Subgroups — C₁₃×#24330 #15710669

Order 3328.

1262 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2058	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal
10	C₁₃×#1864	C₂	1	2	yes	maximal
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	D₄×Q₈×C₁₃	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#475	—	2	4	no	—
25	C₄×C₁₃×SD₁₆	—	2	4	no	—
26	C₂×C₁₃×#106	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#398	—	2	2	no	—
35	C₁₃×#391	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	—	2	1	no	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#384	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	8	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	4	4	no	—
49	C₂²×Q₈×C₁₃	—	4	4	no	—
50	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	4	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	16	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	4	no	—
72	C₄×D₄×C₁₃	—	2	4	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	D₄	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#106	—	2	2	no	—
93	C₁₃×#106	—	2	4	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	2	4	no	—
99	C₄×C₈×C₁₃	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	C₁₃×#95	—	2	2	no	—
103	#24330	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	4	4	no	—
115	C₂×Q₈×C₁₃	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	—	4	2	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
120	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	complemented
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
126	C₂×D₄×C₁₃	#41	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	4	4	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×SD₁₆	—	2	8	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	complemented
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	8	1	no	—
166	C₁₃×C₄⋊C₄	—	8	2	no	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	4	2	no	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
177	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
179	#2582	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2058	C₂×C₁₃	1	2	yes	complemented
181	#2024	C₂×C₁₃	1	2	yes	complemented
182	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1877	C₂×C₁₃	1	2	yes	—
185	#1864	C₂×C₁₃	1	2	yes	—
186	#1802	C₂×C₁₃	1	1	yes	characteristic
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₃	—	2	8	no	—
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	4	16	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	Q₈×C₁₃	—	4	1	no	—
201	Q₈×C₁₃	—	4	8	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	4	16	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	#120	1	2	yes	—
231	C₂×C₄×C₁₃	#120	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
233	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₁₃	—	2	2	no	—
242	C₈×C₁₃	—	4	1	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₂³×Q₈	—	2	1	no	—
245	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
246	D₄×Q₈	—	2	4	no	—
247	D₄×Q₈	—	2	4	no	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₂²⋊Q₈	—	2	2	no	—
252	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	#475	—	2	4	no	—
257	C₄×SD₁₆	—	2	4	no	—
258	C₂×#106	C₂²×C₁₃	1	2	yes	—
259	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#103	C₂²×C₁₃	1	2	yes	—
262	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#102	C₂²×C₁₃	1	2	yes	—
264	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
266	#398	—	2	2	no	—
267	#391	—	2	1	no	—
268	#391	C₂²×C₁₃	1	2	yes	—
269	#389	—	2	1	no	—
270	#389	C₂²×C₁₃	1	2	yes	—
271	#384	C₂²×C₁₃	1	1	yes	characteristic
272	#340	C₂²×C₁₃	1	2	yes	—
273	#340	C₂²×C₁₃	1	2	yes	—
274	#340	C₂²×C₁₃	1	2	yes	—
275	#336	C₂²×C₁₃	1	2	yes	—
276	#336	C₂²×C₁₃	1	2	yes	—
277	C₂²×C₁₃	—	2	4	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
285	C₂²×C₁₃	#548	1	1	yes	characteristic
286	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
287	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
288	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂²×C₁₃	#577	1	1	yes	characteristic
290	C₂²×C₁₃	#578	1	1	yes	characteristic
291	C₄×C₁₃	—	2	4	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	8	2	no	—
298	C₄×C₁₃	—	8	1	no	—
299	C₄×C₁₃	#450	1	4	yes	—
300	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
301	C₄×C₁₃	#536	1	1	yes	characteristic
302	C₄×C₁₃	#548	1	1	yes	characteristic
303	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
304	C₂²×Q₈	—	2	8	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	—	4	4	no	—
308	C₂²×Q₈	—	4	4	no	—
309	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
317	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	—	2	4	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
324	C₂²⋊Q₈	—	2	8	no	—
325	C₂²⋊Q₈	—	2	16	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	D₄×C₁₃	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
351	#106	—	2	2	no	—
352	#106	—	2	4	no	—
353	C₄⋊C₈	—	2	2	no	—
354	#103	—	2	2	no	—
355	#103	—	2	4	no	—
356	#102	—	2	2	no	—
357	#102	—	2	4	no	—
358	C₄×C₈	—	2	2	no	—
359	#95	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂×C₁₃	—	4	4	no	—
363	C₂×C₁₃	#2409	1	1	yes	characteristic
364	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
365	C₂×C₁₃	#3013	1	1	yes	characteristic
366	C₂×C₁₃	#3359	1	1	yes	characteristic
367	C₂×C₁₃	#3373	1	1	yes	characteristic
368	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
369	C₂×C₁₃	#3386	1	1	yes	characteristic
370	C₂⁴	—	2	1	no	—
371	C₂×Q₈	—	2	8	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	—	4	32	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	C₁₃×SD₁₆	1	4	yes	complemented
386	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	complemented
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
392	C₂×D₄	C₁₃×#41	1	2	yes	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	SD₁₆	—	2	8	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	complemented
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	8	1	no	—
432	C₄⋊C₄	—	8	2	no	—
433	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	4	2	no	—
440	C₄²	C₂×D₄×C₁₃	1	2	yes	—
441	C₄²	C₂×D₄×C₁₃	1	2	yes	—
442	C₁₃	#24330	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	16	no	—
455	Q₈	—	4	8	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	16	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	C₁₃×#120	1	2	yes	—
487	C₂×C₄	C₁₃×#120	1	2	yes	—
488	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
489	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
490	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
496	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
508	C₂²	C₁₃×#548	1	1	yes	characteristic
509	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
510	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
511	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
512	C₂²	C₁₃×#577	1	1	yes	characteristic
513	C₂²	C₁₃×#578	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	2	no	—
522	C₄	C₁₃×#450	1	4	yes	—
523	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
524	C₄	C₁₃×#536	1	1	yes	characteristic
525	C₄	C₁₃×#548	1	1	yes	characteristic
526	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
527	C₂	—	4	4	no	—
528	C₂	C₁₃×#2409	1	1	yes	characteristic
529	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
530	C₂	C₁₃×#3013	1	1	yes	characteristic
531	C₂	C₁₃×#3359	1	1	yes	characteristic
532	C₂	C₁₃×#3373	1	1	yes	characteristic
533	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
534	C₂	C₁₃×#3386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#475	C₂	semidirect
4. C₁₃×#2582	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
6. C₁₃×#2024	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1984	C₂	semidirect
57. C₂×C₁₃×SD₁₆	Q₈	semidirect
103. #24330	C₁₃	direct (N × H)
119. C₂×Q₈×C₁₃	SD₁₆	semidirect
120. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
152. C₂×C₈×C₁₃	C₂×Q₈	semidirect
177. C₂×#475	C₂×C₁₃	semidirect
179. #2582	C₂×C₁₃	semidirect
180. #2058	C₂×C₁₃	semidirect
181. #2024	C₂×C₁₃	semidirect
182. #1990	C₂×C₁₃	semidirect
183. #1984	C₂×C₁₃	semidirect
316. C₂×SD₁₆	Q₈×C₁₃	semidirect
385. C₂×Q₈	C₁₃×SD₁₆	semidirect
386. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
418. C₂×C₈	C₂×Q₈×C₁₃	semidirect
442. C₁₃	#24330	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#475	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2582	2
C₁₃×#2058	2
C₁₃×#2024	2
C₁₃×#1990	2
C₁₃×#1984	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1802	2
#24330	13

Subgroups — C13×#24330 #15710669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24330 #15710669