Subgroups — C₁₃×#10408 #15696747

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#127	—	2	1	no	—
9	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#121	—	2	1	no	—
11	C₂×C₁₃×#121	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	—	2	1	no	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#102	—	2	1	no	—
17	C₂×C₁₃×#102	—	2	2	no	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#392	—	2	2	no	—
20	C₁₃×#390	—	2	1	no	—
21	C₁₃×#384	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#340	—	2	1	no	—
24	C₁₃×#340	—	2	1	no	—
25	C₁₃×#331	—	2	2	no	—
26	C₁₃×D₄⋊C₈	—	2	2	no	—
27	C₂²×D₄×C₁₃	—	2	2	no	—
28	C₂²×D₄×C₁₃	—	2	2	no	—
29	C₂²×D₄×C₁₃	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	2	1	no	—
31	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃	D₄	1	2	yes	—
33	C₂³×C₄×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₁₃×#127	—	2	1	no	—
38	C₁₃×#127	—	2	1	no	—
39	C₁₃×#127	—	2	1	no	—
40	C₁₃×#127	—	2	1	no	—
41	C₁₃×#127	—	4	2	no	—
42	C₁₃×#127	—	4	2	no	—
43	C₁₃×#121	—	4	2	no	—
44	C₁₃×#121	—	4	2	no	—
45	C₁₃×#121	—	4	2	no	—
46	C₁₃×#121	—	4	2	no	—
47	C₄×D₄×C₁₃	—	2	1	no	—
48	C₄×D₄×C₁₃	—	2	1	no	—
49	C₄×D₄×C₁₃	—	2	1	no	—
50	C₄×D₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#107	—	4	2	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
67	C₁₃×#102	—	4	4	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₄×C₈×C₁₃	—	2	1	no	—
70	C₄×C₈×C₁₃	—	2	1	no	—
71	C₁₃×#95	—	2	1	no	—
72	#10408	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	1	no	—
74	C₂⁴×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	2	1	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	1	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	4	no	—
85	C₂×D₄×C₁₃	—	4	4	no	—
86	C₂×D₄×C₁₃	—	4	4	no	—
87	C₂×D₄×C₁₃	—	4	4	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	8	2	no	—
101	C₂×D₄×C₁₃	—	8	2	no	—
102	C₂×D₄×C₁₃	D₈	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	4	1	no	—
119	C₂×C₈×C₁₃	—	4	1	no	—
120	C₂×C₈×C₁₃	—	4	1	no	—
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	—	4	1	no	—
123	C₂×C₈×C₁₃	—	4	1	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₄⋊C₄	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	4	1	no	—
134	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
135	C₁₃×C₄⋊C₄	SD₁₆	1	2	yes	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₁₃×C₂²⋊C₄	—	4	1	no	—
140	C₄²×C₁₃	—	4	1	no	—
141	C₄²×C₁₃	—	4	1	no	—
142	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₃	#41	1	1	yes	characteristic
144	C₄²×C₁₃	#41	1	1	yes	characteristic
145	C₄²×C₁₃	#41	1	1	yes	characteristic
146	#2541	C₂×C₁₃	1	1	yes	characteristic
147	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂×#331	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	4	1	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	#120	1	1	yes	characteristic
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	4	no	—
171	D₄×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	4	1	no	—
173	D₄×C₁₃	—	8	2	no	—
174	D₄×C₁₃	—	8	8	no	—
175	D₄×C₁₃	—	8	8	no	—
176	D₄×C₁₃	—	8	1	no	—
177	D₄×C₁₃	—	8	1	no	—
178	D₄×C₁₃	—	8	1	no	—
179	D₄×C₁₃	—	8	1	no	—
180	D₄×C₁₃	—	8	1	no	—
181	D₄×C₁₃	—	8	1	no	—
182	D₄×C₁₃	—	8	1	no	—
183	D₄×C₁₃	—	8	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	8	1	no	—
196	C₂×C₄×C₁₃	—	8	1	no	—
197	C₂×C₄×C₁₃	—	8	1	no	—
198	C₂×C₄×C₁₃	—	8	1	no	—
199	C₂×C₄×C₁₃	—	8	1	no	—
200	C₂×C₄×C₁₃	—	8	1	no	—
201	C₂×C₄×C₁₃	—	8	1	no	—
202	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
203	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
212	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
216	C₈×C₁₃	—	4	2	no	—
217	C₈×C₁₃	—	4	2	no	—
218	C₈×C₁₃	—	8	1	no	—
219	C₂×#127	—	2	1	no	—
220	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#121	—	2	1	no	—
222	C₂×#121	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#107	—	2	1	no	—
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#102	—	2	1	no	—
228	C₂×#102	—	2	2	no	—
229	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	#392	—	2	2	no	—
231	#390	—	2	1	no	—
232	#384	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
234	#340	—	2	1	no	—
235	#340	—	2	1	no	—
236	#331	—	2	2	no	—
237	D₄⋊C₈	—	2	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	—	8	1	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	#394	1	1	yes	characteristic
253	C₂²×C₁₃	#447	1	1	yes	characteristic
254	C₂²×C₁₃	#447	1	1	yes	characteristic
255	C₂²×C₁₃	#450	1	1	yes	characteristic
256	C₂²×C₁₃	#452	1	1	yes	characteristic
257	C₂²×C₁₃	#453	1	1	yes	characteristic
258	C₂²×C₁₃	#455	1	1	yes	characteristic
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	1	no	—
264	C₄×C₁₃	—	16	1	no	—
265	C₄×C₁₃	#459	1	1	yes	characteristic
266	C₄×C₁₃	#460	1	1	yes	characteristic
267	C₄×C₁₃	#466	1	1	yes	characteristic
268	C₄×C₁₃	#468	1	1	yes	characteristic
269	C₄×C₁₃	#480	1	1	yes	characteristic
270	C₄×C₁₃	#482	1	1	yes	characteristic
271	C₄×C₁₃	#486	1	1	yes	characteristic
272	C₄×C₁₃	#490	1	1	yes	characteristic
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
278	C₂²×D₄	D₄×C₁₃	1	2	yes	—
279	C₂³×C₄	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	—	4	2	no	—
288	#127	—	4	2	no	—
289	#121	—	4	2	no	—
290	#121	—	4	2	no	—
291	#121	—	4	2	no	—
292	#121	—	4	2	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
308	#107	—	4	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
313	#102	—	4	4	no	—
314	#102	—	4	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	#95	—	2	1	no	—
318	C₂×C₁₃	—	8	2	no	—
319	C₂×C₁₃	—	16	2	no	—
320	C₂×C₁₃	#1619	1	1	yes	characteristic
321	C₂×C₁₃	#1631	1	1	yes	characteristic
322	C₂×C₁₃	#1639	1	1	yes	characteristic
323	C₂×C₁₃	#1641	1	1	yes	characteristic
324	C₂×C₁₃	#2033	1	1	yes	characteristic
325	C₂×C₁₃	#2037	1	1	yes	characteristic
326	C₂×C₁₃	#2041	1	1	yes	characteristic
327	C₂⁴	—	2	1	no	—
328	C₂⁴	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	8	2	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	C₁₃×D₈	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
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	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	no	—
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
389	C₄⋊C₄	C₁₃×SD₁₆	1	2	yes	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₄²	C₁₃×#41	1	1	yes	characteristic
398	C₄²	C₁₃×#41	1	1	yes	characteristic
399	C₄²	C₁₃×#41	1	1	yes	characteristic
400	C₁₃	#10408	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	C₁₃×#120	1	1	yes	characteristic
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	1	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	8	no	—
423	D₄	—	8	8	no	—
424	D₄	—	8	1	no	—
425	D₄	—	8	1	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	1	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	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	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	—	8	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	1	no	—
448	C₂×C₄	—	8	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
451	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
452	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
453	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
454	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
455	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
456	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
457	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
458	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
459	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
460	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
462	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	8	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	C₁₃×#394	1	1	yes	characteristic
482	C₂²	C₁₃×#447	1	1	yes	characteristic
483	C₂²	C₁₃×#447	1	1	yes	characteristic
484	C₂²	C₁₃×#450	1	1	yes	characteristic
485	C₂²	C₁₃×#452	1	1	yes	characteristic
486	C₂²	C₁₃×#453	1	1	yes	characteristic
487	C₂²	C₁₃×#455	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	1	no	—
493	C₄	—	16	1	no	—
494	C₄	C₁₃×#459	1	1	yes	characteristic
495	C₄	C₁₃×#460	1	1	yes	characteristic
496	C₄	C₁₃×#466	1	1	yes	characteristic
497	C₄	C₁₃×#468	1	1	yes	characteristic
498	C₄	C₁₃×#480	1	1	yes	characteristic
499	C₄	C₁₃×#482	1	1	yes	characteristic
500	C₄	C₁₃×#486	1	1	yes	characteristic
501	C₄	C₁₃×#490	1	1	yes	characteristic
502	C₂	—	8	2	no	—
503	C₂	—	16	2	no	—
504	C₂	C₁₃×#1619	1	1	yes	characteristic
505	C₂	C₁₃×#1631	1	1	yes	characteristic
506	C₂	C₁₃×#1639	1	1	yes	characteristic
507	C₂	C₁₃×#1641	1	1	yes	characteristic
508	C₂	C₁₃×#2033	1	1	yes	characteristic
509	C₂	C₁₃×#2037	1	1	yes	characteristic
510	C₂	C₁₃×#2041	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#2541	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1957	C₂	semidirect
3. C₁₃×#1947	C₂	semidirect
4. C₁₃×#1802	C₂	semidirect
5. C₂×C₁₃×#331	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
66. C₁₃×C₄⋊C₈	D₄	semidirect
72. #10408	C₁₃	direct (N × H)
147. #1957	C₂×C₁₃	semidirect
148. #1947	C₂×C₁₃	semidirect
149. #1802	C₂×C₁₃	semidirect
150. C₂×#331	C₂×C₁₃	semidirect
151. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
152. #1279	C₂×C₁₃	semidirect
312. C₄⋊C₈	D₄×C₁₃	semidirect
400. C₁₃	#10408	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×#2541	2
C₁₃×#1957	2
C₁₃×#1947	2
C₁₃×#1802	2
C₂×C₁₃×#331	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10408	13

Subgroups — C13×#10408 #15696747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10408 #15696747