Subgroups — C₁₃×#24184 #15710523

Order 3328.

1462 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×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2011	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1879	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
15	C₁₃×#550	—	2	4	no	—
16	C₁₃×#550	—	2	4	no	—
17	C₂×C₁₃×#127	C₂²	1	2	yes	—
18	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×#121	—	2	1	no	—
21	C₂×C₁₃×#121	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#459	—	2	4	no	—
27	C₄×C₁₃×D₈	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#396	—	2	2	no	—
38	C₁₃×#390	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#384	C₂²	1	1	yes	characteristic
41	C₁₃×#380	—	2	1	no	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂×C₁₃×#41	—	4	4	no	—
48	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	—	2	2	no	—
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	—	2	1	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₂×C₁₃×D₈	—	2	4	no	—
62	C₂×C₁₃×D₈	—	2	4	no	—
63	C₂×C₁₃×D₈	—	2	2	no	—
64	C₂×C₁₃×D₈	—	4	2	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#127	—	2	4	no	—
69	C₁₃×#127	—	2	4	no	—
70	C₁₃×#127	—	2	2	no	—
71	C₁₃×#127	D₄	1	4	yes	—
72	C₁₃×C₂²⋊Q₈	—	4	4	no	—
73	C₁₃×#121	—	2	8	no	—
74	C₁₃×#121	—	2	16	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	4	no	—
78	C₄×D₄×C₁₃	—	2	4	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	D₄	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#107	—	2	2	no	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#102	—	2	4	no	—
102	C₁₃×#102	—	2	4	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	4	2	no	—
105	C₁₃×#102	—	4	2	no	—
106	C₄×C₈×C₁₃	—	2	2	no	—
107	C₁₃×#95	—	2	2	no	—
108	#24184	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	1	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	1	no	—
112	C₁₃×#41	—	4	32	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	D₈	1	4	yes	complemented
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	4	4	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	8	1	no	—
140	C₂×D₄×C₁₃	—	8	1	no	—
141	C₂×D₄×C₁₃	—	8	2	no	—
142	C₂×D₄×C₁₃	—	8	2	no	—
143	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₁₃	#41	1	2	yes	complemented
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×D₈	—	2	8	no	—
164	C₁₃×D₈	—	4	8	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	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	#41	1	2	yes	complemented
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	4	2	no	—
182	C₁₃×C₄⋊C₄	—	4	4	no	—
183	C₁₃×C₄⋊C₄	—	8	1	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	4	2	no	—
188	C₁₃×C₂²⋊C₄	—	4	4	no	—
189	C₁₃×C₂²⋊C₄	—	8	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2538	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#2041	C₂×C₁₃	1	2	yes	complemented
199	#2011	C₂×C₁₃	1	2	yes	complemented
200	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1879	C₂×C₁₃	1	2	yes	complemented
203	#1862	C₂×C₁₃	1	2	yes	complemented
204	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	4	1	no	—
221	C₂³×C₁₃	—	4	2	no	—
222	C₂³×C₁₃	—	4	1	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	8	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	2	4	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	4	16	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	8	no	—
242	D₄×C₁₃	—	8	4	no	—
243	D₄×C₁₃	—	8	8	no	—
244	C₂×C₄×C₁₃	—	2	2	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	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	16	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	8	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	8	4	no	—
263	C₂×C₄×C₁₃	#120	1	2	yes	—
264	C₂×C₄×C₁₃	#120	1	2	yes	—
265	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
266	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
267	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	2	no	—
277	C₂²×#41	—	2	1	no	—
278	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
280	#550	—	2	4	no	—
281	#550	—	2	4	no	—
282	C₂×#127	C₂²×C₁₃	1	2	yes	—
283	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊Q₈	—	2	1	no	—
285	C₂×#121	—	2	1	no	—
286	C₂×#121	—	2	2	no	—
287	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
289	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
291	#459	—	2	4	no	—
292	C₄×D₈	—	2	4	no	—
293	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₁₃	1	2	yes	—
296	C₂×#102	C₂²×C₁₃	1	2	yes	—
297	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#102	C₂²×C₁₃	1	2	yes	—
300	C₂×#102	C₂²×C₁₃	1	2	yes	—
301	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
302	#396	—	2	2	no	—
303	#390	C₂²×C₁₃	1	2	yes	—
304	#389	C₂²×C₁₃	1	2	yes	—
305	#384	C₂²×C₁₃	1	1	yes	characteristic
306	#380	—	2	1	no	—
307	#340	C₂²×C₁₃	1	2	yes	—
308	#336	C₂²×C₁₃	1	2	yes	—
309	#336	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	2	no	—
321	C₂²×C₁₃	—	8	2	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	—	8	2	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	2	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
332	C₂²×C₁₃	#548	1	1	yes	characteristic
333	C₂²×C₁₃	#550	1	1	yes	characteristic
334	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
335	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₂²×C₁₃	#576	1	1	yes	characteristic
337	C₂²×C₁₃	#577	1	1	yes	characteristic
338	C₄×C₁₃	—	2	4	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	8	2	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	#447	1	4	yes	—
345	C₄×C₁₃	#525	1	1	yes	characteristic
346	C₄×C₁₃	#537	1	1	yes	characteristic
347	C₄×C₁₃	#546	1	1	yes	characteristic
348	C₄×C₁₃	#547	1	1	yes	characteristic
349	C₂×#41	—	2	8	no	—
350	C₂×#41	—	4	4	no	—
351	C₂×#41	—	4	4	no	—
352	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
358	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×D₈	—	2	2	no	—
365	C₂×D₈	—	2	4	no	—
366	C₂×D₈	—	2	4	no	—
367	C₂×D₈	—	2	2	no	—
368	C₂×D₈	—	4	2	no	—
369	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	#127	—	2	4	no	—
373	#127	—	2	4	no	—
374	#127	—	2	2	no	—
375	#127	D₄×C₁₃	1	4	yes	—
376	C₂²⋊Q₈	—	4	4	no	—
377	#121	—	2	8	no	—
378	#121	—	2	16	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	D₄×C₁₃	1	4	yes	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	2	no	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
402	#107	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	4	no	—
406	#102	—	2	4	no	—
407	#102	—	2	2	no	—
408	#102	—	4	2	no	—
409	#102	—	4	2	no	—
410	C₄×C₈	—	2	2	no	—
411	#95	—	2	2	no	—
412	C₂×C₁₃	—	8	2	no	—
413	C₂×C₁₃	—	8	2	no	—
414	C₂×C₁₃	—	8	4	no	—
415	C₂×C₁₃	#2407	1	1	yes	characteristic
416	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
417	C₂×C₁₃	#3012	1	1	yes	characteristic
418	C₂×C₁₃	#3358	1	1	yes	characteristic
419	C₂×C₁₃	#3366	1	1	yes	characteristic
420	C₂×C₁₃	#3391	1	1	yes	characteristic
421	C₂×C₁₃	#3397	1	1	yes	characteristic
422	C₂⁴	—	2	1	no	—
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	2	1	no	—
425	#41	—	4	32	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	C₁₃×D₈	1	4	yes	complemented
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	8	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	8	1	no	—
453	C₂×D₄	—	8	1	no	—
454	C₂×D₄	—	8	2	no	—
455	C₂×D₄	—	8	2	no	—
456	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
457	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂×D₄	C₁₃×#41	1	2	yes	complemented
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	2	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
476	D₈	—	2	8	no	—
477	D₈	—	4	8	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	C₁₃×#41	1	2	yes	complemented
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	4	no	—
496	C₄⋊C₄	—	8	1	no	—
497	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	4	no	—
502	C₂²⋊C₄	—	8	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	2	no	—
505	C₄²	C₂×D₄×C₁₃	1	2	yes	—
506	C₄²	C₂×D₄×C₁₃	1	2	yes	—
507	C₁₃	#24184	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	2	4	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	Q₈	—	2	8	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	16	no	—
538	D₄	—	4	8	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	8	4	no	—
546	D₄	—	8	8	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	16	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	C₁₃×#120	1	2	yes	—
567	C₂×C₄	C₁₃×#120	1	2	yes	—
568	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
569	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
570	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
574	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
575	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	8	2	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	2	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	2	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
602	C₂²	C₁₃×#548	1	1	yes	characteristic
603	C₂²	C₁₃×#550	1	1	yes	characteristic
604	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
605	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
606	C₂²	C₁₃×#576	1	1	yes	characteristic
607	C₂²	C₁₃×#577	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	4	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	8	2	no	—
613	C₄	—	8	1	no	—
614	C₄	C₁₃×#447	1	4	yes	—
615	C₄	C₁₃×#525	1	1	yes	characteristic
616	C₄	C₁₃×#537	1	1	yes	characteristic
617	C₄	C₁₃×#546	1	1	yes	characteristic
618	C₄	C₁₃×#547	1	1	yes	characteristic
619	C₂	—	8	4	no	—
620	C₂	—	8	2	no	—
621	C₂	—	8	2	no	—
622	C₂	C₁₃×#2407	1	1	yes	characteristic
623	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
624	C₂	C₁₃×#3012	1	1	yes	characteristic
625	C₂	C₁₃×#3358	1	1	yes	characteristic
626	C₂	C₁₃×#3366	1	1	yes	characteristic
627	C₂	C₁₃×#3391	1	1	yes	characteristic
628	C₂	C₁₃×#3397	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#550	C₂	semidirect
2. C₂×C₁₃×#459	C₂	semidirect
3. C₂×C₄×C₁₃×D₈	C₂	semidirect
4. C₁₃×#2538	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#2011	C₂	semidirect
7. C₁₃×#1984	C₂	semidirect
8. C₁₃×#1957	C₂	semidirect
9. C₁₃×#1879	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
108. #24184	C₁₃	direct (N × H)
115. C₂×Q₈×C₁₃	D₈	semidirect
145. C₂×D₄×C₁₃	#41	semidirect
173. C₂×C₈×C₁₃	#41	semidirect
194. C₂×#550	C₂×C₁₃	semidirect
195. C₂×#459	C₂×C₁₃	semidirect
196. C₂×C₄×D₈	C₂×C₁₃	semidirect
197. #2538	C₂×C₁₃	semidirect
198. #2041	C₂×C₁₃	semidirect
199. #2011	C₂×C₁₃	semidirect
200. #1984	C₂×C₁₃	semidirect
201. #1957	C₂×C₁₃	semidirect
202. #1879	C₂×C₁₃	semidirect
203. #1862	C₂×C₁₃	semidirect
204. #1802	C₂×C₁₃	semidirect
428. C₂×Q₈	C₁₃×D₈	semidirect
458. C₂×D₄	C₁₃×#41	semidirect
486. C₂×C₈	C₁₃×#41	semidirect
507. C₁₃	#24184	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×#550	2
C₂×C₁₃×#459	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2538	2
C₁₃×#2041	2
C₁₃×#2011	2
C₁₃×#1984	2
C₁₃×#1957	2
C₁₃×#1879	2
C₁₃×#1862	2
C₁₃×#1802	2
#24184	13

Subgroups — C13×#24184 #15710523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24184 #15710523