Subgroups — C₁₃×#32959 #15719298

Order 3328.

1720 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1804	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	—	2	1	no	—
14	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₃	—	2	8	no	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#478	—	2	8	no	—
24	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#387	—	2	1	no	—
37	C₁₃×#385	—	2	1	no	—
38	C₁₃×#385	—	2	1	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	complemented
43	C₁₃×#340	C₂²	1	2	yes	complemented
44	C₁₃×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	—	2	4	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	8	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	—	4	4	no	—
57	C₂³×C₄×C₁₃	—	4	4	no	—
58	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#125	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	8	no	—
65	C₄×D₄×C₁₃	—	2	8	no	—
66	C₄×D₄×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	D₄	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	4	no	—
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#107	—	2	4	no	—
92	C₁₃×#106	—	2	4	no	—
93	C₁₃×C₄⋊C₈	—	2	4	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×C₂²⋊C₈	—	2	2	no	—
99	C₁₃×C₂²⋊C₈	—	2	2	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	—	2	1	no	—
105	C₁₃×#95	—	2	1	no	—
106	#32959	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	4	2	no	—
112	C₂⁴×C₁₃	—	4	2	no	—
113	C₂⁴×C₁₃	—	4	2	no	—
114	C₂⁴×C₁₃	—	4	2	no	—
115	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	16	no	—
119	C₂×D₄×C₁₃	—	2	16	no	—
120	C₂×D₄×C₁₃	—	2	4	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
126	C₂×D₄×C₁₃	#41	1	4	yes	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	4	1	no	—
143	C₂²×C₄×C₁₃	—	4	32	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	—	4	4	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₁₃	#41	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	4	2	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	4	2	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	C₂×D₄	1	4	yes	—
183	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
184	C₂×#478	C₂×C₁₃	1	2	yes	complemented
185	#2851	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#1864	C₂×C₁₃	1	2	yes	complemented
187	#1862	C₂×C₁₃	1	2	yes	complemented
188	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1804	C₂×C₁₃	1	2	yes	complemented
191	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1786	C₂×C₁₃	1	1	yes	characteristic
193	#1786	C₂×C₁₃	1	1	yes	characteristic
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	16	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	4	no	—
201	C₂³×C₁₃	—	2	4	no	—
202	C₂³×C₁₃	—	4	8	no	—
203	C₂³×C₁₃	—	4	8	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	—	4	8	no	—
206	C₂³×C₁₃	—	4	8	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	8	no	—
212	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
213	C₂³×C₁₃	#135	1	2	yes	—
214	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
215	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	D₄×C₁₃	—	2	16	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	16	no	—
238	C₂×C₄×C₁₃	—	4	16	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	#120	1	2	yes	—
255	C₂×C₄×C₁₃	#120	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
257	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
262	C₈×C₁₃	—	4	2	no	—
263	C₈×C₁₃	—	4	2	no	—
264	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂⁴×C₄	—	2	1	no	—
266	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
267	C₂×C₄×D₄	—	2	8	no	—
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	—	2	1	no	—
270	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	—	2	1	no	—
274	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
275	#478	—	2	8	no	—
276	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
277	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
278	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
279	C₂×#102	C₂²×C₁₃	1	2	yes	—
280	C₂×#102	C₂²×C₁₃	1	2	yes	—
281	C₂×#102	C₂²×C₁₃	1	2	yes	—
282	C₂×#102	C₂²×C₁₃	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
285	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#387	—	2	1	no	—
288	#387	—	2	1	no	—
289	#385	—	2	1	no	—
290	#385	—	2	1	no	—
291	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	#380	C₂²×C₁₃	1	1	yes	characteristic
293	#380	C₂²×C₁₃	1	1	yes	characteristic
294	#340	C₂²×C₁₃	1	2	yes	complemented
295	#340	C₂²×C₁₃	1	2	yes	complemented
296	#336	C₂²×C₁₃	1	2	yes	complemented
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	4	32	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	#478	1	4	yes	complemented
312	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
314	C₂²×C₁₃	#525	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²×C₁₃	#575	1	1	yes	characteristic
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	—	8	1	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	—	8	1	no	—
329	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
330	C₄×C₁₃	#525	1	2	yes	—
331	C₂⁵	—	2	1	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	—	2	4	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
338	C₂³×C₄	—	2	8	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	2	2	no	—
341	C₂³×C₄	—	2	2	no	—
342	C₂³×C₄	—	4	4	no	—
343	C₂³×C₄	—	4	4	no	—
344	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
348	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
349	#125	—	2	4	no	—
350	C₄×D₄	—	2	8	no	—
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	D₄×C₁₃	1	8	yes	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	8	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₄²	—	2	4	no	—
373	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	#107	—	2	4	no	—
378	#106	—	2	4	no	—
379	C₄⋊C₈	—	2	4	no	—
380	#102	—	2	4	no	—
381	#102	—	2	4	no	—
382	#102	—	2	4	no	—
383	#102	—	2	4	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	C₂×C₁₃	—	2	4	no	—
393	C₂×C₁₃	—	4	8	no	—
394	C₂×C₁₃	#2848	1	1	yes	characteristic
395	C₂×C₁₃	#3002	1	1	yes	characteristic
396	C₂×C₁₃	#3003	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
398	C₂×C₁₃	#3077	1	1	yes	characteristic
399	C₂×C₁₃	#3105	1	1	yes	characteristic
400	C₂×C₁₃	#3114	1	1	yes	characteristic
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	2	no	—
407	C₂⁴	—	4	2	no	—
408	C₂⁴	—	4	2	no	—
409	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
419	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
420	C₂×D₄	C₁₃×#41	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	32	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
450	C₂²×C₄	C₁₃×#41	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	C₂×D₄×C₁₃	1	4	yes	—
477	C₁₃	#32959	1	1	yes	characteristic, direct product factor, Sylow
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	16	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	8	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
497	C₂³	C₁₃×#135	1	2	yes	—
498	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
499	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	D₄	—	2	16	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	16	no	—
522	C₂×C₄	—	4	16	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	C₁₃×#120	1	2	yes	—
539	C₂×C₄	C₁₃×#120	1	2	yes	—
540	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
541	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
545	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	8	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	C₁₃×#478	1	4	yes	complemented
563	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
564	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
565	C₂²	C₁₃×#525	1	1	yes	characteristic
566	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
567	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
568	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
569	C₂²	C₁₃×#575	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	4	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
581	C₄	C₁₃×#525	1	2	yes	—
582	C₂	—	2	4	no	—
583	C₂	—	4	8	no	—
584	C₂	C₁₃×#2848	1	1	yes	characteristic
585	C₂	C₁₃×#3002	1	1	yes	characteristic
586	C₂	C₁₃×#3003	1	1	yes	characteristic
587	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
588	C₂	C₁₃×#3077	1	1	yes	characteristic
589	C₂	C₁₃×#3105	1	1	yes	characteristic
590	C₂	C₁₃×#3114	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#478	C₂	semidirect
3. C₁₃×#2851	C₂	semidirect
4. C₁₃×#1864	C₂	semidirect
5. C₁₃×#1862	C₂	semidirect
6. C₁₃×#1853	C₂	semidirect
7. C₁₃×#1852	C₂	semidirect
8. C₁₃×#1804	C₂	semidirect
9. C₁₃×#1797	C₂	semidirect
14. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₁₃×#107	C₂²	semidirect
25. C₂×C₁₃×#106	C₂²	semidirect
26. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
39. C₁₃×#382	C₂²	semidirect
42. C₁₃×#340	C₂²	semidirect
43. C₁₃×#340	C₂²	semidirect
44. C₁₃×#336	C₂²	semidirect
106. #32959	C₁₃	direct (N × H)
184. C₂×#478	C₂×C₁₃	semidirect
185. #2851	C₂×C₁₃	semidirect
186. #1864	C₂×C₁₃	semidirect
187. #1862	C₂×C₁₃	semidirect
188. #1853	C₂×C₁₃	semidirect
189. #1852	C₂×C₁₃	semidirect
190. #1804	C₂×C₁₃	semidirect
191. #1797	C₂×C₁₃	semidirect
266. C₂×#125	C₂²×C₁₃	semidirect
276. C₂×#107	C₂²×C₁₃	semidirect
277. C₂×#106	C₂²×C₁₃	semidirect
278. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
285. #389	C₂²×C₁₃	semidirect
286. #389	C₂²×C₁₃	semidirect
291. #382	C₂²×C₁₃	semidirect
294. #340	C₂²×C₁₃	semidirect
295. #340	C₂²×C₁₃	semidirect
296. #336	C₂²×C₁₃	semidirect
311. C₂²×C₁₃	#478	semidirect
477. C₁₃	#32959	direct (N × H)
562. C₂²	C₁₃×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃	2
C₂×C₁₃×#478	2
C₁₃×#2851	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1804	2
C₁₃×#1797	2
C₁₃×#1786	2
#32959	13

Subgroups — C13×#32959 #15719298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32959 #15719298