Subgroups — C₁₃×#24118 #15710457

Order 3328.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2000	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1853	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#554	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	—	2	1	no	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#476	—	2	4	no	—
27	C₄×C₁₃×SD₁₆	—	2	4	no	—
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×#106	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	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#394	—	2	2	no	—
39	C₁₃×#384	C₂²	1	1	yes	characteristic
40	C₁₃×#380	—	2	1	no	—
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	4	yes	complemented
61	C₁₃×#125	—	2	8	no	—
62	C₁₃×C₂²⋊Q₈	—	2	16	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	4	2	no	—
67	C₁₃×#121	—	4	4	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
70	C₄×D₄×C₁₃	—	2	8	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#106	—	2	2	no	—
96	C₁₃×#106	—	2	4	no	—
97	C₁₃×C₄⋊C₈	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	4	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#102	—	2	4	no	—
102	C₁₃×C₂²⋊C₈	—	2	4	no	—
103	C₁₃×C₂²⋊C₈	—	4	2	no	—
104	C₄×C₈×C₁₃	—	2	2	no	—
105	C₁₃×#95	—	2	2	no	—
106	#24118	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	1	no	—
108	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₃	—	2	4	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	8	1	no	—
116	C₂×Q₈×C₁₃	—	8	1	no	—
117	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	8	2	no	—
128	C₂×D₄×C₁₃	SD₁₆	1	4	yes	complemented
129	C₂×D₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	—	4	2	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	8	2	no	—
146	C₂²×C₄×C₁₃	—	8	2	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×SD₁₆	—	2	8	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	#41	1	2	yes	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	4	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	8	1	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₃×C₂²⋊C₄	—	2	8	no	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	4	4	no	—
179	C₁₃×C₂²⋊C₄	—	4	4	no	—
180	C₁₃×C₂²⋊C₄	—	4	2	no	—
181	C₄²×C₁₃	—	2	4	no	—
182	C₄²×C₁₃	C₂×D₄	1	2	yes	—
183	C₄²×C₁₃	C₂×D₄	1	2	yes	—
184	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2537	C₂×C₁₃	1	1	yes	characteristic
188	#2035	C₂×C₁₃	1	2	yes	complemented
189	#2000	C₂×C₁₃	1	2	yes	complemented
190	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1874	C₂×C₁₃	1	2	yes	complemented
193	#1853	C₂×C₁₃	1	2	yes	complemented
194	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	—	4	1	no	—
207	C₂³×C₁₃	—	4	1	no	—
208	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	4	1	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	8	4	no	—
215	D₄×C₁₃	—	2	2	no	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	2	8	no	—
218	D₄×C₁₃	—	4	1	no	—
219	D₄×C₁₃	—	4	1	no	—
220	D₄×C₁₃	—	8	8	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	8	8	no	—
246	C₂×C₄×C₁₃	—	8	4	no	—
247	C₂×C₄×C₁₃	#120	1	2	yes	—
248	C₂×C₄×C₁₃	#120	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
250	C₂×C₄×C₁₃	#137	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	4	1	no	—
259	C₈×C₁₃	—	4	2	no	—
260	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
261	#554	—	2	4	no	—
262	#554	—	2	4	no	—
263	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#125	—	2	1	no	—
265	C₂×C₂²⋊Q₈	—	2	2	no	—
266	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂×#121	—	2	1	no	—
268	C₂×#121	C₂²×C₁₃	1	2	yes	—
269	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×D₄	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
274	#476	—	2	4	no	—
275	C₄×SD₁₆	—	2	4	no	—
276	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#106	C₂²×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#103	C₂²×C₁₃	1	2	yes	—
281	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#102	C₂²×C₁₃	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
285	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
286	#394	—	2	2	no	—
287	#384	C₂²×C₁₃	1	1	yes	characteristic
288	#380	—	2	1	no	—
289	#380	C₂²×C₁₃	1	2	yes	—
290	#340	C₂²×C₁₃	1	2	yes	—
291	#340	C₂²×C₁₃	1	2	yes	—
292	#340	C₂²×C₁₃	1	2	yes	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	2	4	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	8	1	no	—
306	C₂²×C₁₃	—	8	1	no	—
307	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
308	C₂²×C₁₃	#546	1	1	yes	characteristic
309	C₂²×C₁₃	#547	1	1	yes	characteristic
310	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
312	C₂²×C₁₃	#576	1	1	yes	characteristic
313	C₂²×C₁₃	#577	1	1	yes	characteristic
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	8	1	no	—
320	C₄×C₁₃	—	8	2	no	—
321	C₄×C₁₃	#448	1	4	yes	—
322	C₄×C₁₃	#525	1	1	yes	characteristic
323	C₄×C₁₃	#537	1	1	yes	characteristic
324	C₄×C₁₃	#548	1	1	yes	characteristic
325	C₄×C₁₃	#550	1	1	yes	characteristic
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
330	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	2	no	—
341	C₄⋊Q₈	D₄×C₁₃	1	4	yes	complemented
342	#125	—	2	8	no	—
343	C₂²⋊Q₈	—	2	16	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	—	2	4	no	—
346	#121	—	2	4	no	—
347	#121	—	4	2	no	—
348	#121	—	4	4	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
351	C₄×D₄	—	2	8	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#106	—	2	2	no	—
377	#106	—	2	4	no	—
378	C₄⋊C₈	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	4	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	4	no	—
383	C₂²⋊C₈	—	2	4	no	—
384	C₂²⋊C₈	—	4	2	no	—
385	C₄×C₈	—	2	2	no	—
386	#95	—	2	2	no	—
387	C₂×C₁₃	—	4	4	no	—
388	C₂×C₁₃	—	8	2	no	—
389	C₂×C₁₃	#2407	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
391	C₂×C₁₃	#3012	1	1	yes	characteristic
392	C₂×C₁₃	#3295	1	1	yes	characteristic
393	C₂×C₁₃	#3331	1	1	yes	characteristic
394	C₂×C₁₃	#3335	1	1	yes	characteristic
395	C₂×C₁₃	#3357	1	1	yes	characteristic
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	8	1	no	—
405	C₂×Q₈	—	8	1	no	—
406	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	8	2	no	—
417	C₂×D₄	C₁₃×SD₁₆	1	4	yes	complemented
418	C₂×D₄	C₁₃×#41	1	2	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	8	2	no	—
435	C₂²×C₄	—	8	2	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	SD₁₆	—	2	8	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	C₁₃×#41	1	2	yes	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₄⋊C₄	—	8	1	no	—
463	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	4	4	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₄²	—	2	4	no	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₂×D₄×C₁₃	1	2	yes	—
473	C₁₃	#24118	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	2	2	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	8	4	no	—
494	D₄	—	2	8	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	8	8	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	8	8	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	C₁₃×#120	1	2	yes	—
527	C₂×C₄	C₁₃×#120	1	2	yes	—
528	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
529	C₂×C₄	C₁₃×#137	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
533	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
534	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
554	C₂²	C₁₃×#546	1	1	yes	characteristic
555	C₂²	C₁₃×#547	1	1	yes	characteristic
556	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
557	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
558	C₂²	C₁₃×#576	1	1	yes	characteristic
559	C₂²	C₁₃×#577	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	2	no	—
566	C₄	—	8	1	no	—
567	C₄	C₁₃×#448	1	4	yes	—
568	C₄	C₁₃×#525	1	1	yes	characteristic
569	C₄	C₁₃×#537	1	1	yes	characteristic
570	C₄	C₁₃×#548	1	1	yes	characteristic
571	C₄	C₁₃×#550	1	1	yes	characteristic
572	C₂	—	4	4	no	—
573	C₂	—	8	2	no	—
574	C₂	C₁₃×#2407	1	1	yes	characteristic
575	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
576	C₂	C₁₃×#3012	1	1	yes	characteristic
577	C₂	C₁₃×#3295	1	1	yes	characteristic
578	C₂	C₁₃×#3331	1	1	yes	characteristic
579	C₂	C₁₃×#3335	1	1	yes	characteristic
580	C₂	C₁₃×#3357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2537	C₂
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×#554	C₂	semidirect
2. C₂×C₁₃×#476	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#2035	C₂	semidirect
6. C₁₃×#2000	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1954	C₂	semidirect
9. C₁₃×#1874	C₂	semidirect
10. C₁₃×#1853	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
60. C₁₃×C₄⋊Q₈	D₄	semidirect
69. C₄×Q₈×C₁₃	D₄	semidirect
106. #24118	C₁₃	direct (N × H)
128. C₂×D₄×C₁₃	SD₁₆	semidirect
184. C₂×#554	C₂×C₁₃	semidirect
185. C₂×#476	C₂×C₁₃	semidirect
186. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
188. #2035	C₂×C₁₃	semidirect
189. #2000	C₂×C₁₃	semidirect
190. #1990	C₂×C₁₃	semidirect
191. #1954	C₂×C₁₃	semidirect
192. #1874	C₂×C₁₃	semidirect
193. #1853	C₂×C₁₃	semidirect
194. #1803	C₂×C₁₃	semidirect
341. C₄⋊Q₈	D₄×C₁₃	semidirect
350. C₄×Q₈	D₄×C₁₃	semidirect
417. C₂×D₄	C₁₃×SD₁₆	semidirect
473. C₁₃	#24118	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×#554	2
C₂×C₁₃×#476	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2537	2
C₁₃×#2035	2
C₁₃×#2000	2
C₁₃×#1990	2
C₁₃×#1954	2
C₁₃×#1874	2
C₁₃×#1853	2
C₁₃×#1803	2
#24118	13

Subgroups — C13×#24118 #15710457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24118 #15710457