Subgroups — C₁₃×#26111 #15712450

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2087	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1862	C₂	1	2	yes	maximal
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1804	C₂	1	2	yes	maximal
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#400	—	2	2	no	—
23	C₁₃×#389	—	2	1	no	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#385	—	2	2	no	—
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#382	—	2	1	no	—
30	C₁₃×#382	C₂²	1	2	yes	—
31	C₁₃×#380	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₄×D₄×C₁₃	—	2	4	no	—
48	C₄×D₄×C₁₃	—	2	2	no	—
49	C₄×D₄×C₁₃	—	4	2	no	—
50	C₄×D₄×C₁₃	Q₈	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	4	4	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	—	4	2	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	4	2	no	—
73	C₁₃×#102	—	2	2	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#102	—	2	2	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₁₃×#95	—	2	1	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	D₄	1	2	yes	—
83	#26111	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
89	C₂×D₄×C₁₃	#41	1	2	yes	—
90	C₂×D₄×C₁₃	#41	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	4	no	—
98	C₂²×C₄×C₁₃	—	4	4	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	—	8	2	no	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	8	1	no	—
131	C₁₃×C₄⋊C₄	—	8	1	no	—
132	C₁₃×C₄⋊C₄	—	8	2	no	—
133	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	4	2	no	—
139	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
140	C₄²×C₁₃	#41	1	2	yes	—
141	#2571	C₂×C₁₃	1	1	yes	characteristic, complemented
142	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
143	#2101	C₂×C₁₃	1	2	yes	complemented
144	#2087	C₂×C₁₃	1	2	yes	complemented
145	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1862	C₂×C₁₃	1	2	yes	—
148	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1804	C₂×C₁₃	1	2	yes	—
150	#1802	C₂×C₁₃	1	1	yes	characteristic
151	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	#125	1	4	yes	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	8	8	no	—
189	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₁₃	#135	1	2	yes	—
192	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₁₃	—	4	1	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
204	C₂²×C₄⋊C₄	—	2	1	no	—
205	C₂×#107	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
208	C₂×#102	C₂²×C₁₃	1	2	yes	—
209	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
212	#400	—	2	2	no	—
213	#389	—	2	1	no	—
214	#389	C₂²×C₁₃	1	2	yes	—
215	#389	C₂²×C₁₃	1	2	yes	—
216	#385	—	2	2	no	—
217	#384	C₂²×C₁₃	1	1	yes	characteristic
218	#384	C₂²×C₁₃	1	1	yes	characteristic
219	#382	—	2	1	no	—
220	#382	C₂²×C₁₃	1	2	yes	—
221	#380	—	2	1	no	—
222	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
224	#340	C₂²×C₁₃	1	2	yes	—
225	#340	C₂²×C₁₃	1	2	yes	—
226	#340	C₂²×C₁₃	1	2	yes	—
227	#340	C₂²×C₁₃	1	1	yes	characteristic
228	#340	C₂²×C₁₃	1	2	yes	—
229	#340	C₂²×C₁₃	1	1	yes	characteristic
230	#336	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₁₃	—	2	4	no	—
232	C₂²×C₁₃	—	4	2	no	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
239	C₂²×C₁₃	#546	1	1	yes	characteristic
240	C₂²×C₁₃	#548	1	1	yes	characteristic
241	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₁₃	#576	1	1	yes	characteristic
244	C₂²×C₁₃	#578	1	1	yes	characteristic
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	—	8	1	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	#478	1	4	yes	—
254	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
255	C₄×C₁₃	#544	1	1	yes	characteristic
256	C₄×C₁₃	#552	1	1	yes	characteristic
257	C₄×C₁₃	#553	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	4	2	no	—
267	C₄×D₄	Q₈×C₁₃	1	4	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	4	4	no	—
275	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	#107	—	4	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	4	2	no	—
290	#102	—	2	4	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	D₄×C₁₃	1	2	yes	—
300	C₂×C₁₃	—	4	4	no	—
301	C₂×C₁₃	#2442	1	1	yes	characteristic
302	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
303	C₂×C₁₃	#3083	1	1	yes	characteristic
304	C₂×C₁₃	#3302	1	1	yes	characteristic
305	C₂×C₁₃	#3325	1	1	yes	characteristic
306	C₂×C₁₃	#3361	1	1	yes	characteristic
307	C₂×C₁₃	#3367	1	1	yes	characteristic
308	C₂⁴	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
313	C₂×D₄	C₁₃×#41	1	2	yes	—
314	C₂×D₄	C₁₃×#41	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	8	2	no	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	1	no	—
355	C₄⋊C₄	—	8	1	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	4	2	no	—
363	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
364	C₄²	C₁₃×#41	1	2	yes	—
365	C₁₃	#26111	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	C₁₃×#125	1	4	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
404	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
405	C₂×C₄	C₁₃×#135	1	2	yes	—
406	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
407	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
409	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
411	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
424	C₂²	C₁₃×#546	1	1	yes	characteristic
425	C₂²	C₁₃×#548	1	1	yes	characteristic
426	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
427	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
428	C₂²	C₁₃×#576	1	1	yes	characteristic
429	C₂²	C₁₃×#578	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	1	no	—
438	C₄	C₁₃×#478	1	4	yes	—
439	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
440	C₄	C₁₃×#544	1	1	yes	characteristic
441	C₄	C₁₃×#552	1	1	yes	characteristic
442	C₄	C₁₃×#553	1	1	yes	characteristic
443	C₂	—	4	4	no	—
444	C₂	C₁₃×#2442	1	1	yes	characteristic
445	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
446	C₂	C₁₃×#3083	1	1	yes	characteristic
447	C₂	C₁₃×#3302	1	1	yes	characteristic
448	C₂	C₁₃×#3325	1	1	yes	characteristic
449	C₂	C₁₃×#3361	1	1	yes	characteristic
450	C₂	C₁₃×#3367	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
1. C₁₃×#2571	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
5. C₁₃×#1947	C₂	semidirect
6. C₁₃×#1939	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
83. #26111	C₁₃	direct (N × H)
141. #2571	C₂×C₁₃	semidirect
143. #2101	C₂×C₁₃	semidirect
144. #2087	C₂×C₁₃	semidirect
145. #1947	C₂×C₁₃	semidirect
146. #1939	C₂×C₁₃	semidirect
148. #1834	C₂×C₁₃	semidirect
365. C₁₃	#26111	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2571	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2101	2
C₁₃×#2087	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1862	2
C₁₃×#1834	2
C₁₃×#1804	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#26111	13

Subgroups — C13×#26111 #15712450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26111 #15712450