Subgroups — C₁₃×#18654 #15704993

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3229	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
5	C₁₃×#1650	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1648	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#137	—	2	1	no	—
11	C₁₃×#557	—	2	1	no	—
12	C₁₃×#557	C₂²	1	2	yes	—
13	C₁₃×#556	—	2	1	no	—
14	C₁₃×#556	C₂²	1	2	yes	—
15	C₁₃×#552	—	2	2	no	—
16	C₁₃×#552	—	2	2	no	—
17	C₁₃×#541	—	2	2	no	—
18	C₁₃×#536	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	—	2	1	no	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#519	—	2	1	no	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#500	—	2	2	no	—
27	C₁₃×#500	C₂²	1	4	yes	—
28	C₁₃×#498	—	2	1	no	—
29	C₁₃×#487	—	2	1	no	—
30	C₁₃×#483	—	2	2	no	—
31	C₁₃×#475	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×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₁₃×#137	—	4	4	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×#126	—	2	4	no	—
65	C₁₃×#126	—	2	4	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	—	2	1	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#123	—	2	4	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	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	1	no	—
78	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	1	no	—
86	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#117	—	2	4	no	—
94	C₁₃×#117	—	2	2	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	—	2	2	no	—
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	D₄	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	8	no	—
106	C₁₃×#106	—	2	4	no	—
107	C₁₃×C₄⋊C₈	—	2	1	no	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	C₂³	1	2	yes	—
117	#18654	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	4	1	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	—	4	2	no	—
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	4	4	no	—
142	C₁₃×SD₁₆	—	4	4	no	—
143	C₁₃×M₁₆	—	4	2	no	—
144	C₂×C₈×C₁₃	—	2	4	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	4	1	no	—
165	C₁₃×C₄⋊C₄	—	4	1	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₄²×C₁₃	—	2	4	no	—
177	C₄²×C₁₃	—	2	4	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
186	#3509	C₂×C₁₃	1	1	yes	characteristic
187	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#3039	C₂×C₁₃	1	1	yes	characteristic
190	#1650	C₂×C₁₃	1	4	yes	complemented
191	#1648	C₂×C₁₃	1	4	yes	complemented
192	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1476	C₂×C₁₃	1	1	yes	characteristic
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	#120	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	4	2	no	—
205	Q₈×C₁₃	—	4	2	no	—
206	Q₈×C₁₃	—	8	2	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#135	1	2	yes	—
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₃	—	2	4	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₂×#137	—	2	1	no	—
236	#557	—	2	1	no	—
237	#557	C₂²×C₁₃	1	2	yes	—
238	#556	—	2	1	no	—
239	#556	C₂²×C₁₃	1	2	yes	—
240	#552	—	2	2	no	—
241	#552	—	2	2	no	—
242	#541	—	2	2	no	—
243	#536	—	2	1	no	—
244	#533	—	2	1	no	—
245	#533	—	2	1	no	—
246	#533	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	#519	—	2	1	no	—
250	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
251	#500	—	2	2	no	—
252	#500	C₂²×C₁₃	1	4	yes	—
253	#498	—	2	1	no	—
254	#487	—	2	1	no	—
255	#483	—	2	2	no	—
256	#475	C₂²×C₁₃	1	4	yes	—
257	#462	—	2	1	no	—
258	#462	C₂²×C₁₃	1	2	yes	—
259	#461	—	2	1	no	—
260	#461	C₂²×C₁₃	1	2	yes	—
261	#431	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#107	—	2	2	no	—
263	#423	C₂²×C₁₃	1	1	yes	characteristic
264	#419	—	2	1	no	—
265	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
266	#332	C₂²×C₁₃	1	4	yes	—
267	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
268	Q₈⋊C₈	C₂²×C₁₃	1	4	yes	—
269	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	4	1	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	#449	1	2	yes	—
276	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
277	C₄×C₁₃	—	2	1	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	—	4	1	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	#449	1	2	yes	—
287	C₄×C₁₃	#456	1	2	yes	—
288	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
289	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₄×C₁₃	#578	1	2	yes	—
291	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	—	2	1	no	—
294	#137	—	4	4	no	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
309	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
310	#126	—	2	4	no	—
311	#126	—	2	4	no	—
312	#125	—	2	2	no	—
313	#125	—	2	4	no	—
314	#125	—	2	2	no	—
315	#125	—	2	4	no	—
316	#125	—	2	1	no	—
317	#124	—	2	2	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
338	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
339	#117	—	2	4	no	—
340	#117	—	2	2	no	—
341	#117	—	2	1	no	—
342	#117	—	2	2	no	—
343	#117	—	2	1	no	—
344	#117	D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
351	#107	—	2	8	no	—
352	#106	—	2	4	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
355	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
356	#103	—	2	4	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₄×C₈	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₄×C₈	C₂³×C₁₃	1	2	yes	—
363	C₂×C₁₃	—	2	2	no	—
364	C₂×C₁₃	—	8	1	no	—
365	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
366	C₂×C₁₃	#3011	1	1	yes	characteristic
367	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	4	1	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	2	no	—
377	C₂×Q₈	—	4	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	Q₁₆	—	4	4	no	—
392	SD₁₆	—	4	4	no	—
393	M₁₆	—	4	2	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₁₃	#18654	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	1	no	—
438	C₂³	C₁₃×#120	1	1	yes	characteristic
439	Q₈	—	2	1	no	—
440	Q₈	—	2	1	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	8	2	no	—
449	D₄	—	2	1	no	—
450	D₄	—	2	1	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
467	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
468	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
469	C₂×C₄	C₁₃×#135	1	2	yes	—
470	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₈	—	2	4	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	C₁₃×#449	1	2	yes	—
483	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	4	no	—
492	C₄	—	8	2	no	—
493	C₄	C₁₃×#449	1	2	yes	—
494	C₄	C₁₃×#456	1	2	yes	—
495	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
496	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
497	C₄	C₁₃×#578	1	2	yes	—
498	C₂	—	2	2	no	—
499	C₂	—	8	1	no	—
500	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
501	C₂	C₁₃×#3011	1	1	yes	characteristic
502	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	C₂×C₁₃×#41	D₄
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×#3229	C₂	semidirect
3. C₂×C₁₃×#500	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1648	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1493	C₂	semidirect
117. #18654	C₁₃	direct (N × H)
187. #3229	C₂×C₁₃	semidirect
188. C₂×#500	C₂×C₁₃	semidirect
190. #1650	C₂×C₁₃	semidirect
191. #1648	C₂×C₁₃	semidirect
192. #1546	C₂×C₁₃	semidirect
193. #1493	C₂×C₁₃	semidirect
436. C₁₃	#18654	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×#3509	2
C₁₃×#3229	2
C₂×C₁₃×#500	2
C₁₃×#3039	2
C₁₃×#1650	2
C₁₃×#1648	2
C₁₃×#1546	2
C₁₃×#1493	2
C₁₃×#1476	2
#18654	13

Subgroups — C13×#18654 #15704993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18654 #15704993