Subgroups — C₁₃×#25569 #15711908

Order 3328.

1306 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1874	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	C₁₃×#554	—	2	4	no	—
12	C₁₃×#554	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	—	2	1	no	—
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₁₃×#486	—	2	4	no	—
25	C₁₃×#460	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	4	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#392	—	2	2	no	—
33	C₁₃×#390	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	4	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂×C₁₃×SD₁₆	—	2	4	no	—
47	C₂×C₁₃×SD₁₆	—	4	4	no	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	D₄	1	4	yes	complemented
52	C₁₃×#127	—	2	2	no	—
53	C₁₃×#127	—	2	2	no	—
54	C₁₃×#127	—	4	4	no	—
55	C₁₃×#125	—	2	8	no	—
56	C₁₃×C₂²⋊Q₈	—	2	16	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₁₃×#121	—	2	8	no	—
60	C₁₃×#121	—	4	4	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	D₄	1	4	yes	complemented
63	C₄×D₄×C₁₃	—	2	8	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
78	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	2	8	no	—
86	C₁₃×C₂²⋊C₈	—	4	4	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	#25569	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	2	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₁₃	—	2	4	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	8	2	no	—
97	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	4	8	no	—
105	C₂×D₄×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	8	2	no	—
111	C₂×D₄×C₁₃	—	8	4	no	—
112	C₂×D₄×C₁₃	SD₁₆	1	4	yes	complemented
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	8	4	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×SD₁₆	—	4	8	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
143	C₁₃×C₄⋊C₄	#41	1	4	yes	—
144	C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	8	no	—
147	C₄²×C₁₃	—	2	4	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2541	C₂×C₁₃	1	1	yes	characteristic
155	#2000	C₂×C₁₃	1	4	yes	complemented
156	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1874	C₂×C₁₃	1	4	yes	complemented
159	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
170	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	8	4	no	—
175	D₄×C₁₃	—	2	8	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	4	no	—
179	D₄×C₁₃	—	8	4	no	—
180	D₄×C₁₃	—	8	16	no	—
181	D₄×C₁₃	—	8	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	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	4	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	8	8	no	—
198	C₂×C₄×C₁₃	#120	1	2	yes	—
199	C₂×C₄×C₁₃	#120	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₁₃	—	4	2	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
209	#554	—	2	4	no	—
210	#554	—	2	4	no	—
211	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#127	—	2	1	no	—
213	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#125	—	2	1	no	—
215	C₂×C₂²⋊Q₈	—	2	2	no	—
216	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
217	C₂×#121	C₂²×C₁₃	1	4	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×D₄	—	2	1	no	—
220	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
222	#486	—	2	4	no	—
223	#460	—	2	4	no	—
224	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	4	yes	—
227	C₂×#102	C₂²×C₁₃	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
229	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	#392	—	2	2	no	—
231	#390	—	2	1	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	4	yes	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	8	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	8	4	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	—	8	4	no	—
245	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
246	C₂²×C₁₃	#546	1	2	yes	—
247	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
249	C₂²×C₁₃	#576	1	2	yes	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	#448	1	4	yes	—
257	C₄×C₁₃	#532	1	1	yes	characteristic
258	C₄×C₁₃	#535	1	1	yes	characteristic
259	C₄×C₁₃	#550	1	2	yes	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×D₄	—	2	4	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
266	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×SD₁₆	—	2	4	no	—
270	C₂×SD₁₆	—	4	4	no	—
271	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	D₄×C₁₃	1	4	yes	complemented
275	#127	—	2	2	no	—
276	#127	—	2	2	no	—
277	#127	—	4	4	no	—
278	#125	—	2	8	no	—
279	C₂²⋊Q₈	—	2	16	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	#121	—	2	8	no	—
283	#121	—	4	4	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	D₄×C₁₃	1	4	yes	complemented
286	C₄×D₄	—	2	8	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	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	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	#103	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	2	8	no	—
309	C₂²⋊C₈	—	4	4	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	1	no	—
312	C₂×C₁₃	—	4	4	no	—
313	C₂×C₁₃	—	16	2	no	—
314	C₂×C₁₃	#2431	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
316	C₂×C₁₃	#3008	1	1	yes	characteristic
317	C₂×C₁₃	#3295	1	2	yes	—
318	C₂×C₁₃	#3333	1	2	yes	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	—	8	4	no	—
341	C₂×D₄	C₁₃×SD₁₆	1	4	yes	complemented
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	8	4	no	—
352	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	SD₁₆	—	4	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	4	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
372	C₄⋊C₄	C₁₃×#41	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	8	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂×D₄×C₁₃	1	2	yes	—
379	C₄²	C₂×D₄×C₁₃	1	2	yes	—
380	C₁₃	#25569	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
391	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	16	no	—
402	D₄	—	8	4	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	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₁₃×#120	1	2	yes	—
420	C₂×C₄	C₁₃×#120	1	2	yes	—
421	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
422	C₂×C₄	C₁₃×#137	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
426	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
440	C₂²	C₁₃×#546	1	2	yes	—
441	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
442	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
443	C₂²	C₁₃×#576	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	C₁₃×#448	1	4	yes	—
451	C₄	C₁₃×#532	1	1	yes	characteristic
452	C₄	C₁₃×#535	1	1	yes	characteristic
453	C₄	C₁₃×#550	1	2	yes	—
454	C₂	—	4	4	no	—
455	C₂	—	16	2	no	—
456	C₂	C₁₃×#2431	1	1	yes	characteristic
457	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
458	C₂	C₁₃×#3008	1	1	yes	characteristic
459	C₂	C₁₃×#3295	1	2	yes	—
460	C₂	C₁₃×#3333	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2541	C₂
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
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#486	C₂	semidirect
3. C₂×C₁₃×#460	C₂	semidirect
5. C₁₃×#2000	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1874	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
51. C₁₃×C₄⋊Q₈	D₄	semidirect
62. C₄×Q₈×C₁₃	D₄	semidirect
89. #25569	C₁₃	direct (N × H)
112. C₂×D₄×C₁₃	SD₁₆	semidirect
151. C₂×#554	C₂×C₁₃	semidirect
152. C₂×#486	C₂×C₁₃	semidirect
153. C₂×#460	C₂×C₁₃	semidirect
155. #2000	C₂×C₁₃	semidirect
156. #1987	C₂×C₁₃	semidirect
157. #1954	C₂×C₁₃	semidirect
158. #1874	C₂×C₁₃	semidirect
159. C₄×#103	C₂×C₁₃	semidirect
274. C₄⋊Q₈	D₄×C₁₃	semidirect
285. C₄×Q₈	D₄×C₁₃	semidirect
341. C₂×D₄	C₁₃×SD₁₆	semidirect
380. C₁₃	#25569	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₂×C₁₃×#486	2
C₂×C₁₃×#460	2
C₁₃×#2541	2
C₁₃×#2000	2
C₁₃×#1987	2
C₁₃×#1954	2
C₁₃×#1874	2
C₄×C₁₃×#103	2
#25569	13

Subgroups — C13×#25569 #15711908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25569 #15711908