Subgroups — C₁₃×#17686 #15704025

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1533	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1531	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1524	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#559	—	2	2	no	—
11	C₁₃×#556	—	2	2	no	—
12	C₁₃×#551	—	2	2	no	—
13	C₁₃×#551	—	2	2	no	—
14	C₁₃×#542	C₄	1	2	yes	—
15	C₁₃×#542	C₄	1	2	yes	—
16	C₁₃×#536	C₄	1	1	yes	characteristic
17	C₁₃×#535	C₄	1	1	yes	characteristic
18	C₁₃×#533	C₂²	1	1	yes	characteristic
19	C₁₃×#529	C₂²	1	2	yes	—
20	C₁₃×#529	C₂²	1	2	yes	—
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₁₃×#519	C₄	1	1	yes	characteristic
23	C₁₃×#518	C₄	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#446	—	2	2	no	—
26	C₁₃×#435	—	2	2	no	—
27	C₁₃×#435	—	2	2	no	—
28	C₈×D₄×C₁₃	—	2	2	no	—
29	C₁₃×#432	C₂²	1	2	yes	—
30	C₁₃×#432	C₂²	1	2	yes	complemented
31	C₁₃×#432	C₂²	1	2	yes	complemented
32	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#97	C₂²	1	2	yes	—
34	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
35	C₁₃×#330	C₂²	1	2	yes	complemented
36	C₁₃×#330	C₂²	1	2	yes	complemented
37	C₁₃×#330	C₂²	1	2	yes	complemented
38	C₁₃×#330	C₂²	1	2	yes	complemented
39	C₁₃×#329	C₂²	1	1	yes	characteristic
40	C₁₃×#329	C₂²	1	2	yes	—
41	C₁₃×#329	C₂²	1	1	yes	characteristic
42	C₁₃×#329	C₂²	1	2	yes	—
43	C₁₃×#329	C₂²	1	1	yes	characteristic
44	C₁₃×#329	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₁₃×#127	—	2	1	no	—
54	C₁₃×#126	—	2	2	no	—
55	C₁₃×#126	—	2	2	no	—
56	C₁₃×#126	—	2	2	no	—
57	C₁₃×#126	—	2	2	no	—
58	C₁₃×#125	C₂³	1	2	yes	—
59	C₁₃×#124	—	2	1	no	—
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#124	—	2	2	no	—
62	C₁₃×#124	—	2	2	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
66	C₁₃×#124	C₂³	1	1	yes	characteristic
67	C₁₃×#124	C₂³	1	1	yes	characteristic
68	C₁₃×#123	—	2	2	no	—
69	C₁₃×#123	—	2	2	no	—
70	C₁₃×#123	—	2	2	no	—
71	C₁₃×#123	—	2	2	no	—
72	C₁₃×#123	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×C₂²⋊Q₈	—	2	2	no	—
76	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
78	C₁₃×#121	C₂×C₄	1	2	yes	—
79	C₁₃×#121	C₂×C₄	1	2	yes	—
80	C₁₃×#120	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
84	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₁₃	D₄	1	2	yes	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
90	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
91	C₄×D₄×C₁₃	D₄	1	2	yes	—
92	C₄×D₄×C₁₃	D₄	1	2	yes	—
93	C₄×D₄×C₁₃	D₄	1	2	yes	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	—	2	2	no	—
97	C₁₃×#117	—	2	2	no	—
98	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#117	C₂×C₄	1	2	yes	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₈	—	2	2	no	—
108	C₁₃×C₄⋊C₈	—	2	2	no	—
109	C₁₃×C₄⋊C₈	—	2	2	no	—
110	C₁₃×C₂²⋊C₈	—	2	2	no	—
111	C₁₃×C₂²⋊C₈	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	2	no	—
113	C₁₃×#97	—	2	2	no	—
114	C₁₃×#97	—	2	2	no	—
115	C₁₃×#97	C₂³	1	2	yes	—
116	C₁₃×#97	C₂³	1	2	yes	—
117	C₁₃×#97	C₂³	1	2	yes	—
118	C₁₃×#97	C₂³	1	2	yes	—
119	C₄×C₈×C₁₃	—	2	2	no	—
120	#17686	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	1	no	—
122	C₁₃×#41	—	4	2	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	4	2	no	—
133	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₁₃×M₁₆	—	4	4	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	4	4	no	—
151	C₂×C₈×C₁₃	—	4	4	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
164	C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
177	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
178	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
180	C₄²×C₁₃	—	2	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
185	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂×D₄	1	2	yes	—
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	C₂×D₄	1	2	yes	—
189	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
190	#3510	C₂×C₁₃	1	1	yes	characteristic
191	#2970	C₂×C₁₃	1	2	yes	complemented
192	#1535	C₂×C₁₃	1	2	yes	complemented
193	#1533	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1532	C₂×C₁₃	1	2	yes	complemented
195	#1531	C₂×C₁₃	1	2	yes	complemented
196	#1529	C₂×C₁₃	1	2	yes	complemented
197	#1524	C₂×C₁₃	1	2	yes	complemented
198	C₂×#329	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	8	2	no	—
203	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	Q₈×C₁₃	—	4	1	no	—
206	Q₈×C₁₃	—	4	2	no	—
207	Q₈×C₁₃	—	4	1	no	—
208	Q₈×C₁₃	—	4	1	no	—
209	Q₈×C₁₃	—	8	2	no	—
210	D₄×C₁₃	—	2	4	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	8	2	no	—
216	D₄×C₁₃	—	8	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	8	2	no	—
228	C₂×C₄×C₁₃	—	8	2	no	—
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₈×C₁₃	—	2	4	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₈×C₁₃	—	4	2	no	—
239	C₈×C₁₃	—	4	2	no	—
240	#559	—	2	2	no	—
241	#556	—	2	2	no	—
242	#551	—	2	2	no	—
243	#551	—	2	2	no	—
244	#542	C₄×C₁₃	1	2	yes	—
245	#542	C₄×C₁₃	1	2	yes	—
246	#536	C₄×C₁₃	1	1	yes	characteristic
247	#535	C₄×C₁₃	1	1	yes	characteristic
248	#533	C₂²×C₁₃	1	1	yes	characteristic
249	#529	C₂²×C₁₃	1	2	yes	—
250	#529	C₂²×C₁₃	1	2	yes	—
251	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
252	#519	C₄×C₁₃	1	1	yes	characteristic
253	#518	C₄×C₁₃	1	1	yes	characteristic
254	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
255	#446	—	2	2	no	—
256	#435	—	2	2	no	—
257	#435	—	2	2	no	—
258	C₈×D₄	—	2	2	no	—
259	#432	C₂²×C₁₃	1	2	yes	—
260	#432	C₂²×C₁₃	1	2	yes	complemented
261	#432	C₂²×C₁₃	1	2	yes	complemented
262	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
263	C₂×#97	C₂²×C₁₃	1	2	yes	—
264	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
265	#330	C₂²×C₁₃	1	2	yes	complemented
266	#330	C₂²×C₁₃	1	2	yes	complemented
267	#330	C₂²×C₁₃	1	2	yes	complemented
268	#330	C₂²×C₁₃	1	2	yes	complemented
269	#329	C₂²×C₁₃	1	1	yes	characteristic
270	#329	C₂²×C₁₃	1	2	yes	—
271	#329	C₂²×C₁₃	1	1	yes	characteristic
272	#329	C₂²×C₁₃	1	2	yes	—
273	#329	C₂²×C₁₃	1	1	yes	characteristic
274	#329	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	4	1	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	16	2	no	—
284	C₂²×C₁₃	#413	1	2	yes	—
285	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
300	C₂×M₁₆	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
305	#127	—	2	1	no	—
306	#126	—	2	2	no	—
307	#126	—	2	2	no	—
308	#126	—	2	2	no	—
309	#126	—	2	2	no	—
310	#125	C₂³×C₁₃	1	2	yes	—
311	#124	—	2	1	no	—
312	#124	—	2	1	no	—
313	#124	—	2	2	no	—
314	#124	—	2	2	no	—
315	#124	—	2	2	no	—
316	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
317	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
318	#124	C₂³×C₁₃	1	1	yes	characteristic
319	#124	C₂³×C₁₃	1	1	yes	characteristic
320	#123	—	2	2	no	—
321	#123	—	2	2	no	—
322	#123	—	2	2	no	—
323	#123	—	2	2	no	—
324	#123	—	2	2	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	2	no	—
328	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
329	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
330	#121	C₂×C₄×C₁₃	1	2	yes	—
331	#121	C₂×C₄×C₁₃	1	2	yes	—
332	#120	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
336	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
337	C₄×Q₈	D₄×C₁₃	1	2	yes	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
342	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
343	C₄×D₄	D₄×C₁₃	1	2	yes	—
344	C₄×D₄	D₄×C₁₃	1	2	yes	—
345	C₄×D₄	D₄×C₁₃	1	2	yes	—
346	#117	—	2	1	no	—
347	#117	—	2	1	no	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
351	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
352	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
353	#117	C₂×C₄×C₁₃	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	—	2	2	no	—
361	C₄⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	2	no	—
365	#97	—	2	2	no	—
366	#97	—	2	2	no	—
367	#97	C₂³×C₁₃	1	2	yes	—
368	#97	C₂³×C₁₃	1	2	yes	—
369	#97	C₂³×C₁₃	1	2	yes	—
370	#97	C₂³×C₁₃	1	2	yes	—
371	C₄×C₈	—	2	2	no	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	—	4	2	no	—
374	C₂×C₁₃	—	8	1	no	—
375	C₂×C₁₃	—	8	1	no	—
376	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
377	C₂×C₁₃	#2901	1	2	yes	—
378	C₂⁴	—	2	1	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
384	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
385	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
391	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
402	M₁₆	—	4	4	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	4	no	—
408	C₂×C₈	—	4	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
417	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
418	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
419	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
420	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
435	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
436	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
442	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₁₃	1	2	yes	—
444	C₄²	C₂×D₄×C₁₃	1	2	yes	—
445	C₄²	C₂×D₄×C₁₃	1	2	yes	—
446	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₁₃	#17686	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
453	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
454	Q₈	—	4	1	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	8	2	no	—
459	D₄	—	2	4	no	—
460	D₄	—	4	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
480	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
481	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
482	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₈	—	2	4	no	—
486	C₈	—	4	2	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	16	2	no	—
498	C₂²	C₁₃×#413	1	2	yes	—
499	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	2	no	—
513	C₂	—	8	1	no	—
514	C₂	—	8	1	no	—
515	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
516	C₂	C₁₃×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#535	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#1535	C₂	semidirect
4. C₁₃×#1533	C₂	semidirect
5. C₁₃×#1532	C₂	semidirect
6. C₁₃×#1531	C₂	semidirect
7. C₁₃×#1529	C₂	semidirect
8. C₁₃×#1524	C₂	semidirect
9. C₂×C₁₃×#329	C₂	semidirect
30. C₁₃×#432	C₂²	semidirect
31. C₁₃×#432	C₂²	semidirect
32. C₄×C₁₃×M₁₆	C₂²	semidirect
34. C₂×C₁₃×#97	C₂²	semidirect
35. C₁₃×#330	C₂²	semidirect
36. C₁₃×#330	C₂²	semidirect
37. C₁₃×#330	C₂²	semidirect
38. C₁₃×#330	C₂²	semidirect
120. #17686	C₁₃	direct (N × H)
191. #2970	C₂×C₁₃	semidirect
192. #1535	C₂×C₁₃	semidirect
193. #1533	C₂×C₁₃	semidirect
194. #1532	C₂×C₁₃	semidirect
195. #1531	C₂×C₁₃	semidirect
196. #1529	C₂×C₁₃	semidirect
197. #1524	C₂×C₁₃	semidirect
198. C₂×#329	C₂×C₁₃	semidirect
260. #432	C₂²×C₁₃	semidirect
261. #432	C₂²×C₁₃	semidirect
262. C₄×M₁₆	C₂²×C₁₃	semidirect
264. C₂×#97	C₂²×C₁₃	semidirect
265. #330	C₂²×C₁₃	semidirect
266. #330	C₂²×C₁₃	semidirect
267. #330	C₂²×C₁₃	semidirect
268. #330	C₂²×C₁₃	semidirect
447. C₁₃	#17686	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×#3510	2
C₁₃×#2970	2
C₁₃×#1535	2
C₁₃×#1533	2
C₁₃×#1532	2
C₁₃×#1531	2
C₁₃×#1529	2
C₁₃×#1524	2
C₂×C₁₃×#329	2
#17686	13

Subgroups — C13×#17686 #15704025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17686 #15704025