Subgroups — C₁₃×#26480 #15712819

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#498	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×#2451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
15	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#498	—	2	4	no	—
23	C₄×C₁₃×SD₁₆	—	2	4	no	—
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	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×#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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#398	—	2	1	no	—
40	C₁₃×#396	—	2	1	no	—
41	C₁₃×#395	—	2	1	no	—
42	C₁₃×#393	—	2	1	no	—
43	C₁₃×#391	—	2	1	no	—
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#390	C₂²	1	1	yes	characteristic
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#387	—	2	1	no	—
53	C₁₃×#385	—	2	1	no	—
54	C₄×C₁₃×C₄⋊C₄	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×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	—	2	1	no	—
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	Q₈	1	4	yes	complemented
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊Q₈	—	2	2	no	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	4	1	no	—
76	C₁₃×C₄⋊Q₈	—	4	1	no	—
77	C₁₃×C₂²⋊Q₈	—	4	4	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	4	1	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	4	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#106	—	2	2	no	—
107	C₁₃×#106	—	2	2	no	—
108	C₁₃×#106	—	2	2	no	—
109	C₁₃×#106	—	2	2	no	—
110	C₁₃×#106	D₄	1	4	yes	—
111	C₁₃×C₄⋊C₈	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#103	—	4	1	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	2	no	—
117	C₁₃×#102	—	4	1	no	—
118	C₄×C₈×C₁₃	—	2	2	no	—
119	C₄×C₈×C₁₃	—	2	2	no	—
120	C₄×C₈×C₁₃	—	2	2	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	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	D₄	1	1	yes	characteristic
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	#26480	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×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	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	—	4	2	no	—
141	C₂×Q₈×C₁₃	—	4	2	no	—
142	C₂×Q₈×C₁₃	—	8	1	no	—
143	C₂×Q₈×C₁₃	—	8	1	no	—
144	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
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	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	8	1	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×SD₁₆	—	2	8	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
179	C₂×C₈×C₁₃	#41	1	2	yes	—
180	C₂×C₈×C₁₃	#41	1	2	yes	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	2	no	—
195	C₁₃×C₄⋊C₄	—	4	2	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	8	1	no	—
198	C₁₃×C₄⋊C₄	—	8	1	no	—
199	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
200	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₂²⋊C₄	—	4	2	no	—
203	C₁₃×C₂²⋊C₄	—	4	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	8	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	4	2	no	—
214	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
216	#2452	C₂×C₁₃	1	1	yes	characteristic
217	#2451	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2065	C₂×C₁₃	1	1	yes	characteristic
220	#2024	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2023	C₂×C₁₃	1	1	yes	characteristic
222	#1968	C₂×C₁₃	1	1	yes	characteristic
223	#1968	C₂×C₁₃	1	1	yes	characteristic
224	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1864	C₂×C₁₃	1	1	yes	characteristic
228	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	2	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	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	8	4	no	—
242	Q₈×C₁₃	—	8	4	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	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	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	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	—	4	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	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	8	4	no	—
283	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
284	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
285	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
286	C₂×C₄×C₁₃	#135	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
297	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊Q₈	—	2	1	no	—
301	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
303	#498	—	2	4	no	—
304	C₄×SD₁₆	—	2	4	no	—
305	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
320	#398	—	2	1	no	—
321	#396	—	2	1	no	—
322	#395	—	2	1	no	—
323	#393	—	2	1	no	—
324	#391	—	2	1	no	—
325	#391	C₂²×C₁₃	1	1	yes	characteristic
326	#391	C₂²×C₁₃	1	1	yes	characteristic
327	#390	C₂²×C₁₃	1	1	yes	characteristic
328	#390	C₂²×C₁₃	1	1	yes	characteristic
329	#389	C₂²×C₁₃	1	1	yes	characteristic
330	#389	C₂²×C₁₃	1	1	yes	characteristic
331	#389	C₂²×C₁₃	1	1	yes	characteristic
332	#389	C₂²×C₁₃	1	1	yes	characteristic
333	#387	—	2	1	no	—
334	#385	—	2	1	no	—
335	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
336	#340	C₂²×C₁₃	1	1	yes	characteristic
337	#340	C₂²×C₁₃	1	1	yes	characteristic
338	#340	C₂²×C₁₃	1	1	yes	characteristic
339	#340	C₂²×C₁₃	1	1	yes	characteristic
340	#336	C₂²×C₁₃	1	1	yes	characteristic
341	#336	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	2	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	#532	1	1	yes	characteristic
350	C₂²×C₁₃	D₄²	1	1	yes	characteristic
351	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
352	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
353	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
354	C₂²×C₁₃	#577	1	1	yes	characteristic
355	C₂²×C₁₃	#577	1	1	yes	characteristic
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	1	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
370	C₄×C₁₃	#542	1	1	yes	characteristic
371	C₄×C₁₃	#548	1	1	yes	characteristic
372	C₄×C₁₃	#554	1	1	yes	characteristic
373	C₂²×Q₈	—	2	1	no	—
374	C₂²×Q₈	—	2	1	no	—
375	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	2	no	—
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	4	1	no	—
388	C₄⋊Q₈	—	4	1	no	—
389	C₂²⋊Q₈	—	4	4	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	4	1	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	4	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	#106	—	2	2	no	—
419	#106	—	2	2	no	—
420	#106	—	2	2	no	—
421	#106	—	2	2	no	—
422	#106	D₄×C₁₃	1	4	yes	—
423	C₄⋊C₈	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	2	2	no	—
426	#103	—	4	1	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	4	1	no	—
430	C₄×C₈	—	2	2	no	—
431	C₄×C₈	—	2	2	no	—
432	C₄×C₈	—	2	2	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	D₄×C₁₃	1	1	yes	characteristic
442	#95	D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₁₃	—	8	2	no	—
444	C₂×C₁₃	#2452	1	1	yes	characteristic
445	C₂×C₁₃	#3167	1	1	yes	characteristic
446	C₂×C₁₃	#3173	1	1	yes	characteristic
447	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
448	C₂×C₁₃	#3282	1	1	yes	characteristic
449	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
450	C₂×C₁₃	#3381	1	1	yes	characteristic
451	C₂⁴	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	4	2	no	—
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	8	1	no	—
462	C₂×Q₈	—	8	1	no	—
463	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	SD₁₆	—	2	8	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
497	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
498	C₂×C₈	C₁₃×#41	1	2	yes	—
499	C₂×C₈	C₁₃×#41	1	2	yes	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	8	1	no	—
517	C₄⋊C₄	—	8	1	no	—
518	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
519	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
520	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	8	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	4	2	no	—
533	C₁₃	#26480	1	1	yes	characteristic, direct product factor, Sylow
534	C₂³	—	2	2	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	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	8	4	no	—
547	Q₈	—	8	4	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	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	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	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	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	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	C₂×C₁₃×SD₁₆	1	2	yes	—
589	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
590	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
591	C₂×C₄	C₁₃×#135	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
595	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
596	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
598	C₈	—	2	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	C₁₃×#532	1	1	yes	characteristic
610	C₂²	D₄²×C₁₃	1	1	yes	characteristic
611	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
612	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
613	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
614	C₂²	C₁₃×#577	1	1	yes	characteristic
615	C₂²	C₁₃×#577	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	—	8	1	no	—
629	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
630	C₄	C₁₃×#542	1	1	yes	characteristic
631	C₄	C₁₃×#548	1	1	yes	characteristic
632	C₄	C₁₃×#554	1	1	yes	characteristic
633	C₂	—	8	2	no	—
634	C₂	C₁₃×#2452	1	1	yes	characteristic
635	C₂	C₁₃×#3167	1	1	yes	characteristic
636	C₂	C₁₃×#3173	1	1	yes	characteristic
637	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
638	C₂	C₁₃×#3282	1	1	yes	characteristic
639	C₂	Q₈×C₁₃×SD₁₆	1	1	yes	characteristic
640	C₂	C₁₃×#3381	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×#498	C₂	semidirect
4. C₁₃×#2451	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
11. C₁₃×#1941	C₂	semidirect
12. C₁₃×#1941	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
15. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
68. C₂×C₁₃×SD₁₆	Q₈	semidirect
131. #26480	C₁₃	direct (N × H)
199. C₁₃×C₄⋊C₄	SD₁₆	semidirect
214. C₂×#498	C₂×C₁₃	semidirect
217. #2451	C₂×C₁₃	semidirect
218. #2066	C₂×C₁₃	semidirect
220. #2024	C₂×C₁₃	semidirect
224. #1941	C₂×C₁₃	semidirect
225. #1941	C₂×C₁₃	semidirect
226. #1865	C₂×C₁₃	semidirect
228. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
296. C₈×C₁₃	C₂²⋊Q₈	semidirect
380. C₂×SD₁₆	Q₈×C₁₃	semidirect
518. C₄⋊C₄	C₁₃×SD₁₆	semidirect
533. C₁₃	#26480	direct (N × H)
601. C₈	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#498	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2452	2
C₁₃×#2451	2
C₁₃×#2066	2
C₁₃×#2065	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1968	2
C₁₃×#1941	2
C₁₃×#1865	2
C₁₃×#1864	2
C₈×C₁₃×C₄⋊C₄	2
#26480	13

Subgroups — C13×#26480 #15712819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26480 #15712819