Subgroups — C₁₃×#24578 #15710917

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2501	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1948	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#123	—	2	1	no	—
14	C₂×C₁₃×#123	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₁₃×#481	—	2	4	no	—
19	C₂×C₁₃×#106	—	2	4	no	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₃×#399	—	2	2	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#384	C₂²	1	2	yes	—
34	C₁₃×#380	—	2	1	no	—
35	C₁₃×#380	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×#123	—	4	4	no	—
54	C₁₃×#123	—	4	4	no	—
55	C₁₃×#121	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	D₄	1	2	yes	—
92	#24578	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₁₃	—	2	8	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	#41	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	4	no	—
140	C₁₃×C₄⋊C₄	—	8	2	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
143	C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	SD₁₆	1	4	yes	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	8	2	no	—
152	C₂×#481	C₂×C₁₃	1	1	yes	characteristic
153	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2501	C₂×C₁₃	1	1	yes	characteristic
155	#2345	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2084	C₂×C₁₃	1	2	yes	complemented
157	#2065	C₂×C₁₃	1	2	yes	complemented
158	#1948	C₂×C₁₃	1	2	yes	complemented
159	#1926	C₂×C₁₃	1	2	yes	complemented
160	#1893	C₂×C₁₃	1	1	yes	characteristic
161	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	#121	1	2	yes	—
171	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
172	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	4	1	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	8	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	8	4	no	—
201	C₂×C₄×C₁₃	—	8	4	no	—
202	C₂×C₄×C₁₃	#121	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
208	C₈×C₁₃	—	2	4	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#123	—	2	1	no	—
213	C₂×#123	—	2	1	no	—
214	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	#481	—	2	4	no	—
218	C₂×#106	—	2	4	no	—
219	C₂×#106	C₂²×C₁₃	1	2	yes	—
220	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#106	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
224	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#102	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
228	#399	—	2	2	no	—
229	#390	C₂²×C₁₃	1	2	yes	—
230	#389	C₂²×C₁₃	1	2	yes	—
231	#387	—	2	2	no	—
232	#384	C₂²×C₁₃	1	2	yes	—
233	#380	—	2	1	no	—
234	#380	C₂²×C₁₃	1	1	yes	characteristic
235	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
236	C₄×C₂²⋊C₄	—	2	1	no	—
237	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	2	yes	—
241	#336	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	1	no	—
249	C₂²×C₁₃	—	8	1	no	—
250	C₂²×C₁₃	—	8	1	no	—
251	C₂²×C₁₃	#460	1	4	yes	—
252	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
253	C₂²×C₁₃	#547	1	2	yes	—
254	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₁₃	#577	1	2	yes	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	#525	1	1	yes	characteristic
266	C₄×C₁₃	#536	1	1	yes	characteristic
267	C₄×C₁₃	#552	1	2	yes	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
278	#123	—	4	4	no	—
279	#123	—	4	4	no	—
280	#121	—	2	2	no	—
281	#121	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
304	#106	—	2	4	no	—
305	#106	—	2	4	no	—
306	#106	—	2	2	no	—
307	#106	—	2	2	no	—
308	C₄⋊C₈	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	1	no	—
316	#95	D₄×C₁₃	1	2	yes	—
317	C₂×C₁₃	—	2	4	no	—
318	C₂×C₁₃	—	16	1	no	—
319	C₂×C₁₃	#2413	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#460	1	1	yes	characteristic
321	C₂×C₁₃	#3042	1	1	yes	characteristic
322	C₂×C₁₃	#3335	1	2	yes	—
323	C₂×C₁₃	#3345	1	2	yes	—
324	C₂⁴	—	2	1	no	—
325	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	8	2	no	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₁₃×#41	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	C₂×C₈	—	2	8	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₁₃×#41	1	4	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	C₁₃×SD₁₆	1	4	yes	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	8	2	no	—
383	C₁₃	#24578	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₁₃×#121	1	2	yes	—
392	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
393	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	8	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	C₁₃×#121	1	2	yes	—
424	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
427	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
428	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
429	C₈	—	2	4	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₁₃×#460	1	4	yes	—
442	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
443	C₂²	C₁₃×#547	1	2	yes	—
444	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
445	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₂²	C₁₃×#577	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	C₁₃×#525	1	1	yes	characteristic
456	C₄	C₁₃×#536	1	1	yes	characteristic
457	C₄	C₁₃×#552	1	2	yes	—
458	C₂	—	2	4	no	—
459	C₂	—	16	1	no	—
460	C₂	C₁₃×#2413	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#460	1	1	yes	characteristic
462	C₂	C₁₃×#3042	1	1	yes	characteristic
463	C₂	C₁₃×#3335	1	2	yes	—
464	C₂	C₁₃×#3345	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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
2. C₂²×C₁₃×#106	C₂	semidirect
4. C₁₃×#2345	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1948	C₂	semidirect
8. C₁₃×#1926	C₂	semidirect
10. C₁₃×#1850	C₂	semidirect
11. C₁₃×#1823	C₂	semidirect
92. #24578	C₁₃	direct (N × H)
153. C₂²×#106	C₂×C₁₃	semidirect
155. #2345	C₂×C₁₃	semidirect
156. #2084	C₂×C₁₃	semidirect
157. #2065	C₂×C₁₃	semidirect
158. #1948	C₂×C₁₃	semidirect
159. #1926	C₂×C₁₃	semidirect
161. #1850	C₂×C₁₃	semidirect
162. #1823	C₂×C₁₃	semidirect
383. C₁₃	#24578	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×#481	2
C₂²×C₁₃×#106	2
C₁₃×#2501	2
C₁₃×#2345	2
C₁₃×#2084	2
C₁₃×#2065	2
C₁₃×#1948	2
C₁₃×#1926	2
C₁₃×#1893	2
C₁₃×#1850	2
C₁₃×#1823	2
#24578	13

Subgroups — C13×#24578 #15710917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24578 #15710917