Subgroups — C₁₃×#26264 #15712603

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2445	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#123	—	2	2	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#493	—	2	4	no	—
19	C₁₃×#442	—	2	4	no	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#394	—	2	2	no	—
31	C₁₃×#394	—	2	2	no	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#389	C₂²	1	2	yes	—
36	C₁₃×#386	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	—	2	2	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	4	no	—
47	C₂×C₁₃×D₈	—	2	2	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	4	2	no	—
54	C₂×C₁₃×D₈	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#127	—	2	4	no	—
60	C₁₃×#127	—	4	2	no	—
61	C₁₃×#123	—	4	8	no	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	—	4	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	4	2	no	—
83	C₁₃×#102	—	4	2	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₁₃×#97	—	2	2	no	—
86	C₁₃×#97	—	2	2	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	2	yes	—
90	#26264	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	2	no	—
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	4	4	no	—
105	C₂×D₄×C₁₃	—	4	4	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	8	2	no	—
109	C₂×D₄×C₁₃	—	8	2	no	—
110	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	—	8	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×D₈	—	2	8	no	—
122	C₁₃×D₈	—	4	8	no	—
123	C₁₃×D₈	—	4	4	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃	#41	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₂×C₈×C₁₃	#41	1	2	yes	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	8	2	no	—
147	C₁₃×C₂²⋊C₄	—	8	2	no	—
148	C₁₃×C₂²⋊C₄	—	8	2	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	2	1	no	—
154	C₄²×C₁₃	—	2	1	no	—
155	C₂×#493	C₂×C₁₃	1	1	yes	characteristic
156	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2445	C₂×C₁₃	1	2	yes	complemented
158	#2054	C₂×C₁₃	1	2	yes	complemented
159	#2041	C₂×C₁₃	1	2	yes	complemented
160	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1879	C₂×C₁₃	1	2	yes	complemented
165	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂³×C₁₃	—	2	4	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	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	8	8	no	—
190	D₄×C₁₃	—	8	8	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	8	8	no	—
207	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₈×C₁₃	—	2	2	no	—
215	C₈×C₁₃	—	4	1	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₈×C₁₃	#123	1	4	yes	complemented
218	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
220	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#127	C₂²×C₁₃	1	2	yes	—
222	C₂×#123	—	2	2	no	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
224	#493	—	2	4	no	—
225	#442	—	2	4	no	—
226	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#102	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×#102	C₂²×C₁₃	1	2	yes	—
232	C₂×#102	C₂²×C₁₃	1	2	yes	—
233	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
236	#394	—	2	2	no	—
237	#394	—	2	2	no	—
238	#390	C₂²×C₁₃	1	2	yes	—
239	#390	C₂²×C₁₃	1	2	yes	—
240	#390	C₂²×C₁₃	1	2	yes	—
241	#389	C₂²×C₁₃	1	2	yes	—
242	#386	—	2	2	no	—
243	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	#340	C₂²×C₁₃	1	2	yes	—
245	#336	C₂²×C₁₃	1	1	yes	characteristic
246	#336	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	8	2	no	—
254	C₂²×C₁₃	—	8	2	no	—
255	C₂²×C₁₃	—	8	2	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	2	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	—	8	2	no	—
261	C₂²×C₁₃	#532	1	1	yes	characteristic
262	C₂²×C₁₃	D₄²	1	1	yes	characteristic
263	C₂²×C₁₃	#550	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
265	C₂²×C₁₃	#576	1	2	yes	—
266	C₄×C₁₃	—	2	4	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	—	8	2	no	—
272	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
273	C₄×C₁₃	#540	1	1	yes	characteristic
274	C₄×C₁₃	#546	1	1	yes	characteristic
275	C₄×C₁₃	#559	1	1	yes	characteristic
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
279	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
280	C₂³×C₄	—	2	2	no	—
281	C₂×D₈	—	2	4	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	4	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	4	2	no	—
289	C₂×D₈	D₄×C₁₃	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	#127	—	2	4	no	—
295	#127	—	4	2	no	—
296	#123	—	4	8	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	4	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	#106	—	2	2	no	—
314	#106	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	#102	—	2	4	no	—
317	#102	—	4	2	no	—
318	#102	—	4	2	no	—
319	#102	—	4	2	no	—
320	#97	—	2	2	no	—
321	#97	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	D₄×C₁₃	1	2	yes	—
325	C₂×C₁₃	—	8	4	no	—
326	C₂×C₁₃	—	16	2	no	—
327	C₂×C₁₃	#2445	1	1	yes	characteristic
328	C₂×C₁₃	#3176	1	1	yes	characteristic
329	C₂×C₁₃	#3184	1	1	yes	characteristic
330	C₂×C₁₃	#3264	1	2	yes	—
331	C₂×C₁₃	#3399	1	2	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	8	2	no	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
362	D₈	—	2	8	no	—
363	D₈	—	4	8	no	—
364	D₈	—	4	4	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×C₈	C₁₃×#41	1	2	yes	—
375	C₂×C₈	C₁₃×#41	1	2	yes	—
376	C₂×C₈	C₁₃×#41	1	2	yes	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	8	2	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₁₃	#26264	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	8	no	—
421	D₄	—	8	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	8	no	—
438	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
441	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
442	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
443	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	C₁₃×#123	1	4	yes	complemented
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₁₃×#532	1	1	yes	characteristic
464	C₂²	D₄²×C₁₃	1	1	yes	characteristic
465	C₂²	C₁₃×#550	1	1	yes	characteristic
466	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
467	C₂²	C₁₃×#576	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	1	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
475	C₄	C₁₃×#540	1	1	yes	characteristic
476	C₄	C₁₃×#546	1	1	yes	characteristic
477	C₄	C₁₃×#559	1	1	yes	characteristic
478	C₂	—	8	4	no	—
479	C₂	—	16	2	no	—
480	C₂	C₁₃×#2445	1	1	yes	characteristic
481	C₂	C₁₃×#3176	1	1	yes	characteristic
482	C₂	C₁₃×#3184	1	1	yes	characteristic
483	C₂	C₁₃×#3264	1	2	yes	—
484	C₂	C₁₃×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#493	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊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×#2445	C₂	semidirect
4. C₁₃×#2054	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#1972	C₂	semidirect
7. C₁₃×#1972	C₂	semidirect
8. C₁₃×#1972	C₂	semidirect
9. C₁₃×#1941	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₁₃×#1771	C₂	semidirect
90. #26264	C₁₃	direct (N × H)
156. C₂×#442	C₂×C₁₃	semidirect
157. #2445	C₂×C₁₃	semidirect
158. #2054	C₂×C₁₃	semidirect
159. #2041	C₂×C₁₃	semidirect
160. #1972	C₂×C₁₃	semidirect
161. #1972	C₂×C₁₃	semidirect
162. #1972	C₂×C₁₃	semidirect
163. #1941	C₂×C₁₃	semidirect
164. #1879	C₂×C₁₃	semidirect
165. #1771	C₂×C₁₃	semidirect
217. C₈×C₁₃	#123	semidirect
396. C₁₃	#26264	direct (N × H)
448. 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×#493	2
C₂×C₁₃×#442	2
C₁₃×#2445	2
C₁₃×#2054	2
C₁₃×#2041	2
C₁₃×#1972	2
C₁₃×#1941	2
C₁₃×#1879	2
C₁₃×#1771	2
#26264	13

Subgroups — C13×#26264 #15712603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26264 #15712603