Subgroups — C₁₃×#26716 #15713055

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2445	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	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	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#123	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
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	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×#97	C₂²	1	1	yes	characteristic
32	C₁₃×#394	—	2	1	no	—
33	C₁₃×#394	—	2	1	no	—
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#390	C₂²	1	1	yes	characteristic
37	C₁₃×#389	—	2	1	no	—
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×#387	—	2	1	no	—
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#386	—	2	1	no	—
44	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₄×C₁₃×C₄⋊C₄	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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#127	—	2	2	no	—
69	C₁₃×#127	—	4	1	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	—	2	2	no	—
72	C₁₃×#123	—	4	4	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	4	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	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#106	—	4	1	no	—
103	C₁₃×C₄⋊C₈	—	4	1	no	—
104	C₁₃×#102	—	2	2	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×#97	—	4	1	no	—
113	C₁₃×#95	—	2	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	D₄	1	1	yes	characteristic
120	C₁₃×#95	D₄	1	1	yes	characteristic
121	#26716	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	—	2	1	no	—
123	C₂⁴×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
136	C₂×D₄×C₁₃	—	4	2	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	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	—	8	1	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
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	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	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	—	4	1	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	—	8	1	no	—
186	C₁₃×C₄⋊C₄	#41	1	2	yes	—
187	C₁₃×C₄⋊C₄	#41	1	2	yes	—
188	C₁₃×C₄⋊C₄	#41	1	2	yes	—
189	C₁₃×C₂²⋊C₄	—	4	2	no	—
190	C₁₃×C₂²⋊C₄	—	4	2	no	—
191	C₁₃×C₂²⋊C₄	—	4	2	no	—
192	C₁₃×C₂²⋊C₄	—	4	2	no	—
193	C₁₃×C₂²⋊C₄	—	8	1	no	—
194	C₁₃×C₂²⋊C₄	—	8	1	no	—
195	C₁₃×C₂²⋊C₄	—	8	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₄²×C₁₃	—	8	1	no	—
204	C₄²×C₁₃	—	8	1	no	—
205	#2445	C₂×C₁₃	1	1	yes	characteristic
206	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2041	C₂×C₁₃	1	1	yes	characteristic
209	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1982	C₂×C₁₃	1	1	yes	characteristic
212	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1925	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1917	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1762	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	4	1	no	—
222	C₂³×C₁₃	—	4	1	no	—
223	C₂³×C₁₃	—	4	1	no	—
224	C₂³×C₁₃	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	4	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	8	4	no	—
244	D₄×C₁₃	—	8	4	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	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	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	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	—	4	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	—	8	4	no	—
281	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
282	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#123	—	2	1	no	—
295	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#102	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×#97	C₂²×C₁₃	1	1	yes	characteristic
308	#394	—	2	1	no	—
309	#394	—	2	1	no	—
310	#390	C₂²×C₁₃	1	1	yes	characteristic
311	#390	C₂²×C₁₃	1	1	yes	characteristic
312	#390	C₂²×C₁₃	1	1	yes	characteristic
313	#389	—	2	1	no	—
314	#389	C₂²×C₁₃	1	1	yes	characteristic
315	#389	C₂²×C₁₃	1	1	yes	characteristic
316	#389	C₂²×C₁₃	1	1	yes	characteristic
317	#387	—	2	1	no	—
318	#387	—	2	1	no	—
319	#386	—	2	1	no	—
320	C₄×C₄⋊C₄	—	2	1	no	—
321	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
322	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
325	#340	C₂²×C₁₃	1	1	yes	characteristic
326	#340	C₂²×C₁₃	1	1	yes	characteristic
327	#340	C₂²×C₁₃	1	1	yes	characteristic
328	#340	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#336	C₂²×C₁₃	1	1	yes	characteristic
332	#336	C₂²×C₁₃	1	1	yes	characteristic
333	#336	C₂²×C₁₃	1	1	yes	characteristic
334	#336	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	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	#525	1	1	yes	characteristic
350	C₂²×C₁₃	#546	1	1	yes	characteristic
351	C₂²×C₁₃	#548	1	1	yes	characteristic
352	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₂²×C₁₃	#575	1	1	yes	characteristic
354	C₂²×C₁₃	#576	1	1	yes	characteristic
355	C₂²×C₁₃	#577	1	1	yes	characteristic
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	#529	1	1	yes	characteristic
369	C₄×C₁₃	#542	1	1	yes	characteristic
370	C₄×C₁₃	#552	1	1	yes	characteristic
371	C₄×C₁₃	#559	1	1	yes	characteristic
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	#127	—	2	2	no	—
382	#127	—	4	1	no	—
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	#123	—	4	4	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	4	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	#107	—	2	2	no	—
415	#106	—	4	1	no	—
416	C₄⋊C₈	—	4	1	no	—
417	#102	—	2	2	no	—
418	#102	—	2	2	no	—
419	#102	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	2	2	no	—
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	—	4	1	no	—
425	#97	—	4	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	D₄×C₁₃	1	1	yes	characteristic
433	#95	D₄×C₁₃	1	1	yes	characteristic
434	C₂×C₁₃	—	8	2	no	—
435	C₂×C₁₃	—	16	1	no	—
436	C₂×C₁₃	#2458	1	1	yes	characteristic
437	C₂×C₁₃	#3115	1	1	yes	characteristic
438	C₂×C₁₃	#3119	1	1	yes	characteristic
439	C₂×C₁₃	#3310	1	1	yes	characteristic
440	C₂×C₁₃	#3322	1	1	yes	characteristic
441	C₂×C₁₃	#3366	1	1	yes	characteristic
442	C₂×C₁₃	#3371	1	1	yes	characteristic
443	C₂⁴	—	2	1	no	—
444	C₂⁴	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	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	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	8	1	no	—
461	C₂×D₄	—	8	1	no	—
462	C₂×D₄	C₁₃×#41	1	2	yes	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	8	1	no	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
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	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	4	1	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	8	1	no	—
507	C₄⋊C₄	C₁₃×#41	1	2	yes	—
508	C₄⋊C₄	C₁₃×#41	1	2	yes	—
509	C₄⋊C₄	C₁₃×#41	1	2	yes	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	8	1	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₂²⋊C₄	—	8	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	2	no	—
524	C₄²	—	8	1	no	—
525	C₄²	—	8	1	no	—
526	C₁₃	#26716	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	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	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	4	no	—
551	D₄	—	8	4	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	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	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	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	—	8	4	no	—
588	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
589	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
590	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
593	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	8	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	C₁₃×#525	1	1	yes	characteristic
614	C₂²	C₁₃×#546	1	1	yes	characteristic
615	C₂²	C₁₃×#548	1	1	yes	characteristic
616	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
617	C₂²	C₁₃×#575	1	1	yes	characteristic
618	C₂²	C₁₃×#576	1	1	yes	characteristic
619	C₂²	C₁₃×#577	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	2	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	C₁₃×#529	1	1	yes	characteristic
633	C₄	C₁₃×#542	1	1	yes	characteristic
634	C₄	C₁₃×#552	1	1	yes	characteristic
635	C₄	C₁₃×#559	1	1	yes	characteristic
636	C₂	—	8	2	no	—
637	C₂	—	16	1	no	—
638	C₂	C₁₃×#2458	1	1	yes	characteristic
639	C₂	C₁₃×#3115	1	1	yes	characteristic
640	C₂	C₁₃×#3119	1	1	yes	characteristic
641	C₂	C₁₃×#3310	1	1	yes	characteristic
642	C₂	C₁₃×#3322	1	1	yes	characteristic
643	C₂	C₁₃×#3366	1	1	yes	characteristic
644	C₂	C₁₃×#3371	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
2. C₁₃×#2370	C₂	semidirect
3. C₁₃×#2088	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
8. C₁₃×#1936	C₂	semidirect
9. C₁₃×#1926	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1925	C₂	semidirect
12. C₁₃×#1918	C₂	semidirect
13. C₁₃×#1917	C₂	semidirect
14. C₁₃×#1864	C₂	semidirect
15. C₁₃×#1762	C₂	semidirect
121. #26716	C₁₃	direct (N × H)
206. #2370	C₂×C₁₃	semidirect
207. #2088	C₂×C₁₃	semidirect
209. #2025	C₂×C₁₃	semidirect
210. #2025	C₂×C₁₃	semidirect
212. #1936	C₂×C₁₃	semidirect
213. #1926	C₂×C₁₃	semidirect
214. #1925	C₂×C₁₃	semidirect
215. #1925	C₂×C₁₃	semidirect
216. #1918	C₂×C₁₃	semidirect
217. #1917	C₂×C₁₃	semidirect
218. #1864	C₂×C₁₃	semidirect
219. #1762	C₂×C₁₃	semidirect
526. C₁₃	#26716	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×#2445	2
C₁₃×#2370	2
C₁₃×#2088	2
C₁₃×#2041	2
C₁₃×#2025	2
C₁₃×#1982	2
C₁₃×#1936	2
C₁₃×#1926	2
C₁₃×#1925	2
C₁₃×#1918	2
C₁₃×#1917	2
C₁₃×#1864	2
C₁₃×#1762	2
#26716	13

Subgroups — C13×#26716 #15713055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26716 #15713055