Subgroups — C₁₃×#24736 #15711075

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1958	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#464	—	2	4	no	—
27	C₁₃×#464	—	2	4	no	—
28	C₁₃×#462	—	2	4	no	—
29	C₄×C₁₃×Q₁₆	—	2	4	no	—
30	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#396	—	2	1	no	—
46	C₁₃×#396	—	2	1	no	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#389	—	2	1	no	—
50	C₁₃×#389	—	2	1	no	—
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#382	—	2	1	no	—
56	C₁₃×#382	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	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	C₂³	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	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	2	2	no	—
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×Q₁₆	—	2	2	no	—
71	C₂×C₁₃×Q₁₆	—	2	2	no	—
72	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
73	C₂×C₁₃×SD₁₆	—	2	2	no	—
74	C₂×C₁₃×SD₁₆	—	2	2	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	—	2	2	no	—
81	C₁₃×C₄⋊Q₈	—	4	1	no	—
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	—	2	2	no	—
85	C₁₃×#124	—	4	1	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	4	1	no	—
92	C₄×Q₈×C₁₃	—	4	1	no	—
93	C₄×Q₈×C₁₃	D₄	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₄²×C₁₃	—	2	1	no	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	—	2	1	no	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	—	2	2	no	—
122	C₁₃×C₄⋊C₈	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	2	no	—
125	C₁₃×#103	—	2	2	no	—
126	C₁₃×#103	—	2	2	no	—
127	C₁₃×#103	—	2	2	no	—
128	C₁₃×#103	—	2	2	no	—
129	C₁₃×#103	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	4	1	no	—
132	C₁₃×#102	—	2	2	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	4	1	no	—
135	C₄×C₈×C₁₃	—	2	2	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	C₁₃×#95	D₄	1	1	yes	characteristic
143	C₁₃×#95	D₄	1	1	yes	characteristic
144	#24736	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×Q₈×C₁₃	#41	1	2	yes	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×Q₁₆	—	2	8	no	—
185	C₁₃×Q₁₆	—	4	4	no	—
186	C₁₃×SD₁₆	—	4	4	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	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	4	1	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	—	4	2	no	—
212	C₁₃×C₄⋊C₄	—	4	2	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	4	2	no	—
215	C₁₃×C₄⋊C₄	—	4	2	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	C₄²×C₁₃	—	2	4	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	—	4	2	no	—
230	C₄²×C₁₃	—	4	2	no	—
231	C₄²×C₁₃	C₂×D₄	1	2	yes	—
232	C₄²×C₁₃	#41	1	2	yes	—
233	C₂×#464	C₂×C₁₃	1	1	yes	characteristic
234	C₂×#464	C₂×C₁₃	1	1	yes	characteristic
235	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2545	C₂×C₁₃	1	1	yes	characteristic
238	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2067	C₂×C₁₃	1	1	yes	characteristic
241	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2042	C₂×C₁₃	1	1	yes	characteristic
243	#1958	C₂×C₁₃	1	1	yes	characteristic
244	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1880	C₂×C₁₃	1	1	yes	characteristic
246	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₁₃	—	2	2	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	2	2	no	—
259	Q₈×C₁₃	—	2	2	no	—
260	Q₈×C₁₃	—	2	2	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	1	no	—
263	Q₈×C₁₃	—	4	1	no	—
264	Q₈×C₁₃	—	4	1	no	—
265	Q₈×C₁₃	—	4	1	no	—
266	Q₈×C₁₃	—	4	1	no	—
267	Q₈×C₁₃	#121	1	4	yes	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	D₄×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	1	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	2	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	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	#121	1	2	yes	—
309	C₂×C₄×C₁₃	#121	1	2	yes	—
310	C₂×C₄×C₁₃	#135	1	2	yes	—
311	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
317	C₈×C₁₃	—	2	2	no	—
318	C₈×C₁₃	—	4	1	no	—
319	C₈×C₁₃	—	4	1	no	—
320	C₈×C₁₃	—	4	1	no	—
321	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
331	#464	—	2	4	no	—
332	#464	—	2	4	no	—
333	#462	—	2	4	no	—
334	C₄×Q₁₆	—	2	4	no	—
335	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#103	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×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
350	#396	—	2	1	no	—
351	#396	—	2	1	no	—
352	#391	C₂²×C₁₃	1	1	yes	characteristic
353	#390	C₂²×C₁₃	1	1	yes	characteristic
354	#389	—	2	1	no	—
355	#389	—	2	1	no	—
356	#389	C₂²×C₁₃	1	1	yes	characteristic
357	#389	C₂²×C₁₃	1	1	yes	characteristic
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#382	—	2	1	no	—
361	#382	C₂²×C₁₃	1	1	yes	characteristic
362	C₄×C₄⋊C₄	—	2	1	no	—
363	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
364	#340	C₂²×C₁₃	1	1	yes	characteristic
365	#340	C₂²×C₁₃	1	1	yes	characteristic
366	#336	C₂²×C₁₃	1	1	yes	characteristic
367	#336	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	—	8	1	no	—
371	C₂²×C₁₃	—	8	1	no	—
372	C₂²×C₁₃	—	8	1	no	—
373	C₂²×C₁₃	—	8	1	no	—
374	C₂²×C₁₃	—	8	1	no	—
375	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
376	C₂²×C₁₃	D₄²	1	1	yes	characteristic
377	C₂²×C₁₃	#548	1	1	yes	characteristic
378	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
379	C₂²×C₁₃	#575	1	1	yes	characteristic
380	C₂²×C₁₃	#578	1	1	yes	characteristic
381	C₂²×C₁₃	#578	1	1	yes	characteristic
382	C₄×C₁₃	—	2	4	no	—
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	2	2	no	—
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	1	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	2	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	—	8	1	no	—
394	C₄×C₁₃	—	8	1	no	—
395	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
396	C₄×C₁₃	#537	1	1	yes	characteristic
397	C₄×C₁₃	#547	1	1	yes	characteristic
398	C₄×C₁₃	#553	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	2	2	no	—
406	C₂×Q₁₆	—	2	2	no	—
407	C₂×Q₁₆	—	2	2	no	—
408	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
409	C₂×SD₁₆	—	2	2	no	—
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄⋊Q₈	—	2	2	no	—
417	C₄⋊Q₈	—	4	1	no	—
418	#124	—	2	2	no	—
419	#124	—	2	2	no	—
420	#124	—	2	2	no	—
421	#124	—	4	1	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	2	2	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	4	1	no	—
428	C₄×Q₈	—	4	1	no	—
429	C₄×Q₈	D₄×C₁₃	1	4	yes	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
457	#107	—	2	2	no	—
458	C₄⋊C₈	—	2	2	no	—
459	C₄⋊C₈	—	2	2	no	—
460	C₄⋊C₈	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	#103	—	4	1	no	—
468	#102	—	2	2	no	—
469	#102	—	2	2	no	—
470	#102	—	4	1	no	—
471	C₄×C₈	—	2	2	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	D₄×C₁₃	1	1	yes	characteristic
479	#95	D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₁₃	—	16	1	no	—
481	C₂×C₁₃	#2416	1	1	yes	characteristic
482	C₂×C₁₃	#3035	1	1	yes	characteristic
483	C₂×C₁₃	#3044	1	1	yes	characteristic
484	C₂×C₁₃	#3277	1	1	yes	characteristic
485	C₂×C₁₃	#3285	1	1	yes	characteristic
486	C₂×C₁₃	#3364	1	1	yes	characteristic
487	C₂×C₁₃	#3377	1	1	yes	characteristic
488	C₂⁴	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
504	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
505	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
506	C₂×Q₈	C₁₃×#41	1	2	yes	—
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	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	Q₁₆	—	2	8	no	—
528	Q₁₆	—	4	4	no	—
529	SD₁₆	—	4	4	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	2	no	—
574	C₄²	C₂×D₄×C₁₃	1	2	yes	—
575	C₄²	C₁₃×#41	1	2	yes	—
576	C₁₃	#24736	1	1	yes	characteristic, direct product factor, Sylow
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	2	2	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	—	4	1	no	—
594	Q₈	—	4	1	no	—
595	Q₈	—	4	1	no	—
596	Q₈	C₁₃×#121	1	4	yes	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	C₁₃×#121	1	2	yes	—
638	C₂×C₄	C₁₃×#121	1	2	yes	—
639	C₂×C₄	C₁₃×#135	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
642	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
643	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
644	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
658	C₂²	D₄²×C₁₃	1	1	yes	characteristic
659	C₂²	C₁₃×#548	1	1	yes	characteristic
660	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
661	C₂²	C₁₃×#575	1	1	yes	characteristic
662	C₂²	C₁₃×#578	1	1	yes	characteristic
663	C₂²	C₁₃×#578	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	—	8	1	no	—
677	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
678	C₄	C₁₃×#537	1	1	yes	characteristic
679	C₄	C₁₃×#547	1	1	yes	characteristic
680	C₄	C₁₃×#553	1	1	yes	characteristic
681	C₂	—	16	1	no	—
682	C₂	C₁₃×#2416	1	1	yes	characteristic
683	C₂	C₁₃×#3035	1	1	yes	characteristic
684	C₂	C₁₃×#3044	1	1	yes	characteristic
685	C₂	C₁₃×#3277	1	1	yes	characteristic
686	C₂	C₁₃×#3285	1	1	yes	characteristic
687	C₂	C₁₃×#3364	1	1	yes	characteristic
688	C₂	C₁₃×#3377	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
3. C₂×C₁₃×#462	C₂	semidirect
4. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
6. C₁₃×#2351	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
9. C₁₃×#2043	C₂	semidirect
12. C₁₃×#1939	C₂	semidirect
14. C₁₃×#1878	C₂	semidirect
15. C₁₃×#1805	C₂	semidirect
144. #24736	C₁₃	direct (N × H)
235. C₂×#462	C₂×C₁₃	semidirect
236. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
238. #2351	C₂×C₁₃	semidirect
239. #2068	C₂×C₁₃	semidirect
241. #2043	C₂×C₁₃	semidirect
244. #1939	C₂×C₁₃	semidirect
246. #1878	C₂×C₁₃	semidirect
247. #1805	C₂×C₁₃	semidirect
576. C₁₃	#24736	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×#464	2
C₂×C₁₃×#462	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2545	2
C₁₃×#2351	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2043	2
C₁₃×#2042	2
C₁₃×#1958	2
C₁₃×#1939	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1805	2
#24736	13

Subgroups — C13×#24736 #15711075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24736 #15711075