Subgroups — C₁₃×#17670 #15704009

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1535	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1529	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1528	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1527	C₂	1	2	yes	maximal, complemented
8	C₁₃×#529	—	2	1	no	—
9	C₁₃×#529	—	2	1	no	—
10	C₁₃×#529	—	2	1	no	—
11	C₁₃×#529	—	2	1	no	—
12	C₁₃×#529	C₄	1	2	yes	—
13	C₁₃×#529	C₄	1	2	yes	—
14	C₁₃×#529	C₂²	1	2	yes	—
15	C₁₃×#529	C₂²	1	2	yes	—
16	C₂×C₁₃×#126	—	2	1	no	—
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#123	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	—	2	1	no	—
24	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
25	C₂×C₁₃×#117	—	2	1	no	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#432	C₂²	1	2	yes	—
28	C₁₃×#432	C₂²	1	2	yes	complemented
29	C₁₃×#432	C₂²	1	2	yes	complemented
30	C₁₃×#432	C₂²	1	2	yes	complemented
31	C₁₃×#431	—	2	1	no	—
32	C₁₃×#431	—	2	1	no	—
33	C₁₃×#431	—	2	1	no	—
34	C₁₃×#431	—	2	1	no	—
35	C₁₃×#423	—	2	1	no	—
36	C₁₃×#423	—	2	1	no	—
37	C₁₃×#407	—	2	1	no	—
38	C₁₃×#407	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
40	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
41	C₁₃×#330	C₂²	1	8	yes	complemented
42	C₁₃×#329	C₂²	1	8	yes	complemented
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₁₃×#126	—	2	2	no	—
53	C₁₃×#126	—	2	2	no	—
54	C₁₃×#126	—	2	2	no	—
55	C₁₃×#126	—	2	2	no	—
56	C₁₃×#125	—	2	1	no	—
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×#125	C₂×C₄	1	2	yes	—
59	C₁₃×#125	C₂³	1	2	yes	—
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#124	—	2	1	no	—
62	C₁₃×#124	C₂×C₄	1	2	yes	—
63	C₁₃×#124	C₂³	1	2	yes	—
64	C₁₃×#123	—	2	2	no	—
65	C₁₃×#123	—	2	2	no	—
66	C₁₃×#123	—	2	2	no	—
67	C₁₃×#123	—	2	2	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₁₃×C₂²⋊Q₈	—	2	1	no	—
70	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₁₃×#121	—	2	1	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	C₂×C₄	1	2	yes	—
75	C₁₃×#121	C₂×C₄	1	2	yes	—
76	C₄×Q₈×C₁₃	—	2	1	no	—
77	C₄×Q₈×C₁₃	—	2	1	no	—
78	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	1	no	—
85	C₄×D₄×C₁₃	—	2	1	no	—
86	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
87	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
88	C₁₃×#117	—	2	2	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	—	2	2	no	—
91	C₁₃×#117	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×C₄⋊C₈	—	2	2	no	—
119	C₁₃×C₄⋊C₈	—	2	2	no	—
120	C₁₃×C₂²⋊C₈	—	2	2	no	—
121	C₁₃×C₂²⋊C₈	—	2	2	no	—
122	C₁₃×C₂²⋊C₈	—	2	2	no	—
123	C₁₃×C₂²⋊C₈	—	2	2	no	—
124	C₁₃×#97	C₂³	1	4	yes	—
125	C₁₃×#97	C₂³	1	4	yes	—
126	C₄×C₈×C₁₃	—	2	2	no	—
127	C₄×C₈×C₁₃	—	2	2	no	—
128	#17670	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	4	2	no	—
133	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₁₃×M₁₆	—	4	4	no	—
168	C₁₃×M₁₆	—	4	4	no	—
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
183	C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	—	2	2	no	—
195	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
212	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1535	C₂×C₁₃	1	4	yes	complemented
215	#1529	C₂×C₁₃	1	4	yes	complemented
216	#1528	C₂×C₁₃	1	2	yes	complemented
217	#1527	C₂×C₁₃	1	2	yes	complemented
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	—	4	2	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	Q₈×C₁₃	—	4	2	no	—
229	Q₈×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₃	—	4	4	no	—
273	C₈×C₁₃	—	4	4	no	—
274	#529	—	2	1	no	—
275	#529	—	2	1	no	—
276	#529	—	2	1	no	—
277	#529	—	2	1	no	—
278	#529	C₄×C₁₃	1	2	yes	—
279	#529	C₄×C₁₃	1	2	yes	—
280	#529	C₂²×C₁₃	1	2	yes	—
281	#529	C₂²×C₁₃	1	2	yes	—
282	C₂×#126	—	2	1	no	—
283	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#123	—	2	1	no	—
286	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
287	C₂×#121	C₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄×D₄	—	2	1	no	—
290	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
291	C₂×#117	—	2	1	no	—
292	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
293	#432	C₂²×C₁₃	1	2	yes	—
294	#432	C₂²×C₁₃	1	2	yes	complemented
295	#432	C₂²×C₁₃	1	2	yes	complemented
296	#432	C₂²×C₁₃	1	2	yes	complemented
297	#431	—	2	1	no	—
298	#431	—	2	1	no	—
299	#431	—	2	1	no	—
300	#431	—	2	1	no	—
301	#423	—	2	1	no	—
302	#423	—	2	1	no	—
303	#407	—	2	1	no	—
304	#407	—	2	1	no	—
305	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
306	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
307	#330	C₂²×C₁₃	1	8	yes	complemented
308	#329	C₂²×C₁₃	1	8	yes	complemented
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	8	4	no	—
322	C₂²×C₁₃	#421	1	2	yes	—
323	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	2	no	—
337	C₄×C₁₃	#413	1	2	yes	—
338	C₄×C₁₃	#421	1	2	yes	—
339	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
344	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	#126	—	2	2	no	—
349	#126	—	2	2	no	—
350	#126	—	2	2	no	—
351	#126	—	2	2	no	—
352	#125	—	2	1	no	—
353	#125	—	2	1	no	—
354	#125	C₂×C₄×C₁₃	1	2	yes	—
355	#125	C₂³×C₁₃	1	2	yes	—
356	#124	—	2	1	no	—
357	#124	—	2	1	no	—
358	#124	C₂×C₄×C₁₃	1	2	yes	—
359	#124	C₂³×C₁₃	1	2	yes	—
360	#123	—	2	2	no	—
361	#123	—	2	2	no	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
367	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	C₂×C₄×C₁₃	1	2	yes	—
371	#121	C₂×C₄×C₁₃	1	2	yes	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
375	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
383	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
384	#117	—	2	2	no	—
385	#117	—	2	2	no	—
386	#117	—	2	2	no	—
387	#117	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	—	2	2	no	—
413	C₄⋊C₈	—	2	2	no	—
414	C₄⋊C₈	—	2	2	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	—	2	2	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	C₂²⋊C₈	—	2	2	no	—
420	#97	C₂³×C₁₃	1	4	yes	—
421	#97	C₂³×C₁₃	1	4	yes	—
422	C₄×C₈	—	2	2	no	—
423	C₄×C₈	—	2	2	no	—
424	C₂×C₁₃	—	2	2	no	—
425	C₂×C₁₃	—	4	1	no	—
426	C₂×C₁₃	—	4	1	no	—
427	C₂×C₁₃	—	8	2	no	—
428	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
429	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
430	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
431	C₂⁴	—	2	1	no	—
432	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
453	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
454	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
456	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	M₁₆	—	4	4	no	—
470	M₁₆	—	4	4	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	—	2	4	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
484	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
498	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
499	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
500	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
501	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
502	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
503	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
504	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
505	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₁₃	#17670	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
523	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
557	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₈	—	4	4	no	—
569	C₈	—	4	4	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	8	4	no	—
583	C₂²	C₁₃×#421	1	2	yes	—
584	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	C₁₃×#413	1	2	yes	—
599	C₄	C₁₃×#421	1	2	yes	—
600	C₂	—	2	2	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	8	2	no	—
604	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
605	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
606	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2920	C₂	semidirect
3. C₁₃×#2920	C₂	semidirect
4. C₁₃×#1535	C₂	semidirect
5. C₁₃×#1529	C₂	semidirect
6. C₁₃×#1528	C₂	semidirect
7. C₁₃×#1527	C₂	semidirect
28. C₁₃×#432	C₂²	semidirect
29. C₁₃×#432	C₂²	semidirect
30. C₁₃×#432	C₂²	semidirect
40. C₄×C₁₃×M₁₆	C₂²	semidirect
41. C₁₃×#330	C₂²	semidirect
42. C₁₃×#329	C₂²	semidirect
128. #17670	C₁₃	direct (N × H)
212. #2920	C₂×C₁₃	semidirect
213. #2920	C₂×C₁₃	semidirect
214. #1535	C₂×C₁₃	semidirect
215. #1529	C₂×C₁₃	semidirect
216. #1528	C₂×C₁₃	semidirect
217. #1527	C₂×C₁₃	semidirect
294. #432	C₂²×C₁₃	semidirect
295. #432	C₂²×C₁₃	semidirect
296. #432	C₂²×C₁₃	semidirect
306. C₄×M₁₆	C₂²×C₁₃	semidirect
307. #330	C₂²×C₁₃	semidirect
308. #329	C₂²×C₁₃	semidirect
513. C₁₃	#17670	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×#529	2
C₁₃×#2920	2
C₁₃×#1535	2
C₁₃×#1529	2
C₁₃×#1528	2
C₁₃×#1527	2
#17670	13

Subgroups — C13×#17670 #15704009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17670 #15704009