Subgroups — C₁₃×#26110 #15712449

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2100	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2088	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1864	C₂	1	2	yes	maximal
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1802	C₂	1	2	yes	maximal
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	—	2	1	no	—
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	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#398	—	2	2	no	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#385	—	2	2	no	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	2	yes	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
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	C₁₃×#125	—	4	4	no	—
48	C₄×D₄×C₁₃	—	2	4	no	—
49	C₄×D₄×C₁₃	—	2	2	no	—
50	C₄×D₄×C₁₃	—	4	2	no	—
51	C₄×D₄×C₁₃	Q₈	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	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	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#106	—	4	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×C₄⋊C₈	—	4	2	no	—
76	C₁₃×#102	—	2	2	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×#102	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	D₄	1	2	yes	—
84	#26110	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	2	1	no	—
89	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂×D₄×C₁₃	#41	1	2	yes	—
91	C₂×D₄×C₁₃	#41	1	2	yes	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	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	—	4	4	no	—
102	C₂²×C₄×C₁₃	—	8	2	no	—
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	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	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	4	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	8	1	no	—
133	C₁₃×C₄⋊C₄	—	8	1	no	—
134	C₁₃×C₄⋊C₄	—	8	2	no	—
135	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
136	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
143	C₄²×C₁₃	#41	1	2	yes	—
144	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
145	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
146	#2100	C₂×C₁₃	1	2	yes	complemented
147	#2088	C₂×C₁₃	1	2	yes	complemented
148	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1864	C₂×C₁₃	1	2	yes	—
151	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1802	C₂×C₁₃	1	2	yes	—
153	#1802	C₂×C₁₃	1	1	yes	characteristic
154	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	2	no	—
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	#125	1	4	yes	complemented
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	8	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	8	8	no	—
191	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
194	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	4	1	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₂×#125	—	2	1	no	—
206	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	—	2	1	no	—
209	C₂×#106	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
212	C₂×#102	C₂²×C₁₃	1	2	yes	—
213	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
216	#398	—	2	2	no	—
217	#389	—	2	1	no	—
218	#389	C₂²×C₁₃	1	2	yes	—
219	#389	C₂²×C₁₃	1	2	yes	—
220	#385	—	2	2	no	—
221	#384	C₂²×C₁₃	1	1	yes	characteristic
222	#384	C₂²×C₁₃	1	2	yes	—
223	#384	C₂²×C₁₃	1	1	yes	characteristic
224	#380	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	2	yes	—
228	#340	C₂²×C₁₃	1	2	yes	—
229	#340	C₂²×C₁₃	1	2	yes	—
230	#340	C₂²×C₁₃	1	1	yes	characteristic
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	1	yes	characteristic
233	#336	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	#546	1	1	yes	characteristic
243	C₂²×C₁₃	#548	1	1	yes	characteristic
244	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂²×C₁₃	#576	1	1	yes	characteristic
247	C₂²×C₁₃	#578	1	1	yes	characteristic
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	—	8	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	#476	1	4	yes	—
257	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
258	C₄×C₁₃	#544	1	1	yes	characteristic
259	C₄×C₁₃	#552	1	1	yes	characteristic
260	C₄×C₁₃	#553	1	1	yes	characteristic
261	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	—	2	2	no	—
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	#125	—	4	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	4	2	no	—
271	C₄×D₄	Q₈×C₁₃	1	4	yes	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	4	4	no	—
281	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	#106	—	4	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	4	2	no	—
296	#102	—	2	4	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	D₄×C₁₃	1	2	yes	—
304	C₂×C₁₃	—	4	4	no	—
305	C₂×C₁₃	#2442	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
307	C₂×C₁₃	#3083	1	1	yes	characteristic
308	C₂×C₁₃	#3295	1	1	yes	characteristic
309	C₂×C₁₃	#3330	1	1	yes	characteristic
310	C₂×C₁₃	#3359	1	1	yes	characteristic
311	C₂×C₁₃	#3366	1	1	yes	characteristic
312	C₂⁴	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
317	C₂×D₄	C₁₃×#41	1	2	yes	—
318	C₂×D₄	C₁₃×#41	1	2	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	—	8	1	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
363	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
370	C₄²	C₁₃×#41	1	2	yes	—
371	C₁₃	#26110	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	C₁₃×#125	1	4	yes	complemented
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
409	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
410	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
411	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
412	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
413	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
417	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
430	C₂²	C₁₃×#546	1	1	yes	characteristic
431	C₂²	C₁₃×#548	1	1	yes	characteristic
432	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
433	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₂²	C₁₃×#576	1	1	yes	characteristic
435	C₂²	C₁₃×#578	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	C₁₃×#476	1	4	yes	—
445	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
446	C₄	C₁₃×#544	1	1	yes	characteristic
447	C₄	C₁₃×#552	1	1	yes	characteristic
448	C₄	C₁₃×#553	1	1	yes	characteristic
449	C₂	—	4	4	no	—
450	C₂	C₁₃×#2442	1	1	yes	characteristic
451	C₂	C₂×C₁₃×#476	1	1	yes	characteristic
452	C₂	C₁₃×#3083	1	1	yes	characteristic
453	C₂	C₁₃×#3295	1	1	yes	characteristic
454	C₂	C₁₃×#3330	1	1	yes	characteristic
455	C₂	C₁₃×#3359	1	1	yes	characteristic
456	C₂	C₁₃×#3366	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×#2552	C₂	semidirect
3. C₁₃×#2100	C₂	semidirect
4. C₁₃×#2088	C₂	semidirect
5. C₁₃×#1948	C₂	semidirect
6. C₁₃×#1939	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
84. #26110	C₁₃	direct (N × H)
144. #2552	C₂×C₁₃	semidirect
146. #2100	C₂×C₁₃	semidirect
147. #2088	C₂×C₁₃	semidirect
148. #1948	C₂×C₁₃	semidirect
149. #1939	C₂×C₁₃	semidirect
151. #1834	C₂×C₁₃	semidirect
166. D₄×C₁₃	#125	semidirect
371. C₁₃	#26110	direct (N × H)
383. D₄	C₁₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2552	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2100	2
C₁₃×#2088	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1864	2
C₁₃×#1834	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#26110	13

Subgroups — C13×#26110 #15712449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26110 #15712449