Subgroups — C₁₃×#24965 #15711304

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2075	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1823	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#121	—	2	1	no	—
13	C₂×C₁₃×#121	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#394	—	2	2	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#385	—	2	2	no	—
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#380	—	2	1	no	—
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×#121	—	2	4	no	—
51	C₁₃×#121	—	4	2	no	—
52	C₁₃×#121	—	4	4	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	2	2	no	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	4	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	4	2	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	4	2	no	—
83	C₁₃×C₂²⋊C₈	—	4	2	no	—
84	C₁₃×C₂²⋊C₈	—	4	2	no	—
85	C₄×C₈×C₁₃	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	#24965	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	4	4	no	—
100	C₂×D₄×C₁₃	—	4	4	no	—
101	C₂×D₄×C₁₃	—	8	2	no	—
102	C₂×D₄×C₁₃	D₈	1	4	yes	—
103	C₂×D₄×C₁₃	#41	1	2	yes	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	—	8	2	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	8	1	no	—
148	C₁₃×C₄⋊C₄	—	8	1	no	—
149	C₁₃×C₄⋊C₄	#41	1	2	yes	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	4	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₄²×C₁₃	—	4	2	no	—
156	C₄²×C₁₃	#41	1	2	yes	—
157	C₄²×C₁₃	#41	1	2	yes	—
158	#2537	C₂×C₁₃	1	1	yes	characteristic
159	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2075	C₂×C₁₃	1	2	yes	complemented
161	#2033	C₂×C₁₃	1	2	yes	complemented
162	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1874	C₂×C₁₃	1	2	yes	complemented
165	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1823	C₂×C₁₃	1	2	yes	complemented
167	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	C₂×D₈	1	4	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	8	no	—
187	D₄×C₁₃	—	4	1	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	8	8	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	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	8	8	no	—
215	C₂×C₄×C₁₃	—	8	4	no	—
216	C₂×C₄×C₁₃	#123	1	2	yes	—
217	C₂×C₄×C₁₃	#123	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
219	C₂×C₄×C₁₃	#137	1	2	yes	—
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
226	C₈×C₁₃	—	4	2	no	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	1	no	—
229	C₂×#121	—	2	1	no	—
230	C₂×#121	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
235	C₂×#107	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#102	C₂²×C₁₃	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
243	#394	—	2	2	no	—
244	#389	—	2	1	no	—
245	#385	—	2	2	no	—
246	#384	C₂²×C₁₃	1	1	yes	characteristic
247	#384	C₂²×C₁₃	1	1	yes	characteristic
248	#380	—	2	1	no	—
249	#380	C₂²×C₁₃	1	2	yes	—
250	#380	C₂²×C₁₃	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	#340	C₂²×C₁₃	1	2	yes	—
253	#340	C₂²×C₁₃	1	1	yes	characteristic
254	#340	C₂²×C₁₃	1	2	yes	—
255	#340	C₂²×C₁₃	1	1	yes	characteristic
256	#340	C₂²×C₁₃	1	2	yes	—
257	#340	C₂²×C₁₃	1	2	yes	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	2	4	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	—	8	1	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
273	C₂²×C₁₃	#546	1	1	yes	characteristic
274	C₂²×C₁₃	#546	1	1	yes	characteristic
275	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
276	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
277	C₂²×C₁₃	#577	1	1	yes	characteristic
278	C₂²×C₁₃	#577	1	1	yes	characteristic
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	#480	1	4	yes	—
287	C₄×C₁₃	#529	1	1	yes	characteristic
288	C₄×C₁₃	#540	1	1	yes	characteristic
289	C₄×C₁₃	#553	1	1	yes	characteristic
290	C₄×C₁₃	#555	1	1	yes	characteristic
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
300	#121	—	2	4	no	—
301	#121	—	4	2	no	—
302	#121	—	4	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	4	4	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
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	—	4	2	no	—
315	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
328	#107	—	4	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	4	2	no	—
333	C₂²⋊C₈	—	4	2	no	—
334	C₂²⋊C₈	—	4	2	no	—
335	C₄×C₈	—	2	2	no	—
336	#95	—	2	1	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	C₂×C₁₃	—	4	4	no	—
340	C₂×C₁₃	—	8	2	no	—
341	C₂×C₁₃	#2420	1	1	yes	characteristic
342	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
343	C₂×C₁₃	#3099	1	1	yes	characteristic
344	C₂×C₁₃	#3294	1	1	yes	characteristic
345	C₂×C₁₃	#3294	1	1	yes	characteristic
346	C₂×C₁₃	#3329	1	1	yes	characteristic
347	C₂×C₁₃	#3331	1	1	yes	characteristic
348	C₂⁴	—	2	1	no	—
349	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂×D₄	C₁₃×D₈	1	4	yes	—
361	C₂×D₄	C₁₃×#41	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	8	1	no	—
406	C₄⋊C₄	—	8	1	no	—
407	C₄⋊C₄	C₁₃×#41	1	2	yes	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₄²	—	4	2	no	—
414	C₄²	C₁₃×#41	1	2	yes	—
415	C₄²	C₁₃×#41	1	2	yes	—
416	C₁₃	#24965	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂×C₁₃×D₈	1	4	yes	—
431	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	D₄	—	2	8	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	8	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	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	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	C₁₃×#123	1	2	yes	—
465	C₂×C₄	C₁₃×#123	1	2	yes	—
466	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
467	C₂×C₄	C₁₃×#137	1	2	yes	—
468	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
469	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
470	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
472	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
474	C₈	—	4	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	4	1	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
492	C₂²	C₁₃×#546	1	1	yes	characteristic
493	C₂²	C₁₃×#546	1	1	yes	characteristic
494	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
495	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
496	C₂²	C₁₃×#577	1	1	yes	characteristic
497	C₂²	C₁₃×#577	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	8	1	no	—
502	C₄	—	8	2	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	1	no	—
505	C₄	C₁₃×#480	1	4	yes	—
506	C₄	C₁₃×#529	1	1	yes	characteristic
507	C₄	C₁₃×#540	1	1	yes	characteristic
508	C₄	C₁₃×#553	1	1	yes	characteristic
509	C₄	C₁₃×#555	1	1	yes	characteristic
510	C₂	—	4	4	no	—
511	C₂	—	8	2	no	—
512	C₂	C₁₃×#2420	1	1	yes	characteristic
513	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
514	C₂	C₁₃×#3099	1	1	yes	characteristic
515	C₂	C₁₃×#3294	1	1	yes	characteristic
516	C₂	C₁₃×#3294	1	1	yes	characteristic
517	C₂	C₁₃×#3329	1	1	yes	characteristic
518	C₂	C₁₃×#3331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
3. C₁₃×#2075	C₂	semidirect
4. C₁₃×#2033	C₂	semidirect
5. C₁₃×#1954	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
7. C₁₃×#1874	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
9. C₁₃×#1823	C₂	semidirect
10. C₁₃×#1802	C₂	semidirect
11. C₄×C₁₃×#102	C₂	semidirect
89. #24965	C₁₃	direct (N × H)
159. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
160. #2075	C₂×C₁₃	semidirect
161. #2033	C₂×C₁₃	semidirect
162. #1954	C₂×C₁₃	semidirect
163. #1947	C₂×C₁₃	semidirect
164. #1874	C₂×C₁₃	semidirect
165. #1834	C₂×C₁₃	semidirect
166. #1823	C₂×C₁₃	semidirect
167. #1802	C₂×C₁₃	semidirect
168. C₄×#102	C₂×C₁₃	semidirect
416. C₁₃	#24965	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×#2537	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2075	2
C₁₃×#2033	2
C₁₃×#1954	2
C₁₃×#1947	2
C₁₃×#1874	2
C₁₃×#1834	2
C₁₃×#1823	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#24965	13

Subgroups — C13×#24965 #15711304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24965 #15711304