Subgroups — C₁₃×#26041 #15712380

Order 3328.

862 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×#478	C₂	1	2	yes	maximal
2	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2087	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
16	C₁₃×#478	—	2	8	no	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#398	—	2	2	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#385	—	2	2	no	—
31	C₁₃×#384	—	2	1	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#380	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#125	—	2	4	no	—
49	C₁₃×#125	—	4	2	no	—
50	C₄×D₄×C₁₃	—	2	4	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	4	2	no	—
53	C₄×D₄×C₁₃	Q₈	1	4	yes	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#106	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	D₄	1	4	yes	—
82	C₁₃×#102	Q₈	1	4	yes	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	D₄	1	2	yes	—
88	#26041	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
95	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	4	4	no	—
103	C₂²×C₄×C₁₃	—	4	4	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	8	2	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	8	1	no	—
136	C₁₃×C₄⋊C₄	—	8	1	no	—
137	C₁₃×C₄⋊C₄	—	8	2	no	—
138	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
139	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	4	2	no	—
146	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
147	C₄²×C₁₃	#41	1	2	yes	—
148	C₂×#478	C₂×C₁₃	1	2	yes	—
149	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
150	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
151	#2087	C₂×C₁₃	1	2	yes	complemented
152	#2059	C₂×C₁₃	1	2	yes	complemented
153	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1862	C₂×C₁₃	1	2	yes	—
156	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1802	C₂×C₁₃	1	1	yes	characteristic
158	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	C₄⋊Q₈	1	4	yes	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	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	8	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	—	8	8	no	—
196	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₁₃	#135	1	2	yes	—
199	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×Q₈	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	—	2	2	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₂×#125	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	—	2	1	no	—
213	#478	—	2	8	no	—
214	C₂×#107	C₂²×C₁₃	1	2	yes	—
215	C₂×#107	C₂²×C₁₃	1	2	yes	—
216	C₂×#106	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	#398	—	2	2	no	—
224	#389	—	2	1	no	—
225	#389	C₂²×C₁₃	1	2	yes	—
226	#389	C₂²×C₁₃	1	2	yes	—
227	#385	—	2	2	no	—
228	#384	—	2	1	no	—
229	#384	C₂²×C₁₃	1	1	yes	characteristic
230	#384	C₂²×C₁₃	1	1	yes	characteristic
231	#380	—	2	1	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	#340	C₂²×C₁₃	1	2	yes	—
235	#340	C₂²×C₁₃	1	1	yes	characteristic
236	#340	C₂²×C₁₃	1	1	yes	characteristic
237	#340	C₂²×C₁₃	1	2	yes	—
238	#336	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
247	C₂²×C₁₃	D₄²	1	1	yes	characteristic
248	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂²×C₁₃	#576	1	1	yes	characteristic
252	C₂²×C₁₃	#578	1	1	yes	characteristic
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	#478	1	4	yes	complemented
262	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
263	C₄×C₁₃	#544	1	1	yes	characteristic
264	C₄×C₁₃	#547	1	1	yes	characteristic
265	C₄×C₁₃	#554	1	1	yes	characteristic
266	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	#125	—	2	4	no	—
273	#125	—	4	2	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	4	2	no	—
277	C₄×D₄	Q₈×C₁₃	1	4	yes	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	4	4	no	—
287	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	#107	—	2	4	no	—
300	#107	—	4	2	no	—
301	#106	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#102	—	2	4	no	—
305	#102	D₄×C₁₃	1	4	yes	—
306	#102	Q₈×C₁₃	1	4	yes	—
307	C₄×C₈	—	2	2	no	—
308	#95	—	2	1	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	D₄×C₁₃	1	2	yes	—
312	C₂×C₁₃	—	4	4	no	—
313	C₂×C₁₃	#2440	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
315	C₂×C₁₃	#3083	1	1	yes	characteristic
316	C₂×C₁₃	#3274	1	1	yes	characteristic
317	C₂×C₁₃	#3283	1	1	yes	characteristic
318	C₂×C₁₃	#3380	1	1	yes	characteristic
319	C₂×C₁₃	#3386	1	1	yes	characteristic
320	C₂⁴	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
326	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	—	8	2	no	—
369	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
371	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	4	2	no	—
377	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
378	C₄²	C₁₃×#41	1	2	yes	—
379	C₁₃	#26041	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	D₄	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	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	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	8	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	—	8	8	no	—
417	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
418	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
419	C₂×C₄	C₁₃×#135	1	2	yes	—
420	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×Q₈×C₁₃	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	—	2	2	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂²	D₄²×C₁₃	1	1	yes	characteristic
439	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
440	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
441	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
442	C₂²	C₁₃×#576	1	1	yes	characteristic
443	C₂²	C₁₃×#578	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₁₃×#478	1	4	yes	complemented
453	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
454	C₄	C₁₃×#544	1	1	yes	characteristic
455	C₄	C₁₃×#547	1	1	yes	characteristic
456	C₄	C₁₃×#554	1	1	yes	characteristic
457	C₂	—	4	4	no	—
458	C₂	C₁₃×#2440	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
460	C₂	C₁₃×#3083	1	1	yes	characteristic
461	C₂	C₁₃×#3274	1	1	yes	characteristic
462	C₂	C₁₃×#3283	1	1	yes	characteristic
463	C₂	C₁₃×#3380	1	1	yes	characteristic
464	C₂	C₁₃×#3386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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. C₁₃×#2552	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#1948	C₂	semidirect
7. C₁₃×#1939	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
88. #26041	C₁₃	direct (N × H)
149. #2552	C₂×C₁₃	semidirect
151. #2087	C₂×C₁₃	semidirect
152. #2059	C₂×C₁₃	semidirect
153. #1948	C₂×C₁₃	semidirect
154. #1939	C₂×C₁₃	semidirect
156. #1845	C₂×C₁₃	semidirect
261. C₄×C₁₃	#478	semidirect
379. C₁₃	#26041	direct (N × H)
452. C₄	C₁₃×#478	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#478	2
C₁₃×#2552	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2087	2
C₁₃×#2059	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1862	2
C₁₃×#1845	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#26041	13

Subgroups — C13×#26041 #15712380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26041 #15712380