Subgroups — C₁₃×#25925 #15712264

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3040	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2028	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2027	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1883	C₂	1	2	yes	maximal
10	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
14	C₁₃×#557	—	2	2	no	—
15	C₁₃×#554	—	2	2	no	—
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#544	—	2	2	no	—
18	C₁₃×#544	C₂²	1	2	yes	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	—	2	1	no	—
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₁₃×#520	C₂²	1	2	yes	—
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₁₃×#489	—	2	2	no	—
27	C₁₃×#488	—	2	1	no	—
28	C₁₃×#488	—	2	1	no	—
29	C₁₃×#464	—	2	2	no	—
30	C₁₃×#463	—	2	2	no	—
31	C₁₃×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#419	C₂²	1	1	yes	characteristic
34	C₁₃×#419	C₂²	1	2	yes	—
35	C₁₃×#418	C₂²	1	1	yes	characteristic
36	C₁₃×#418	C₂²	1	2	yes	—
37	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	2	yes	—
40	C₁₃×#388	—	2	4	no	—
41	C₄³×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#343	C₂²	1	2	yes	—
44	C₁₃×#339	C₂²	1	2	yes	—
45	C₁₃×#339	C₂²	1	2	yes	—
46	C₁₃×#339	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#137	—	2	4	no	—
51	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×SD₁₆	—	2	1	no	—
54	C₂×C₁₃×SD₁₆	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
63	C₁₃×#125	—	2	4	no	—
64	C₁₃×#125	—	2	4	no	—
65	C₁₃×#125	—	2	2	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₁₃×#125	—	2	1	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	D₄	1	1	yes	characteristic
71	C₁₃×#125	D₄	1	1	yes	characteristic
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	1	no	—
74	C₁₃×#124	—	2	1	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	4	no	—
77	C₁₃×C₂²⋊Q₈	—	2	4	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₄×Q₈×C₁₃	—	2	4	no	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	D₄	1	2	yes	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	D₄	1	2	yes	—
88	C₁₃×#117	—	2	2	no	—
89	C₁₃×#117	—	2	1	no	—
90	C₁₃×#117	C₂³	1	1	yes	characteristic
91	C₁₃×#117	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	—	2	2	no	—
100	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×#104	—	2	4	no	—
104	C₁₃×#103	—	2	2	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#97	—	2	1	no	—
111	C₄×C₈×C₁₃	—	2	1	no	—
112	C₁₃×#95	—	2	4	no	—
113	#25925	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁴×C₁₃	—	2	1	no	—
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	#41	1	4	yes	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×Q₁₆	—	4	2	no	—
139	C₁₃×SD₁₆	—	4	2	no	—
140	C₁₃×SD₁₆	—	4	2	no	—
141	C₁₃×D₈	—	4	2	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	1	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	8	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	4	4	no	—
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3040	C₂×C₁₃	1	1	yes	characteristic
184	#2861	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2028	C₂×C₁₃	1	2	yes	complemented
186	#2027	C₂×C₁₃	1	2	yes	complemented
187	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1994	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1883	C₂×C₁₃	1	2	yes	—
190	#1882	C₂×C₁₃	1	2	yes	complemented
191	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	4	1	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	Q₈×C₁₃	—	8	2	no	—
202	Q₈×C₁₃	—	8	4	no	—
203	Q₈×C₁₃	#124	1	2	yes	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	2	1	no	—
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	#124	1	2	yes	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	—	8	4	no	—
225	C₂×C₄×C₁₃	#120	1	2	yes	—
226	C₂×C₄×C₁₃	#120	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
231	C₈×C₁₃	—	4	1	no	—
232	C₈×C₁₃	—	4	1	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
236	#557	—	2	2	no	—
237	#554	—	2	2	no	—
238	#554	—	2	4	no	—
239	#544	—	2	2	no	—
240	#544	C₂²×C₁₃	1	2	yes	—
241	#533	—	2	1	no	—
242	#533	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#125	—	2	1	no	—
244	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
246	#520	C₂²×C₁₃	1	2	yes	—
247	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
248	#489	—	2	2	no	—
249	#488	—	2	1	no	—
250	#488	—	2	1	no	—
251	#464	—	2	2	no	—
252	#463	—	2	2	no	—
253	#423	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#104	C₂²×C₁₃	1	2	yes	—
255	#419	C₂²×C₁₃	1	2	yes	—
256	#419	C₂²×C₁₃	1	1	yes	characteristic
257	#418	C₂²×C₁₃	1	2	yes	—
258	#418	C₂²×C₁₃	1	1	yes	characteristic
259	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
260	#391	C₂²×C₁₃	1	2	yes	—
261	#390	C₂²×C₁₃	1	2	yes	—
262	#388	—	2	4	no	—
263	C₄³	C₂²×C₁₃	1	1	yes	characteristic
264	#343	C₂²×C₁₃	1	2	yes	—
265	#343	C₂²×C₁₃	1	2	yes	—
266	#339	C₂²×C₁₃	1	2	yes	—
267	#339	C₂²×C₁₃	1	2	yes	—
268	#339	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	8	4	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	—	8	2	no	—
275	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
276	C₂²×C₁₃	#548	1	2	yes	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	8	1	no	—
286	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
287	C₄×C₁₃	#536	1	1	yes	characteristic
288	C₄×C₁₃	#548	1	2	yes	—
289	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
292	#137	—	2	4	no	—
293	AGL(1,ℤ/8)	—	2	4	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×SD₁₆	—	2	1	no	—
296	C₂×SD₁₆	—	2	1	no	—
297	C₂×D₈	—	2	1	no	—
298	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
301	C₄⋊Q₈	—	2	4	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
305	#125	—	2	4	no	—
306	#125	—	2	4	no	—
307	#125	—	2	2	no	—
308	#125	—	2	2	no	—
309	#125	—	2	1	no	—
310	#125	—	2	1	no	—
311	#125	—	2	2	no	—
312	#125	D₄×C₁₃	1	1	yes	characteristic
313	#125	D₄×C₁₃	1	1	yes	characteristic
314	#124	—	2	2	no	—
315	#124	—	2	1	no	—
316	#124	—	2	1	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	D₄×C₁₃	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	4	no	—
329	C₄×D₄	D₄×C₁₃	1	2	yes	—
330	#117	—	2	2	no	—
331	#117	—	2	1	no	—
332	#117	C₂³×C₁₃	1	1	yes	characteristic
333	#117	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	4	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	C₄⋊C₈	—	2	2	no	—
345	#104	—	2	4	no	—
346	#103	—	2	2	no	—
347	#103	—	2	2	no	—
348	#103	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	2	no	—
351	#102	—	2	2	no	—
352	#97	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	#95	—	2	4	no	—
355	C₂×C₁₃	—	2	2	no	—
356	C₂×C₁₃	—	4	2	no	—
357	C₂×C₁₃	—	16	1	no	—
358	C₂×C₁₃	#2436	1	1	yes	characteristic
359	C₂×C₁₃	#3018	1	2	yes	—
360	C₂⁴	—	2	1	no	—
361	#41	—	2	2	no	—
362	#41	C₁₃×#41	1	4	yes	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	Q₁₆	—	4	2	no	—
385	SD₁₆	—	4	2	no	—
386	SD₁₆	—	4	2	no	—
387	D₈	—	4	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	8	no	—
415	C₂²⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	4	no	—
424	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₃	1	2	yes	—
427	C₁₃	#25925	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	1	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	2	no	—
432	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	8	2	no	—
438	Q₈	—	8	4	no	—
439	Q₈	C₁₃×#124	1	2	yes	—
440	D₄	—	2	4	no	—
441	D₄	—	2	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	2	no	—
445	D₄	C₁₃×#124	1	2	yes	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	C₁₃×#120	1	2	yes	—
462	C₂×C₄	C₁₃×#120	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
466	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	1	no	—
476	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
477	C₂²	C₁₃×#548	1	2	yes	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	1	no	—
487	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
488	C₄	C₁₃×#536	1	1	yes	characteristic
489	C₄	C₁₃×#548	1	2	yes	—
490	C₂	—	2	2	no	—
491	C₂	—	4	2	no	—
492	C₂	—	16	1	no	—
493	C₂	C₁₃×#2436	1	1	yes	characteristic
494	C₂	C₁₃×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3504	C₂	semidirect
2. C₁₃×#3140	C₂	semidirect
4. C₁₃×#2861	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#2027	C₂	semidirect
7. C₁₃×#1998	C₂	semidirect
8. C₁₃×#1994	C₂	semidirect
10. C₁₃×#1882	C₂	semidirect
11. C₄×C₁₃×#104	C₂	semidirect
113. #25925	C₁₃	direct (N × H)
181. #3504	C₂×C₁₃	semidirect
182. #3140	C₂×C₁₃	semidirect
184. #2861	C₂×C₁₃	semidirect
185. #2028	C₂×C₁₃	semidirect
186. #2027	C₂×C₁₃	semidirect
187. #1998	C₂×C₁₃	semidirect
188. #1994	C₂×C₁₃	semidirect
190. #1882	C₂×C₁₃	semidirect
191. C₄×#104	C₂×C₁₃	semidirect
427. C₁₃	#25925	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×#3504	2
C₁₃×#3140	2
C₁₃×#3040	2
C₁₃×#2861	2
C₁₃×#2028	2
C₁₃×#2027	2
C₁₃×#1998	2
C₁₃×#1994	2
C₁₃×#1883	2
C₁₃×#1882	2
C₄×C₁₃×#104	2
#25925	13

Subgroups — C13×#25925 #15712264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25925 #15712264