Subgroups — C₁₃×#24972 #15711311

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 476 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	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2077	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1873	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1825	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	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#396	—	2	2	no	—
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#388	—	2	2	no	—
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
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	C₂³	1	2	yes	—
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×C₂²⋊Q₈	—	2	4	no	—
48	C₁₃×C₂²⋊Q₈	—	4	2	no	—
49	C₄×Q₈×C₁₃	—	2	2	no	—
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₁₃×#117	—	2	4	no	—
54	C₁₃×#117	—	4	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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	D₄	1	2	yes	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#106	—	4	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	4	2	no	—
81	C₁₃×C₂²⋊C₈	—	4	2	no	—
82	C₁₃×C₂²⋊C₈	—	4	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	#24972	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
89	C₂×Q₈×C₁₃	—	2	1	no	—
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	#41	1	2	yes	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	8	1	no	—
138	C₁₃×C₄⋊C₄	—	8	1	no	—
139	C₁₃×C₄⋊C₄	#41	1	2	yes	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	8	2	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	—	4	2	no	—
148	C₄²×C₁₃	#41	1	2	yes	—
149	C₄²×C₁₃	#41	1	2	yes	—
150	#2538	C₂×C₁₃	1	1	yes	characteristic
151	#2354	C₂×C₁₃	1	1	yes	characteristic
152	#2077	C₂×C₁₃	1	2	yes	complemented
153	#2035	C₂×C₁₃	1	2	yes	complemented
154	#1954	C₂×C₁₃	1	1	yes	characteristic
155	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1873	C₂×C₁₃	1	2	yes	complemented
157	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1825	C₂×C₁₃	1	2	yes	complemented
159	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	Q₈×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	4	4	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	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	—	4	1	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	2	no	—
186	C₂×C₄×C₁₃	—	4	2	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	—	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	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	#123	1	2	yes	—
202	C₂×C₄×C₁₃	#123	1	2	yes	—
203	C₂×C₄×C₁₃	#135	1	2	yes	—
204	C₂×C₄×C₁₃	#137	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#117	C₂²×C₁₃	1	2	yes	—
218	C₂×#106	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	#396	—	2	2	no	—
227	#390	—	2	1	no	—
228	#390	—	2	1	no	—
229	#389	—	2	1	no	—
230	#388	—	2	2	no	—
231	#384	C₂²×C₁₃	1	1	yes	characteristic
232	#384	C₂²×C₁₃	1	1	yes	characteristic
233	#380	C₂²×C₁₃	1	2	yes	—
234	#380	C₂²×C₁₃	1	2	yes	—
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	1	yes	characteristic
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
251	C₂²×C₁₃	#546	1	1	yes	characteristic
252	C₂²×C₁₃	#546	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
255	C₂²×C₁₃	#577	1	1	yes	characteristic
256	C₂²×C₁₃	#577	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	8	1	no	—
262	C₄×C₁₃	—	8	1	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	#485	1	4	yes	—
266	C₄×C₁₃	#529	1	1	yes	characteristic
267	C₄×C₁₃	#540	1	1	yes	characteristic
268	C₄×C₁₃	#553	1	1	yes	characteristic
269	C₄×C₁₃	#555	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	4	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	#117	—	2	4	no	—
283	#117	—	4	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	#106	—	4	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	4	2	no	—
310	C₂²⋊C₈	—	4	2	no	—
311	C₂²⋊C₈	—	4	2	no	—
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	C₂×C₁₃	—	8	2	no	—
317	C₂×C₁₃	#2420	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#485	1	1	yes	characteristic
319	C₂×C₁₃	#3099	1	1	yes	characteristic
320	C₂×C₁₃	#3304	1	1	yes	characteristic
321	C₂×C₁₃	#3304	1	1	yes	characteristic
322	C₂×C₁₃	#3329	1	1	yes	characteristic
323	C₂×C₁₃	#3331	1	1	yes	characteristic
324	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	C₁₃×#41	1	2	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	C₁₃×#41	1	2	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	8	2	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₄²	—	4	4	no	—
382	C₄²	—	4	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₁₃×#41	1	2	yes	—
385	C₄²	C₁₃×#41	1	2	yes	—
386	C₁₃	#24972	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	D₄	—	4	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	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	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	C₁₃×#123	1	2	yes	—
428	C₂×C₄	C₁₃×#123	1	2	yes	—
429	C₂×C₄	C₁₃×#135	1	2	yes	—
430	C₂×C₄	C₁₃×#137	1	2	yes	—
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
435	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
448	C₂²	C₁₃×#546	1	1	yes	characteristic
449	C₂²	C₁₃×#546	1	1	yes	characteristic
450	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
451	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
452	C₂²	C₁₃×#577	1	1	yes	characteristic
453	C₂²	C₁₃×#577	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₁₃×#485	1	4	yes	—
463	C₄	C₁₃×#529	1	1	yes	characteristic
464	C₄	C₁₃×#540	1	1	yes	characteristic
465	C₄	C₁₃×#553	1	1	yes	characteristic
466	C₄	C₁₃×#555	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₁₃×#2420	1	1	yes	characteristic
469	C₂	C₂×C₁₃×#485	1	1	yes	characteristic
470	C₂	C₁₃×#3099	1	1	yes	characteristic
471	C₂	C₁₃×#3304	1	1	yes	characteristic
472	C₂	C₁₃×#3304	1	1	yes	characteristic
473	C₂	C₁₃×#3329	1	1	yes	characteristic
474	C₂	C₁₃×#3331	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×#2077	C₂	semidirect
4. C₁₃×#2035	C₂	semidirect
6. C₁₃×#1948	C₂	semidirect
7. C₁₃×#1873	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
9. C₁₃×#1825	C₂	semidirect
10. C₁₃×#1803	C₂	semidirect
11. C₄×C₁₃×#103	C₂	semidirect
87. #24972	C₁₃	direct (N × H)
152. #2077	C₂×C₁₃	semidirect
153. #2035	C₂×C₁₃	semidirect
155. #1948	C₂×C₁₃	semidirect
156. #1873	C₂×C₁₃	semidirect
157. #1834	C₂×C₁₃	semidirect
158. #1825	C₂×C₁₃	semidirect
159. #1803	C₂×C₁₃	semidirect
160. C₄×#103	C₂×C₁₃	semidirect
386. C₁₃	#24972	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
C₁₃×#2354	2
C₁₃×#2077	2
C₁₃×#2035	2
C₁₃×#1954	2
C₁₃×#1948	2
C₁₃×#1873	2
C₁₃×#1834	2
C₁₃×#1825	2
C₁₃×#1803	2
C₄×C₁₃×#103	2
#24972	13

Subgroups — C13×#24972 #15711311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24972 #15711311