Subgroups — C₁₃×#24782 #15711121

Order 3328.

1124 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2416	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	2	no	—
16	C₂×C₁₃×#121	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₁₃×#469	—	2	4	no	—
21	C₁₃×#466	—	2	4	no	—
22	C₁₃×#435	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	—	2	4	no	—
25	C₂×C₁₃×#106	C₂²	1	2	yes	—
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×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#394	—	2	2	no	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#386	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₃	—	2	2	no	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#121	—	2	4	no	—
64	C₁₃×#121	—	2	4	no	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	4	2	no	—
67	C₁₃×#121	—	4	8	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#107	—	2	2	no	—
87	C₁₃×#106	—	2	2	no	—
88	C₁₃×#106	—	2	4	no	—
89	C₁₃×#106	D₄	1	4	yes	complemented
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	4	no	—
93	C₁₃×#102	—	4	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#24782	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	—	2	2	no	—
101	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	8	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	4	4	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	8	2	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	#41	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×D₈	—	4	4	no	—
141	C₁₃×M₁₆	—	4	4	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	8	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	#41	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	4	no	—
167	C₁₃×C₂²⋊C₄	—	4	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	8	2	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2416	C₂×C₁₃	1	2	yes	complemented
178	#2065	C₂×C₁₃	1	2	yes	complemented
179	#2034	C₂×C₁₃	1	2	yes	complemented
180	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1944	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1874	C₂×C₁₃	1	2	yes	complemented
183	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	2	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	#121	1	2	yes	—
200	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	D₄×C₁₃	—	4	4	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	8	8	no	—
208	D₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	8	8	no	—
236	C₂×C₄×C₁₃	#121	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	4	1	no	—
245	C₈×C₁₃	—	4	1	no	—
246	C₈×C₁₃	#121	1	4	yes	complemented
247	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#121	—	2	2	no	—
251	C₂×#121	C₂²×C₁₃	1	2	yes	—
252	C₂×#121	C₂²×C₁₃	1	2	yes	—
253	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
255	#469	—	2	4	no	—
256	#466	—	2	4	no	—
257	#435	—	2	4	no	—
258	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#106	—	2	4	no	—
260	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#106	C₂²×C₁₃	1	2	yes	—
262	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#102	C₂²×C₁₃	1	2	yes	—
265	C₂×#102	C₂²×C₁₃	1	2	yes	—
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
270	#396	—	2	2	no	—
271	#394	—	2	2	no	—
272	#390	C₂²×C₁₃	1	2	yes	—
273	#389	C₂²×C₁₃	1	2	yes	—
274	#386	—	2	2	no	—
275	#380	C₂²×C₁₃	1	2	yes	—
276	#340	C₂²×C₁₃	1	2	yes	—
277	#340	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₁₃	—	2	4	no	—
279	C₂²×C₁₃	—	2	2	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	—	8	2	no	—
288	C₂²×C₁₃	—	8	2	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	—	8	2	no	—
292	C₂²×C₁₃	—	8	2	no	—
293	C₂²×C₁₃	—	8	2	no	—
294	C₂²×C₁₃	#469	1	4	yes	complemented
295	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
296	C₂²×C₁₃	D₄²	1	1	yes	characteristic
297	C₂²×C₁₃	#547	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
299	C₂²×C₁₃	#577	1	2	yes	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	4	1	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₄×C₁₃	—	4	1	no	—
304	C₄×C₁₃	—	4	1	no	—
305	C₄×C₁₃	—	8	2	no	—
306	C₄×C₁₃	—	8	2	no	—
307	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
308	C₄×C₁₃	#537	1	1	yes	characteristic
309	C₄×C₁₃	#548	1	1	yes	characteristic
310	C₄×C₁₃	#553	1	1	yes	characteristic
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
314	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
327	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	#121	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	4	2	no	—
335	#121	—	4	8	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	4	2	no	—
342	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
354	#107	—	2	2	no	—
355	#106	—	2	2	no	—
356	#106	—	2	4	no	—
357	#106	D₄×C₁₃	1	4	yes	complemented
358	C₄⋊C₈	—	2	2	no	—
359	#102	—	2	4	no	—
360	#102	—	2	4	no	—
361	#102	—	4	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	#97	—	2	2	no	—
365	#95	—	2	2	no	—
366	#95	—	2	2	no	—
367	C₂×C₁₃	—	2	4	no	—
368	C₂×C₁₃	—	8	1	no	—
369	C₂×C₁₃	—	16	2	no	—
370	C₂×C₁₃	#2416	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#469	1	1	yes	characteristic
372	C₂×C₁₃	#3060	1	1	yes	characteristic
373	C₂×C₁₃	#3265	1	2	yes	—
374	C₂×C₁₃	#3345	1	2	yes	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	8	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	8	2	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₂²×C₄	C₁₃×#41	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
415	D₈	—	4	4	no	—
416	M₁₆	—	4	4	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	8	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
427	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
429	C₂×C₈	C₁₃×#41	1	2	yes	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	8	2	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₁₃	#24782	1	1	yes	characteristic, direct product factor, Sylow
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₁₃×#121	1	2	yes	—
465	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	8	8	no	—
473	D₄	—	8	8	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	C₁₃×#121	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
505	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
506	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	C₁₃×#121	1	4	yes	complemented
512	C₂²	—	2	4	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₁₃×#469	1	4	yes	complemented
529	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
530	C₂²	D₄²×C₁₃	1	1	yes	characteristic
531	C₂²	C₁₃×#547	1	1	yes	characteristic
532	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
533	C₂²	C₁₃×#577	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	8	2	no	—
540	C₄	—	8	2	no	—
541	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
542	C₄	C₁₃×#537	1	1	yes	characteristic
543	C₄	C₁₃×#548	1	1	yes	characteristic
544	C₄	C₁₃×#553	1	1	yes	characteristic
545	C₂	—	2	4	no	—
546	C₂	—	8	1	no	—
547	C₂	—	16	2	no	—
548	C₂	C₁₃×#2416	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#469	1	1	yes	characteristic
550	C₂	C₁₃×#3060	1	1	yes	characteristic
551	C₂	C₁₃×#3265	1	2	yes	—
552	C₂	C₁₃×#3345	1	2	yes	—

	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#469	C₂	semidirect
2. C₂×C₁₃×#466	C₂	semidirect
3. C₂×C₁₃×#435	C₂	semidirect
4. C₂²×C₁₃×#106	C₂	semidirect
5. C₁₃×#2416	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#1972	C₂	semidirect
9. C₁₃×#1944	C₂	semidirect
10. C₁₃×#1874	C₂	semidirect
11. C₁₃×#1809	C₂	semidirect
58. C₂²×C₈×C₁₃	D₄	semidirect
89. C₁₃×#106	D₄	semidirect
99. #24782	C₁₃	direct (N × H)
173. C₂×#469	C₂×C₁₃	semidirect
174. C₂×#466	C₂×C₁₃	semidirect
175. C₂×#435	C₂×C₁₃	semidirect
176. C₂²×#106	C₂×C₁₃	semidirect
177. #2416	C₂×C₁₃	semidirect
178. #2065	C₂×C₁₃	semidirect
179. #2034	C₂×C₁₃	semidirect
180. #1972	C₂×C₁₃	semidirect
181. #1944	C₂×C₁₃	semidirect
182. #1874	C₂×C₁₃	semidirect
183. #1809	C₂×C₁₃	semidirect
246. C₈×C₁₃	#121	semidirect
294. C₂²×C₁₃	#469	semidirect
326. C₂²×C₈	D₄×C₁₃	semidirect
357. #106	D₄×C₁₃	semidirect
448. C₁₃	#24782	direct (N × H)
511. C₈	C₁₃×#121	semidirect
528. C₂²	C₁₃×#469	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#435	2
C₂²×C₁₃×#106	2
C₁₃×#2416	2
C₁₃×#2065	2
C₁₃×#2034	2
C₁₃×#1972	2
C₁₃×#1944	2
C₁₃×#1874	2
C₁₃×#1809	2
#24782	13

Subgroups — C13×#24782 #15711121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24782 #15711121