Subgroups — C₁₃×#23808 #15710147

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2011	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#442	—	2	4	no	—
27	C₁₃×#440	—	2	4	no	—
28	C₄×C₁₃×SD₁₆	—	2	4	no	—
29	C₄×C₁₃×D₈	—	2	4	no	—
30	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#390	C₂²	1	1	yes	characteristic
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#388	—	2	2	no	—
49	C₁₃×#386	—	2	2	no	—
50	C₁₃×#386	—	2	2	no	—
51	C₁₃×#385	—	2	2	no	—
52	C₁₃×#384	C₂²	1	1	yes	characteristic
53	C₁₃×#382	C₂²	1	1	yes	characteristic
54	C₁₃×#376	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	2	no	—
72	C₂×C₁₃×SD₁₆	—	2	2	no	—
73	C₂×C₁₃×D₈	—	2	2	no	—
74	C₂×C₁₃×D₈	—	2	2	no	—
75	C₂×C₁₃×D₈	—	2	2	no	—
76	C₂×C₁₃×D₈	—	2	2	no	—
77	C₂×C₁₃×D₈	—	2	2	no	—
78	C₂×C₁₃×D₈	—	2	2	no	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#124	—	2	2	no	—
86	C₁₃×#124	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×#107	—	2	2	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#102	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#97	D₄	1	4	yes	complemented
125	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
126	C₁₃×#95	—	2	2	no	—
127	C₁₃×#95	—	2	2	no	—
128	C₁₃×#95	D₄	1	2	yes	—
129	C₁₃×#95	D₄	1	2	yes	—
130	#23808	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	#41	1	2	yes	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
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	—	8	2	no	—
157	C₂×D₄×C₁₃	—	8	2	no	—
158	C₂×D₄×C₁₃	#41	1	2	yes	—
159	C₂×D₄×C₁₃	#41	1	2	yes	—
160	C₂×D₄×C₁₃	#41	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	8	2	no	—
170	C₂²×C₄×C₁₃	—	8	2	no	—
171	C₂²×C₄×C₁₃	—	8	2	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×SD₁₆	—	2	8	no	—
178	C₁₃×SD₁₆	—	2	8	no	—
179	C₁₃×D₈	—	2	8	no	—
180	C₁₃×D₈	—	2	8	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	8	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	8	2	no	—
208	C₁₃×C₂²⋊C₄	—	8	2	no	—
209	C₁₃×C₂²⋊C₄	—	8	2	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	4	2	no	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2328	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2097	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2094	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2093	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2014	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2012	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#2012	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2011	C₂×C₁₃	1	1	yes	characteristic
231	#1746	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	2	no	—
242	C₂³×C₁₃	—	4	2	no	—
243	C₂³×C₁₃	—	4	2	no	—
244	C₂³×C₁₃	—	4	2	no	—
245	C₂³×C₁₃	—	4	2	no	—
246	C₂³×C₁₃	—	4	2	no	—
247	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₁₃	—	2	2	no	—
249	Q₈×C₁₃	—	2	2	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	2	2	no	—
253	D₄×C₁₃	—	2	2	no	—
254	D₄×C₁₃	—	2	2	no	—
255	D₄×C₁₃	—	2	2	no	—
256	D₄×C₁₃	—	2	2	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	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	8	8	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	8	4	no	—
285	C₂×C₄×C₁₃	—	8	4	no	—
286	C₂×C₄×C₁₃	—	8	4	no	—
287	C₂×C₄×C₁₃	#127	1	2	yes	—
288	C₂×C₄×C₁₃	#127	1	2	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₈×C₁₃	—	2	2	no	—
296	C₈×C₁₃	—	2	2	no	—
297	C₈×C₁₃	—	2	2	no	—
298	C₈×C₁₃	—	2	2	no	—
299	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	#442	—	2	4	no	—
310	#440	—	2	4	no	—
311	C₄×SD₁₆	—	2	4	no	—
312	C₄×D₈	—	2	4	no	—
313	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
327	#391	C₂²×C₁₃	1	1	yes	characteristic
328	#390	C₂²×C₁₃	1	1	yes	characteristic
329	#390	C₂²×C₁₃	1	1	yes	characteristic
330	#390	C₂²×C₁₃	1	1	yes	characteristic
331	#388	—	2	2	no	—
332	#386	—	2	2	no	—
333	#386	—	2	2	no	—
334	#385	—	2	2	no	—
335	#384	C₂²×C₁₃	1	1	yes	characteristic
336	#382	C₂²×C₁₃	1	1	yes	characteristic
337	#376	C₂²×C₁₃	1	1	yes	characteristic
338	#336	C₂²×C₁₃	1	1	yes	characteristic
339	#336	C₂²×C₁₃	1	1	yes	characteristic
340	#336	C₂²×C₁₃	1	1	yes	characteristic
341	#336	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₁₃	—	4	4	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	2	no	—
346	C₂²×C₁₃	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	8	2	no	—
349	C₂²×C₁₃	—	8	2	no	—
350	C₂²×C₁₃	—	8	2	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	—	8	1	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	—	8	1	no	—
357	C₂²×C₁₃	#525	1	1	yes	characteristic
358	C₂²×C₁₃	#525	1	1	yes	characteristic
359	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
360	C₂²×C₁₃	#576	1	2	yes	—
361	C₂²×C₁₃	#577	1	2	yes	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	2	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	#525	1	1	yes	characteristic
372	C₄×C₁₃	#525	1	1	yes	characteristic
373	C₄×C₁₃	#525	1	1	yes	characteristic
374	C₄×C₁₃	#525	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×D₄	—	2	2	no	—
377	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×D₈	—	2	2	no	—
390	C₂×D₈	—	2	2	no	—
391	C₂×D₈	—	2	2	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×D₈	—	2	2	no	—
394	C₂×D₈	—	2	2	no	—
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	#127	—	2	2	no	—
400	#127	—	2	2	no	—
401	#124	—	2	2	no	—
402	#124	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	#107	—	2	2	no	—
429	#107	—	2	2	no	—
430	#106	—	2	2	no	—
431	#106	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#102	—	2	2	no	—
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	#97	D₄×C₁₃	1	4	yes	complemented
441	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
442	#95	—	2	2	no	—
443	#95	—	2	2	no	—
444	#95	D₄×C₁₃	1	2	yes	—
445	#95	D₄×C₁₃	1	2	yes	—
446	C₂×C₁₃	—	8	2	no	—
447	C₂×C₁₃	—	8	2	no	—
448	C₂×C₁₃	—	8	2	no	—
449	C₂×C₁₃	#2397	1	1	yes	characteristic
450	C₂×C₁₃	#3118	1	2	yes	—
451	C₂×C₁₃	#3119	1	2	yes	—
452	C₂×C₁₃	#3154	1	1	yes	characteristic
453	C₂×C₁₃	#3155	1	1	yes	characteristic
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	2	1	no	—
456	C₂⁴	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	C₁₃×#41	1	2	yes	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	1	no	—
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	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
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	—	8	2	no	—
480	C₂×D₄	—	8	2	no	—
481	C₂×D₄	C₁₃×#41	1	2	yes	—
482	C₂×D₄	C₁₃×#41	1	2	yes	—
483	C₂×D₄	C₁₃×#41	1	2	yes	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	8	2	no	—
493	C₂²×C₄	—	8	2	no	—
494	C₂²×C₄	—	8	2	no	—
495	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	SD₁₆	—	2	8	no	—
501	SD₁₆	—	2	8	no	—
502	D₈	—	2	8	no	—
503	D₈	—	2	8	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
513	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
514	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	—	8	2	no	—
526	C₂²⋊C₄	—	2	8	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	8	2	no	—
531	C₂²⋊C₄	—	8	2	no	—
532	C₂²⋊C₄	—	8	2	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	4	2	no	—
538	C₄²	C₂×D₄×C₁₃	1	2	yes	—
539	C₄²	C₂×D₄×C₁₃	1	2	yes	—
540	C₁₃	#23808	1	1	yes	characteristic, direct product factor, Sylow
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	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	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	8	8	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	C₁₃×#127	1	2	yes	—
597	C₂×C₄	C₁₃×#127	1	2	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
601	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
602	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	2	2	no	—
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	8	2	no	—
615	C₂²	—	8	2	no	—
616	C₂²	—	8	2	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	C₁₃×#525	1	1	yes	characteristic
624	C₂²	C₁₃×#525	1	1	yes	characteristic
625	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
626	C₂²	C₁₃×#576	1	2	yes	—
627	C₂²	C₁₃×#577	1	2	yes	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₁₃×#525	1	1	yes	characteristic
638	C₄	C₁₃×#525	1	1	yes	characteristic
639	C₄	C₁₃×#525	1	1	yes	characteristic
640	C₄	C₁₃×#525	1	1	yes	characteristic
641	C₂	—	8	2	no	—
642	C₂	—	8	2	no	—
643	C₂	—	8	2	no	—
644	C₂	C₁₃×#2397	1	1	yes	characteristic
645	C₂	C₁₃×#3118	1	2	yes	—
646	C₂	C₁₃×#3119	1	2	yes	—
647	C₂	C₁₃×#3154	1	1	yes	characteristic
648	C₂	C₁₃×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#442	C₂	semidirect
2. C₂×C₁₃×#440	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. C₂×C₄×C₁₃×D₈	C₂	semidirect
5. C₁₃×#2328	C₂	semidirect
6. C₁₃×#2326	C₂	semidirect
7. C₁₃×#2097	C₂	semidirect
8. C₁₃×#2094	C₂	semidirect
9. C₁₃×#2093	C₂	semidirect
10. C₁₃×#2092	C₂	semidirect
11. C₁₃×#2014	C₂	semidirect
12. C₁₃×#2012	C₂	semidirect
13. C₁₃×#2012	C₂	semidirect
15. C₁₃×#1746	C₂	semidirect
124. C₁₃×#97	D₄	semidirect
125. C₄×C₈×C₁₃	D₄	semidirect
130. #23808	C₁₃	direct (N × H)
217. C₂×#442	C₂×C₁₃	semidirect
218. C₂×#440	C₂×C₁₃	semidirect
219. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
220. C₂×C₄×D₈	C₂×C₁₃	semidirect
221. #2328	C₂×C₁₃	semidirect
222. #2326	C₂×C₁₃	semidirect
223. #2097	C₂×C₁₃	semidirect
224. #2094	C₂×C₁₃	semidirect
225. #2093	C₂×C₁₃	semidirect
226. #2092	C₂×C₁₃	semidirect
227. #2014	C₂×C₁₃	semidirect
228. #2012	C₂×C₁₃	semidirect
229. #2012	C₂×C₁₃	semidirect
231. #1746	C₂×C₁₃	semidirect
440. #97	D₄×C₁₃	semidirect
441. C₄×C₈	D₄×C₁₃	semidirect
540. C₁₃	#23808	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×C₁₃×#442	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2328	2
C₁₃×#2326	2
C₁₃×#2097	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2092	2
C₁₃×#2014	2
C₁₃×#2012	2
C₁₃×#2011	2
C₁₃×#1746	2
#23808	13

Subgroups — C13×#23808 #15710147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23808 #15710147