Subgroups — C₁₃×#25923 #15712262

Order 3328.

1014 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2028	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1882	C₂	1	4	yes	maximal
9	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#137	C₂²	1	2	yes	—
11	Q₈²×C₁₃	—	2	1	no	—
12	C₁₃×#557	—	2	1	no	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#554	—	2	2	no	—
15	D₄×Q₈×C₁₃	—	2	2	no	—
16	D₄×Q₈×C₁₃	—	2	1	no	—
17	C₁₃×#544	—	2	2	no	—
18	C₁₃×#544	C₂²	1	2	yes	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#520	C₂²	1	2	yes	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#491	—	2	2	no	—
27	C₁₃×#487	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#462	—	2	1	no	—
30	C₁₃×#462	—	2	1	no	—
31	C₁₃×#461	—	2	1	no	—
32	C₁₃×#461	—	2	1	no	—
33	C₁₃×#423	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#104	C₂²	1	2	yes	—
35	C₁₃×#419	C₂²	1	2	yes	—
36	C₁₃×#419	C₂²	1	4	yes	—
37	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×#391	—	2	2	no	—
39	C₁₃×#391	C₂²	1	4	yes	—
40	C₁₃×#382	—	2	2	no	—
41	C₄³×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#343	C₂²	1	4	yes	—
43	C₁₃×#339	C₂²	1	4	yes	—
44	C₁₃×#339	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×#137	—	2	8	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
69	C₁₃×#125	—	2	4	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	—	2	2	no	—
72	C₁₃×#125	D₄	1	2	yes	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	1	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	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	1	no	—
84	C₄×Q₈×C₁₃	—	2	1	no	—
85	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	4	no	—
91	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
93	C₁₃×#117	—	2	2	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	C₂³	1	1	yes	characteristic
96	C₁₃×#117	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	—	2	1	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×#104	—	2	4	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#103	—	2	4	no	—
114	C₁₃×#103	—	2	4	no	—
115	C₁₃×#97	—	2	1	no	—
116	C₄×C₈×C₁₃	—	2	1	no	—
117	C₁₃×#95	—	2	8	no	—
118	#25923	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₁₃×#41	—	2	2	no	—
120	C₁₃×#41	#41	1	4	yes	—
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	4	4	no	—
131	C₂×Q₈×C₁₃	—	8	4	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×Q₁₆	—	4	4	no	—
146	C₁₃×SD₁₆	—	4	4	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	4	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₄²×C₁₃	—	2	4	no	—
180	C₄²×C₁₃	—	2	4	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	2	no	—
185	C₄²×C₁₃	—	2	2	no	—
186	C₄²×C₁₃	—	2	2	no	—
187	C₄²×C₁₃	—	4	2	no	—
188	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
192	#3503	C₂×C₁₃	1	1	yes	characteristic
193	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3039	C₂×C₁₃	1	1	yes	characteristic
195	#2862	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#2028	C₂×C₁₃	1	4	yes	complemented
197	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1994	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1882	C₂×C₁₃	1	4	yes	—
200	C₄×#104	C₂×C₁₃	1	1	yes	characteristic
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	—	4	4	no	—
205	Q₈×C₁₃	—	4	2	no	—
206	Q₈×C₁₃	—	4	2	no	—
207	Q₈×C₁₃	—	4	2	no	—
208	Q₈×C₁₃	—	4	2	no	—
209	Q₈×C₁₃	—	4	4	no	—
210	Q₈×C₁₃	—	8	2	no	—
211	Q₈×C₁₃	—	8	4	no	—
212	Q₈×C₁₃	#124	1	2	yes	—
213	D₄×C₁₃	—	2	4	no	—
214	D₄×C₁₃	—	2	1	no	—
215	D₄×C₁₃	#124	1	2	yes	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	8	4	no	—
234	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
241	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
242	C₈×C₁₃	—	4	2	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₂×#137	C₂²×C₁₃	1	2	yes	—
245	Q₈²	—	2	1	no	—
246	#557	—	2	1	no	—
247	#554	—	2	1	no	—
248	#554	—	2	2	no	—
249	D₄×Q₈	—	2	2	no	—
250	D₄×Q₈	—	2	1	no	—
251	#544	—	2	2	no	—
252	#544	C₂²×C₁₃	1	2	yes	—
253	#533	—	2	1	no	—
254	#533	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	#520	C₂²×C₁₃	1	2	yes	—
259	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
260	#491	—	2	2	no	—
261	#487	—	2	1	no	—
262	#487	—	2	1	no	—
263	#462	—	2	1	no	—
264	#462	—	2	1	no	—
265	#461	—	2	1	no	—
266	#461	—	2	1	no	—
267	#423	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#104	C₂²×C₁₃	1	2	yes	—
269	#419	C₂²×C₁₃	1	4	yes	—
270	#419	C₂²×C₁₃	1	2	yes	—
271	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	#391	—	2	2	no	—
273	#391	C₂²×C₁₃	1	4	yes	—
274	#382	—	2	2	no	—
275	C₄³	C₂²×C₁₃	1	1	yes	characteristic
276	#343	C₂²×C₁₃	1	4	yes	—
277	#339	C₂²×C₁₃	1	4	yes	—
278	#339	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
285	C₂²×C₁₃	#548	1	2	yes	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	4	4	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	#455	1	2	yes	—
297	C₄×C₁₃	#456	1	2	yes	—
298	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
299	C₄×C₁₃	#536	1	1	yes	characteristic
300	C₄×C₁₃	#548	1	2	yes	—
301	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
304	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
305	#137	—	2	8	no	—
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
309	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
324	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
325	#125	—	2	4	no	—
326	#125	—	2	2	no	—
327	#125	—	2	2	no	—
328	#125	D₄×C₁₃	1	2	yes	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
342	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
348	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
349	#117	—	2	2	no	—
350	#117	—	2	1	no	—
351	#117	C₂³×C₁₃	1	1	yes	characteristic
352	#117	C₂³×C₁₃	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	2	1	no	—
366	#104	—	2	4	no	—
367	#103	—	2	2	no	—
368	#103	—	2	2	no	—
369	#103	—	2	4	no	—
370	#103	—	2	4	no	—
371	#97	—	2	1	no	—
372	C₄×C₈	—	2	1	no	—
373	#95	—	2	8	no	—
374	C₂×C₁₃	—	2	2	no	—
375	C₂×C₁₃	—	4	2	no	—
376	C₂×C₁₃	#2436	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
378	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
379	#41	—	2	2	no	—
380	#41	C₁₃×#41	1	4	yes	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	—	8	4	no	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	Q₁₆	—	4	4	no	—
406	SD₁₆	—	4	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	4	no	—
409	M₁₆	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₄²	—	2	4	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	4	2	no	—
448	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₁₃	#25923	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	1	no	—
454	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	Q₈	—	2	1	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	4	no	—
462	Q₈	—	8	2	no	—
463	Q₈	—	8	4	no	—
464	Q₈	C₁₃×#124	1	2	yes	—
465	D₄	—	2	4	no	—
466	D₄	—	2	1	no	—
467	D₄	C₁₃×#124	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	4	no	—
486	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
487	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
488	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
489	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
493	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
502	C₂²	C₁₃×#548	1	2	yes	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	—	8	2	no	—
513	C₄	C₁₃×#455	1	2	yes	—
514	C₄	C₁₃×#456	1	2	yes	—
515	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
516	C₄	C₁₃×#536	1	1	yes	characteristic
517	C₄	C₁₃×#548	1	2	yes	—
518	C₂	—	2	2	no	—
519	C₂	—	4	2	no	—
520	C₂	C₁₃×#2436	1	1	yes	characteristic
521	C₂	C₂×C₁₃×#455	1	1	yes	characteristic
522	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3139	C₂	semidirect
4. C₁₃×#2862	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#1997	C₂	semidirect
7. C₁₃×#1994	C₂	semidirect
118. #25923	C₁₃	direct (N × H)
193. #3139	C₂×C₁₃	semidirect
195. #2862	C₂×C₁₃	semidirect
196. #2028	C₂×C₁₃	semidirect
197. #1997	C₂×C₁₃	semidirect
198. #1994	C₂×C₁₃	semidirect
452. C₁₃	#25923	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×#3503	2
C₁₃×#3139	2
C₁₃×#3039	2
C₁₃×#2862	2
C₁₃×#2028	2
C₁₃×#1997	2
C₁₃×#1994	2
C₁₃×#1882	2
C₄×C₁₃×#104	2
#25923	13

Subgroups — C13×#25923 #15712262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25923 #15712262