Subgroups — C₁₃×#26477 #15712816

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1983	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1959	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1940	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
15	C₁₃×#1776	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#479	—	2	4	no	—
22	C₁₃×#478	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	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×#103	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×#97	C₂²	1	1	yes	characteristic
39	C₁₃×#398	—	2	1	no	—
40	C₁₃×#398	—	2	1	no	—
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#389	—	2	1	no	—
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#384	—	2	1	no	—
50	C₁₃×#384	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	4	1	no	—
71	C₁₃×#125	—	4	1	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	Q₈	1	4	yes	—
74	C₄×Q₈×C₁₃	—	2	2	no	—
75	C₄×Q₈×C₁₃	—	4	1	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	4	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	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	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	—	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×#107	—	2	2	no	—
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#107	—	2	2	no	—
109	C₁₃×#106	D₄	1	4	yes	—
110	C₁₃×C₄⋊C₈	—	2	2	no	—
111	C₁₃×C₄⋊C₈	—	2	2	no	—
112	C₁₃×C₄⋊C₈	—	2	2	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#103	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	4	1	no	—
117	C₁₃×#102	—	2	2	no	—
118	C₁₃×#102	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	4	1	no	—
121	C₁₃×#97	—	2	2	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	D₄	1	1	yes	characteristic
129	C₁₃×#95	D₄	1	1	yes	characteristic
130	#26477	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂×Q₈×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	C₂×Q₈	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	1	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	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₃	—	8	1	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	4	1	no	—
183	C₁₃×C₄⋊C₄	—	4	1	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	—	4	2	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	8	1	no	—
191	C₁₃×C₄⋊C₄	—	8	1	no	—
192	C₁₃×C₄⋊C₄	—	8	1	no	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	#41	1	2	yes	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₁₃×C₂²⋊C₄	—	8	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	4	2	no	—
206	C₄²×C₁₃	—	4	2	no	—
207	C₄²×C₁₃	—	8	1	no	—
208	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
209	C₄²×C₁₃	#41	1	2	yes	—
210	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#478	C₂×C₁₃	1	1	yes	characteristic
212	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2367	C₂×C₁₃	1	1	yes	characteristic
214	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2067	C₂×C₁₃	1	1	yes	characteristic
216	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2025	C₂×C₁₃	1	1	yes	characteristic
218	#1983	C₂×C₁₃	1	1	yes	characteristic
219	#1959	C₂×C₁₃	1	1	yes	characteristic
220	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1862	C₂×C₁₃	1	1	yes	characteristic
224	#1776	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	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	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	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	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	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
279	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
287	C₈×C₁₃	—	2	2	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
296	#479	—	2	4	no	—
297	#478	—	2	4	no	—
298	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#391	C₂²×C₁₃	1	1	yes	characteristic
317	#390	C₂²×C₁₃	1	1	yes	characteristic
318	#389	—	2	1	no	—
319	#389	C₂²×C₁₃	1	1	yes	characteristic
320	#389	C₂²×C₁₃	1	1	yes	characteristic
321	#388	—	2	1	no	—
322	#388	—	2	1	no	—
323	#385	—	2	1	no	—
324	#384	—	2	1	no	—
325	#384	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	—	2	1	no	—
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#336	C₂²×C₁₃	1	1	yes	characteristic
335	#336	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
344	C₂²×C₁₃	D₄²	1	1	yes	characteristic
345	C₂²×C₁₃	#548	1	1	yes	characteristic
346	C₂²×C₁₃	#575	1	1	yes	characteristic
347	C₂²×C₁₃	#575	1	1	yes	characteristic
348	C₂²×C₁₃	#576	1	1	yes	characteristic
349	C₂²×C₁₃	#578	1	1	yes	characteristic
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	—	8	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	#532	1	1	yes	characteristic
364	C₄×C₁₃	#542	1	1	yes	characteristic
365	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
366	C₄×C₁₃	#554	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
374	#125	—	2	2	no	—
375	#125	—	2	2	no	—
376	#125	—	4	1	no	—
377	#125	—	4	1	no	—
378	#124	—	2	2	no	—
379	#124	Q₈×C₁₃	1	4	yes	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	4	1	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	4	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	#107	—	2	2	no	—
413	#107	—	2	2	no	—
414	#107	—	2	2	no	—
415	#106	D₄×C₁₃	1	4	yes	—
416	C₄⋊C₈	—	2	2	no	—
417	C₄⋊C₈	—	2	2	no	—
418	C₄⋊C₈	—	2	2	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	4	1	no	—
423	#102	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	4	1	no	—
427	#97	—	2	2	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	D₄×C₁₃	1	1	yes	characteristic
435	#95	D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	8	2	no	—
437	C₂×C₁₃	#2452	1	1	yes	characteristic
438	C₂×C₁₃	#3080	1	1	yes	characteristic
439	C₂×C₁₃	#3083	1	1	yes	characteristic
440	C₂×C₁₃	#3268	1	1	yes	characteristic
441	C₂×C₁₃	#3269	1	1	yes	characteristic
442	C₂×C₁₃	#3370	1	1	yes	characteristic
443	C₂×C₁₃	#3377	1	1	yes	characteristic
444	C₂⁴	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	8	1	no	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	—	8	1	no	—
505	C₄⋊C₄	—	8	1	no	—
506	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
507	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
508	C₄⋊C₄	C₁₃×#41	1	2	yes	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	8	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	8	1	no	—
521	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
522	C₄²	C₁₃×#41	1	2	yes	—
523	C₁₃	#26477	1	1	yes	characteristic, direct product factor, Sylow
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	Q₈	—	2	2	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	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	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	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	—	8	4	no	—
578	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
579	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
583	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
584	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
586	C₈	—	2	2	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
598	C₂²	D₄²×C₁₃	1	1	yes	characteristic
599	C₂²	C₁₃×#548	1	1	yes	characteristic
600	C₂²	C₁₃×#575	1	1	yes	characteristic
601	C₂²	C₁₃×#575	1	1	yes	characteristic
602	C₂²	C₁₃×#576	1	1	yes	characteristic
603	C₂²	C₁₃×#578	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	C₁₃×#532	1	1	yes	characteristic
618	C₄	C₁₃×#542	1	1	yes	characteristic
619	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
620	C₄	C₁₃×#554	1	1	yes	characteristic
621	C₂	—	8	2	no	—
622	C₂	C₁₃×#2452	1	1	yes	characteristic
623	C₂	C₁₃×#3080	1	1	yes	characteristic
624	C₂	C₁₃×#3083	1	1	yes	characteristic
625	C₂	C₁₃×#3268	1	1	yes	characteristic
626	C₂	C₁₃×#3269	1	1	yes	characteristic
627	C₂	C₁₃×#3370	1	1	yes	characteristic
628	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
1. C₂×C₁₃×#479	C₂	semidirect
3. C₁₃×#2552	C₂	semidirect
5. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2026	C₂	semidirect
11. C₁₃×#1947	C₂	semidirect
12. C₁₃×#1940	C₂	semidirect
13. C₁₃×#1863	C₂	semidirect
15. C₁₃×#1776	C₂	semidirect
130. #26477	C₁₃	direct (N × H)
210. C₂×#479	C₂×C₁₃	semidirect
212. #2552	C₂×C₁₃	semidirect
214. #2068	C₂×C₁₃	semidirect
216. #2026	C₂×C₁₃	semidirect
220. #1947	C₂×C₁₃	semidirect
221. #1940	C₂×C₁₃	semidirect
222. #1863	C₂×C₁₃	semidirect
224. #1776	C₂×C₁₃	semidirect
523. C₁₃	#26477	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×#479	2
C₂×C₁₃×#478	2
C₁₃×#2552	2
C₁₃×#2367	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1983	2
C₁₃×#1959	2
C₁₃×#1947	2
C₁₃×#1940	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1776	2
#26477	13

Subgroups — C13×#26477 #15712816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26477 #15712816