Subgroups — C₁₃×#24588 #15710927

Order 3328.

800 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₁₃×#484	—	2	4	no	—
22	C₁₃×#428	—	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×#107	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×C₄⋊C₈	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₁₃×#397	—	2	1	no	—
37	C₁₃×#397	—	2	1	no	—
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#387	—	2	1	no	—
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#384	C₂²	1	1	yes	characteristic
47	C₁₃×#382	C₂²	1	1	yes	characteristic
48	C₁₃×#381	—	2	1	no	—
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₂²⋊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×#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	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	—	2	2	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	—	2	2	no	—
75	C₁₃×#117	—	4	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	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	D₄	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#107	—	2	2	no	—
103	C₁₃×#107	—	2	2	no	—
104	C₁₃×#107	—	2	2	no	—
105	C₁₃×#106	—	2	2	no	—
106	C₁₃×#106	—	2	2	no	—
107	C₁₃×C₄⋊C₈	—	2	2	no	—
108	C₁₃×C₄⋊C₈	—	2	2	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	2	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	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	D₄	1	1	yes	characteristic
126	C₁₃×#95	D₄	1	1	yes	characteristic
127	#24588	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×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	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	2	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	#41	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₁₃×M₁₆	—	2	8	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
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	#41	1	2	yes	—
170	C₂×C₈×C₁₃	#41	1	2	yes	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	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	C₂×D₄	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	4	1	no	—
193	C₁₃×C₂²⋊C₄	—	4	2	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	4	2	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₂×#484	C₂×C₁₃	1	1	yes	characteristic
204	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
205	#2499	C₂×C₁₃	1	1	yes	characteristic
206	#2344	C₂×C₁₃	1	1	yes	characteristic
207	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1928	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1894	C₂×C₁₃	1	1	yes	characteristic
216	#1851	C₂×C₁₃	1	1	yes	characteristic
217	#1825	C₂×C₁₃	1	1	yes	characteristic
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	1	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	#121	1	2	yes	—
225	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	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	1	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	—	4	8	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	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	#121	1	2	yes	—
273	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
280	C₈×C₁₃	—	2	2	no	—
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#117	—	2	1	no	—
287	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
289	#484	—	2	4	no	—
290	#428	—	2	4	no	—
291	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	#397	—	2	1	no	—
305	#397	—	2	1	no	—
306	#391	C₂²×C₁₃	1	1	yes	characteristic
307	#391	C₂²×C₁₃	1	1	yes	characteristic
308	#389	C₂²×C₁₃	1	1	yes	characteristic
309	#389	C₂²×C₁₃	1	1	yes	characteristic
310	#387	—	2	1	no	—
311	#387	—	2	1	no	—
312	#387	—	2	1	no	—
313	#387	—	2	1	no	—
314	#384	C₂²×C₁₃	1	1	yes	characteristic
315	#382	C₂²×C₁₃	1	1	yes	characteristic
316	#381	—	2	1	no	—
317	#380	C₂²×C₁₃	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
321	#340	C₂²×C₁₃	1	1	yes	characteristic
322	#340	C₂²×C₁₃	1	1	yes	characteristic
323	#340	C₂²×C₁₃	1	1	yes	characteristic
324	#340	C₂²×C₁₃	1	1	yes	characteristic
325	#340	C₂²×C₁₃	1	1	yes	characteristic
326	#340	C₂²×C₁₃	1	1	yes	characteristic
327	#336	C₂²×C₁₃	1	1	yes	characteristic
328	#336	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
337	C₂²×C₁₃	#547	1	1	yes	characteristic
338	C₂²×C₁₃	#547	1	1	yes	characteristic
339	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂²×C₁₃	#575	1	1	yes	characteristic
341	C₂²×C₁₃	#578	1	1	yes	characteristic
342	C₂²×C₁₃	#578	1	1	yes	characteristic
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	#525	1	1	yes	characteristic
357	C₄×C₁₃	#536	1	1	yes	characteristic
358	C₄×C₁₃	#552	1	1	yes	characteristic
359	C₄×C₁₃	#552	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	4	4	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#107	—	2	2	no	—
401	#107	—	2	2	no	—
402	#107	—	2	2	no	—
403	#107	—	2	2	no	—
404	#106	—	2	2	no	—
405	#106	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	C₄⋊C₈	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	D₄×C₁₃	1	1	yes	characteristic
425	#95	D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₁₃	—	4	2	no	—
427	C₂×C₁₃	#2413	1	1	yes	characteristic
428	C₂×C₁₃	#3036	1	1	yes	characteristic
429	C₂×C₁₃	#3044	1	1	yes	characteristic
430	C₂×C₁₃	#3343	1	1	yes	characteristic
431	C₂×C₁₃	#3349	1	1	yes	characteristic
432	C₂×C₁₃	#3352	1	1	yes	characteristic
433	C₂×C₁₃	#3353	1	1	yes	characteristic
434	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₁₃×#41	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
464	M₁₆	—	2	8	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	C₁₃×#41	1	2	yes	—
476	C₂×C₈	C₁₃×#41	1	2	yes	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
496	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₁₃	#24588	1	1	yes	characteristic, direct product factor, Sylow
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	C₁₃×#121	1	2	yes	—
517	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	8	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	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	C₁₃×#121	1	2	yes	—
565	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
568	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
570	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	2	2	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
584	C₂²	C₁₃×#547	1	1	yes	characteristic
585	C₂²	C₁₃×#547	1	1	yes	characteristic
586	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
587	C₂²	C₁₃×#575	1	1	yes	characteristic
588	C₂²	C₁₃×#578	1	1	yes	characteristic
589	C₂²	C₁₃×#578	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₁₃×#525	1	1	yes	characteristic
604	C₄	C₁₃×#536	1	1	yes	characteristic
605	C₄	C₁₃×#552	1	1	yes	characteristic
606	C₄	C₁₃×#552	1	1	yes	characteristic
607	C₂	—	4	2	no	—
608	C₂	C₁₃×#2413	1	1	yes	characteristic
609	C₂	C₁₃×#3036	1	1	yes	characteristic
610	C₂	C₁₃×#3044	1	1	yes	characteristic
611	C₂	C₁₃×#3343	1	1	yes	characteristic
612	C₂	C₁₃×#3349	1	1	yes	characteristic
613	C₂	C₁₃×#3352	1	1	yes	characteristic
614	C₂	C₁₃×#3353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2083	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2066	C₂	semidirect
9. C₁₃×#1949	C₂	semidirect
10. C₁₃×#1947	C₂	semidirect
11. C₁₃×#1928	C₂	semidirect
12. C₁₃×#1927	C₂	semidirect
127. #24588	C₁₃	direct (N × H)
207. #2085	C₂×C₁₃	semidirect
208. #2083	C₂×C₁₃	semidirect
209. #2068	C₂×C₁₃	semidirect
210. #2066	C₂×C₁₃	semidirect
211. #1949	C₂×C₁₃	semidirect
212. #1947	C₂×C₁₃	semidirect
213. #1928	C₂×C₁₃	semidirect
214. #1927	C₂×C₁₃	semidirect
509. C₁₃	#24588	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×#484	2
C₂×C₁₃×#428	2
C₁₃×#2499	2
C₁₃×#2344	2
C₁₃×#2085	2
C₁₃×#2083	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#1949	2
C₁₃×#1947	2
C₁₃×#1928	2
C₁₃×#1927	2
C₁₃×#1894	2
C₁₃×#1851	2
C₁₃×#1825	2
#24588	13

Subgroups — C13×#24588 #15710927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24588 #15710927