Subgroups — C₁₃×#18650 #15704989

Order 3328.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1649	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1647	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	C₂×C₁₃×#137	—	2	1	no	—
12	D₄×Q₈×C₁₃	—	2	1	no	—
13	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#547	—	2	2	no	—
15	C₁₃×#547	—	2	1	no	—
16	C₁₃×#547	—	2	2	no	—
17	C₁₃×#547	C₂²	1	2	yes	—
18	C₁₃×#536	—	2	2	no	—
19	C₁₃×#536	—	2	1	no	—
20	C₁₃×#532	—	2	1	no	—
21	C₁₃×#532	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#500	—	2	2	no	—
27	C₁₃×#500	—	2	1	no	—
28	C₁₃×#500	C₂²	1	4	yes	—
29	C₁₃×#486	—	2	1	no	—
30	C₁₃×#480	—	2	2	no	—
31	C₁₃×#474	C₂²	1	4	yes	—
32	C₁₃×#462	—	2	1	no	—
33	C₁₃×#462	C₂²	1	2	yes	—
34	C₁₃×#461	—	2	1	no	—
35	C₁₃×#461	C₂²	1	2	yes	—
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#107	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#419	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
45	C₁₃×2₋¹⁺⁴	—	4	4	no	—
46	C₁₃×2₋¹⁺⁴	—	4	4	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	4	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	2	no	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₁₃×#137	—	4	4	no	—
57	C₂×C₁₃×Q₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₁₃×#127	D₄	1	1	yes	characteristic
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#123	—	2	4	no	—
77	C₁₃×#123	—	2	4	no	—
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#121	D₄	1	2	yes	—
87	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	C₂³	1	2	yes	—
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	D₄	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	8	no	—
108	C₁₃×#107	—	2	4	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#102	—	2	4	no	—
115	C₁₃×C₂²⋊C₈	—	2	1	no	—
116	C₄×C₈×C₁₃	—	2	1	no	—
117	C₄×C₈×C₁₃	—	2	1	no	—
118	C₄×C₈×C₁₃	C₂³	1	2	yes	—
119	#18650	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	4	8	no	—
122	C₁₃×#41	—	4	16	no	—
123	C₁₃×#41	—	4	4	no	—
124	C₁₃×#41	—	4	4	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₁₃×#41	—	4	2	no	—
127	C₁₃×#41	D₈	1	4	yes	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	4	8	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	—	4	4	no	—
136	C₂×Q₈×C₁₃	—	4	1	no	—
137	C₂×Q₈×C₁₃	—	4	2	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	—	4	2	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	4	1	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	4	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×M₁₆	—	4	2	no	—
163	C₂×C₈×C₁₃	—	2	4	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	4	1	no	—
178	C₁₃×C₄⋊C₄	—	4	1	no	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	#3499	C₂×C₁₃	1	1	yes	characteristic
198	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1649	C₂×C₁₃	1	4	yes	complemented
202	#1647	C₂×C₁₃	1	4	yes	complemented
203	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×C₁₃	—	2	1	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	#120	1	1	yes	characteristic
209	Q₈×C₁₃	—	2	1	no	—
210	Q₈×C₁₃	—	4	8	no	—
211	Q₈×C₁₃	—	4	2	no	—
212	Q₈×C₁₃	—	4	2	no	—
213	Q₈×C₁₃	—	4	2	no	—
214	Q₈×C₁₃	—	4	4	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	Q₈×C₁₃	—	4	2	no	—
217	Q₈×C₁₃	—	8	2	no	—
218	Q₈×C₁₃	C₂×D₈	1	2	yes	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	2	1	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	4	8	no	—
223	D₄×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	4	2	no	—
226	D₄×C₁₃	C₂×D₈	1	2	yes	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	8	2	no	—
244	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
248	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₁₃	—	2	4	no	—
253	C₈×C₁₃	—	4	2	no	—
254	C₈×C₁₃	—	4	2	no	—
255	C₂×2₋¹⁺⁴	—	2	1	no	—
256	C₂×#137	—	2	1	no	—
257	D₄×Q₈	—	2	1	no	—
258	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
259	#547	—	2	2	no	—
260	#547	—	2	1	no	—
261	#547	—	2	2	no	—
262	#547	C₂²×C₁₃	1	2	yes	—
263	#536	—	2	2	no	—
264	#536	—	2	1	no	—
265	#532	—	2	1	no	—
266	#532	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	—	2	1	no	—
268	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
271	#500	—	2	2	no	—
272	#500	—	2	1	no	—
273	#500	C₂²×C₁₃	1	4	yes	—
274	#486	—	2	1	no	—
275	#480	—	2	2	no	—
276	#474	C₂²×C₁₃	1	4	yes	—
277	#462	—	2	1	no	—
278	#462	C₂²×C₁₃	1	2	yes	—
279	#461	—	2	1	no	—
280	#461	C₂²×C₁₃	1	2	yes	—
281	#431	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#107	—	2	2	no	—
283	#423	C₂²×C₁₃	1	1	yes	characteristic
284	#419	—	2	1	no	—
285	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
286	#332	C₂²×C₁₃	1	4	yes	—
287	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
288	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
289	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	4	1	no	—
294	C₂²×C₁₃	—	4	1	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	#447	1	2	yes	—
299	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	1	no	—
306	C₄×C₁₃	—	4	1	no	—
307	C₄×C₁₃	—	8	2	no	—
308	C₄×C₁₃	#447	1	2	yes	—
309	C₄×C₁₃	#456	1	2	yes	—
310	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
311	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₄×C₁₃	#578	1	2	yes	—
313	2₋¹⁺⁴	—	4	4	no	—
314	2₋¹⁺⁴	—	4	4	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
320	C₂²×Q₈	—	2	2	no	—
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	—	2	1	no	—
324	#137	—	4	4	no	—
325	C₂×Q₁₆	—	2	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
338	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
339	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
340	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
341	#127	D₄×C₁₃	1	1	yes	characteristic
342	#124	—	2	2	no	—
343	#124	—	2	1	no	—
344	#123	—	2	4	no	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	1	no	—
354	#121	D₄×C₁₃	1	2	yes	—
355	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
356	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
363	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₄×D₄	C₂³×C₁₃	1	2	yes	—
365	#117	—	2	1	no	—
366	#117	D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#107	—	2	8	no	—
376	#107	—	2	4	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#102	—	2	4	no	—
383	C₂²⋊C₈	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	C₄×C₈	C₂³×C₁₃	1	2	yes	—
387	C₂×C₁₃	—	2	2	no	—
388	C₂×C₁₃	—	4	2	no	—
389	C₂×C₁₃	—	8	2	no	—
390	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
391	C₂×C₁₃	#3011	1	1	yes	characteristic
392	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
393	#41	—	2	2	no	—
394	#41	—	4	8	no	—
395	#41	—	4	16	no	—
396	#41	—	4	4	no	—
397	#41	—	4	4	no	—
398	#41	—	4	2	no	—
399	#41	—	4	2	no	—
400	#41	C₁₃×D₈	1	4	yes	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	1	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	—	4	2	no	—
414	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	Q₁₆	—	4	4	no	—
434	SD₁₆	—	4	4	no	—
435	M₁₆	—	4	2	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
470	C₁₃	#18650	1	1	yes	characteristic, direct product factor, Sylow
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	C₁₃×#120	1	1	yes	characteristic
474	Q₈	—	2	1	no	—
475	Q₈	—	4	8	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	4	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	8	2	no	—
483	Q₈	C₂×C₁₃×D₈	1	2	yes	—
484	D₄	—	2	4	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	4	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	4	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	C₂×C₁₃×D₈	1	2	yes	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
510	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
511	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
512	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
513	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	C₈	—	2	4	no	—
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	C₁₃×#447	1	2	yes	—
529	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
530	C₄	—	2	1	no	—
531	C₄	—	2	1	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	8	2	no	—
538	C₄	C₁₃×#447	1	2	yes	—
539	C₄	C₁₃×#456	1	2	yes	—
540	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
541	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
542	C₄	C₁₃×#578	1	2	yes	—
543	C₂	—	2	2	no	—
544	C₂	—	4	2	no	—
545	C₂	—	8	2	no	—
546	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
547	C₂	C₁₃×#3011	1	1	yes	characteristic
548	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3226	C₂	semidirect
3. C₂×C₁₃×#500	C₂	semidirect
4. C₁₃×#3039	C₂	semidirect
5. C₁₃×#1649	C₂	semidirect
6. C₁₃×#1647	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1492	C₂	semidirect
9. C₁₃×#1476	C₂	semidirect
119. #18650	C₁₃	direct (N × H)
198. #3226	C₂×C₁₃	semidirect
199. C₂×#500	C₂×C₁₃	semidirect
200. #3039	C₂×C₁₃	semidirect
201. #1649	C₂×C₁₃	semidirect
202. #1647	C₂×C₁₃	semidirect
203. #1546	C₂×C₁₃	semidirect
204. #1492	C₂×C₁₃	semidirect
205. #1476	C₂×C₁₃	semidirect
470. C₁₃	#18650	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×#3499	2
C₁₃×#3226	2
C₂×C₁₃×#500	2
C₁₃×#3039	2
C₁₃×#1649	2
C₁₃×#1647	2
C₁₃×#1546	2
C₁₃×#1492	2
C₁₃×#1476	2
#18650	13

Subgroups — C13×#18650 #15704989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18650 #15704989