Finite Group Databasebeta

← C3×#10602336 #14302042

Subgroups — C3×#10602336 #14302042

Order 1920.

1196 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#4099C211yesmaximal, characteristic
3C3×#65536C211yesmaximal, characteristic, complemented
4C2×C3×#3938C212yesmaximal, complemented
5C3×#64747C212yesmaximal, complemented
6#10602336C311yesmaximal, characteristic, direct product factor, Hall
7C25×C3×C5C2211yescharacteristic
8C23×C3×C4×C5—21no—
9C22×C3×C22⋊D5C412yescomplemented
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4—24no—
13C2×C3×C5×C22⋊C4C2212yes—
14C3×#4099—21no—
15C3×#4099—22no—
16C3×#4099—21no—
17C2×C3×C22⋊Dic5—22no—
18C2×C3×C22⋊Dic5C412yescomplemented
19C2×C3×C22⋊Dic5C2212yes—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C3×#3938—24no—
22C3×#1898—51nomaximal, Hall
23C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
24C2×#4099C2×C311yescharacteristic
25#65536C2×C311yescharacteristic, complemented
26C2×#3938C2×C312yescomplemented
27#64747C2×C312yescomplemented
28C24×C3×C5—22no—
29C24×C3×C5—22no—
30C24×C3×C5—44no—
31C24×C3×C5C2×C412yes—
32C24×C3×C5D411yescharacteristic
33C24×C3×C5D412yes—
34C24×C3×C5D411yescharacteristic
35C24×C3×C5C2311yescharacteristic
36C23×C3×D5C2×C411yescharacteristic, complemented
37C22×C3×C4×C5—24no—
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5—44no—
40C2×C3×C22⋊D5—22no—
41C2×C3×C22⋊D5—22no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—22no—
45C2×C3×C22⋊D5—22no—
46C2×C3×C22⋊D5—44no—
47C22×C3×Dic5—22no—
48C22×C3×Dic5C2×C411yescharacteristic, complemented
49C22×C3×Dic5C2×C412yescomplemented
50C3×C5×C22⋊C4—24no—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4D414yescomplemented
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—22no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—22no—
58C3×C22⋊Dic5—22no—
59C3×C22⋊Dic5—44no—
60C2×C3×#120—51no—
61C22×C3×C22⋊C4D511yescharacteristic, complemented
62C2×C3×#99—52no—
63C3×#379—51no—
64C3×#342—52no—
65C25×C5C22×C311yescharacteristic
66C23×C4×C5—21no—
67C22×C22⋊D5C3×C412yescomplemented
68C22×C22⋊D5C22×C311yescharacteristic
69C2×C5×C22⋊C4—21no—
70C2×C5×C22⋊C4—24no—
71C2×C5×C22⋊C4C22×C312yes—
72#4099—22no—
73#4099—21no—
74#4099—21no—
75C2×C22⋊Dic5—22no—
76C2×C22⋊Dic5C3×C412yescomplemented
77C2×C22⋊Dic5C22×C312yes—
78C2×C22⋊Dic5C22×C311yescharacteristic
79#3938—24no—
80#1898—51noSylow
81C23×C3×C5—24no—
82C23×C3×C5—21no—
83C23×C3×C5—21no—
84C23×C3×C5—24no—
85C23×C3×C5—24no—
86C23×C3×C5—24no—
87C23×C3×C5—21no—
88C23×C3×C5—24no—
89C23×C3×C5—21no—
90C23×C3×C5—42no—
91C23×C3×C5—42no—
92C23×C3×C5—42no—
93C23×C3×C5—42no—
94C23×C3×C5—48no—
95C23×C3×C5—48no—
96C23×C3×C5C22⋊C412yes—
97C23×C3×C5C22⋊C412yes—
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C23×C3×C5C2×D411yescharacteristic
101C23×C3×C5C2×D412yes—
102C23×C3×C5#4112yes—
103C22×C3×D5—21no—
104C22×C3×D5—22no—
105C22×C3×D5—42no—
106C2×C3×C4×C5—24no—
107C2×C3×C4×C5—48no—
108C2×C3×C4×C5—44no—
109C3×C22⋊D5—44no—
110C3×C22⋊D5—44no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—42no—
113C3×C22⋊D5—41no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5—44no—
119C2×C3×Dic5—42no—
120C25×C3C2×D511yescharacteristic
121C22×C3×D4—51no—
122C22×C3×D4—52no—
123C23×C3×C4—21no—
124C3×#120—102no—
125C3×#120—101no—
126C3×#120—101no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4—52no—
130C2×C3×C22⋊C4—51no—
131C2×C3×C22⋊C4—52no—
132C2×C3×C22⋊C4—102no—
133C2×C3×C22⋊C4C2×D512yes—
134C3×#99—104no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—44no—
138C24×C5C2×C3×C412yes—
139C24×C5C3×D412yes—
140C24×C5C3×D411yescharacteristic
141C24×C5C3×D411yescharacteristic
142C24×C5C23×C311yescharacteristic
143C23×D5C2×C3×C411yescharacteristic, complemented
144C22×C4×C5—24no—
145C22×C4×C5—22no—
146C22×C4×C5—44no—
147C2×C22⋊D5—22no—
148C2×C22⋊D5—22no—
149C2×C22⋊D5—21no—
150C2×C22⋊D5—21no—
151C2×C22⋊D5—22no—
152C2×C22⋊D5—22no—
153C2×C22⋊D5—44no—
154C22×Dic5—22no—
155C22×Dic5C2×C3×C411yescharacteristic, complemented
156C22×Dic5C2×C3×C412yescomplemented
157C5×C22⋊C4—24no—
158C5×C22⋊C4—22no—
159C5×C22⋊C4C3×D414yescomplemented
160C22⋊Dic5—22no—
161C22⋊Dic5—22no—
162C22⋊Dic5—21no—
163C22⋊Dic5—21no—
164C22⋊Dic5—22no—
165C22⋊Dic5—22no—
166C22⋊Dic5—44no—
167C2×#120—51no—
168C22×C22⋊C4C3×D511yescharacteristic, complemented
169C2×#99—52no—
170#379—51no—
171#342—52no—
172C22×C3×C5—24no—
173C22×C3×C5—24no—
174C22×C3×C5—22no—
175C22×C3×C5—22no—
176C22×C3×C5—22no—
177C22×C3×C5—22no—
178C22×C3×C5—22no—
179C22×C3×C5—22no—
180C22×C3×C5—22no—
181C22×C3×C5—22no—
182C22×C3×C5—42no—
183C22×C3×C5—42no—
184C22×C3×C5—48no—
185C22×C3×C5—48no—
186C22×C3×C5—42no—
187C22×C3×C5—42no—
188C22×C3×C5#9914yescomplemented
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5C4×D412yes—
191C22×C3×C5#12011yescharacteristic
192C22×C3×C5#12112yes—
193C22×C3×C5#12311yescharacteristic
194C2×C3×D5—41no—
195C2×C3×D5—42no—
196C2×C3×D5—82no—
197C3×C4×C5—44no—
198C3×Dic5—41no—
199C3×Dic5—42no—
200C3×Dic5—82no—
201C24×C3—22no—
202C24×C3—22no—
203C24×C3—44no—
204C24×C3—51no—
205C24×C3C4×D512yes—
206C24×C3D2012yes—
207C24×C3C22⋊D511yescharacteristic
208C24×C3C22⋊D511yescharacteristic
209C24×C3C22×D511yescharacteristic
210C2×C3×D4—102no—
211C2×C3×D4—102no—
212C2×C3×D4—101no—
213C2×C3×D4—102no—
214C2×C3×D4—102no—
215C2×C3×D4—101no—
216C2×C3×D4—204no—
217C22×C3×C4—24no—
218C22×C3×C4—22no—
219C22×C3×C4—44no—
220C22×C3×C4—51no—
221C22×C3×C4—52no—
222C22×C3×C4—102no—
223C3×C22⋊C4—24no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—102no—
226C3×C22⋊C4—102no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—101no—
229C3×C22⋊C4—102no—
230C3×C22⋊C4—102no—
231C3×C22⋊C4—204no—
232C3×C22⋊C4C22⋊D514yescomplemented
233C23×C5—24no—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5—24no—
237C23×C5—24no—
238C23×C5—24no—
239C23×C5—21no—
240C23×C5—24no—
241C23×C5—21no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—48no—
247C23×C5—48no—
248C23×C5C3×C22⋊C412yes—
249C23×C5C3×C22⋊C412yes—
250C23×C5C22×C3×C411yescharacteristic
251C23×C5C2×C3×D411yescharacteristic
252C23×C5C2×C3×D411yescharacteristic
253C23×C5C2×C3×D412yes—
254C23×C5C3×#4112yes—
255C22×D5—21no—
256C22×D5—22no—
257C22×D5—42no—
258C2×C4×C5—24no—
259C2×C4×C5—48no—
260C2×C4×C5—44no—
261C22⋊D5—44no—
262C22⋊D5—44no—
263C22⋊D5—41no—
264C22⋊D5—42no—
265C22⋊D5—41no—
266C2×Dic5—21no—
267C2×Dic5—22no—
268C2×Dic5—22no—
269C2×Dic5—42no—
270C2×Dic5—44no—
271C2×Dic5—42no—
272C25C2×C3×D511yescharacteristic
273C22×D4—51no—
274C22×D4—52no—
275C23×C4—21no—
276#120—102no—
277#120—101no—
278#120—101no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—52no—
282C2×C22⋊C4—51no—
283C2×C22⋊C4—52no—
284C2×C22⋊C4—102no—
285C2×C22⋊C4C2×C3×D512yes—
286#99—104no—
287C2×C3×C5—22no—
288C2×C3×C5—21no—
289C2×C3×C5—22no—
290C2×C3×C5—24no—
291C2×C3×C5—21no—
292C2×C3×C5—42no—
293C2×C3×C5#38611yescharacteristic
294C2×C3×C5C2×#9912yes—
295C3×D5—81no—
296C23×C3—21no—
297C23×C3—24no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3—24no—
303C23×C3—21no—
304C23×C3—24no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—48no—
310C23×C3—48no—
311C23×C3—101no—
312C23×C3—102no—
313C23×C3—202no—
314C23×C3#68512yes—
315C23×C3#68512yes—
316C23×C3C2×C4×D511yescharacteristic
317C23×C3C2×D2011yescharacteristic
318C23×C3#70912yes—
319C23×C3C2×C22⋊D511yescharacteristic
320C23×C3C2×C22⋊D512yes—
321C3×D4—204no—
322C3×D4—201no—
323C3×D4—204no—
324C3×D4—201no—
325C3×D4—202no—
326C2×C3×C4—24no—
327C2×C3×C4—48no—
328C2×C3×C4—44no—
329C2×C3×C4—102no—
330C2×C3×C4—101no—
331C2×C3×C4—102no—
332C2×C3×C4—202no—
333C2×C3×C4—204no—
334C2×C3×C4—202no—
335C22×C5—24no—
336C22×C5—24no—
337C22×C5—22no—
338C22×C5—22no—
339C22×C5—22no—
340C22×C5—22no—
341C22×C5—22no—
342C22×C5—22no—
343C22×C5—22no—
344C22×C5—22no—
345C22×C5—42no—
346C22×C5—42no—
347C22×C5—48no—
348C22×C5—48no—
349C22×C5—42no—
350C22×C5—42no—
351C22×C5C3×#9914yescomplemented
352C22×C5C2×C3×C22⋊C411yescharacteristic
353C22×C5C3×C4×D412yes—
354C22×C5C3×#12011yescharacteristic
355C22×C5C3×#12112yes—
356C22×C5C3×#12311yescharacteristic
357C2×D5—41no—
358C2×D5—42no—
359C2×D5—82no—
360C4×C5—44no—
361Dic5—41no—
362Dic5—42no—
363Dic5—82no—
364C24—22no—
365C24—22no—
366C24—44no—
367C24—51no—
368C24C3×C4×D512yes—
369C24C3×D2012yes—
370C24C3×C22⋊D511yescharacteristic
371C24C3×C22⋊D511yescharacteristic
372C24C22×C3×D511yescharacteristic
373C2×D4—102no—
374C2×D4—102no—
375C2×D4—101no—
376C2×D4—102no—
377C2×D4—102no—
378C2×D4—101no—
379C2×D4—204no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—44no—
383C22×C4—51no—
384C22×C4—52no—
385C22×C4—102no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—102no—
389C22⋊C4—102no—
390C22⋊C4—101no—
391C22⋊C4—101no—
392C22⋊C4—102no—
393C22⋊C4—102no—
394C22⋊C4—204no—
395C22⋊C4C3×C22⋊D514yescomplemented
396C3×C5#189811yescharacteristic, complemented, Hall
397C22×C3—24no—
398C22×C3—24no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—48no—
410C22×C3—48no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—202no—
414C22×C3—201no—
415C22×C3—402no—
416C22×C3#393814yescomplemented
417C22×C3C2×#68511yescharacteristic
418C22×C3C4×C22⋊D512yes—
419C22×C3#407511yescharacteristic
420C22×C3#407612yes—
421C22×C3#409911yescharacteristic
422C3×C4—44no—
423C3×C4—202no—
424C3×C4—201no—
425C3×C4—402no—
426C2×C5—22no—
427C2×C5—21no—
428C2×C5—22no—
429C2×C5—24no—
430C2×C5—21no—
431C2×C5—42no—
432C2×C5C3×#38611yescharacteristic
433C2×C5C2×C3×#9912yes—
434D5—81no—
435C23—21no—
436C23—24no—
437C23—21no—
438C23—21no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—21no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—48no—
449C23—48no—
450C23—101no—
451C23—102no—
452C23—202no—
453C23C3×#68512yes—
454C23C3×#68512yes—
455C23C2×C3×C4×D511yescharacteristic
456C23C2×C3×D2011yescharacteristic
457C23C3×#70912yes—
458C23C2×C3×C22⋊D511yescharacteristic
459C23C2×C3×C22⋊D512yes—
460D4—204no—
461D4—201no—
462D4—204no—
463D4—201no—
464D4—202no—
465C2×C4—24no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—102no—
469C2×C4—101no—
470C2×C4—102no—
471C2×C4—202no—
472C2×C4—204no—
473C2×C4—202no—
474C2×C3—21no—
475C2×C3—22no—
476C2×C3—24no—
477C2×C3—21no—
478C2×C3—22no—
479C2×C3—42no—
480C2×C3—401no—
481C2×C3C2×#393812yes—
482C2×C3#6550211yescharacteristic
483C5C3×#189811yescharacteristic, complemented, Sylow
484C22—24no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—48no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—202no—
501C22—201no—
502C22—402no—
503C22C3×#393814yescomplemented
504C22C2×C3×#68511yescharacteristic
505C22C3×C4×C22⋊D512yes—
506C22C3×#407511yescharacteristic
507C22C3×#407612yes—
508C22C3×#409911yescharacteristic
509C4—44no—
510C4—202no—
511C4—201no—
512C4—402no—
513C3#1060233611yescharacteristic, direct product factor, Sylow
514C2—21no—
515C2—22no—
516C2—24no—
517C2—21no—
518C2—22no—
519C2—42no—
520C2—401no—
521C2C2×C3×#393812yes—
522C2C3×#6550211yescharacteristic
subgroupG/H
centerC22×C3C2×#685
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4099C2
cosocleC24×C5C23×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#1898
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C25×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C22⋊C4C2semidirect
3. C3×#65536C2semidirect
4. C2×C3×#3938C2semidirect
5. C3×#64747C2semidirect
6. #10602336C3direct (N × H)
9. C22×C3×C22⋊D5C4semidirect
18. C2×C3×C22⋊Dic5C4semidirect
23. C22×C5×C22⋊C4C2×C3semidirect
25. #65536C2×C3semidirect
26. C2×#3938C2×C3semidirect
27. #64747C2×C3semidirect
36. C23×C3×D5C2×C4semidirect
48. C22×C3×Dic5C2×C4semidirect
49. C22×C3×Dic5C2×C4semidirect
52. C3×C5×C22⋊C4D4semidirect
61. C22×C3×C22⋊C4D5semidirect
67. C22×C22⋊D5C3×C4semidirect
76. C2×C22⋊Dic5C3×C4semidirect
143. C23×D5C2×C3×C4semidirect
155. C22×Dic5C2×C3×C4semidirect
156. C22×Dic5C2×C3×C4semidirect
159. C5×C22⋊C4C3×D4semidirect
168. C22×C22⋊C4C3×D5semidirect
188. C22×C3×C5#99semidirect
232. C3×C22⋊C4C22⋊D5semidirect
351. C22×C5C3×#99semidirect
395. C22⋊C4C3×C22⋊D5semidirect
396. C3×C5#1898semidirect
416. C22×C3#3938semidirect
483. C5C3×#1898semidirect
503. C22C3×#3938semidirect
513. C3#10602336direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C2×C3×#40992
C3×#655362
C2×C3×#39382
C3×#647472
#106023363
C3×#18985