Subgroups — C₁₃×#24971 #15711310

Order 3328.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2076	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1824	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	—	2	1	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#396	—	2	2	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#385	—	2	2	no	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₁₃×#380	C₂²	1	2	yes	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₂²⋊Q₈	—	2	4	no	—
49	C₁₃×C₂²⋊Q₈	—	4	2	no	—
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	4	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	—	4	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	—	4	2	no	—
82	C₁₃×C₂²⋊C₈	—	4	2	no	—
83	C₁₃×C₂²⋊C₈	—	4	2	no	—
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	#24971	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	#41	1	2	yes	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	Q₁₆	1	4	yes	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	8	1	no	—
143	C₁₃×C₄⋊C₄	—	8	1	no	—
144	C₁₃×C₄⋊C₄	#41	1	2	yes	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	8	2	no	—
149	C₄²×C₁₃	—	4	2	no	—
150	C₄²×C₁₃	—	4	2	no	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₄²×C₁₃	#41	1	2	yes	—
153	#2538	C₂×C₁₃	1	1	yes	characteristic
154	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
155	#2076	C₂×C₁₃	1	2	yes	complemented
156	#2036	C₂×C₁₃	1	2	yes	complemented
157	#1954	C₂×C₁₃	1	1	yes	characteristic
158	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1872	C₂×C₁₃	1	2	yes	complemented
160	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1824	C₂×C₁₃	1	2	yes	complemented
162	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	C₂×Q₁₆	1	4	yes	—
171	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	4	1	no	—
175	Q₈×C₁₃	—	4	1	no	—
176	D₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	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	2	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	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	8	8	no	—
205	C₂×C₄×C₁₃	#123	1	2	yes	—
206	C₂×C₄×C₁₃	#123	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
208	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₈×C₁₃	—	4	2	no	—
216	C₈×C₁₃	—	4	1	no	—
217	C₈×C₁₃	—	4	1	no	—
218	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂×#107	C₂²×C₁₃	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	#396	—	2	2	no	—
232	#390	—	2	1	no	—
233	#389	—	2	1	no	—
234	#389	—	2	1	no	—
235	#385	—	2	2	no	—
236	#384	C₂²×C₁₃	1	1	yes	characteristic
237	#384	C₂²×C₁₃	1	1	yes	characteristic
238	#380	C₂²×C₁₃	1	2	yes	—
239	#380	C₂²×C₁₃	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	1	yes	characteristic
243	#340	C₂²×C₁₃	1	2	yes	—
244	#340	C₂²×C₁₃	1	1	yes	characteristic
245	#340	C₂²×C₁₃	1	2	yes	—
246	#340	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	—	2	4	no	—
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	2	4	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
255	C₂²×C₁₃	#546	1	1	yes	characteristic
256	C₂²×C₁₃	#546	1	1	yes	characteristic
257	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂²×C₁₃	#577	1	1	yes	characteristic
260	C₂²×C₁₃	#577	1	1	yes	characteristic
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	#484	1	4	yes	—
270	C₄×C₁₃	#529	1	1	yes	characteristic
271	C₄×C₁₃	#540	1	1	yes	characteristic
272	C₄×C₁₃	#553	1	1	yes	characteristic
273	C₄×C₁₃	#555	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	4	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	4	4	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	4	2	no	—
297	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	D₄×C₁₃	1	2	yes	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
310	#107	—	4	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	2	2	no	—
314	#103	—	4	2	no	—
315	C₂²⋊C₈	—	4	2	no	—
316	C₂²⋊C₈	—	4	2	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	C₂×C₁₃	—	4	4	no	—
322	C₂×C₁₃	#2420	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#484	1	1	yes	characteristic
324	C₂×C₁₃	#3099	1	1	yes	characteristic
325	C₂×C₁₃	#3299	1	1	yes	characteristic
326	C₂×C₁₃	#3299	1	1	yes	characteristic
327	C₂×C₁₃	#3324	1	1	yes	characteristic
328	C₂×C₁₃	#3332	1	1	yes	characteristic
329	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	C₁₃×#41	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	C₁₃×Q₁₆	1	4	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	8	2	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	8	1	no	—
383	C₄⋊C₄	—	8	1	no	—
384	C₄⋊C₄	C₁₃×#41	1	2	yes	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	4	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	C₁₃×#41	1	2	yes	—
392	C₄²	C₁₃×#41	1	2	yes	—
393	C₁₃	#24971	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	C₂×C₁₃×Q₁₆	1	4	yes	—
401	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	1	no	—
406	D₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	8	8	no	—
435	C₂×C₄	C₁₃×#123	1	2	yes	—
436	C₂×C₄	C₁₃×#123	1	2	yes	—
437	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
438	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
439	C₂×C₄	C₂×C₁₃×#41	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	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
456	C₂²	C₁₃×#546	1	1	yes	characteristic
457	C₂²	C₁₃×#546	1	1	yes	characteristic
458	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
459	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
460	C₂²	C₁₃×#577	1	1	yes	characteristic
461	C₂²	C₁₃×#577	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₁₃×#484	1	4	yes	—
471	C₄	C₁₃×#529	1	1	yes	characteristic
472	C₄	C₁₃×#540	1	1	yes	characteristic
473	C₄	C₁₃×#553	1	1	yes	characteristic
474	C₄	C₁₃×#555	1	1	yes	characteristic
475	C₂	—	4	4	no	—
476	C₂	C₁₃×#2420	1	1	yes	characteristic
477	C₂	C₂×C₁₃×#484	1	1	yes	characteristic
478	C₂	C₁₃×#3099	1	1	yes	characteristic
479	C₂	C₁₃×#3299	1	1	yes	characteristic
480	C₂	C₁₃×#3299	1	1	yes	characteristic
481	C₂	C₁₃×#3324	1	1	yes	characteristic
482	C₂	C₁₃×#3332	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₁₃×#2076	C₂	semidirect
4. C₁₃×#2036	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
7. C₁₃×#1872	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
9. C₁₃×#1824	C₂	semidirect
10. C₁₃×#1803	C₂	semidirect
11. C₄×C₁₃×#103	C₂	semidirect
88. #24971	C₁₃	direct (N × H)
155. #2076	C₂×C₁₃	semidirect
156. #2036	C₂×C₁₃	semidirect
158. #1947	C₂×C₁₃	semidirect
159. #1872	C₂×C₁₃	semidirect
160. #1834	C₂×C₁₃	semidirect
161. #1824	C₂×C₁₃	semidirect
162. #1803	C₂×C₁₃	semidirect
163. C₄×#103	C₂×C₁₃	semidirect
393. C₁₃	#24971	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×#2538	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2076	2
C₁₃×#2036	2
C₁₃×#1954	2
C₁₃×#1947	2
C₁₃×#1872	2
C₁₃×#1834	2
C₁₃×#1824	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#24971	13

Subgroups — C13×#24971 #15711310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24971 #15711310