Subgroups — C₁₃×#32725 #15719064

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2056	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	2	yes	maximal
9	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2001	C₂	1	2	yes	maximal
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₃×#391	C₂²	1	1	yes	characteristic
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#389	—	2	1	no	—
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#387	—	2	1	no	—
32	C₁₃×#387	—	2	1	no	—
33	C₁₃×#385	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#381	—	2	1	no	—
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	—	2	1	no	—
38	C₁₃×#380	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	—	4	2	no	—
49	C₂×C₁₃×Q₁₆	—	4	2	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	4	2	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	4	2	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#106	—	4	2	no	—
78	C₁₃×C₄⋊C₈	—	4	2	no	—
79	C₁₃×#103	—	4	2	no	—
80	C₁₃×#103	—	4	2	no	—
81	C₁₃×#103	—	4	2	no	—
82	C₁₃×#103	—	4	2	no	—
83	C₁₃×C₂²⋊C₈	—	4	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	#32725	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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×Q₁₆	—	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	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₂²⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	—	4	1	no	—
155	#2857	C₂×C₁₃	1	1	yes	characteristic
156	#2855	C₂×C₁₃	1	1	yes	characteristic
157	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2066	C₂×C₁₃	1	2	yes	complemented
160	#2056	C₂×C₁₃	1	2	yes	complemented
161	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2035	C₂×C₁₃	1	2	yes	—
163	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2001	C₂×C₁₃	1	2	yes	—
165	#1797	C₂×C₁₃	1	1	yes	characteristic
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	#137	1	2	yes	—
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	4	2	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	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	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	#135	1	2	yes	—
215	C₂×C₄×C₁₃	#137	1	2	yes	—
216	C₂×C₄×C₁₃	#137	1	2	yes	—
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
219	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
220	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#106	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
230	C₂×#103	C₂²×C₁₃	1	2	yes	—
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	2	yes	—
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
235	#391	C₂²×C₁₃	1	1	yes	characteristic
236	#391	C₂²×C₁₃	1	2	yes	—
237	#391	C₂²×C₁₃	1	1	yes	characteristic
238	#389	—	2	1	no	—
239	#389	—	2	1	no	—
240	#389	C₂²×C₁₃	1	1	yes	characteristic
241	#389	C₂²×C₁₃	1	1	yes	characteristic
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#385	—	2	1	no	—
245	#384	C₂²×C₁₃	1	1	yes	characteristic
246	#381	—	2	1	no	—
247	#380	—	2	1	no	—
248	#380	—	2	1	no	—
249	#380	C₂²×C₁₃	1	1	yes	characteristic
250	#340	C₂²×C₁₃	1	2	yes	—
251	#340	C₂²×C₁₃	1	2	yes	—
252	#336	C₂²×C₁₃	1	1	yes	characteristic
253	#336	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	4	1	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	#534	1	1	yes	characteristic
262	C₂²×C₁₃	#535	1	1	yes	characteristic
263	C₂²×C₁₃	#537	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
267	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	4	1	no	—
272	C₄×C₁₃	—	4	1	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	—	8	2	no	—
275	C₄×C₁₃	—	8	1	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	#560	1	2	yes	—
280	C₄×C₁₃	#562	1	2	yes	—
281	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×Q₁₆	—	4	2	no	—
287	C₂×Q₁₆	—	4	2	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₄⋊Q₈	—	4	2	no	—
292	C₂²⋊Q₈	—	4	2	no	—
293	C₂²⋊Q₈	—	4	2	no	—
294	C₂²⋊Q₈	—	4	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	4	2	no	—
311	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	#106	—	4	2	no	—
316	C₄⋊C₈	—	4	2	no	—
317	#103	—	4	2	no	—
318	#103	—	4	2	no	—
319	#103	—	4	2	no	—
320	#103	—	4	2	no	—
321	C₂²⋊C₈	—	4	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	C₂×C₁₃	—	4	2	no	—
332	C₂×C₁₃	#2813	1	1	yes	characteristic
333	C₂×C₁₃	#3190	1	1	yes	characteristic
334	C₂×C₁₃	#3195	1	1	yes	characteristic
335	C₂×C₁₃	#3210	1	1	yes	characteristic
336	C₂×C₁₃	#3218	1	1	yes	characteristic
337	C₂×C₁₃	#3248	1	1	yes	characteristic
338	C₂×C₁₃	#3255	1	1	yes	characteristic
339	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
372	Q₁₆	—	4	8	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	1	no	—
400	C₁₃	#32725	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	C₁₃×#137	1	2	yes	—
408	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	C₁₃×#135	1	2	yes	—
450	C₂×C₄	C₁₃×#137	1	2	yes	—
451	C₂×C₄	C₁₃×#137	1	2	yes	—
452	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
454	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
455	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
456	C₈	—	4	2	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₁₃×#534	1	1	yes	characteristic
466	C₂²	C₁₃×#535	1	1	yes	characteristic
467	C₂²	C₁₃×#537	1	1	yes	characteristic
468	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
469	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
470	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	C₁₃×#560	1	2	yes	—
484	C₄	C₁₃×#562	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	C₁₃×#2813	1	1	yes	characteristic
487	C₂	C₁₃×#3190	1	1	yes	characteristic
488	C₂	C₁₃×#3195	1	1	yes	characteristic
489	C₂	C₁₃×#3210	1	1	yes	characteristic
490	C₂	C₁₃×#3218	1	1	yes	characteristic
491	C₂	C₁₃×#3248	1	1	yes	characteristic
492	C₂	C₁₃×#3255	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2099	C₂	semidirect
4. C₁₃×#2096	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
6. C₁₃×#2056	C₂	semidirect
7. C₁₃×#2043	C₂	semidirect
9. C₁₃×#2016	C₂	semidirect
93. #32725	C₁₃	direct (N × H)
157. #2099	C₂×C₁₃	semidirect
158. #2096	C₂×C₁₃	semidirect
159. #2066	C₂×C₁₃	semidirect
160. #2056	C₂×C₁₃	semidirect
161. #2043	C₂×C₁₃	semidirect
163. #2016	C₂×C₁₃	semidirect
400. C₁₃	#32725	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×#2857	2
C₁₃×#2855	2
C₁₃×#2099	2
C₁₃×#2096	2
C₁₃×#2066	2
C₁₃×#2056	2
C₁₃×#2043	2
C₁₃×#2035	2
C₁₃×#2016	2
C₁₃×#2001	2
C₁₃×#1797	2
#32725	13

Subgroups — C13×#32725 #15719064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32725 #15719064