Subgroups — C₁₃×#8425 #15694764

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 484 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×#1981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1477	C₂	1	1	yes	maximal, characteristic
8	Q₈²×C₁₃	C₄	1	2	yes	complemented
9	C₁₃×#557	—	2	1	no	—
10	C₁₃×#554	—	2	2	no	—
11	C₁₃×#554	C₄	1	2	yes	complemented
12	D₄×Q₈×C₁₃	—	2	2	no	—
13	D₄×Q₈×C₁₃	—	2	1	no	—
14	C₁₃×#544	—	2	2	no	—
15	C₁₃×#544	—	2	1	no	—
16	C₁₃×#533	—	2	1	no	—
17	C₁₃×#533	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#520	—	2	1	no	—
21	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₁₃×#431	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#104	—	2	1	no	—
26	C₂×C₁₃×#103	—	2	2	no	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₃×#339	—	2	1	no	—
29	C₁₃×#333	—	2	2	no	—
30	C₁₃×#333	—	2	1	no	—
31	C₁₃×#332	—	2	1	no	—
32	C₁₃×#328	—	2	2	no	—
33	C₁₃×Q₈⋊C₈	—	2	1	no	—
34	C₁₃×D₄⋊C₈	—	2	1	no	—
35	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
38	C₂×C₁₃×M₁₆	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	4	no	—
43	C₁₃×C₄⋊Q₈	—	2	2	no	—
44	C₁₃×C₄⋊Q₈	—	2	2	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
49	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
50	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
51	C₁₃×#125	—	2	2	no	—
52	C₁₃×#125	—	2	4	no	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	4	no	—
60	C₁₃×C₂²⋊Q₈	—	2	1	no	—
61	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	1	no	—
66	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
68	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	—	2	4	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	—	2	1	no	—
78	C₁₃×#117	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	—	2	1	no	—
90	C₁₃×C₄⋊C₈	—	2	1	no	—
91	C₁₃×C₄⋊C₈	—	2	1	no	—
92	C₁₃×#104	—	4	2	no	—
93	C₁₃×#103	—	4	4	no	—
94	C₁₃×C₂²⋊C₈	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	#8425	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₁₃×#41	—	2	1	no	—
99	C₁₃×#41	—	2	1	no	—
100	C₁₃×#41	SD₁₆	1	2	yes	—
101	C₁₃×#41	Q₁₆	1	2	yes	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	4	2	no	—
106	C₂×Q₈×C₁₃	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	8	2	no	—
108	C₂×Q₈×C₁₃	—	8	2	no	—
109	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
111	C₂×Q₈×C₁₃	C₂²⋊C₄	1	4	yes	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₁₃×M₁₆	—	4	1	no	—
124	C₁₃×M₁₆	—	4	1	no	—
125	C₂×C₈×C₁₃	—	4	2	no	—
126	C₂×C₈×C₁₃	—	4	1	no	—
127	C₂×C₈×C₁₃	—	4	1	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	4	1	no	—
146	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
149	C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₁₃	—	2	4	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	1	no	—
159	C₄²×C₁₃	—	4	1	no	—
160	C₄²×C₁₃	—	4	1	no	—
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	#3503	C₂×C₁₃	1	1	yes	characteristic
166	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1806	C₂×C₁₃	1	1	yes	characteristic
168	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1548	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1477	C₂×C₁₃	1	1	yes	characteristic
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	#120	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	1	no	—
175	Q₈×C₁₃	—	4	4	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	Q₈×C₁₃	—	4	1	no	—
179	Q₈×C₁₃	—	4	2	no	—
180	Q₈×C₁₃	—	4	1	no	—
181	Q₈×C₁₃	—	8	4	no	—
182	Q₈×C₁₃	#103	1	2	yes	complemented
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	1	no	—
186	D₄×C₁₃	#103	1	2	yes	complemented
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	8	2	no	—
203	C₂×C₄×C₁₃	—	8	4	no	—
204	C₂×C₄×C₁₃	—	8	1	no	—
205	C₂×C₄×C₁₃	—	8	1	no	—
206	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
214	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
216	C₈×C₁₃	—	8	1	no	—
217	C₈×C₁₃	—	8	1	no	—
218	C₈×C₁₃	—	8	1	no	—
219	Q₈²	C₄×C₁₃	1	2	yes	complemented
220	#557	—	2	1	no	—
221	#554	—	2	2	no	—
222	#554	C₄×C₁₃	1	2	yes	complemented
223	D₄×Q₈	—	2	2	no	—
224	D₄×Q₈	—	2	1	no	—
225	#544	—	2	2	no	—
226	#544	—	2	1	no	—
227	#533	—	2	1	no	—
228	#533	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	—	2	1	no	—
230	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	#520	—	2	1	no	—
232	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
233	#431	C₂²×C₁₃	1	1	yes	characteristic
234	#423	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#104	—	2	1	no	—
237	C₂×#103	—	2	2	no	—
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	#339	—	2	1	no	—
240	#333	—	2	2	no	—
241	#333	—	2	1	no	—
242	#332	—	2	1	no	—
243	#328	—	2	2	no	—
244	Q₈⋊C₈	—	2	1	no	—
245	D₄⋊C₈	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	2	no	—
249	C₂²×C₁₃	—	4	1	no	—
250	C₂²×C₁₃	—	4	1	no	—
251	C₂²×C₁₃	#379	1	1	yes	characteristic
252	C₂²×C₁₃	#448	1	1	yes	characteristic
253	C₂²×C₁₃	#451	1	1	yes	characteristic
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	1	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
265	C₄×C₁₃	#419	1	1	yes	characteristic
266	C₄×C₁₃	#448	1	1	yes	characteristic
267	C₄×C₁₃	#451	1	1	yes	characteristic
268	C₄×C₁₃	#453	1	1	yes	characteristic
269	C₄×C₁₃	#455	1	1	yes	characteristic
270	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
271	C₂²×Q₈	—	2	2	no	—
272	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
283	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
284	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
286	#125	—	2	2	no	—
287	#125	—	2	4	no	—
288	#125	—	2	2	no	—
289	#125	—	2	1	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
303	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
309	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
310	#117	—	2	2	no	—
311	#117	—	2	1	no	—
312	#117	—	2	1	no	—
313	#117	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	#104	—	4	2	no	—
328	#103	—	4	4	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₄×C₈	—	2	1	no	—
331	#95	—	2	1	no	—
332	C₂×C₁₃	—	2	1	no	—
333	C₂×C₁₃	—	2	1	no	—
334	C₂×C₁₃	—	4	2	no	—
335	C₂×C₁₃	#1787	1	1	yes	characteristic
336	C₂×C₁₃	#1792	1	1	yes	characteristic
337	C₂×C₁₃	#1796	1	1	yes	characteristic
338	#41	—	2	1	no	—
339	#41	—	2	1	no	—
340	#41	C₁₃×SD₁₆	1	2	yes	—
341	#41	C₁₃×Q₁₆	1	2	yes	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	8	2	no	—
348	C₂×Q₈	—	8	2	no	—
349	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
351	C₂×Q₈	C₁₃×C₂²⋊C₄	1	4	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	M₁₆	—	4	1	no	—
364	M₁₆	—	4	1	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
387	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₁₃	#8425	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	2	1	no	—
407	C₂³	C₁₃×#120	1	1	yes	characteristic
408	Q₈	—	2	1	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	8	4	no	—
416	Q₈	C₁₃×#103	1	2	yes	complemented
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	1	no	—
420	D₄	C₁₃×#103	1	2	yes	complemented
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	—	8	1	no	—
439	C₂×C₄	—	8	1	no	—
440	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
441	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
444	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
445	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
448	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
449	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
450	C₈	—	8	1	no	—
451	C₈	—	8	1	no	—
452	C₈	—	8	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₁₃×#379	1	1	yes	characteristic
459	C₂²	C₁₃×#448	1	1	yes	characteristic
460	C₂²	C₁₃×#451	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	2	no	—
471	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
472	C₄	C₁₃×#419	1	1	yes	characteristic
473	C₄	C₁₃×#448	1	1	yes	characteristic
474	C₄	C₁₃×#451	1	1	yes	characteristic
475	C₄	C₁₃×#453	1	1	yes	characteristic
476	C₄	C₁₃×#455	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	4	2	no	—
480	C₂	C₁₃×#1787	1	1	yes	characteristic
481	C₂	C₁₃×#1792	1	1	yes	characteristic
482	C₂	C₁₃×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×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×#1981	C₂	semidirect
4. C₁₃×#1550	C₂	semidirect
5. C₁₃×#1548	C₂	semidirect
6. C₁₃×#1503	C₂	semidirect
8. Q₈²×C₁₃	C₄	semidirect
11. C₁₃×#554	C₄	semidirect
97. #8425	C₁₃	direct (N × H)
166. #1981	C₂×C₁₃	semidirect
168. #1550	C₂×C₁₃	semidirect
169. #1548	C₂×C₁₃	semidirect
170. #1503	C₂×C₁₃	semidirect
182. Q₈×C₁₃	#103	semidirect
186. D₄×C₁₃	#103	semidirect
219. Q₈²	C₄×C₁₃	semidirect
222. #554	C₄×C₁₃	semidirect
405. C₁₃	#8425	direct (N × H)
416. Q₈	C₁₃×#103	semidirect
420. D₄	C₁₃×#103	semidirect

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×#1981	2
C₁₃×#1806	2
C₁₃×#1550	2
C₁₃×#1548	2
C₁₃×#1503	2
C₁₃×#1477	2
#8425	13

Subgroups — C13×#8425 #15694764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8425 #15694764