Subgroups — C₁₃×#25221 #15711560

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 728 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	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#123	—	2	1	no	—
19	C₂×C₁₃×#123	—	2	1	no	—
20	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₁₃×#481	—	2	4	no	—
26	C₁₃×#469	—	2	4	no	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#399	—	2	1	no	—
40	C₁₃×#399	—	2	1	no	—
41	C₁₃×#390	—	2	1	no	—
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#386	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	—	2	1	no	—
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×D₈	—	2	2	no	—
69	C₂×C₁₃×D₈	—	2	2	no	—
70	C₂×C₁₃×D₈	—	4	1	no	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	2	2	no	—
73	C₂×C₁₃×M₁₆	—	4	1	no	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#123	—	4	4	no	—
79	C₁₃×#123	—	4	4	no	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	D₄	1	4	yes	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	4	1	no	—
86	C₁₃×#117	—	2	2	no	—
87	C₁₃×#117	—	4	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#106	—	2	2	no	—
119	C₁₃×#106	—	2	2	no	—
120	C₁₃×#106	—	2	2	no	—
121	C₁₃×C₄⋊C₈	—	2	2	no	—
122	C₁₃×C₄⋊C₈	—	4	1	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₁₃×#102	—	2	2	no	—
125	C₁₃×#102	—	2	2	no	—
126	C₁₃×#102	—	2	2	no	—
127	C₁₃×#102	—	2	2	no	—
128	C₁₃×#102	—	4	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	2	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	D₄	1	1	yes	characteristic
133	C₁₃×#95	D₄	1	1	yes	characteristic
134	#25221	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂⁴×C₁₃	—	2	1	no	—
137	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	2	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	8	1	no	—
154	C₂×D₄×C₁₃	—	8	1	no	—
155	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	—	8	1	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	#41	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×D₈	—	4	4	no	—
181	C₁₃×M₁₆	—	4	4	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	#41	1	2	yes	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	2	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	8	1	no	—
210	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
211	C₁₃×C₄⋊C₄	#41	1	2	yes	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	2	no	—
214	C₁₃×C₂²⋊C₄	—	2	2	no	—
215	C₁₃×C₂²⋊C₄	—	4	2	no	—
216	C₁₃×C₂²⋊C₄	—	4	2	no	—
217	C₁₃×C₂²⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	4	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₁₃×C₂²⋊C₄	—	8	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	4	2	no	—
229	C₄²×C₁₃	—	8	1	no	—
230	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#469	C₂×C₁₃	1	1	yes	characteristic
232	#2501	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	#121	1	2	yes	—
266	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	2	2	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	8	4	no	—
276	D₄×C₁₃	—	8	4	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	8	4	no	—
312	C₂×C₄×C₁₃	—	8	4	no	—
313	C₂×C₄×C₁₃	#121	1	2	yes	—
314	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
315	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
322	C₈×C₁₃	—	2	2	no	—
323	C₈×C₁₃	—	4	1	no	—
324	C₈×C₁₃	—	4	1	no	—
325	C₈×C₁₃	—	4	1	no	—
326	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#123	—	2	1	no	—
329	C₂×#123	—	2	1	no	—
330	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	#481	—	2	4	no	—
336	#469	—	2	4	no	—
337	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
349	#399	—	2	1	no	—
350	#399	—	2	1	no	—
351	#390	—	2	1	no	—
352	#390	C₂²×C₁₃	1	1	yes	characteristic
353	#390	C₂²×C₁₃	1	1	yes	characteristic
354	#390	C₂²×C₁₃	1	1	yes	characteristic
355	#389	C₂²×C₁₃	1	1	yes	characteristic
356	#388	—	2	1	no	—
357	#386	—	2	1	no	—
358	#384	C₂²×C₁₃	1	1	yes	characteristic
359	#384	C₂²×C₁₃	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₄×C₂²⋊C₄	—	2	1	no	—
362	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
363	#340	C₂²×C₁₃	1	1	yes	characteristic
364	#340	C₂²×C₁₃	1	1	yes	characteristic
365	#340	C₂²×C₁₃	1	1	yes	characteristic
366	#340	C₂²×C₁₃	1	1	yes	characteristic
367	#340	C₂²×C₁₃	1	1	yes	characteristic
368	#340	C₂²×C₁₃	1	1	yes	characteristic
369	#336	C₂²×C₁₃	1	1	yes	characteristic
370	#336	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₁₃	—	2	2	no	—
372	C₂²×C₁₃	—	2	2	no	—
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	8	1	no	—
384	C₂²×C₁₃	—	8	1	no	—
385	C₂²×C₁₃	—	8	1	no	—
386	C₂²×C₁₃	—	8	1	no	—
387	C₂²×C₁₃	—	8	1	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	—	8	1	no	—
390	C₂²×C₁₃	—	8	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
393	C₂²×C₁₃	#546	1	1	yes	characteristic
394	C₂²×C₁₃	#547	1	1	yes	characteristic
395	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²×C₁₃	#577	1	1	yes	characteristic
398	C₂²×C₁₃	#577	1	1	yes	characteristic
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	4	1	no	—
403	C₄×C₁₃	—	4	1	no	—
404	C₄×C₁₃	—	4	2	no	—
405	C₄×C₁₃	—	4	2	no	—
406	C₄×C₁₃	—	8	1	no	—
407	C₄×C₁₃	—	8	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	#529	1	1	yes	characteristic
411	C₄×C₁₃	#539	1	1	yes	characteristic
412	C₄×C₁₃	#546	1	1	yes	characteristic
413	C₄×C₁₃	#547	1	1	yes	characteristic
414	C₂²×D₄	—	2	1	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂³×C₄	—	2	1	no	—
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×D₈	—	2	2	no	—
422	C₂×D₈	—	2	2	no	—
423	C₂×D₈	—	4	1	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	2	2	no	—
426	C₂×M₁₆	—	4	1	no	—
427	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	#123	—	4	4	no	—
432	#123	—	4	4	no	—
433	#121	—	2	2	no	—
434	#121	—	2	2	no	—
435	#121	—	2	2	no	—
436	#121	D₄×C₁₃	1	4	yes	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	4	1	no	—
439	#117	—	2	2	no	—
440	#117	—	4	1	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	—	2	2	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	#106	—	2	2	no	—
472	#106	—	2	2	no	—
473	#106	—	2	2	no	—
474	C₄⋊C₈	—	2	2	no	—
475	C₄⋊C₈	—	4	1	no	—
476	#102	—	2	2	no	—
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	#102	—	4	1	no	—
482	C₂²⋊C₈	—	2	2	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	D₄×C₁₃	1	1	yes	characteristic
486	#95	D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₁₃	—	4	2	no	—
488	C₂×C₁₃	—	8	2	no	—
489	C₂×C₁₃	—	16	1	no	—
490	C₂×C₁₃	#2425	1	1	yes	characteristic
491	C₂×C₁₃	#3038	1	1	yes	characteristic
492	C₂×C₁₃	#3042	1	1	yes	characteristic
493	C₂×C₁₃	#3306	1	1	yes	characteristic
494	C₂×C₁₃	#3332	1	1	yes	characteristic
495	C₂×C₁₃	#3345	1	1	yes	characteristic
496	C₂×C₁₃	#3354	1	1	yes	characteristic
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	2	1	no	—
499	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	8	1	no	—
516	C₂×D₄	—	8	1	no	—
517	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
538	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₁₃×#41	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
542	D₈	—	4	4	no	—
543	M₁₆	—	4	4	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₁₃×#41	1	2	yes	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	—	8	1	no	—
572	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
573	C₄⋊C₄	C₁₃×#41	1	2	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	8	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	4	2	no	—
591	C₄²	—	8	1	no	—
592	C₁₃	#25221	1	1	yes	characteristic, direct product factor, Sylow
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	C₁₃×#121	1	2	yes	—
614	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	8	4	no	—
624	D₄	—	8	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	8	4	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	C₁₃×#121	1	2	yes	—
662	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
663	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
665	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
666	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
667	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
668	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
670	C₈	—	2	2	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
696	C₂²	C₁₃×#546	1	1	yes	characteristic
697	C₂²	C₁₃×#547	1	1	yes	characteristic
698	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
699	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
700	C₂²	C₁₃×#577	1	1	yes	characteristic
701	C₂²	C₁₃×#577	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	1	no	—
713	C₄	C₁₃×#529	1	1	yes	characteristic
714	C₄	C₁₃×#539	1	1	yes	characteristic
715	C₄	C₁₃×#546	1	1	yes	characteristic
716	C₄	C₁₃×#547	1	1	yes	characteristic
717	C₂	—	4	2	no	—
718	C₂	—	8	2	no	—
719	C₂	—	16	1	no	—
720	C₂	C₁₃×#2425	1	1	yes	characteristic
721	C₂	C₁₃×#3038	1	1	yes	characteristic
722	C₂	C₁₃×#3042	1	1	yes	characteristic
723	C₂	C₁₃×#3306	1	1	yes	characteristic
724	C₂	C₁₃×#3332	1	1	yes	characteristic
725	C₂	C₁₃×#3345	1	1	yes	characteristic
726	C₂	C₁₃×#3354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#469	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#481	C₂	semidirect
3. C₁₃×#2501	C₂	semidirect
4. C₁₃×#2363	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2071	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2054	C₂	semidirect
9. C₁₃×#1948	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1879	C₂	semidirect
12. C₁₃×#1875	C₂	semidirect
13. C₁₃×#1851	C₂	semidirect
14. C₁₃×#1802	C₂	semidirect
15. C₁₃×#1736	C₂	semidirect
134. #25221	C₁₃	direct (N × H)
230. C₂×#481	C₂×C₁₃	semidirect
232. #2501	C₂×C₁₃	semidirect
233. #2363	C₂×C₁₃	semidirect
234. #2084	C₂×C₁₃	semidirect
235. #2071	C₂×C₁₃	semidirect
236. #2065	C₂×C₁₃	semidirect
237. #2054	C₂×C₁₃	semidirect
238. #1948	C₂×C₁₃	semidirect
239. #1926	C₂×C₁₃	semidirect
240. #1879	C₂×C₁₃	semidirect
241. #1875	C₂×C₁₃	semidirect
242. #1851	C₂×C₁₃	semidirect
243. #1802	C₂×C₁₃	semidirect
244. #1736	C₂×C₁₃	semidirect
592. C₁₃	#25221	direct (N × H)

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
C₂×C₁₃×#469	2
C₁₃×#2501	2
C₁₃×#2363	2
C₁₃×#2084	2
C₁₃×#2071	2
C₁₃×#2065	2
C₁₃×#2054	2
C₁₃×#1948	2
C₁₃×#1926	2
C₁₃×#1879	2
C₁₃×#1875	2
C₁₃×#1851	2
C₁₃×#1802	2
C₁₃×#1736	2
#25221	13

Subgroups — C13×#25221 #15711560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25221 #15711560