Subgroups — C₁₃×#26902 #15713241

Order 3328.

872 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2452	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#475	—	2	4	no	—
25	C₄×C₁₃×SD₁₆	—	2	4	no	—
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#396	—	2	1	no	—
39	C₁₃×#393	—	2	1	no	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#389	—	2	1	no	—
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#387	—	2	1	no	—
48	C₁₃×#387	—	2	1	no	—
49	C₁₃×#385	—	2	1	no	—
50	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊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×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	4	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	4	1	no	—
80	C₁₃×C₂²⋊Q₈	—	4	4	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	—	4	1	no	—
84	C₄×Q₈×C₁₃	—	4	1	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	4	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×#106	D₄	1	4	yes	—
114	C₁₃×C₄⋊C₈	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₄×C₈×C₁₃	—	2	2	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	C₁₃×#95	D₄	1	1	yes	characteristic
133	#26902	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	4	2	no	—
146	C₂×Q₈×C₁₃	—	4	2	no	—
147	C₂×Q₈×C₁₃	—	8	1	no	—
148	C₂×Q₈×C₁₃	#41	1	2	yes	—
149	C₂×Q₈×C₁₃	#41	1	2	yes	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	#41	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	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	8	1	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×SD₁₆	—	2	8	no	—
174	C₁₃×SD₁₆	—	4	4	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	2	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	—	4	2	no	—
203	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
204	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	8	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	4	2	no	—
218	C₄²×C₁₃	—	4	2	no	—
219	C₄²×C₁₃	—	4	2	no	—
220	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
222	#2452	C₂×C₁₃	1	1	yes	characteristic
223	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2055	C₂×C₁₃	1	1	yes	characteristic
225	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2013	C₂×C₁₃	1	1	yes	characteristic
228	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1926	C₂×C₁₃	1	1	yes	characteristic
230	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1880	C₂×C₁₃	1	1	yes	characteristic
233	#1877	C₂×C₁₃	1	1	yes	characteristic
234	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	1	no	—
242	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₁₃	—	2	2	no	—
244	Q₈×C₁₃	—	2	2	no	—
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	2	2	no	—
247	Q₈×C₁₃	—	4	1	no	—
248	Q₈×C₁₃	—	4	1	no	—
249	Q₈×C₁₃	—	4	1	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	—	8	4	no	—
252	D₄×C₁₃	—	2	2	no	—
253	D₄×C₁₃	—	2	2	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	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	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	8	4	no	—
293	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
294	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
295	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
302	C₈×C₁₃	—	2	2	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₂²⋊Q₈	—	2	1	no	—
311	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
314	#475	—	2	4	no	—
315	C₄×SD₁₆	—	2	4	no	—
316	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
328	#396	—	2	1	no	—
329	#393	—	2	1	no	—
330	#391	C₂²×C₁₃	1	1	yes	characteristic
331	#391	C₂²×C₁₃	1	1	yes	characteristic
332	#390	C₂²×C₁₃	1	1	yes	characteristic
333	#390	C₂²×C₁₃	1	1	yes	characteristic
334	#389	—	2	1	no	—
335	#389	C₂²×C₁₃	1	1	yes	characteristic
336	#389	C₂²×C₁₃	1	1	yes	characteristic
337	#387	—	2	1	no	—
338	#387	—	2	1	no	—
339	#385	—	2	1	no	—
340	C₄×C₄⋊C₄	—	2	1	no	—
341	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
343	#340	C₂²×C₁₃	1	1	yes	characteristic
344	#340	C₂²×C₁₃	1	1	yes	characteristic
345	#340	C₂²×C₁₃	1	1	yes	characteristic
346	#340	C₂²×C₁₃	1	1	yes	characteristic
347	#336	C₂²×C₁₃	1	1	yes	characteristic
348	#336	C₂²×C₁₃	1	1	yes	characteristic
349	#336	C₂²×C₁₃	1	1	yes	characteristic
350	#336	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	2	no	—
353	C₂²×C₁₃	—	4	2	no	—
354	C₂²×C₁₃	—	8	1	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	—	8	1	no	—
357	C₂²×C₁₃	—	8	1	no	—
358	C₂²×C₁₃	#525	1	1	yes	characteristic
359	C₂²×C₁₃	D₄²	1	1	yes	characteristic
360	C₂²×C₁₃	#548	1	1	yes	characteristic
361	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
362	C₂²×C₁₃	#575	1	1	yes	characteristic
363	C₂²×C₁₃	#577	1	1	yes	characteristic
364	C₂²×C₁₃	#578	1	1	yes	characteristic
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	2	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	#525	1	1	yes	characteristic
379	C₄×C₁₃	#539	1	1	yes	characteristic
380	C₄×C₁₃	#548	1	1	yes	characteristic
381	C₄×C₁₃	#551	1	1	yes	characteristic
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂×SD₁₆	—	2	2	no	—
388	C₂×SD₁₆	—	2	2	no	—
389	C₂×SD₁₆	—	2	2	no	—
390	C₂×SD₁₆	—	2	2	no	—
391	C₂×SD₁₆	—	2	2	no	—
392	C₂×SD₁₆	—	4	1	no	—
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊Q₈	—	2	2	no	—
398	C₄⋊Q₈	—	2	2	no	—
399	C₄⋊Q₈	—	2	2	no	—
400	C₄⋊Q₈	—	4	1	no	—
401	C₂²⋊Q₈	—	4	4	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	4	1	no	—
405	C₄×Q₈	—	4	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	4	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	#106	—	2	2	no	—
434	#106	D₄×C₁₃	1	4	yes	—
435	C₄⋊C₈	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	4	1	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	C₄×C₈	—	2	2	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	D₄×C₁₃	1	1	yes	characteristic
453	#95	D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₁₃	—	8	2	no	—
455	C₂×C₁₃	#2463	1	1	yes	characteristic
456	C₂×C₁₃	#3103	1	1	yes	characteristic
457	C₂×C₁₃	#3121	1	1	yes	characteristic
458	C₂×C₁₃	#3269	1	1	yes	characteristic
459	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
460	C₂×C₁₃	#3359	1	1	yes	characteristic
461	C₂×C₁₃	#3376	1	1	yes	characteristic
462	C₂⁴	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	4	2	no	—
474	C₂×Q₈	—	4	2	no	—
475	C₂×Q₈	—	8	1	no	—
476	C₂×Q₈	C₁₃×#41	1	2	yes	—
477	C₂×Q₈	C₁₃×#41	1	2	yes	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	C₁₃×#41	1	2	yes	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	SD₁₆	—	2	8	no	—
502	SD₁₆	—	4	4	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
515	C₄⋊C₄	—	2	4	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
532	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	8	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	4	2	no	—
546	C₄²	—	4	2	no	—
547	C₄²	—	4	2	no	—
548	C₁₃	#26902	1	1	yes	characteristic, direct product factor, Sylow
549	C₂³	—	2	2	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	2	2	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	8	4	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	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	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	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	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	8	4	no	—
607	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
608	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
609	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
612	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
613	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
614	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	C₁₃×#525	1	1	yes	characteristic
628	C₂²	D₄²×C₁₃	1	1	yes	characteristic
629	C₂²	C₁₃×#548	1	1	yes	characteristic
630	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
631	C₂²	C₁₃×#575	1	1	yes	characteristic
632	C₂²	C₁₃×#577	1	1	yes	characteristic
633	C₂²	C₁₃×#578	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	C₁₃×#525	1	1	yes	characteristic
648	C₄	C₁₃×#539	1	1	yes	characteristic
649	C₄	C₁₃×#548	1	1	yes	characteristic
650	C₄	C₁₃×#551	1	1	yes	characteristic
651	C₂	—	8	2	no	—
652	C₂	C₁₃×#2463	1	1	yes	characteristic
653	C₂	C₁₃×#3103	1	1	yes	characteristic
654	C₂	C₁₃×#3121	1	1	yes	characteristic
655	C₂	C₁₃×#3269	1	1	yes	characteristic
656	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
657	C₂	C₁₃×#3359	1	1	yes	characteristic
658	C₂	C₁₃×#3376	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
1. C₂×C₁₃×#475	C₂	semidirect
4. C₁₃×#2365	C₂	semidirect
6. C₁₃×#2043	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
9. C₁₃×#1933	C₂	semidirect
11. C₁₃×#1919	C₂	semidirect
12. C₁₃×#1916	C₂	semidirect
15. C₁₃×#1865	C₂	semidirect
133. #26902	C₁₃	direct (N × H)
203. C₁₃×C₄⋊C₄	SD₁₆	semidirect
220. C₂×#475	C₂×C₁₃	semidirect
223. #2365	C₂×C₁₃	semidirect
225. #2043	C₂×C₁₃	semidirect
226. #2024	C₂×C₁₃	semidirect
228. #1933	C₂×C₁₃	semidirect
230. #1919	C₂×C₁₃	semidirect
231. #1916	C₂×C₁₃	semidirect
234. #1865	C₂×C₁₃	semidirect
531. C₄⋊C₄	C₁₃×SD₁₆	semidirect
548. C₁₃	#26902	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×#475	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2452	2
C₁₃×#2365	2
C₁₃×#2055	2
C₁₃×#2043	2
C₁₃×#2024	2
C₁₃×#2013	2
C₁₃×#1933	2
C₁₃×#1926	2
C₁₃×#1919	2
C₁₃×#1916	2
C₁₃×#1880	2
C₁₃×#1877	2
C₁₃×#1865	2
#26902	13

Subgroups — C13×#26902 #15713241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26902 #15713241