Subgroups — C₁₃×#25010 #15711349

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#480	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2075	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, 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	C₁₃×#480	—	2	8	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#394	—	2	2	no	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#385	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#380	—	2	1	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₁₃×#380	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#121	—	2	4	no	—
52	C₁₃×#121	—	4	2	no	—
53	C₁₃×#121	—	4	4	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	—	2	2	no	—
58	C₄×D₄×C₁₃	—	4	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×#107	—	2	4	no	—
81	C₁₃×#107	—	4	2	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	D₄	1	4	yes	complemented
86	C₁₃×C₂²⋊C₈	—	2	4	no	—
87	C₁₃×C₂²⋊C₈	—	2	4	no	—
88	C₄×C₈×C₁₃	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#25010	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	4	4	no	—
103	C₂×D₄×C₁₃	—	4	4	no	—
104	C₂×D₄×C₁₃	—	8	2	no	—
105	C₂×D₄×C₁₃	D₈	1	4	yes	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	4	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	8	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	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	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃	#41	1	2	yes	—
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	2	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	4	4	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	8	1	no	—
151	C₁₃×C₄⋊C₄	—	8	1	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₂²⋊C₄	—	2	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	4	no	—
155	C₁₃×C₂²⋊C₄	—	4	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	4	2	no	—
159	C₄²×C₁₃	#41	1	2	yes	—
160	C₄²×C₁₃	#41	1	2	yes	—
161	C₂×#480	C₂×C₁₃	1	2	yes	complemented
162	#2537	C₂×C₁₃	1	1	yes	characteristic
163	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2075	C₂×C₁₃	1	2	yes	complemented
165	#2033	C₂×C₁₃	1	2	yes	complemented
166	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1852	C₂×C₁₃	1	2	yes	complemented
169	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	C₂×D₈	1	4	yes	—
186	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	8	no	—
190	D₄×C₁₃	—	4	1	no	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	8	8	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	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	—	4	2	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	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	8	8	no	—
218	C₂×C₄×C₁₃	—	8	4	no	—
219	C₂×C₄×C₁₃	#123	1	2	yes	—
220	C₂×C₄×C₁₃	#123	1	2	yes	—
221	C₂×C₄×C₁₃	C₂×D₈	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	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	4	2	no	—
232	C₂×#121	—	2	1	no	—
233	C₂×#121	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
238	#480	—	2	8	no	—
239	C₂×#107	C₂²×C₁₃	1	2	yes	—
240	C₂×#107	C₂²×C₁₃	1	2	yes	—
241	C₂×#107	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
249	#394	—	2	2	no	—
250	#389	—	2	1	no	—
251	#385	—	2	2	no	—
252	#384	C₂²×C₁₃	1	1	yes	characteristic
253	#384	C₂²×C₁₃	1	1	yes	characteristic
254	#380	—	2	1	no	—
255	#380	C₂²×C₁₃	1	2	yes	—
256	#380	C₂²×C₁₃	1	2	yes	—
257	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	#340	C₂²×C₁₃	1	2	yes	—
259	#340	C₂²×C₁₃	1	1	yes	characteristic
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	4	no	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	1	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
277	C₂²×C₁₃	D₄²	1	1	yes	characteristic
278	C₂²×C₁₃	#547	1	1	yes	characteristic
279	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
281	C₂²×C₁₃	#576	1	1	yes	characteristic
282	C₂²×C₁₃	#578	1	1	yes	characteristic
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	—	8	1	no	—
288	C₄×C₁₃	—	8	2	no	—
289	C₄×C₁₃	—	8	2	no	—
290	C₄×C₁₃	#480	1	4	yes	complemented
291	C₄×C₁₃	#532	1	1	yes	characteristic
292	C₄×C₁₃	#542	1	1	yes	characteristic
293	C₄×C₁₃	#547	1	1	yes	characteristic
294	C₄×C₁₃	#553	1	1	yes	characteristic
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	#121	—	2	4	no	—
305	#121	—	4	2	no	—
306	#121	—	4	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	4	4	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	2	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	—	4	2	no	—
319	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	#107	—	2	4	no	—
333	#107	—	2	4	no	—
334	#107	—	4	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	#102	—	2	4	no	—
337	#102	—	2	2	no	—
338	#102	D₄×C₁₃	1	4	yes	complemented
339	C₂²⋊C₈	—	2	4	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	C₄×C₈	—	2	2	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	C₂×C₁₃	—	4	4	no	—
346	C₂×C₁₃	—	8	2	no	—
347	C₂×C₁₃	#2422	1	1	yes	characteristic
348	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
349	C₂×C₁₃	#3098	1	1	yes	characteristic
350	C₂×C₁₃	#3276	1	1	yes	characteristic
351	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
352	C₂×C₁₃	#3334	1	1	yes	characteristic
353	C₂×C₁₃	#3357	1	1	yes	characteristic
354	C₂⁴	—	2	1	no	—
355	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂×D₄	C₁₃×D₈	1	4	yes	—
367	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
397	C₂×C₈	C₁₃×#41	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	8	1	no	—
412	C₄⋊C₄	—	8	1	no	—
413	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₄²	—	4	2	no	—
420	C₄²	C₁₃×#41	1	2	yes	—
421	C₄²	C₁₃×#41	1	2	yes	—
422	C₁₃	#25010	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	C₂×C₁₃×D₈	1	4	yes	—
437	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	D₄	—	2	8	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	8	8	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	—	8	4	no	—
470	C₂×C₄	C₁₃×#123	1	2	yes	—
471	C₂×C₄	C₁₃×#123	1	2	yes	—
472	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
473	C₂×C₄	C₁₃×#137	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
477	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
478	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
498	C₂²	D₄²×C₁₃	1	1	yes	characteristic
499	C₂²	C₁₃×#547	1	1	yes	characteristic
500	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
501	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
502	C₂²	C₁₃×#576	1	1	yes	characteristic
503	C₂²	C₁₃×#578	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	C₁₃×#480	1	4	yes	complemented
512	C₄	C₁₃×#532	1	1	yes	characteristic
513	C₄	C₁₃×#542	1	1	yes	characteristic
514	C₄	C₁₃×#547	1	1	yes	characteristic
515	C₄	C₁₃×#553	1	1	yes	characteristic
516	C₂	—	4	4	no	—
517	C₂	—	8	2	no	—
518	C₂	C₁₃×#2422	1	1	yes	characteristic
519	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
520	C₂	C₁₃×#3098	1	1	yes	characteristic
521	C₂	C₁₃×#3276	1	1	yes	characteristic
522	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
523	C₂	C₁₃×#3334	1	1	yes	characteristic
524	C₂	C₁₃×#3357	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
1. C₂×C₁₃×#480	C₂	semidirect
3. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×#2075	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1954	C₂	semidirect
7. C₁₃×#1947	C₂	semidirect
8. C₁₃×#1852	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
10. C₁₃×#1802	C₂	semidirect
11. C₄×C₁₃×#102	C₂	semidirect
85. C₁₃×#102	D₄	semidirect
92. #25010	C₁₃	direct (N × H)
161. C₂×#480	C₂×C₁₃	semidirect
163. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
164. #2075	C₂×C₁₃	semidirect
165. #2033	C₂×C₁₃	semidirect
166. #1954	C₂×C₁₃	semidirect
167. #1947	C₂×C₁₃	semidirect
168. #1852	C₂×C₁₃	semidirect
169. #1845	C₂×C₁₃	semidirect
170. #1802	C₂×C₁₃	semidirect
171. C₄×#102	C₂×C₁₃	semidirect
290. C₄×C₁₃	#480	semidirect
338. #102	D₄×C₁₃	semidirect
422. C₁₃	#25010	direct (N × H)
511. C₄	C₁₃×#480	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#480	2
C₁₃×#2537	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2075	2
C₁₃×#2033	2
C₁₃×#1954	2
C₁₃×#1947	2
C₁₃×#1852	2
C₁₃×#1845	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#25010	13

Subgroups — C13×#25010 #15711349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25010 #15711349