Subgroups — C₁₃×#26232 #15712571

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#481	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	—	2	1	no	—
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₁₃×#481	—	2	8	no	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#392	—	2	2	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#389	—	2	1	no	—
34	C₁₃×#385	—	2	2	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#380	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	—	2	2	no	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#127	—	2	2	no	—
54	C₁₃×#127	—	2	2	no	—
55	C₁₃×#127	—	4	4	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	2	4	no	—
58	C₁₃×#121	—	4	2	no	—
59	C₁₃×#121	—	4	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	4	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	D₄	1	4	yes	complemented
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	4	2	no	—
88	C₁₃×#102	—	4	2	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	—	4	2	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	2	no	—
95	#26232	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	8	1	no	—
115	C₂×D₄×C₁₃	—	8	1	no	—
116	C₂×D₄×C₁₃	—	8	2	no	—
117	C₂×D₄×C₁₃	—	8	2	no	—
118	C₂×D₄×C₁₃	SD₁₆	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	4	4	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	8	2	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	8	1	no	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₁₃×C₄⋊C₄	#41	1	2	yes	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₁₃×C₂²⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	4	4	no	—
163	C₁₃×C₂²⋊C₄	—	4	4	no	—
164	C₄²×C₁₃	—	4	2	no	—
165	C₄²×C₁₃	—	4	2	no	—
166	C₄²×C₁₃	#41	1	2	yes	—
167	C₄²×C₁₃	#41	1	2	yes	—
168	C₂×#481	C₂×C₁₃	1	2	yes	complemented
169	#2541	C₂×C₁₃	1	1	yes	characteristic
170	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2034	C₂×C₁₃	1	2	yes	complemented
172	#2034	C₂×C₁₃	1	2	yes	complemented
173	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1874	C₂×C₁₃	1	2	yes	complemented
178	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	D₄×C₁₃	—	2	8	no	—
195	D₄×C₁₃	—	4	2	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	8	4	no	—
200	D₄×C₁₃	—	8	8	no	—
201	D₄×C₁₃	—	8	8	no	—
202	D₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	8	8	no	—
228	C₂×C₄×C₁₃	#123	1	2	yes	—
229	C₂×C₄×C₁₃	#123	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₂×#127	—	2	1	no	—
242	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#121	C₂²×C₁₃	1	2	yes	—
244	C₂×#121	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
248	#481	—	2	8	no	—
249	C₂×#106	C₂²×C₁₃	1	2	yes	—
250	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#102	C₂²×C₁₃	1	2	yes	—
254	C₂×#102	C₂²×C₁₃	1	2	yes	—
255	C₂×#102	C₂²×C₁₃	1	2	yes	—
256	C₂×#102	C₂²×C₁₃	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
259	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
260	#392	—	2	2	no	—
261	#390	—	2	1	no	—
262	#389	—	2	1	no	—
263	#385	—	2	2	no	—
264	#384	C₂²×C₁₃	1	1	yes	characteristic
265	#380	C₂²×C₁₃	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	#340	C₂²×C₁₃	1	1	yes	characteristic
269	#340	C₂²×C₁₃	1	2	yes	—
270	#340	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₁₃	—	2	4	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	8	2	no	—
279	C₂²×C₁₃	—	8	2	no	—
280	C₂²×C₁₃	—	8	2	no	—
281	C₂²×C₁₃	—	8	2	no	—
282	C₂²×C₁₃	—	8	2	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
286	C₂²×C₁₃	D₄²	1	1	yes	characteristic
287	C₂²×C₁₃	#546	1	1	yes	characteristic
288	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₂²×C₁₃	#576	1	1	yes	characteristic
291	C₂²×C₁₃	#577	1	1	yes	characteristic
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	—	8	2	no	—
299	C₄×C₁₃	#481	1	4	yes	complemented
300	C₄×C₁₃	#532	1	1	yes	characteristic
301	C₄×C₁₃	#540	1	1	yes	characteristic
302	C₄×C₁₃	#550	1	1	yes	characteristic
303	C₄×C₁₃	#559	1	1	yes	characteristic
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
314	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
315	#127	—	2	2	no	—
316	#127	—	2	2	no	—
317	#127	—	4	4	no	—
318	#121	—	2	4	no	—
319	#121	—	2	4	no	—
320	#121	—	4	2	no	—
321	#121	—	4	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	4	4	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
343	#106	—	2	4	no	—
344	#106	—	2	2	no	—
345	#106	D₄×C₁₃	1	4	yes	complemented
346	C₄⋊C₈	—	2	2	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	#102	—	4	2	no	—
350	#102	—	4	2	no	—
351	C₂²⋊C₈	—	2	4	no	—
352	C₂²⋊C₈	—	4	2	no	—
353	C₄×C₈	—	2	2	no	—
354	#95	—	2	1	no	—
355	#95	—	2	1	no	—
356	#95	—	2	2	no	—
357	C₂×C₁₃	—	4	4	no	—
358	C₂×C₁₃	—	16	2	no	—
359	C₂×C₁₃	#2445	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#481	1	1	yes	characteristic
361	C₂×C₁₃	#3096	1	1	yes	characteristic
362	C₂×C₁₃	#3274	1	1	yes	characteristic
363	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
364	C₂×C₁₃	#3295	1	1	yes	characteristic
365	C₂×C₁₃	#3332	1	1	yes	characteristic
366	C₂⁴	—	2	2	no	—
367	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	4	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	8	1	no	—
385	C₂×D₄	—	8	1	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂×D₄	C₁₃×SD₁₆	1	4	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	8	2	no	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	8	1	no	—
427	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₄⋊C₄	C₁₃×#41	1	2	yes	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₄²	—	4	2	no	—
435	C₄²	—	4	2	no	—
436	C₄²	C₁₃×#41	1	2	yes	—
437	C₄²	C₁₃×#41	1	2	yes	—
438	C₁₃	#26232	1	1	yes	characteristic, direct product factor, Sylow
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
453	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	8	no	—
461	D₄	—	8	8	no	—
462	D₄	—	8	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	C₁₃×#123	1	2	yes	—
489	C₂×C₄	C₁₃×#123	1	2	yes	—
490	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
491	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
495	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
496	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
516	C₂²	D₄²×C₁₃	1	1	yes	characteristic
517	C₂²	C₁₃×#546	1	1	yes	characteristic
518	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
519	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
520	C₂²	C₁₃×#576	1	1	yes	characteristic
521	C₂²	C₁₃×#577	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	1	no	—
529	C₄	C₁₃×#481	1	4	yes	complemented
530	C₄	C₁₃×#532	1	1	yes	characteristic
531	C₄	C₁₃×#540	1	1	yes	characteristic
532	C₄	C₁₃×#550	1	1	yes	characteristic
533	C₄	C₁₃×#559	1	1	yes	characteristic
534	C₂	—	4	4	no	—
535	C₂	—	16	2	no	—
536	C₂	C₁₃×#2445	1	1	yes	characteristic
537	C₂	C₂×C₁₃×#481	1	1	yes	characteristic
538	C₂	C₁₃×#3096	1	1	yes	characteristic
539	C₂	C₁₃×#3274	1	1	yes	characteristic
540	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
541	C₂	C₁₃×#3295	1	1	yes	characteristic
542	C₂	C₁₃×#3332	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2541	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×#481	C₂	semidirect
3. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×#2034	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#1982	C₂	semidirect
7. C₁₃×#1957	C₂	semidirect
8. C₁₃×#1954	C₂	semidirect
9. C₁₃×#1948	C₂	semidirect
10. C₁₃×#1874	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
83. C₁₃×#106	D₄	semidirect
95. #26232	C₁₃	direct (N × H)
168. C₂×#481	C₂×C₁₃	semidirect
170. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
171. #2034	C₂×C₁₃	semidirect
172. #2034	C₂×C₁₃	semidirect
173. #1982	C₂×C₁₃	semidirect
174. #1957	C₂×C₁₃	semidirect
175. #1954	C₂×C₁₃	semidirect
176. #1948	C₂×C₁₃	semidirect
177. #1874	C₂×C₁₃	semidirect
178. C₄×#106	C₂×C₁₃	semidirect
299. C₄×C₁₃	#481	semidirect
345. #106	D₄×C₁₃	semidirect
438. C₁₃	#26232	direct (N × H)
529. C₄	C₁₃×#481	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#481	2
C₁₃×#2541	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2034	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1954	2
C₁₃×#1948	2
C₁₃×#1874	2
C₄×C₁₃×#106	2
#26232	13

Subgroups — C13×#26232 #15712571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26232 #15712571