Finite Group Databasebeta

← C4×C13×#557 #15720508

Subgroups — C4×C13×#557 #15720508

Order 3328.

2220 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#557C211yesmaximal, characteristic
2C13×#2370C216yesmaximal
3C13×#2365C213yesmaximal
4C13×#2355C213yesmaximal
5C13×#2351C212yesmaximal
6Q8×C13×C4⋊C4C211yesmaximal, characteristic
7C4×C13×C4⋊Q8C213yesmaximal
8C4×C13×#125C216yesmaximal
9C42×Q8×C13C213yesmaximal
10C42×Q8×C13C211yesmaximal, characteristic
11C42×Q8×C13C212yesmaximal
12C13×#557C4116yesdirect product factor
13C2×C13×C4⋊Q8C2213yes—
14C2×C13×#125C2216yes—
15C2×C4×Q8×C13C2213yes—
16C2×C4×Q8×C13C2212yes—
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2213yes—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2212yes—
21C2×C4×Q8×C13C2213yes—
22C2×C4×Q8×C13C2211yescharacteristic
23C13×#391C2216yes—
24C13×#389C2216yes—
25C13×#389C2216yes—
26C13×#389C2216yes—
27C13×#389C2216yes—
28C13×#387C22112yes—
29C13×#387C22112yes—
30C13×#384C2213yes—
31C13×#382C2216yes—
32C4×C13×C4⋊C4C2211yescharacteristic
33C4×C13×C4⋊C4C2216yes—
34C4×C13×C4⋊C4C2213yes—
35C4×C13×C4⋊C4C2216yes—
36C4×C13×C4⋊C4C2213yes—
37C4×C13×C4⋊C4C2216yes—
38C4×C13×C4⋊C4C2213yes—
39C4×C13×C4⋊C4C2213yes—
40C4×C13×C4⋊C4C2216yes—
41C4×C13×C4⋊C4C2216yes—
42C4×C13×C4⋊C4C2216yes—
43C4×C13×C4⋊C4C2213yes—
44C4×C13×C4⋊C4C2216yes—
45C43×C13C2216yes—
46C43×C13C2213yes—
47C22×Q8×C13C2313yes—
48C22×Q8×C13C2311yescharacteristic
49C13×C4⋊Q8C2×C4124yes—
50C13×#125C2×C4148yes—
51C4×Q8×C13—28no—
52C4×Q8×C13—24no—
53C4×Q8×C13—212no—
54C4×Q8×C13—212no—
55C4×Q8×C13C2×C4116yes—
56C4×Q8×C13C2×C4124yes—
57C4×Q8×C13C2×C418yes—
58C4×Q8×C13Q818yescomplemented
59C2×C13×C4⋊C4C2313yes—
60C2×C13×C4⋊C4C2316yes—
61C2×C13×C4⋊C4C2313yes—
62C2×C13×C4⋊C4C2316yes—
63C2×C13×C4⋊C4C2316yes—
64C2×C13×C4⋊C4C2316yes—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2316yes—
67C2×C13×C4⋊C4C2313yes—
68C2×C13×C4⋊C4C2316yes—
69C2×C13×C4⋊C4C2316yes—
70C2×C13×C4⋊C4C2313yes—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C42×C13C2316yes—
73C2×C42×C13C2313yes—
74C2×C42×C13C2316yes—
75C2×C42×C13C2313yes—
76C2×C42×C13C2313yes—
77C2×C42×C13C2316yes—
78C2×C42×C13C2312yes—
79C2×C42×C13C2316yes—
80C2×C42×C13C2313yes—
81C2×C42×C13C2316yes—
82C2×C42×C13C2313yes—
83C2×C42×C13C2313yes—
84C2×C42×C13C2311yescharacteristic
85C13×#95C2312yes—
86C13×#95C2316yes—
87C13×#95C2316yes—
88C13×#95C2316yes—
89C13×#95C23112yes—
90C13×#95C23112yes—
91C4×#557C1311yesmaximal, characteristic, direct product factor, Sylow
92C2×Q8×C13—26no—
93C2×Q8×C13—26no—
94C2×Q8×C13C22×C4112yes—
95C2×Q8×C13C22×C414yes—
96C2×Q8×C13C2×Q814yes—
97C2×Q8×C13#4114yes—
98C22×C4×C13C2413yes—
99C22×C4×C13C2416yes—
100C22×C4×C13C2412yes—
101C22×C4×C13C2413yes—
102C22×C4×C13C2416yes—
103C22×C4×C13C2413yes—
104C22×C4×C13C2412yes—
105C22×C4×C13C2411yescharacteristic
106C22×C4×C13C2413yes—
107C22×C4×C13C2411yescharacteristic
108C22×C4×C13C2411yescharacteristic
109C13×C4⋊C4—212no—
110C13×C4⋊C4—212no—
111C13×C4⋊C4—26no—
112C13×C4⋊C4—212no—
113C13×C4⋊C4—26no—
114C13×C4⋊C4—46no—
115C13×C4⋊C4C22×C414yes—
116C13×C4⋊C4C22×C4124yes—
117C13×C4⋊C4C22×C4112yes—
118C13×C4⋊C4C22×C4124yes—
119C13×C4⋊C4C22×C4124yes—
120C13×C4⋊C4C2×Q8112yes—
121C13×C4⋊C4#4114yes—
122C42×C13—212no—
123C42×C13—26no—
124C42×C13—212no—
125C42×C13—26no—
126C42×C13—212no—
127C42×C13—24no—
128C42×C13—26no—
129C42×C13—43no—
130C42×C13—46no—
131C42×C13C22×C4124yes—
132C42×C13C22×C4112yes—
133C42×C13C2×Q8112yes—
134C42×C13#4114yes—
135C2×#557C2×C1311yescharacteristic
136#2370C2×C1316yes—
137#2365C2×C1313yes—
138#2355C2×C1313yes—
139#2351C2×C1312yes—
140Q8×C4⋊C4C2×C1311yescharacteristic
141C4×C4⋊Q8C2×C1313yes—
142C4×#125C2×C1316yes—
143C42×Q8C2×C1313yes—
144C42×Q8C2×C1312yes—
145C42×Q8C2×C1311yescharacteristic
146C23×C13C2511yescharacteristic
147Q8×C13—224no—
148Q8×C13C4×Q8116yescomplemented
149C2×C4×C13—23no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—26no—
153C2×C4×C13—26no—
154C2×C4×C13—22no—
155C2×C4×C13—23no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—23no—
159C2×C4×C13—21no—
160C2×C4×C13—23no—
161C2×C4×C13—26no—
162C2×C4×C13—26no—
163C2×C4×C13—23no—
164C2×C4×C13—23no—
165C2×C4×C13—23no—
166C2×C4×C13—26no—
167C2×C4×C13C23×C414yes—
168C2×C4×C13C23×C416yes—
169C2×C4×C13C23×C4112yes—
170C2×C4×C13C23×C416yes—
171C2×C4×C13C23×C412yes—
172C2×C4×C13C22×Q816yes—
173C2×C4×C13C22×Q816yes—
174C2×C4×C13C22×Q812yes—
175C2×C4×C13C2×#4114yes—
176C2×C4×C13C2×#4112yes—
177C2×C4×C13C2×#4116yes—
178C2×C4×C13C2×#4112yes—
179C2×C4×C13C2×#4112yes—
180C2×C4×C13C2×#4112yes—
181C2×C4×C132−1+412yes—
182#557C4×C13116yesdirect product factor
183C2×C4⋊Q8C22×C1313yes—
184C2×#125C22×C1316yes—
185C2×C4×Q8C22×C1313yes—
186C2×C4×Q8C22×C1312yes—
187C2×C4×Q8C22×C1311yescharacteristic
188C2×C4×Q8C22×C1313yes—
189C2×C4×Q8C22×C1311yescharacteristic
190C2×C4×Q8C22×C1312yes—
191C2×C4×Q8C22×C1313yes—
192C2×C4×Q8C22×C1311yescharacteristic
193#391C22×C1316yes—
194#389C22×C1316yes—
195#389C22×C1316yes—
196#389C22×C1316yes—
197#389C22×C1316yes—
198#387C22×C13112yes—
199#387C22×C13112yes—
200#384C22×C1313yes—
201#382C22×C1316yes—
202C4×C4⋊C4C22×C1316yes—
203C4×C4⋊C4C22×C1316yes—
204C4×C4⋊C4C22×C1313yes—
205C4×C4⋊C4C22×C1316yes—
206C4×C4⋊C4C22×C1313yes—
207C4×C4⋊C4C22×C1316yes—
208C4×C4⋊C4C22×C1313yes—
209C4×C4⋊C4C22×C1313yes—
210C4×C4⋊C4C22×C1316yes—
211C4×C4⋊C4C22×C1316yes—
212C4×C4⋊C4C22×C1316yes—
213C4×C4⋊C4C22×C1313yes—
214C4×C4⋊C4C22×C1311yescharacteristic
215C43C22×C1316yes—
216C43C22×C1313yes—
217C22×C13C24×C411yescharacteristic
218C22×C13C23×Q811yescharacteristic
219C22×C13C22×#4111yescharacteristic
220C22×C13C22×#4111yescharacteristic
221C22×C13C22×#4111yescharacteristic
222C22×C13C2×2−1+411yescharacteristic
223C22×C13#58511yescharacteristic
224C4×C13—212no—
225C4×C13—24no—
226C4×C13—26no—
227C4×C13—26no—
228C4×C13—22no—
229C4×C13—24no—
230C4×C13—46no—
231C4×C13—43no—
232C4×C13C2×C4×Q8112yes—
233C4×C13C4×#4114yes—
234C4×C13#55714yesdirect product factor
235C22×Q8C23×C1313yes—
236C22×Q8C23×C1311yescharacteristic
237C4⋊Q8C2×C4×C13124yes—
238#125C2×C4×C13148yes—
239C4×Q8—28no—
240C4×Q8—24no—
241C4×Q8—212no—
242C4×Q8—212no—
243C4×Q8C2×C4×C13116yes—
244C4×Q8C2×C4×C13124yes—
245C4×Q8C2×C4×C1318yes—
246C4×Q8Q8×C1318yescomplemented
247C2×C4⋊C4C23×C1313yes—
248C2×C4⋊C4C23×C1316yes—
249C2×C4⋊C4C23×C1313yes—
250C2×C4⋊C4C23×C1316yes—
251C2×C4⋊C4C23×C1316yes—
252C2×C4⋊C4C23×C1316yes—
253C2×C4⋊C4C23×C1311yescharacteristic
254C2×C4⋊C4C23×C1316yes—
255C2×C4⋊C4C23×C1313yes—
256C2×C4⋊C4C23×C1316yes—
257C2×C4⋊C4C23×C1316yes—
258C2×C4⋊C4C23×C1313yes—
259C2×C4⋊C4C23×C1311yescharacteristic
260C2×C42C23×C1316yes—
261C2×C42C23×C1316yes—
262C2×C42C23×C1313yes—
263C2×C42C23×C1316yes—
264C2×C42C23×C1313yes—
265C2×C42C23×C1312yes—
266C2×C42C23×C1313yes—
267C2×C42C23×C1316yes—
268C2×C42C23×C1313yes—
269C2×C42C23×C1316yes—
270C2×C42C23×C1313yes—
271C2×C42C23×C1313yes—
272C2×C42C23×C1311yescharacteristic
273#95C23×C1312yes—
274#95C23×C1316yes—
275#95C23×C1316yes—
276#95C23×C1316yes—
277#95C23×C13112yes—
278#95C23×C13112yes—
279C2×C13C22×C4×Q811yescharacteristic
280C2×C13C2×C4×#4111yescharacteristic
281C2×C13C4×2−1+411yescharacteristic
282C2×C13C2×#55711yescharacteristic
283C2×C13Q8×#4111yescharacteristic
284C2×C13#348011yescharacteristic
285C2×C13#348211yescharacteristic
286C2×Q8—26no—
287C2×Q8—26no—
288C2×Q8C22×C4×C13112yes—
289C2×Q8C22×C4×C1314yes—
290C2×Q8C2×Q8×C1314yes—
291C2×Q8C13×#4114yes—
292C22×C4C24×C1313yes—
293C22×C4C24×C1316yes—
294C22×C4C24×C1312yes—
295C22×C4C24×C1313yes—
296C22×C4C24×C1316yes—
297C22×C4C24×C1313yes—
298C22×C4C24×C1312yes—
299C22×C4C24×C1311yescharacteristic
300C22×C4C24×C1313yes—
301C22×C4C24×C1311yescharacteristic
302C22×C4C24×C1311yescharacteristic
303C4⋊C4—212no—
304C4⋊C4—212no—
305C4⋊C4—26no—
306C4⋊C4—212no—
307C4⋊C4—26no—
308C4⋊C4—46no—
309C4⋊C4C22×C4×C1314yes—
310C4⋊C4C22×C4×C13124yes—
311C4⋊C4C22×C4×C13112yes—
312C4⋊C4C22×C4×C13124yes—
313C4⋊C4C22×C4×C13124yes—
314C4⋊C4C2×Q8×C13112yes—
315C4⋊C4C13×#4114yes—
316C42—212no—
317C42—26no—
318C42—212no—
319C42—26no—
320C42—212no—
321C42—24no—
322C42—26no—
323C42—43no—
324C42—46no—
325C42C22×C4×C13124yes—
326C42C22×C4×C13112yes—
327C42C2×Q8×C13112yes—
328C42C13×#4114yes—
329C13C4×#55711yescharacteristic, direct product factor, Sylow
330C23C25×C1311yescharacteristic
331Q8—224no—
332Q8C4×Q8×C13116yescomplemented
333C2×C4—23no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—26no—
337C2×C4—26no—
338C2×C4—22no—
339C2×C4—23no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—23no—
343C2×C4—21no—
344C2×C4—23no—
345C2×C4—26no—
346C2×C4—26no—
347C2×C4—23no—
348C2×C4—23no—
349C2×C4—23no—
350C2×C4—26no—
351C2×C4C23×C4×C1314yes—
352C2×C4C23×C4×C1316yes—
353C2×C4C23×C4×C13112yes—
354C2×C4C23×C4×C1316yes—
355C2×C4C23×C4×C1312yes—
356C2×C4C22×Q8×C1316yes—
357C2×C4C22×Q8×C1316yes—
358C2×C4C22×Q8×C1312yes—
359C2×C4C2×C13×#4114yes—
360C2×C4C2×C13×#4112yes—
361C2×C4C2×C13×#4116yes—
362C2×C4C2×C13×#4112yes—
363C2×C4C2×C13×#4112yes—
364C2×C4C2×C13×#4112yes—
365C2×C4C13×2−1+412yes—
366C22C24×C4×C1311yescharacteristic
367C22C23×Q8×C1311yescharacteristic
368C22C22×C13×#4111yescharacteristic
369C22C22×C13×#4111yescharacteristic
370C22C22×C13×#4111yescharacteristic
371C22C2×C13×2−1+411yescharacteristic
372C22C13×#58511yescharacteristic
373C4—212no—
374C4—24no—
375C4—26no—
376C4—26no—
377C4—22no—
378C4—24no—
379C4—46no—
380C4—43no—
381C4C2×C4×Q8×C13112yes—
382C4C4×C13×#4114yes—
383C4C13×#55714yesdirect product factor
384C2C22×C4×Q8×C1311yescharacteristic
385C2C2×C4×C13×#4111yescharacteristic
386C2C4×C13×2−1+411yescharacteristic
387C2C2×C13×#55711yescharacteristic
388C2Q8×C13×#4111yescharacteristic
389C2C13×#348011yescharacteristic
390C2C13×#348211yescharacteristic
subgroupG/H
centerC22×C4×C13C24
commutatorC22C24×C4×C13
Frattini, cosocleC23C25×C13
socle, prime radicalC23×C13C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
12. C13×#557C4direct (N × H)
58. C4×Q8×C13Q8semidirect
91. C4×#557C13direct (N × H)
148. Q8×C13C4×Q8semidirect
182. #557C4×C13direct (N × H)
234. C4×C13#557direct (N × H)
246. C4×Q8Q8×C13semidirect
329. C13C4×#557direct (N × H)
332. Q8C4×Q8×C13semidirect
383. C4C13×#557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5572
C13×#23702
C13×#23652
C13×#23552
C13×#23512
Q8×C13×C4⋊C42
C4×C13×C4⋊Q82
C4×C13×#1252
C42×Q8×C132
C4×#55713