Subgroups — C₁₃×#25848 #15712187

Order 3328.

980 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2059	C₂	1	2	yes	maximal
6	C₁₃×#2058	C₂	1	2	yes	maximal
7	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1865	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#557	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#501	—	2	4	no	—
27	C₁₃×#475	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#106	C₂²	1	2	yes	—
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#395	—	2	1	no	—
37	C₁₃×#391	—	2	1	no	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#384	—	2	1	no	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#336	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	2	8	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×#125	—	2	8	no	—
59	C₁₃×#125	—	2	8	no	—
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×#125	D₄	1	4	yes	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	D₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	—	2	4	no	—
100	C₁₃×#106	—	2	4	no	—
101	C₁₃×#106	—	2	4	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×#103	—	2	4	no	—
104	C₁₃×#103	Q₈	1	8	yes	complemented
105	C₁₃×#97	—	2	2	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	2	no	—
108	C₁₃×#95	—	2	2	no	—
109	#25848	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	4	1	no	—
116	C₂×Q₈×C₁₃	—	4	2	no	—
117	C₂×Q₈×C₁₃	—	4	2	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	—	8	2	no	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	4	2	no	—
158	C₁₃×C₄⋊C₄	—	8	2	no	—
159	C₁₃×C₄⋊C₄	—	8	2	no	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
164	C₄²×C₁₃	—	2	4	no	—
165	C₄²×C₁₃	—	2	4	no	—
166	C₄²×C₁₃	—	2	4	no	—
167	C₄²×C₁₃	—	2	1	no	—
168	C₄²×C₁₃	—	2	1	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	4	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×#557	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#501	C₂×C₁₃	1	1	yes	characteristic
176	C₂×#475	C₂×C₁₃	1	1	yes	characteristic
177	#2567	C₂×C₁₃	1	1	yes	characteristic
178	#2059	C₂×C₁₃	1	2	yes	—
179	#2058	C₂×C₁₃	1	2	yes	—
180	#1989	C₂×C₁₃	1	1	yes	characteristic
181	#1985	C₂×C₁₃	1	1	yes	characteristic
182	#1865	C₂×C₁₃	1	2	yes	—
183	#1863	C₂×C₁₃	1	2	yes	—
184	#1763	C₂×C₁₃	1	1	yes	characteristic
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	2	4	no	—
188	Q₈×C₁₃	—	4	4	no	—
189	Q₈×C₁₃	—	4	8	no	—
190	Q₈×C₁₃	—	8	4	no	—
191	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	#120	1	2	yes	—
221	C₂×C₄×C₁₃	#120	1	2	yes	—
222	C₂×C₄×C₁₃	#137	1	2	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
227	C₈×C₁₃	—	2	4	no	—
228	C₈×C₁₃	—	4	2	no	—
229	#557	—	2	4	no	—
230	#557	—	2	4	no	—
231	C₂×C₄⋊Q₈	—	2	1	no	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#125	—	2	1	no	—
235	C₂×#125	—	2	1	no	—
236	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	#501	—	2	4	no	—
244	#475	—	2	4	no	—
245	C₂×#107	C₂²×C₁₃	1	2	yes	—
246	C₂×#106	C₂²×C₁₃	1	2	yes	—
247	C₂×#106	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×#103	C₂²×C₁₃	1	2	yes	—
251	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
252	#395	—	2	1	no	—
253	#395	—	2	1	no	—
254	#391	—	2	1	no	—
255	#389	C₂²×C₁₃	1	2	yes	—
256	#389	C₂²×C₁₃	1	2	yes	—
257	#384	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	#340	C₂²×C₁₃	1	2	yes	—
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	2	yes	—
262	#336	C₂²×C₁₃	1	2	yes	—
263	#336	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
265	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
266	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
267	C₂²×C₁₃	#575	1	1	yes	characteristic
268	C₂²×C₁₃	#577	1	2	yes	—
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	4	1	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	8	2	no	—
281	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
282	C₄×C₁₃	#536	1	1	yes	characteristic
283	C₄×C₁₃	D₄×Q₈	1	2	yes	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
290	C₄⋊Q₈	—	2	8	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	#125	—	2	8	no	—
296	#125	—	2	8	no	—
297	#125	—	2	2	no	—
298	#125	—	2	2	no	—
299	#125	—	2	2	no	—
300	#125	D₄×C₁₃	1	4	yes	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	D₄×C₁₃	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#107	—	2	4	no	—
337	#106	—	2	4	no	—
338	#106	—	2	4	no	—
339	C₄⋊C₈	—	2	2	no	—
340	#103	—	2	4	no	—
341	#103	Q₈×C₁₃	1	8	yes	complemented
342	#97	—	2	2	no	—
343	#95	—	2	1	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	C₂×C₁₃	#2434	1	1	yes	characteristic
347	C₂×C₁₃	#3007	1	1	yes	characteristic
348	C₂×C₁₃	#3010	1	1	yes	characteristic
349	C₂×C₁₃	#3387	1	2	yes	—
350	C₂×C₁₃	#3388	1	2	yes	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	1	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	8	2	no	—
361	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	8	2	no	—
400	C₄⋊C₄	—	8	2	no	—
401	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂×D₄×C₁₃	1	2	yes	—
414	C₄²	C₂×D₄×C₁₃	1	2	yes	—
415	C₁₃	#25848	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	4	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	8	no	—
421	Q₈	—	8	4	no	—
422	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	C₁₃×#120	1	2	yes	—
452	C₂×C₄	C₁₃×#120	1	2	yes	—
453	C₂×C₄	C₁₃×#137	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
457	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
458	C₈	—	2	4	no	—
459	C₈	—	4	2	no	—
460	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
461	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
462	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
463	C₂²	C₁₃×#575	1	1	yes	characteristic
464	C₂²	C₁₃×#577	1	2	yes	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
478	C₄	C₁₃×#536	1	1	yes	characteristic
479	C₄	D₄×Q₈×C₁₃	1	2	yes	—
480	C₂	C₁₃×#2434	1	1	yes	characteristic
481	C₂	C₁₃×#3007	1	1	yes	characteristic
482	C₂	C₁₃×#3010	1	1	yes	characteristic
483	C₂	C₁₃×#3387	1	2	yes	—
484	C₂	C₁₃×#3388	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
104. C₁₃×#103	Q₈	semidirect
109. #25848	C₁₃	direct (N × H)
341. #103	Q₈×C₁₃	semidirect
415. C₁₃	#25848	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×#557	2
C₂×C₁₃×#501	2
C₂×C₁₃×#475	2
C₁₃×#2567	2
C₁₃×#2059	2
C₁₃×#2058	2
C₁₃×#1989	2
C₁₃×#1985	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1763	2
#25848	13

Subgroups — C13×#25848 #15712187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25848 #15712187