Subgroups — C₁₃×#32741 #15719080

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2086	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2077	C₂	1	2	yes	maximal
6	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2036	C₂	1	2	yes	maximal
10	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₁₃×#391	—	2	1	no	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	C₂²	1	1	yes	characteristic
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	1	yes	characteristic
29	C₁₃×#387	—	2	1	no	—
30	C₁₃×#387	—	2	1	no	—
31	C₁₃×#385	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#381	—	2	1	no	—
34	C₁₃×#380	—	2	1	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	4	2	no	—
51	C₁₃×C₂²⋊Q₈	—	4	2	no	—
52	C₁₃×C₂²⋊Q₈	—	4	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	4	2	no	—
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#107	—	4	2	no	—
74	C₁₃×#106	—	4	2	no	—
75	C₁₃×C₄⋊C₈	—	4	2	no	—
76	C₁₃×#103	—	4	2	no	—
77	C₁₃×#103	—	4	2	no	—
78	C₁₃×C₂²⋊C₈	—	4	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	#32741	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	2	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	4	1	no	—
146	C₄²×C₁₃	—	4	1	no	—
147	#2857	C₂×C₁₃	1	1	yes	characteristic
148	#2855	C₂×C₁₃	1	1	yes	characteristic
149	#2086	C₂×C₁₃	1	2	yes	complemented
150	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2077	C₂×C₁₃	1	2	yes	—
152	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2066	C₂×C₁₃	1	2	yes	complemented
154	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2036	C₂×C₁₃	1	2	yes	—
156	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1797	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	#137	1	2	yes	—
165	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	8	4	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	#135	1	2	yes	—
204	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₁₃	#137	1	2	yes	—
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
208	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	—	2	1	no	—
214	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃	1	2	yes	—
217	C₂×#106	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
222	#391	—	2	1	no	—
223	#391	C₂²×C₁₃	1	1	yes	characteristic
224	#391	C₂²×C₁₃	1	1	yes	characteristic
225	#389	—	2	1	no	—
226	#389	C₂²×C₁₃	1	1	yes	characteristic
227	#389	C₂²×C₁₃	1	2	yes	—
228	#389	C₂²×C₁₃	1	1	yes	characteristic
229	#387	—	2	1	no	—
230	#387	—	2	1	no	—
231	#385	—	2	1	no	—
232	#384	C₂²×C₁₃	1	1	yes	characteristic
233	#381	—	2	1	no	—
234	#380	—	2	1	no	—
235	#380	C₂²×C₁₃	1	1	yes	characteristic
236	#380	C₂²×C₁₃	1	2	yes	—
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	2	yes	—
241	#336	C₂²×C₁₃	1	1	yes	characteristic
242	#336	C₂²×C₁₃	1	1	yes	characteristic
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	1	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	#534	1	1	yes	characteristic
251	C₂²×C₁₃	#536	1	1	yes	characteristic
252	C₂²×C₁₃	#537	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	—	4	1	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	—	8	1	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	#562	1	2	yes	—
269	C₄×C₁₃	#563	1	2	yes	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
273	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
277	C₄⋊Q₈	—	4	2	no	—
278	C₂²⋊Q₈	—	4	2	no	—
279	C₂²⋊Q₈	—	4	4	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₄²	—	4	2	no	—
296	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	#107	—	4	2	no	—
301	#106	—	4	2	no	—
302	C₄⋊C₈	—	4	2	no	—
303	#103	—	4	2	no	—
304	#103	—	4	2	no	—
305	C₂²⋊C₈	—	4	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	1	no	—
311	#95	—	2	1	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	C₂×C₁₃	—	4	2	no	—
316	C₂×C₁₃	#2814	1	1	yes	characteristic
317	C₂×C₁₃	#3188	1	1	yes	characteristic
318	C₂×C₁₃	#3195	1	1	yes	characteristic
319	C₂×C₁₃	#3231	1	1	yes	characteristic
320	C₂×C₁₃	#3239	1	1	yes	characteristic
321	C₂×C₁₃	#3248	1	1	yes	characteristic
322	C₂×C₁₃	#3254	1	1	yes	characteristic
323	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₁₃	#32741	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₁₃×#137	1	2	yes	—
389	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	8	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₁₃×#135	1	2	yes	—
428	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
429	C₂×C₄	C₁₃×#137	1	2	yes	—
430	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
433	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₁₃×#534	1	1	yes	characteristic
444	C₂²	C₁₃×#536	1	1	yes	characteristic
445	C₂²	C₁₃×#537	1	1	yes	characteristic
446	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
447	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
449	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	C₁₃×#562	1	2	yes	—
462	C₄	C₁₃×#563	1	2	yes	—
463	C₂	—	4	2	no	—
464	C₂	C₁₃×#2814	1	1	yes	characteristic
465	C₂	C₁₃×#3188	1	1	yes	characteristic
466	C₂	C₁₃×#3195	1	1	yes	characteristic
467	C₂	C₁₃×#3231	1	1	yes	characteristic
468	C₂	C₁₃×#3239	1	1	yes	characteristic
469	C₂	C₁₃×#3248	1	1	yes	characteristic
470	C₂	C₁₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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
3. C₁₃×#2086	C₂	semidirect
4. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2072	C₂	semidirect
7. C₁₃×#2066	C₂	semidirect
8. C₁₃×#2057	C₂	semidirect
10. C₁₃×#2024	C₂	semidirect
88. #32741	C₁₃	direct (N × H)
149. #2086	C₂×C₁₃	semidirect
150. #2084	C₂×C₁₃	semidirect
152. #2072	C₂×C₁₃	semidirect
153. #2066	C₂×C₁₃	semidirect
154. #2057	C₂×C₁₃	semidirect
156. #2024	C₂×C₁₃	semidirect
381. C₁₃	#32741	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×#2857	2
C₁₃×#2855	2
C₁₃×#2086	2
C₁₃×#2084	2
C₁₃×#2077	2
C₁₃×#2072	2
C₁₃×#2066	2
C₁₃×#2057	2
C₁₃×#2036	2
C₁₃×#2024	2
C₁₃×#1797	2
#32741	13

Subgroups — C13×#32741 #15719080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32741 #15719080