	1	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	4	8	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
402	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	4	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
412	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
413	#117	—	2	2	no	—
414	#117	—	2	1	no	—
415	#117	C₂³×C₁₃	1	1	yes	characteristic
416	#117	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	4	no	—
421	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	4	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	#107	—	2	1	no	—
430	#107	—	2	2	no	—
431	#106	—	2	1	no	—
432	#106	—	2	2	no	—
433	C₄⋊C₈	—	2	1	no	—
434	C₄⋊C₈	—	2	1	no	—
435	#104	—	2	4	no	—
436	#103	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	1	no	—
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#97	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	#95	—	2	1	no	—
445	C₂×C₁₃	—	2	1	no	—
446	C₂×C₁₃	—	2	1	no	—
447	C₂×C₁₃	—	4	2	no	—
448	C₂×C₁₃	—	8	2	no	—
449	C₂×C₁₃	#2409	1	1	yes	characteristic
450	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
451	C₂×C₁₃	#3020	1	1	yes	characteristic
452	C₂⁴	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	C₂×Q₈×C₁₃	1	2	yes	—
456	#41	C₁₃×#41	1	2	yes	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	4	4	no	—
463	C₂×Q₈	—	8	4	no	—
464	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	complemented
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	SD₁₆	—	2	4	no	—
487	D₈	—	2	4	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	2	no	—
490	M₁₆	—	2	1	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	C₂×Q₈×C₁₃	1	2	yes	complemented
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	2	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	4	8	no	—
515	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	4	8	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₁₃	#24320	1	1	yes	characteristic, direct product factor, Sylow
539	C₂³	—	2	1	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	Q₈	—	2	1	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	4	no	—
549	Q₈	—	4	2	no	—
550	Q₈	—	8	2	no	—
551	Q₈	—	8	4	no	—
552	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	complemented
553	D₄	—	2	2	no	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	2	1	no	—
557	D₄	—	2	2	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	complemented
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	8	2	no	—
580	C₂×C₄	—	8	4	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
583	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
584	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
585	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
590	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
591	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	2	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
606	C₂²	C₁₃×#548	1	1	yes	characteristic
607	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	8	1	no	—
619	C₄	C₁₃×#453	1	2	yes	—
620	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
621	C₄	C₁₃×#536	1	1	yes	characteristic
622	C₄	C₁₃×#548	1	1	yes	characteristic
623	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	4	2	no	—
627	C₂	—	8	2	no	—
628	C₂	C₁₃×#2409	1	1	yes	characteristic
629	C₂	C₂×C₁₃×#453	1	1	yes	characteristic
630	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×#3503	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
4. C₁₃×#2542	C₂	semidirect
5. C₁₃×#2060	C₂	semidirect
6. C₁₃×#2027	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1986	C₂	semidirect
10. C₁₃×#1859	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
59. C₁₃×AGL(1,ℤ/8)	Q₈	semidirect
137. #24320	C₁₃	direct (N × H)
158. C₂×D₄×C₁₃	C₂×Q₈	semidirect
179. C₁₃×M₁₆	C₂×Q₈	semidirect
224. #3503	C₂×C₁₃	semidirect
225. #3077	C₂×C₁₃	semidirect
227. #2542	C₂×C₁₃	semidirect
228. #2060	C₂×C₁₃	semidirect
229. #2027	C₂×C₁₃	semidirect
230. #1997	C₂×C₁₃	semidirect
231. #1986	C₂×C₁₃	semidirect
233. #1859	C₂×C₁₃	semidirect
234. #1806	C₂×C₁₃	semidirect
248. Q₈×C₁₃	C₂²⋊Q₈	semidirect
256. D₄×C₁₃	C₂²⋊Q₈	semidirect
367. AGL(1,ℤ/8)	Q₈×C₁₃	semidirect
472. C₂×D₄	C₂×Q₈×C₁₃	semidirect
493. M₁₆	C₂×Q₈×C₁₃	semidirect
538. C₁₃	#24320	direct (N × H)
552. Q₈	C₁₃×C₂²⋊Q₈	semidirect
560. D₄	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3503	2
C₁₃×#3077	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2542	2
C₁₃×#2060	2
C₁₃×#2027	2
C₁₃×#1997	2
C₁₃×#1986	2
C₁₃×#1883	2
C₁₃×#1859	2
C₁₃×#1806	2
#24320	13

Subgroups — C13×#24320 #15710659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24320 #15710659