Subgroups — C₁₃×#26769 #15713108

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₁₃×#400	—	2	1	no	—
34	C₁₃×#398	—	2	1	no	—
35	C₁₃×#390	—	2	1	no	—
36	C₁₃×#390	C₂²	1	1	yes	characteristic
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#386	—	2	1	no	—
44	C₁₃×#386	—	2	1	no	—
45	C₁₃×#384	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#127	—	2	2	no	—
70	C₁₃×#127	—	2	2	no	—
71	C₁₃×#125	—	4	4	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	4	1	no	—
75	C₄×D₄×C₁₃	—	4	1	no	—
76	C₄×D₄×C₁₃	—	4	4	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	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	—	2	2	no	—
103	C₁₃×#106	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	4	1	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	2	2	no	—
111	C₁₃×#102	—	4	1	no	—
112	C₁₃×#102	—	4	1	no	—
113	C₁₃×#97	—	4	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	D₄	1	1	yes	characteristic
121	C₁₃×#95	D₄	1	1	yes	characteristic
122	#26769	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	1	no	—
124	C₂⁴×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	8	1	no	—
140	C₂×D₄×C₁₃	—	8	1	no	—
141	C₂×D₄×C₁₃	#41	1	2	yes	—
142	C₂×D₄×C₁₃	#41	1	2	yes	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₃	—	8	1	no	—
154	C₂²×C₄×C₁₃	—	8	1	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	4	2	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	#41	1	2	yes	—
193	C₁₃×C₄⋊C₄	#41	1	2	yes	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	2	no	—
197	C₁₃×C₂²⋊C₄	—	4	2	no	—
198	C₁₃×C₂²⋊C₄	—	8	1	no	—
199	C₁₃×C₂²⋊C₄	—	8	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	4	2	no	—
207	C₄²×C₁₃	—	4	2	no	—
208	#2506	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2366	C₂×C₁₃	1	1	yes	characteristic
210	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2041	C₂×C₁₃	1	1	yes	characteristic
213	#2041	C₂×C₁₃	1	1	yes	characteristic
214	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1917	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1762	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	8	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	8	4	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	8	4	no	—
283	C₂×C₄×C₁₃	—	8	4	no	—
284	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
285	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
292	C₈×C₁₃	—	4	1	no	—
293	C₈×C₁₃	—	4	1	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#125	—	2	1	no	—
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
313	#400	—	2	1	no	—
314	#398	—	2	1	no	—
315	#390	—	2	1	no	—
316	#390	C₂²×C₁₃	1	1	yes	characteristic
317	#390	C₂²×C₁₃	1	1	yes	characteristic
318	#389	C₂²×C₁₃	1	1	yes	characteristic
319	#389	C₂²×C₁₃	1	1	yes	characteristic
320	#389	C₂²×C₁₃	1	1	yes	characteristic
321	#389	C₂²×C₁₃	1	1	yes	characteristic
322	#387	—	2	1	no	—
323	#386	—	2	1	no	—
324	#386	—	2	1	no	—
325	#384	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#340	C₂²×C₁₃	1	1	yes	characteristic
335	#336	C₂²×C₁₃	1	1	yes	characteristic
336	#336	C₂²×C₁₃	1	1	yes	characteristic
337	#336	C₂²×C₁₃	1	1	yes	characteristic
338	#336	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	8	1	no	—
350	C₂²×C₁₃	—	8	1	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	#525	1	1	yes	characteristic
354	C₂²×C₁₃	#546	1	1	yes	characteristic
355	C₂²×C₁₃	#548	1	1	yes	characteristic
356	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
358	C₂²×C₁₃	#577	1	1	yes	characteristic
359	C₂²×C₁₃	#577	1	1	yes	characteristic
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	#529	1	1	yes	characteristic
373	C₄×C₁₃	#539	1	1	yes	characteristic
374	C₄×C₁₃	#552	1	1	yes	characteristic
375	C₄×C₁₃	#553	1	1	yes	characteristic
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
386	#127	—	2	2	no	—
387	#127	—	2	2	no	—
388	#125	—	4	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	4	1	no	—
392	C₄×D₄	—	4	1	no	—
393	C₄×D₄	—	4	4	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
419	#106	—	2	2	no	—
420	#106	—	2	2	no	—
421	C₄⋊C₈	—	4	1	no	—
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	4	1	no	—
429	#102	—	4	1	no	—
430	#97	—	4	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	D₄×C₁₃	1	1	yes	characteristic
438	#95	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₁₃	—	8	2	no	—
440	C₂×C₁₃	—	8	2	no	—
441	C₂×C₁₃	#2460	1	1	yes	characteristic
442	C₂×C₁₃	#3109	1	1	yes	characteristic
443	C₂×C₁₃	#3123	1	1	yes	characteristic
444	C₂×C₁₃	#3310	1	1	yes	characteristic
445	C₂×C₁₃	#3332	1	1	yes	characteristic
446	C₂×C₁₃	#3368	1	1	yes	characteristic
447	C₂×C₁₃	#3373	1	1	yes	characteristic
448	C₂⁴	—	2	1	no	—
449	C₂⁴	—	2	1	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	8	1	no	—
465	C₂×D₄	—	8	1	no	—
466	C₂×D₄	C₁₃×#41	1	2	yes	—
467	C₂×D₄	C₁₃×#41	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	8	1	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	C₁₃×#41	1	2	yes	—
518	C₄⋊C₄	C₁₃×#41	1	2	yes	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	8	1	no	—
524	C₂²⋊C₄	—	8	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	4	2	no	—
533	C₁₃	#26769	1	1	yes	characteristic, direct product factor, Sylow
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	8	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	8	4	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
596	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
597	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
598	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
601	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	C₁₃×#525	1	1	yes	characteristic
622	C₂²	C₁₃×#546	1	1	yes	characteristic
623	C₂²	C₁₃×#548	1	1	yes	characteristic
624	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
625	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
626	C₂²	C₁₃×#577	1	1	yes	characteristic
627	C₂²	C₁₃×#577	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	C₁₃×#529	1	1	yes	characteristic
641	C₄	C₁₃×#539	1	1	yes	characteristic
642	C₄	C₁₃×#552	1	1	yes	characteristic
643	C₄	C₁₃×#553	1	1	yes	characteristic
644	C₂	—	8	2	no	—
645	C₂	—	8	2	no	—
646	C₂	C₁₃×#2460	1	1	yes	characteristic
647	C₂	C₁₃×#3109	1	1	yes	characteristic
648	C₂	C₁₃×#3123	1	1	yes	characteristic
649	C₂	C₁₃×#3310	1	1	yes	characteristic
650	C₂	C₁₃×#3332	1	1	yes	characteristic
651	C₂	C₁₃×#3368	1	1	yes	characteristic
652	C₂	C₁₃×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2506	C₂	semidirect
3. C₁₃×#2071	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1936	C₂	semidirect
8. C₁₃×#1926	C₂	semidirect
9. C₁₃×#1919	C₂	semidirect
10. C₁₃×#1919	C₂	semidirect
11. C₁₃×#1917	C₂	semidirect
12. C₁₃×#1864	C₂	semidirect
13. C₁₃×#1864	C₂	semidirect
14. C₁₃×#1802	C₂	semidirect
15. C₁₃×#1762	C₂	semidirect
122. #26769	C₁₃	direct (N × H)
208. #2506	C₂×C₁₃	semidirect
210. #2071	C₂×C₁₃	semidirect
211. #2065	C₂×C₁₃	semidirect
214. #1936	C₂×C₁₃	semidirect
215. #1926	C₂×C₁₃	semidirect
216. #1919	C₂×C₁₃	semidirect
217. #1919	C₂×C₁₃	semidirect
218. #1917	C₂×C₁₃	semidirect
219. #1864	C₂×C₁₃	semidirect
220. #1864	C₂×C₁₃	semidirect
221. #1802	C₂×C₁₃	semidirect
222. #1762	C₂×C₁₃	semidirect
533. C₁₃	#26769	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×#2506	2
C₁₃×#2366	2
C₁₃×#2071	2
C₁₃×#2065	2
C₁₃×#2041	2
C₁₃×#1936	2
C₁₃×#1926	2
C₁₃×#1919	2
C₁₃×#1917	2
C₁₃×#1864	2
C₁₃×#1802	2
C₁₃×#1762	2
#26769	13

Subgroups — C13×#26769 #15713108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26769 #15713108