Subgroups — C₁₃×#60943 #15747282

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	2	yes	maximal
2	C₁₃×#3249	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3230	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3209	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3189	C₂	1	4	yes	maximal
6	C₁₃×#3170	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3104	C₂	1	8	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#533	—	2	2	no	—
10	C₁₃×#533	—	2	2	no	—
11	C₁₃×#533	—	2	2	no	—
12	C₁₃×#533	—	2	2	no	—
13	C₁₃×#533	C₂²	1	4	yes	—
14	C₁₃×#533	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	4	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	—	2	2	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
24	C₂×C₁₃×#117	—	2	2	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	4	yes	complemented
27	C₁₃×#494	C₂²	1	4	yes	complemented
28	C₁₃×#487	C₂²	1	8	yes	complemented
29	C₁₃×#484	C₂²	1	16	yes	—
30	C₁₃×#477	C₂²	1	16	yes	complemented
31	C₁₃×#467	C₂²	1	16	yes	—
32	C₁₃×#462	C₂²	1	16	yes	complemented
33	C₁₃×#451	C₂²	1	16	yes	—
34	C₄×C₁₃×Q₁₆	C₂²	1	16	yes	complemented
35	C₁₃×#431	C₂²	1	4	yes	—
36	C₁₃×#431	C₂²	1	4	yes	—
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
55	C₁₃×#125	—	2	4	no	—
56	C₁₃×#125	—	2	4	no	—
57	C₁₃×#125	—	2	4	no	—
58	C₁₃×#125	—	2	4	no	—
59	C₁₃×C₂²⋊Q₈	—	2	4	no	—
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	4	no	—
69	C₄×Q₈×C₁₃	—	2	4	no	—
70	C₄×Q₈×C₁₃	—	2	4	no	—
71	C₄×Q₈×C₁₃	—	2	4	no	—
72	C₄×Q₈×C₁₃	—	2	4	no	—
73	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
74	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
75	C₁₃×#117	—	2	4	no	—
76	C₁₃×#117	—	2	4	no	—
77	C₁₃×#117	—	2	4	no	—
78	C₁₃×#117	—	2	4	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
86	C₂×C₄²×C₁₃	—	2	4	no	—
87	C₂×C₄²×C₁₃	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃	D₄	1	2	yes	—
89	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₁₃×#107	C₂³	1	16	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
97	C₁₃×#103	C₂³	1	32	yes	—
98	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
99	C₄×C₈×C₁₃	C₂³	1	4	yes	—
100	C₄×C₈×C₁₃	C₂³	1	4	yes	—
101	#60943	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	4	8	no	—
107	C₂×Q₈×C₁₃	—	4	8	no	—
108	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	Q₁₆	1	8	yes	complemented
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	4	16	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
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	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	4	no	—
140	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
141	C₁₃×C₂²⋊C₄	—	2	8	no	—
142	C₁₃×C₂²⋊C₄	—	2	8	no	—
143	C₄²×C₁₃	—	2	8	no	—
144	C₄²×C₁₃	—	2	8	no	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂×D₄	1	2	yes	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	C₂×D₄	1	2	yes	—
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₄²×C₁₃	C₂⁴	1	2	yes	—
154	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂×#533	C₂×C₁₃	1	2	yes	—
156	#3249	C₂×C₁₃	1	4	yes	complemented
157	#3230	C₂×C₁₃	1	4	yes	complemented
158	#3209	C₂×C₁₃	1	4	yes	complemented
159	#3189	C₂×C₁₃	1	4	yes	—
160	#3170	C₂×C₁₃	1	4	yes	complemented
161	#3104	C₂×C₁₃	1	8	yes	complemented
162	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
168	Q₈×C₁₃	—	2	16	no	—
169	Q₈×C₁₃	—	4	8	no	—
170	Q₈×C₁₃	—	4	8	no	—
171	Q₈×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	8	no	—
184	C₂×C₄×C₁₃	C₂×Q₁₆	1	8	yes	—
185	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
186	C₂×C₄×C₁₃	C₂×Q₁₆	1	8	yes	—
187	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₃	—	2	8	no	—
198	#533	—	2	2	no	—
199	#533	—	2	2	no	—
200	#533	—	2	2	no	—
201	#533	—	2	2	no	—
202	#533	C₂²×C₁₃	1	4	yes	—
203	#533	C₂²×C₁₃	1	4	yes	—
204	#533	C₂²×C₁₃	1	4	yes	—
205	#533	C₂²×C₁₃	1	4	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
208	C₂×#125	—	2	2	no	—
209	C₂×C₂²⋊Q₈	—	2	2	no	—
210	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
211	C₂×C₄×Q₈	—	2	2	no	—
212	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
213	C₂×#117	—	2	2	no	—
214	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
215	#500	C₂²×C₁₃	1	4	yes	complemented
216	#494	C₂²×C₁₃	1	4	yes	complemented
217	#487	C₂²×C₁₃	1	8	yes	complemented
218	#484	C₂²×C₁₃	1	16	yes	—
219	#477	C₂²×C₁₃	1	16	yes	complemented
220	#467	C₂²×C₁₃	1	16	yes	—
221	#462	C₂²×C₁₃	1	16	yes	complemented
222	#451	C₂²×C₁₃	1	16	yes	—
223	C₄×Q₁₆	C₂²×C₁₃	1	16	yes	complemented
224	#431	C₂²×C₁₃	1	4	yes	—
225	#431	C₂²×C₁₃	1	4	yes	—
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
235	C₂²×C₁₃	C₂²×Q₁₆	1	4	yes	—
236	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	4	8	no	—
242	C₄×C₁₃	—	4	8	no	—
243	C₄×C₁₃	C₂²×Q₁₆	1	4	yes	—
244	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
245	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
246	C₄×C₁₃	#575	1	2	yes	—
247	C₄×C₁₃	#585	1	2	yes	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
250	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
251	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
254	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	2	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
260	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
261	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
262	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
263	#125	—	2	4	no	—
264	#125	—	2	4	no	—
265	#125	—	2	4	no	—
266	#125	—	2	4	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	4	no	—
269	C₂²⋊Q₈	—	2	4	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
274	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
282	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
283	#117	—	2	4	no	—
284	#117	—	2	4	no	—
285	#117	—	2	4	no	—
286	#117	—	2	4	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	—	2	4	no	—
295	C₂×C₄²	D₄×C₁₃	1	2	yes	—
296	C₂×C₄²	D₄×C₁₃	1	2	yes	—
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	C₂³×C₁₃	1	16	yes	—
304	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
305	#103	C₂³×C₁₃	1	32	yes	—
306	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
307	C₄×C₈	C₂³×C₁₃	1	4	yes	—
308	C₄×C₈	C₂³×C₁₃	1	4	yes	—
309	C₂×C₁₃	—	2	4	no	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	#3449	1	1	yes	characteristic
312	C₂×C₁₃	C₂³×Q₁₆	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
314	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	4	8	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₁₃×Q₁₆	1	8	yes	complemented
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	Q₁₆	—	4	16	no	—
339	C₂×C₈	—	4	4	no	—
340	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₄²	—	2	8	no	—
356	C₄²	—	2	8	no	—
357	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₁₃	1	2	yes	—
359	C₄²	C₂×D₄×C₁₃	1	2	yes	—
360	C₄²	C₂×D₄×C₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₃	1	2	yes	—
362	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₁₃	1	2	yes	—
364	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
365	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
366	C₄²	C₂⁴×C₁₃	1	2	yes	—
367	C₁₃	#60943	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
371	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
373	Q₈	—	2	16	no	—
374	Q₈	—	4	8	no	—
375	Q₈	—	4	8	no	—
376	Q₈	—	4	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	C₂×C₁₃×Q₁₆	1	8	yes	—
390	C₂×C₄	C₂×C₁₃×Q₁₆	1	8	yes	—
391	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
392	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
402	C₈	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	4	no	—
408	C₂²	C₂²×C₁₃×Q₁₆	1	2	yes	—
409	C₂²	C₂²×C₁₃×Q₁₆	1	4	yes	—
410	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	8	no	—
416	C₄	—	4	8	no	—
417	C₄	C₂²×C₁₃×Q₁₆	1	4	yes	—
418	C₄	C₂²×C₁₃×Q₁₆	1	2	yes	—
419	C₄	C₂²×C₁₃×Q₁₆	1	2	yes	—
420	C₄	C₁₃×#575	1	2	yes	—
421	C₄	C₁₃×#585	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	2	2	no	—
424	C₂	C₁₃×#3449	1	1	yes	characteristic
425	C₂	C₂³×C₁₃×Q₁₆	1	1	yes	characteristic
426	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3249	C₂	semidirect
3. C₁₃×#3230	C₂	semidirect
4. C₁₃×#3209	C₂	semidirect
6. C₁₃×#3170	C₂	semidirect
7. C₁₃×#3104	C₂	semidirect
26. C₁₃×#500	C₂²	semidirect
27. C₁₃×#494	C₂²	semidirect
28. C₁₃×#487	C₂²	semidirect
30. C₁₃×#477	C₂²	semidirect
32. C₁₃×#462	C₂²	semidirect
34. C₄×C₁₃×Q₁₆	C₂²	semidirect
101. #60943	C₁₃	direct (N × H)
113. C₂²×C₄×C₁₃	Q₁₆	semidirect
156. #3249	C₂×C₁₃	semidirect
157. #3230	C₂×C₁₃	semidirect
158. #3209	C₂×C₁₃	semidirect
160. #3170	C₂×C₁₃	semidirect
161. #3104	C₂×C₁₃	semidirect
215. #500	C₂²×C₁₃	semidirect
216. #494	C₂²×C₁₃	semidirect
217. #487	C₂²×C₁₃	semidirect
219. #477	C₂²×C₁₃	semidirect
221. #462	C₂²×C₁₃	semidirect
223. C₄×Q₁₆	C₂²×C₁₃	semidirect
325. C₂²×C₄	C₁₃×Q₁₆	semidirect
367. C₁₃	#60943	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×#533	2
C₁₃×#3249	2
C₁₃×#3230	2
C₁₃×#3209	2
C₁₃×#3189	2
C₁₃×#3170	2
C₁₃×#3104	2
C₂×C₁₃×#431	2
#60943	13

Subgroups — C13×#60943 #15747282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60943 #15747282