Subgroups — C₁₃×#18756 #15705095

Order 3328.

1224 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1647	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1625	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
12	C₁₃×#547	—	2	2	no	—
13	C₁₃×#547	—	2	2	no	—
14	C₁₃×#547	—	2	2	no	—
15	C₁₃×#547	C₂²	1	4	yes	—
16	C₁₃×#532	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#123	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₁₃×#500	C₂²	1	2	yes	complemented
25	C₁₃×#486	C₂²	1	2	yes	complemented
26	C₁₃×#480	—	2	1	no	—
27	C₁₃×#480	—	2	2	no	—
28	C₁₃×#474	—	2	2	no	—
29	C₁₃×#474	C₂²	1	2	yes	complemented
30	C₁₃×#463	—	2	2	no	—
31	C₁₃×#461	C₂²	1	2	yes	complemented
32	C₁₃×#459	C₂²	1	2	yes	complemented
33	C₁₃×#459	C₂²	1	2	yes	complemented
34	C₁₃×#447	—	2	1	no	—
35	C₄×C₁₃×D₈	—	2	2	no	—
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#431	C₂²	1	1	yes	characteristic
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#417	—	2	1	no	—
40	C₁₃×#332	C₂²	1	4	yes	complemented
41	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂×C₁₃×#41	—	4	4	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×#127	C₂³	1	1	yes	characteristic
66	C₁₃×#124	—	2	1	no	—
67	C₁₃×#123	—	2	8	no	—
68	C₁₃×#123	—	2	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	4	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×#121	—	2	4	no	—
72	C₁₃×#121	—	2	4	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₄×D₄×C₁₃	—	2	1	no	—
77	C₄×D₄×C₁₃	—	2	1	no	—
78	C₄×D₄×C₁₃	—	2	1	no	—
79	C₄×D₄×C₁₃	—	2	1	no	—
80	C₄×D₄×C₁₃	—	2	1	no	—
81	C₄×D₄×C₁₃	D₄	1	2	yes	—
82	C₄×D₄×C₁₃	D₄	1	2	yes	—
83	C₄×D₄×C₁₃	C₂³	1	2	yes	—
84	C₄×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	—	2	2	no	—
97	C₁₃×#107	—	2	4	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	—	2	1	no	—
100	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
102	C₁₃×#103	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	4	no	—
107	C₁₃×C₂²⋊C₈	—	2	1	no	—
108	C₁₃×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₈×C₁₃	—	2	1	no	—
110	C₄×C₈×C₁₃	C₂³	1	2	yes	—
111	#18756	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	1	no	—
113	C₂⁴×C₁₃	—	2	1	no	—
114	C₁₃×#41	—	4	8	no	—
115	C₁₃×#41	—	4	16	no	—
116	C₁₃×#41	—	4	8	no	—
117	C₁₃×#41	—	4	2	no	—
118	C₁₃×#41	—	4	2	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	4	2	no	—
123	C₂×Q₈×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	4	2	no	—
132	C₂×D₄×C₁₃	—	4	8	no	—
133	C₂×D₄×C₁₃	—	4	1	no	—
134	C₂×D₄×C₁₃	D₈	1	4	yes	complemented
135	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	—	2	8	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	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	1	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₁₃×SD₁₆	—	4	4	no	—
154	C₁₃×D₈	—	4	4	no	—
155	C₁₃×D₈	—	4	4	no	—
156	C₁₃×M₁₆	—	4	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
171	C₁₃×C₂²⋊C₄	—	2	8	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	—	4	1	no	—
177	C₁₃×C₂²⋊C₄	—	4	1	no	—
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#1647	C₂×C₁₃	1	4	yes	complemented
187	#1625	C₂×C₁₃	1	4	yes	complemented
188	#1546	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1486	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1478	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	#120	1	1	yes	characteristic
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	—	4	4	no	—
204	Q₈×C₁₃	—	4	1	no	—
205	Q₈×C₁₃	—	4	1	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	4	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	4	16	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	8	2	no	—
217	D₄×C₁₃	C₂×D₈	1	4	yes	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	16	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	4	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	4	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	8	2	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	C₂×D₈	1	2	yes	—
238	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₈×C₁₃	—	4	2	no	—
243	C₈×C₁₃	—	4	2	no	—
244	C₈×C₁₃	—	4	2	no	—
245	C₂²×#41	—	2	1	no	—
246	C₂×AGL(1,ℤ/8)	—	2	1	no	—
247	#547	—	2	2	no	—
248	#547	—	2	2	no	—
249	#547	—	2	2	no	—
250	#547	C₂²×C₁₃	1	4	yes	—
251	#532	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#123	—	2	2	no	—
254	C₂×C₂²⋊Q₈	—	2	1	no	—
255	C₂×#121	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	—	2	1	no	—
259	#500	C₂²×C₁₃	1	2	yes	complemented
260	#486	C₂²×C₁₃	1	2	yes	complemented
261	#480	—	2	1	no	—
262	#480	—	2	2	no	—
263	#474	—	2	2	no	—
264	#474	C₂²×C₁₃	1	2	yes	complemented
265	#463	—	2	2	no	—
266	#461	C₂²×C₁₃	1	2	yes	complemented
267	#459	C₂²×C₁₃	1	2	yes	complemented
268	#459	C₂²×C₁₃	1	2	yes	complemented
269	#447	—	2	1	no	—
270	C₄×D₈	—	2	2	no	—
271	#431	C₂²×C₁₃	1	1	yes	characteristic
272	#431	C₂²×C₁₃	1	1	yes	characteristic
273	#423	C₂²×C₁₃	1	1	yes	characteristic
274	#417	—	2	1	no	—
275	#332	C₂²×C₁₃	1	4	yes	complemented
276	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
277	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	4	8	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	8	4	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	—	8	1	no	—
290	C₂²×C₁₃	—	8	1	no	—
291	C₂²×C₁₃	#447	1	2	yes	—
292	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	#447	1	2	yes	—
301	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
302	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₄×C₁₃	#575	1	2	yes	—
304	C₂×#41	—	2	4	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	4	4	no	—
308	C₂×#41	—	4	4	no	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	AGL(1,ℤ/8)	—	4	4	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
324	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
326	#127	C₂³×C₁₃	1	1	yes	characteristic
327	#124	—	2	1	no	—
328	#123	—	2	8	no	—
329	#123	—	2	8	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	D₄×C₁₃	1	2	yes	—
343	C₄×D₄	D₄×C₁₃	1	2	yes	—
344	C₄×D₄	C₂³×C₁₃	1	2	yes	—
345	C₄×D₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	#107	—	2	2	no	—
358	#107	—	2	4	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
362	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
363	#103	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	4	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	1	no	—
370	C₄×C₈	—	2	1	no	—
371	C₄×C₈	C₂³×C₁₃	1	2	yes	—
372	C₂×C₁₃	—	2	2	no	—
373	C₂×C₁₃	—	4	4	no	—
374	C₂×C₁₃	—	8	2	no	—
375	C₂×C₁₃	—	16	1	no	—
376	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
377	C₂×C₁₃	#3005	1	1	yes	characteristic
378	C₂×C₁₃	#3020	1	1	yes	characteristic
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	1	no	—
381	#41	—	4	16	no	—
382	#41	—	4	8	no	—
383	#41	—	4	8	no	—
384	#41	—	4	2	no	—
385	#41	—	4	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	1	no	—
401	C₂×D₄	C₁₃×D₈	1	4	yes	complemented
402	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	SD₁₆	—	4	4	no	—
421	D₈	—	4	4	no	—
422	D₈	—	4	4	no	—
423	M₁₆	—	4	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₁₃	#18756	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	4	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₁₃×#120	1	1	yes	characteristic
460	Q₈	—	4	4	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	16	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	C₂×C₁₃×D₈	1	4	yes	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
494	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
495	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
496	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
497	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	1	no	—
517	C₂²	C₁₃×#447	1	2	yes	—
518	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₁₃×#447	1	2	yes	—
527	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
528	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
529	C₄	C₁₃×#575	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	4	4	no	—
532	C₂	—	8	2	no	—
533	C₂	—	16	1	no	—
534	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
535	C₂	C₁₃×#3005	1	1	yes	characteristic
536	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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
1. C₂×C₁₃×#547	C₂	semidirect
2. C₁₃×#3226	C₂	semidirect
3. C₁₃×#3100	C₂	semidirect
4. C₁₃×#3036	C₂	semidirect
5. C₁₃×#1647	C₂	semidirect
6. C₁₃×#1625	C₂	semidirect
7. C₁₃×#1546	C₂	semidirect
8. C₁₃×#1486	C₂	semidirect
9. C₁₃×#1478	C₂	semidirect
24. C₁₃×#500	C₂²	semidirect
25. C₁₃×#486	C₂²	semidirect
29. C₁₃×#474	C₂²	semidirect
31. C₁₃×#461	C₂²	semidirect
32. C₁₃×#459	C₂²	semidirect
33. C₁₃×#459	C₂²	semidirect
40. C₁₃×#332	C₂²	semidirect
41. C₁₃×D₄⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
111. #18756	C₁₃	direct (N × H)
134. C₂×D₄×C₁₃	D₈	semidirect
182. C₂×#547	C₂×C₁₃	semidirect
183. #3226	C₂×C₁₃	semidirect
184. #3100	C₂×C₁₃	semidirect
185. #3036	C₂×C₁₃	semidirect
186. #1647	C₂×C₁₃	semidirect
187. #1625	C₂×C₁₃	semidirect
188. #1546	C₂×C₁₃	semidirect
189. #1486	C₂×C₁₃	semidirect
190. #1478	C₂×C₁₃	semidirect
259. #500	C₂²×C₁₃	semidirect
260. #486	C₂²×C₁₃	semidirect
264. #474	C₂²×C₁₃	semidirect
266. #461	C₂²×C₁₃	semidirect
267. #459	C₂²×C₁₃	semidirect
268. #459	C₂²×C₁₃	semidirect
275. #332	C₂²×C₁₃	semidirect
276. D₄⋊C₈	C₂²×C₁₃	semidirect
277. D₄⋊C₈	C₂²×C₁₃	semidirect
401. C₂×D₄	C₁₃×D₈	semidirect
449. C₁₃	#18756	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#547	2
C₁₃×#3226	2
C₁₃×#3100	2
C₁₃×#3036	2
C₁₃×#1647	2
C₁₃×#1625	2
C₁₃×#1546	2
C₁₃×#1486	2
C₁₃×#1478	2
#18756	13

Subgroups — C13×#18756 #15705095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18756 #15705095