Subgroups — C₁₃×#24206 #15710545

Order 3328.

1140 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₁₃×#559	—	2	4	no	—
20	C₁₃×#559	—	2	4	no	—
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#464	—	2	4	no	—
34	C₁₃×#440	—	2	4	no	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
48	C₁₃×#398	—	2	1	no	—
49	C₁₃×#398	—	2	1	no	—
50	C₁₃×#391	—	2	1	no	—
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#389	—	2	1	no	—
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	1	yes	characteristic
56	C₁₃×#384	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	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	2	no	—
73	C₂×C₁₃×Q₁₆	—	2	2	no	—
74	C₂×C₁₃×Q₁₆	—	4	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	4	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#124	—	2	8	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	D₄	1	4	yes	—
92	C₁₃×#123	—	2	8	no	—
93	C₁₃×#123	—	2	8	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	D₄	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#107	—	2	2	no	—
130	C₁₃×C₄⋊C₈	—	2	2	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	4	1	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#102	—	4	1	no	—
139	C₁₃×#102	—	4	1	no	—
140	C₁₃×#102	—	4	1	no	—
141	C₁₃×#97	—	2	2	no	—
142	C₁₃×#95	—	2	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	#24206	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	1	no	—
150	C₂⁴×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	4	1	no	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₁₃	#41	1	2	yes	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	4	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	4	2	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	—	8	1	no	—
181	C₂×D₄×C₁₃	—	8	1	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	8	1	no	—
193	C₂²×C₄×C₁₃	—	8	1	no	—
194	C₂²×C₄×C₁₃	—	8	1	no	—
195	C₂²×C₄×C₁₃	—	8	1	no	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×Q₁₆	—	4	4	no	—
204	C₁₃×SD₁₆	—	2	8	no	—
205	C₁₃×SD₁₆	—	4	4	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	#41	1	2	yes	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	4	2	no	—
230	C₁₃×C₄⋊C₄	—	4	2	no	—
231	C₁₃×C₄⋊C₄	—	8	1	no	—
232	C₁₃×C₄⋊C₄	—	8	1	no	—
233	C₁₃×C₄⋊C₄	—	8	1	no	—
234	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₄²×C₁₃	—	2	4	no	—
242	C₄²×C₁₃	—	2	1	no	—
243	C₄²×C₁₃	—	2	1	no	—
244	C₄²×C₁₃	—	2	1	no	—
245	C₄²×C₁₃	—	2	1	no	—
246	C₄²×C₁₃	—	4	2	no	—
247	C₄²×C₁₃	C₂×D₄	1	2	yes	—
248	C₄²×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
250	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2582	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2041	C₂×C₁₃	1	1	yes	characteristic
255	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2014	C₂×C₁₃	1	1	yes	characteristic
257	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1959	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	—	4	1	no	—
277	C₂³×C₁₃	—	4	1	no	—
278	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₁₃	—	2	2	no	—
280	Q₈×C₁₃	—	2	2	no	—
281	Q₈×C₁₃	—	2	2	no	—
282	Q₈×C₁₃	—	2	2	no	—
283	Q₈×C₁₃	—	4	4	no	—
284	Q₈×C₁₃	—	4	1	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	Q₈×C₁₃	—	4	1	no	—
287	Q₈×C₁₃	—	4	1	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	2	no	—
291	D₄×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	4	8	no	—
293	D₄×C₁₃	—	4	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	4	1	no	—
296	D₄×C₁₃	—	4	1	no	—
297	D₄×C₁₃	—	8	4	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	8	4	no	—
332	C₂×C₄×C₁₃	—	8	4	no	—
333	C₂×C₄×C₁₃	#120	1	2	yes	—
334	C₂×C₄×C₁₃	#120	1	2	yes	—
335	C₂×C₄×C₁₃	#137	1	2	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
342	C₈×C₁₃	—	2	2	no	—
343	C₈×C₁₃	—	4	1	no	—
344	C₈×C₁₃	—	4	1	no	—
345	C₈×C₁₃	—	4	1	no	—
346	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
349	#559	—	2	4	no	—
350	#559	—	2	4	no	—
351	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#124	—	2	1	no	—
353	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#123	—	2	1	no	—
356	C₂×#123	—	2	1	no	—
357	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×D₄	—	2	1	no	—
361	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
363	#464	—	2	4	no	—
364	#440	—	2	4	no	—
365	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
378	#398	—	2	1	no	—
379	#398	—	2	1	no	—
380	#391	—	2	1	no	—
381	#391	C₂²×C₁₃	1	1	yes	characteristic
382	#391	C₂²×C₁₃	1	1	yes	characteristic
383	#389	—	2	1	no	—
384	#389	C₂²×C₁₃	1	1	yes	characteristic
385	#389	C₂²×C₁₃	1	1	yes	characteristic
386	#384	C₂²×C₁₃	1	1	yes	characteristic
387	#340	C₂²×C₁₃	1	1	yes	characteristic
388	#340	C₂²×C₁₃	1	1	yes	characteristic
389	#336	C₂²×C₁₃	1	1	yes	characteristic
390	#336	C₂²×C₁₃	1	1	yes	characteristic
391	#336	C₂²×C₁₃	1	1	yes	characteristic
392	#336	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	2	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	8	1	no	—
400	C₂²×C₁₃	—	8	1	no	—
401	C₂²×C₁₃	—	8	1	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	—	8	1	no	—
406	C₂²×C₁₃	—	8	1	no	—
407	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
408	C₂²×C₁₃	#548	1	1	yes	characteristic
409	C₂²×C₁₃	#550	1	1	yes	characteristic
410	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
411	C₂²×C₁₃	#575	1	1	yes	characteristic
412	C₂²×C₁₃	#576	1	1	yes	characteristic
413	C₂²×C₁₃	#577	1	1	yes	characteristic
414	C₄×C₁₃	—	2	2	no	—
415	C₄×C₁₃	—	2	2	no	—
416	C₄×C₁₃	—	2	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	4	1	no	—
421	C₄×C₁₃	—	4	1	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	—	8	1	no	—
424	C₄×C₁₃	—	8	1	no	—
425	C₄×C₁₃	—	8	1	no	—
426	C₄×C₁₃	#525	1	1	yes	characteristic
427	C₄×C₁₃	#537	1	1	yes	characteristic
428	C₄×C₁₃	#546	1	1	yes	characteristic
429	C₄×C₁₃	#547	1	1	yes	characteristic
430	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	—	2	1	no	—
435	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂×Q₁₆	—	2	2	no	—
440	C₂×Q₁₆	—	2	2	no	—
441	C₂×Q₁₆	—	4	1	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	—	4	1	no	—
448	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
452	#127	—	2	2	no	—
453	#127	—	2	2	no	—
454	#124	—	2	8	no	—
455	#124	—	2	2	no	—
456	#124	—	2	2	no	—
457	#124	—	2	2	no	—
458	#124	D₄×C₁₃	1	4	yes	—
459	#123	—	2	8	no	—
460	#123	—	2	8	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×D₄	—	2	8	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	D₄×C₁₃	1	4	yes	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
496	#107	—	2	2	no	—
497	C₄⋊C₈	—	2	2	no	—
498	#103	—	2	2	no	—
499	#103	—	2	2	no	—
500	#103	—	2	2	no	—
501	#103	—	4	1	no	—
502	#102	—	2	2	no	—
503	#102	—	2	2	no	—
504	#102	—	2	2	no	—
505	#102	—	4	1	no	—
506	#102	—	4	1	no	—
507	#102	—	4	1	no	—
508	#97	—	2	2	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	C₂×C₁₃	—	8	2	no	—
516	C₂×C₁₃	—	8	2	no	—
517	C₂×C₁₃	#2407	1	1	yes	characteristic
518	C₂×C₁₃	#3007	1	1	yes	characteristic
519	C₂×C₁₃	#3012	1	1	yes	characteristic
520	C₂×C₁₃	#3371	1	1	yes	characteristic
521	C₂×C₁₃	#3375	1	1	yes	characteristic
522	C₂×C₁₃	#3400	1	1	yes	characteristic
523	C₂×C₁₃	#3403	1	1	yes	characteristic
524	C₂⁴	—	2	1	no	—
525	C₂⁴	—	2	1	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	4	1	no	—
539	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
540	C₂×Q₈	C₁₃×#41	1	2	yes	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	8	1	no	—
556	C₂×D₄	—	8	1	no	—
557	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
558	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	8	1	no	—
568	C₂²×C₄	—	8	1	no	—
569	C₂²×C₄	—	8	1	no	—
570	C₂²×C₄	—	8	1	no	—
571	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
578	Q₁₆	—	4	4	no	—
579	SD₁₆	—	2	8	no	—
580	SD₁₆	—	4	4	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	C₁₃×#41	1	2	yes	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	8	1	no	—
607	C₄⋊C₄	—	8	1	no	—
608	C₄⋊C₄	—	8	1	no	—
609	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	4	2	no	—
622	C₄²	C₂×D₄×C₁₃	1	2	yes	—
623	C₄²	C₂×D₄×C₁₃	1	2	yes	—
624	C₁₃	#24206	1	1	yes	characteristic, direct product factor, Sylow
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	2	2	no	—
653	D₄	—	4	8	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	8	4	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₁₃×#120	1	2	yes	—
695	C₂×C₄	C₁₃×#120	1	2	yes	—
696	C₂×C₄	C₁₃×#137	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
700	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
701	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
703	C₈	—	2	2	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
722	C₂²	C₁₃×#548	1	1	yes	characteristic
723	C₂²	C₁₃×#550	1	1	yes	characteristic
724	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
725	C₂²	C₁₃×#575	1	1	yes	characteristic
726	C₂²	C₁₃×#576	1	1	yes	characteristic
727	C₂²	C₁₃×#577	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	8	1	no	—
738	C₄	—	8	1	no	—
739	C₄	—	8	1	no	—
740	C₄	C₁₃×#525	1	1	yes	characteristic
741	C₄	C₁₃×#537	1	1	yes	characteristic
742	C₄	C₁₃×#546	1	1	yes	characteristic
743	C₄	C₁₃×#547	1	1	yes	characteristic
744	C₂	—	8	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₁₃×#2407	1	1	yes	characteristic
747	C₂	C₁₃×#3007	1	1	yes	characteristic
748	C₂	C₁₃×#3012	1	1	yes	characteristic
749	C₂	C₁₃×#3371	1	1	yes	characteristic
750	C₂	C₁₃×#3375	1	1	yes	characteristic
751	C₂	C₁₃×#3400	1	1	yes	characteristic
752	C₂	C₁₃×#3403	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#464	C₂	semidirect
3. C₂×C₁₃×#440	C₂	semidirect
4. C₁₃×#2582	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2015	C₂	semidirect
9. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1959	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
12. C₁₃×#1877	C₂	semidirect
13. C₁₃×#1863	C₂	semidirect
14. C₁₃×#1862	C₂	semidirect
15. C₁₃×#1802	C₂	semidirect
148. #24206	C₁₃	direct (N × H)
250. C₂×#464	C₂×C₁₃	semidirect
251. C₂×#440	C₂×C₁₃	semidirect
252. #2582	C₂×C₁₃	semidirect
253. #2042	C₂×C₁₃	semidirect
255. #2015	C₂×C₁₃	semidirect
257. #1985	C₂×C₁₃	semidirect
258. #1959	C₂×C₁₃	semidirect
259. #1878	C₂×C₁₃	semidirect
260. #1877	C₂×C₁₃	semidirect
261. #1863	C₂×C₁₃	semidirect
262. #1862	C₂×C₁₃	semidirect
263. #1802	C₂×C₁₃	semidirect
624. C₁₃	#24206	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×#559	2
C₂×C₁₃×#464	2
C₂×C₁₃×#440	2
C₁₃×#2582	2
C₁₃×#2042	2
C₁₃×#2041	2
C₁₃×#2015	2
C₁₃×#2014	2
C₁₃×#1985	2
C₁₃×#1959	2
C₁₃×#1878	2
C₁₃×#1877	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1802	2
#24206	13

Subgroups — C13×#24206 #15710545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24206 #15710545