Subgroups — C₁₃×#25887 #15712226

Order 3328.

1386 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2034	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1788	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₁₃×#550	—	2	4	no	—
12	C₁₃×#550	—	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×#124	—	2	1	no	—
17	C₂×C₁₃×#121	—	2	2	no	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#486	—	2	4	no	—
23	C₁₃×#475	—	2	4	no	—
24	C₂×C₁₃×#106	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	4	yes	—
29	C₂×C₁₃×#102	C₂²	1	4	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#397	—	2	2	no	—
33	C₁₃×#391	—	2	1	no	—
34	C₁₃×#380	C₂²	1	4	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂×C₁₃×#41	—	2	4	no	—
38	C₂×C₁₃×#41	—	2	4	no	—
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	—	4	4	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×#127	—	2	8	no	—
56	C₁₃×#127	—	2	2	no	—
57	C₁₃×#127	D₄	1	4	yes	—
58	C₁₃×#124	—	4	4	no	—
59	C₁₃×#121	—	2	16	no	—
60	C₁₃×#121	—	2	4	no	—
61	C₁₃×#121	—	2	4	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	D₄	1	4	yes	—
64	C₄×D₄×C₁₃	—	2	8	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₄×D₄×C₁₃	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#102	—	2	8	no	—
84	C₁₃×#102	—	4	4	no	—
85	C₁₃×C₂²⋊C₈	—	4	4	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	4	no	—
89	#25887	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	C₁₃×#41	—	4	16	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₁₃×#41	—	4	8	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₁₃	#41	1	4	yes	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	4	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	4	8	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	—	8	2	no	—
116	C₂×D₄×C₁₃	—	8	4	no	—
117	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	4	8	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	4	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	2	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	8	no	—
149	C₄²×C₁₃	—	2	4	no	—
150	C₄²×C₁₃	—	4	2	no	—
151	C₄²×C₁₃	C₂×D₄	1	2	yes	—
152	C₄²×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
154	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2547	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2034	C₂×C₁₃	1	4	yes	complemented
158	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1788	C₂×C₁₃	1	4	yes	complemented
161	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	4	no	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	4	no	—
175	Q₈×C₁₃	—	8	4	no	—
176	Q₈×C₁₃	#124	1	4	yes	complemented
177	D₄×C₁₃	—	2	8	no	—
178	D₄×C₁₃	—	4	16	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	4	no	—
182	D₄×C₁₃	—	4	8	no	—
183	D₄×C₁₃	—	8	4	no	—
184	D₄×C₁₃	—	8	8	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	4	16	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	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	2	no	—
202	C₂×C₄×C₁₃	#120	1	2	yes	—
203	C₂×C₄×C₁₃	#120	1	2	yes	—
204	C₂×C₄×C₁₃	#135	1	2	yes	—
205	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₂²×#41	C₂²×C₁₃	1	2	yes	—
213	#550	—	2	4	no	—
214	#550	—	2	4	no	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#127	—	2	1	no	—
217	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	2	no	—
220	C₂×#121	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
224	#486	—	2	4	no	—
225	#475	—	2	4	no	—
226	C₂×#106	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₃	1	2	yes	—
229	C₂×#103	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	4	yes	—
231	C₂×#102	C₂²×C₁₃	1	4	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
233	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
234	#397	—	2	2	no	—
235	#391	—	2	1	no	—
236	#380	C₂²×C₁₃	1	4	yes	—
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	#340	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	8	4	no	—
248	C₂²×C₁₃	—	8	4	no	—
249	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
250	C₂²×C₁₃	#546	1	2	yes	—
251	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₁₃	#577	1	2	yes	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	#449	1	4	yes	—
261	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
262	C₄×C₁₃	#535	1	1	yes	characteristic
263	C₄×C₁₃	#546	1	2	yes	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	—	2	4	no	—
266	C₂×#41	—	2	8	no	—
267	C₂×#41	—	4	4	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	#127	—	2	8	no	—
283	#127	—	2	2	no	—
284	#127	D₄×C₁₃	1	4	yes	—
285	#124	—	4	4	no	—
286	#121	—	2	16	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	D₄×C₁₃	1	4	yes	—
291	C₄×D₄	—	2	8	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	4	no	—
302	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	#106	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	2	4	no	—
309	#103	—	2	4	no	—
310	#102	—	2	8	no	—
311	#102	—	4	4	no	—
312	C₂²⋊C₈	—	4	4	no	—
313	C₄×C₈	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	4	no	—
316	C₂×C₁₃	—	8	2	no	—
317	C₂×C₁₃	—	8	4	no	—
318	C₂×C₁₃	#2435	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
320	C₂×C₁₃	#3009	1	1	yes	characteristic
321	C₂×C₁₃	#3304	1	2	yes	—
322	C₂×C₁₃	#3332	1	2	yes	—
323	C₂⁴	—	2	2	no	—
324	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
325	#41	—	4	16	no	—
326	#41	—	4	8	no	—
327	#41	—	4	8	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×Q₈	C₁₃×#41	1	4	yes	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	8	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	4	no	—
350	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	4	8	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂×D₄×C₁₃	1	2	yes	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₁₃	#25887	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	8	4	no	—
401	Q₈	C₁₃×#124	1	4	yes	complemented
402	D₄	—	2	8	no	—
403	D₄	—	4	16	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	4	no	—
409	D₄	—	8	8	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	16	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₁₃×#120	1	2	yes	—
428	C₂×C₄	C₁₃×#120	1	2	yes	—
429	C₂×C₄	C₁₃×#135	1	2	yes	—
430	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
434	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	8	4	no	—
447	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
448	C₂²	C₁₃×#546	1	2	yes	—
449	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
450	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂²	C₁₃×#577	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	2	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	2	no	—
458	C₄	C₁₃×#449	1	4	yes	—
459	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
460	C₄	C₁₃×#535	1	1	yes	characteristic
461	C₄	C₁₃×#546	1	2	yes	—
462	C₂	—	8	2	no	—
463	C₂	—	8	4	no	—
464	C₂	C₁₃×#2435	1	1	yes	characteristic
465	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
466	C₂	C₁₃×#3009	1	1	yes	characteristic
467	C₂	C₁₃×#3304	1	2	yes	—
468	C₂	C₁₃×#3332	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#550	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
2. C₂×C₁₃×#486	C₂	semidirect
3. C₂×C₁₃×#475	C₂	semidirect
4. C₁₃×#2547	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#1982	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1788	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
89. #25887	C₁₃	direct (N × H)
154. C₂×#486	C₂×C₁₃	semidirect
155. C₂×#475	C₂×C₁₃	semidirect
156. #2547	C₂×C₁₃	semidirect
157. #2034	C₂×C₁₃	semidirect
158. #1982	C₂×C₁₃	semidirect
159. #1954	C₂×C₁₃	semidirect
160. #1788	C₂×C₁₃	semidirect
161. C₄×#103	C₂×C₁₃	semidirect
176. Q₈×C₁₃	#124	semidirect
386. C₁₃	#25887	direct (N × H)
401. Q₈	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#550	2
C₂×C₁₃×#486	2
C₂×C₁₃×#475	2
C₁₃×#2547	2
C₁₃×#2034	2
C₁₃×#1982	2
C₁₃×#1954	2
C₁₃×#1788	2
C₄×C₁₃×#103	2
#25887	13

Subgroups — C13×#25887 #15712226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25887 #15712226