Subgroups — C₁₃×#25046 #15711385

Order 3328.

944 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×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2422	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1753	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	C₂×C₁₃×#123	—	2	2	no	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#469	—	2	4	no	—
18	C₁₃×#442	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#397	—	2	2	no	—
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#385	—	2	2	no	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	D₄	1	4	yes	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#123	—	4	8	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	4	2	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	4	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	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#106	—	2	2	no	—
76	C₁₃×#106	—	2	2	no	—
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×C₂²⋊C₈	—	2	2	no	—
82	C₁₃×#97	—	2	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	D₄	1	2	yes	—
87	#25046	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	4	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	—	8	2	no	—
98	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	8	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×D₈	—	2	8	no	—
116	C₁₃×M₁₆	—	4	4	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₂×C₈×C₁₃	#41	1	2	yes	—
128	C₂×C₈×C₁₃	#41	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	8	2	no	—
138	C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	—	4	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₂×#469	C₂×C₁₃	1	1	yes	characteristic
149	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2422	C₂×C₁₃	1	2	yes	complemented
151	#2071	C₂×C₁₃	1	2	yes	complemented
152	#2034	C₂×C₁₃	1	2	yes	complemented
153	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1864	C₂×C₁₃	1	2	yes	complemented
156	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	2	4	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	8	8	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	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	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	8	8	no	—
199	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	C₈×C₁₃	#123	1	4	yes	complemented
210	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#123	—	2	2	no	—
213	C₂×#121	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
215	#469	—	2	4	no	—
216	#442	—	2	4	no	—
217	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×#102	C₂²×C₁₃	1	2	yes	—
223	C₂×#102	C₂²×C₁₃	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	#397	—	2	2	no	—
228	#394	—	2	2	no	—
229	#390	C₂²×C₁₃	1	2	yes	—
230	#389	C₂²×C₁₃	1	2	yes	—
231	#385	—	2	2	no	—
232	#384	C₂²×C₁₃	1	2	yes	—
233	#380	C₂²×C₁₃	1	2	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	2	yes	—
236	#340	C₂²×C₁₃	1	2	yes	—
237	#336	C₂²×C₁₃	1	1	yes	characteristic
238	#336	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	#532	1	1	yes	characteristic
252	C₂²×C₁₃	D₄²	1	1	yes	characteristic
253	C₂²×C₁₃	#547	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
255	C₂²×C₁₃	#577	1	2	yes	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
263	C₄×C₁₃	#542	1	1	yes	characteristic
264	C₄×C₁₃	#547	1	1	yes	characteristic
265	C₄×C₁₃	#553	1	1	yes	characteristic
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×D₈	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	D₄×C₁₃	1	4	yes	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	#123	—	4	8	no	—
281	#121	—	2	4	no	—
282	#121	—	4	2	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	—	4	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	#106	—	2	2	no	—
302	#106	—	4	2	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	#97	—	2	2	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	D₄×C₁₃	1	2	yes	—
312	C₂×C₁₃	—	8	1	no	—
313	C₂×C₁₃	—	8	4	no	—
314	C₂×C₁₃	#2422	1	1	yes	characteristic
315	C₂×C₁₃	#3173	1	1	yes	characteristic
316	C₂×C₁₃	#3184	1	1	yes	characteristic
317	C₂×C₁₃	#3272	1	2	yes	—
318	C₂×C₁₃	#3345	1	2	yes	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	8	2	no	—
329	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	8	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
346	D₈	—	2	8	no	—
347	M₁₆	—	4	4	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
357	C₂×C₈	C₁₃×#41	1	2	yes	—
358	C₂×C₈	C₁₃×#41	1	2	yes	—
359	C₂×C₈	C₁₃×#41	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₁₃	#25046	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	1	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	8	8	no	—
420	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	1	no	—
430	C₈	C₁₃×#123	1	4	yes	complemented
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₁₃×#532	1	1	yes	characteristic
444	C₂²	D₄²×C₁₃	1	1	yes	characteristic
445	C₂²	C₁₃×#547	1	1	yes	characteristic
446	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
447	C₂²	C₁₃×#577	1	2	yes	—
448	C₄	—	2	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
455	C₄	C₁₃×#542	1	1	yes	characteristic
456	C₄	C₁₃×#547	1	1	yes	characteristic
457	C₄	C₁₃×#553	1	1	yes	characteristic
458	C₂	—	8	1	no	—
459	C₂	—	8	4	no	—
460	C₂	C₁₃×#2422	1	1	yes	characteristic
461	C₂	C₁₃×#3173	1	1	yes	characteristic
462	C₂	C₁₃×#3184	1	1	yes	characteristic
463	C₂	C₁₃×#3272	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×#469	C₂
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. C₂×C₁₃×#442	C₂	semidirect
3. C₁₃×#2422	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#1970	C₂	semidirect
7. C₁₃×#1943	C₂	semidirect
8. C₁₃×#1864	C₂	semidirect
9. C₁₃×#1844	C₂	semidirect
10. C₁₃×#1809	C₂	semidirect
11. C₁₃×#1753	C₂	semidirect
87. #25046	C₁₃	direct (N × H)
149. C₂×#442	C₂×C₁₃	semidirect
150. #2422	C₂×C₁₃	semidirect
151. #2071	C₂×C₁₃	semidirect
152. #2034	C₂×C₁₃	semidirect
153. #1970	C₂×C₁₃	semidirect
154. #1943	C₂×C₁₃	semidirect
155. #1864	C₂×C₁₃	semidirect
156. #1844	C₂×C₁₃	semidirect
157. #1809	C₂×C₁₃	semidirect
158. #1753	C₂×C₁₃	semidirect
209. C₈×C₁₃	#123	semidirect
379. C₁₃	#25046	direct (N × H)
430. C₈	C₁₃×#123	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×#442	2
C₁₃×#2422	2
C₁₃×#2071	2
C₁₃×#2034	2
C₁₃×#1970	2
C₁₃×#1943	2
C₁₃×#1864	2
C₁₃×#1844	2
C₁₃×#1809	2
C₁₃×#1753	2
#25046	13

Subgroups — C13×#25046 #15711385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25046 #15711385