Finite Group Databasebeta

← C3×#10605792 #14327985

Subgroups — C3×#10605792 #14327985

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C3×#65246C212yesmaximal
5C3×#65233C212yesmaximal, complemented
6C3×#64958C212yesmaximal, complemented
7C3×#64955C211yesmaximal, characteristic, complemented
8C3×#64953C211yesmaximal, characteristic, complemented
9C3×#64939C211yesmaximal, characteristic, complemented
10C3×#64938C212yesmaximal, complemented
11C3×#64938C211yesmaximal, characteristic, complemented
12#10605792C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2212yes—
17C2×C3×C22⋊Dic5C2212yes—
18C2×C3×C22⋊Dic5C2211yescharacteristic
19C3×C4×C22⋊D5C418yescomplemented
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×#683C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30C3×C5×#95C2211yescharacteristic
31C3×C5×#95C2212yes—
32C3×C5×#95C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36C3×#3963C2212yes—
37C3×#2357—51nomaximal, Hall
38C2×C4×C22⋊D5C2×C311yescharacteristic
39C5×#381C2×C311yescharacteristic, complemented
40C4×C22⋊Dic5C2×C311yescharacteristic, complemented
41#65246C2×C312yes—
42#65233C2×C312yescomplemented
43#64958C2×C312yescomplemented
44#64955C2×C311yescharacteristic, complemented
45#64953C2×C311yescharacteristic, complemented
46#64939C2×C311yescharacteristic, complemented
47#64938C2×C312yescomplemented
48#64938C2×C311yescharacteristic, complemented
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—42no—
66C2×C3×C4×D5C2×C414yes—
67C3×C5×C22⋊C4—42no—
68C3×C22⋊Dic5—24no—
69C3×C22⋊Dic5C2×C414yes—
70C3×#685—24no—
71C3×#685—42no—
72C3×#685C2×C414yes—
73C3×#683—24no—
74C3×#683—24no—
75C3×#683C2×C414yes—
76C3×C4×Dic5—24no—
77C3×C4×Dic5—42no—
78C3×C4×Dic5—42no—
79C3×C4×Dic5C2×C414yes—
80C2×C3×C4×D4—51no—
81C3×#390—52no—
82C3×#388—52no—
83C3×#388—52no—
84C3×#382—51no—
85C3×#381—51no—
86C3×#381D511yescharacteristic, complemented
87C3×C4×C4⋊C4—51no—
88C3×C4×C4⋊C4—52no—
89C3×C4×C22⋊C4—51no—
90C3×C4×C22⋊C4—51no—
91C23×C4×C5C22×C311yescharacteristic
92C22×C22⋊D5C22×C311yescharacteristic
93C22×C4×D5C22×C311yescharacteristic
94C2×C5×C22⋊C4C22×C312yes—
95C2×C22⋊Dic5C22×C312yes—
96C2×C22⋊Dic5C22×C311yescharacteristic
97C4×C22⋊D5C3×C418yescomplemented
98C2×#685C22×C312yes—
99C2×#685C22×C312yes—
100C2×#685C22×C311yescharacteristic
101C2×#683C22×C312yes—
102C2×#683C22×C312yes—
103C2×#683C22×C311yescharacteristic
104C2×C4×Dic5C22×C312yes—
105C2×C4×Dic5C22×C312yes—
106C2×C4×Dic5C22×C312yes—
107C2×C4×Dic5C22×C311yescharacteristic
108C5×#95C22×C311yescharacteristic
109C5×#95C22×C312yes—
110C5×#95C22×C311yescharacteristic
111#3963C22×C312yes—
112#3963C22×C311yescharacteristic
113#3963C22×C311yescharacteristic
114#3963C22×C312yes—
115#2357—51noSylow
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—22no—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—44no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C3×C22⋊D5—28no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5C22×C412yes—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5#4114yes—
150C2×C3×Dic5#4112yes—
151C2×C3×Dic5#4112yes—
152C3×C4×D5—44no—
153C22×C3×D4—51no—
154C23×C3×C4—51no—
155C23×C3×C4C2×D511yescharacteristic
156C3×C4×D4—58no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—52no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4—52no—
163C2×C3×C22⋊C4—52no—
164C2×C3×C22⋊C4—52no—
165C2×C3×C22⋊C4C2×D512yes—
166C2×C3×C42—51no—
167C2×C3×C42—52no—
168C2×C3×C42—52no—
169C2×C3×C42—52no—
170C3×#95—51no—
171C3×#95—51no—
172C3×#95—52no—
173C3×#95—52no—
174C3×#95C2×D511yescharacteristic
175C3×#95C2×D511yescharacteristic
176C3×#95C2×D512yes—
177C24×C5C23×C311yescharacteristic
178C23×D5C23×C311yescharacteristic
179C22×C4×C5—42no—
180C22×C4×C5C2×C3×C414yes—
181C22×C4×C5C23×C312yes—
182C22×C4×C5C23×C312yes—
183C22×C4×C5C23×C311yescharacteristic
184C22×C4×C5C23×C311yescharacteristic
185C2×C22⋊D5—22no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5C2×C3×C414yes—
188C22×Dic5C23×C312yes—
189C22×Dic5C23×C311yescharacteristic
190C22×Dic5C23×C311yescharacteristic
191C22×Dic5C23×C312yes—
192C22×Dic5C23×C311yescharacteristic
193C2×C4×D5—42no—
194C2×C4×D5C2×C3×C414yes—
195C5×C22⋊C4—42no—
196C22⋊Dic5—24no—
197C22⋊Dic5C2×C3×C414yes—
198#685—24no—
199#685—42no—
200#685C2×C3×C414yes—
201#683—24no—
202#683—24no—
203#683C2×C3×C414yes—
204C4×Dic5—24no—
205C4×Dic5—42no—
206C4×Dic5—42no—
207C4×Dic5C2×C3×C414yes—
208C2×C4×D4—51no—
209#390—52no—
210#388—52no—
211#388—52no—
212#382—51no—
213#381—51no—
214#381C3×D511yescharacteristic, complemented
215C4×C4⋊C4—51no—
216C4×C4⋊C4—52no—
217C4×C22⋊C4—51no—
218C4×C22⋊C4—51no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—42no—
223C22×C3×C5—42no—
224C22×C3×C5C23×C411yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4112yes—
228C22×C3×C5H(5,𝔽2)12yes—
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C3×C4×C5—22no—
235C3×C4×C5—22no—
236C3×C4×C5—42no—
237C3×C4×C5—42no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C3×Dic5—24no—
241C3×Dic5—42no—
242C3×Dic5#11714yes—
243C24×C3—51no—
244C24×C3C22×D511yescharacteristic
245C2×C3×D4—54no—
246C2×C3×D4—102no—
247C2×C3×D4—102no—
248C22×C3×C4—42no—
249C22×C3×C4—51no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—52no—
253C22×C3×C4—54no—
254C22×C3×C4—52no—
255C22×C3×C4—202no—
256C22×C3×C4C4×D514yes—
257C22×C3×C4C22×D512yes—
258C22×C3×C4C22×D512yes—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D511yescharacteristic
261C3×C4⋊C4—54no—
262C3×C4⋊C4—104no—
263C3×C4⋊C4—104no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4—54no—
266C3×C22⋊C4—54no—
267C3×C22⋊C4—104no—
268C3×C22⋊C4—104no—
269C3×C22⋊C4—202no—
270C3×C42—54no—
271C3×C42—104no—
272C3×C42—202no—
273C3×C42—202no—
274C23×C5—22no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—22no—
278C23×C5C22×C3×C412yes—
279C23×C5C24×C311yescharacteristic
280C22×D5—22no—
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—22no—
284C22×D5C22×C3×C412yes—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—44no—
294C2×C4×C5C22×C3×C412yes—
295C2×C4×C5C22×C3×C412yes—
296C22⋊D5—28no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5C22×C3×C412yes—
305C2×Dic5C22×C3×C412yes—
306C2×Dic5C22×C3×C412yes—
307C2×Dic5C3×#4114yes—
308C2×Dic5C3×#4112yes—
309C2×Dic5C3×#4112yes—
310C4×D5—44no—
311C22×D4—51no—
312C23×C4—51no—
313C23×C4C2×C3×D511yescharacteristic
314C4×D4—58no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—52no—
317C2×C4⋊C4—52no—
318C2×C22⋊C4—51no—
319C2×C22⋊C4—51no—
320C2×C22⋊C4—52no—
321C2×C22⋊C4—52no—
322C2×C22⋊C4—52no—
323C2×C22⋊C4C2×C3×D512yes—
324C2×C42—51no—
325C2×C42—52no—
326C2×C42—52no—
327C2×C42—52no—
328#95—51no—
329#95—51no—
330#95—52no—
331#95—52no—
332#95C2×C3×D511yescharacteristic
333#95C2×C3×D511yescharacteristic
334#95C2×C3×D512yes—
335C2×C3×C5—42no—
336C2×C3×C5C2×#11711yescharacteristic
337C2×C3×C5C4×#4111yescharacteristic
338C2×C3×C5#51811yescharacteristic
339C2×C3×C5#55312yes—
340C2×C3×C5#55912yes—
341C3×D5—42no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—52no—
347C23×C3—102no—
348C23×C3—102no—
349C23×C3—101no—
350C23×C3—101no—
351C23×C3C2×C4×D512yes—
352C23×C3C23×D511yescharacteristic
353C3×D4—108no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—44no—
363C2×C3×C4—52no—
364C2×C3×C4—52no—
365C2×C3×C4—52no—
366C2×C3×C4—52no—
367C2×C3×C4—52no—
368C2×C3×C4—54no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—102no—
375C2×C3×C4—102no—
376C2×C3×C4—204no—
377C2×C3×C4C2×C4×D512yes—
378C2×C3×C4C2×C4×D512yes—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5C23×C3×C411yescharacteristic
385C22×C5C2×C3×#4111yescharacteristic
386C22×C5C2×C3×#4112yes—
387C22×C5C2×C3×#4111yescharacteristic
388C22×C5C3×H(5,𝔽2)12yes—
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—22no—
392C2×D5—42no—
393C2×D5—42no—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—42no—
397C4×C5—42no—
398Dic5—22no—
399Dic5—22no—
400Dic5—24no—
401Dic5—42no—
402Dic5C3×#11714yes—
403C24—51no—
404C24C22×C3×D511yescharacteristic
405C2×D4—54no—
406C2×D4—102no—
407C2×D4—102no—
408C22×C4—42no—
409C22×C4—51no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—52no—
413C22×C4—54no—
414C22×C4—52no—
415C22×C4—202no—
416C22×C4C3×C4×D514yes—
417C22×C4C22×C3×D512yes—
418C22×C4C22×C3×D512yes—
419C22×C4C22×C3×D511yescharacteristic
420C22×C4C22×C3×D511yescharacteristic
421C4⋊C4—54no—
422C4⋊C4—104no—
423C4⋊C4—104no—
424C22⋊C4—42no—
425C22⋊C4—54no—
426C22⋊C4—54no—
427C22⋊C4—104no—
428C22⋊C4—104no—
429C22⋊C4—202no—
430C42—54no—
431C42—104no—
432C42—202no—
433C42—202no—
434C3×C5#235711yescharacteristic, complemented, Hall
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3—102no—
443C22×C3—202no—
444C22×C3—202no—
445C22×C3C22×C4×D511yescharacteristic
446C22×C3#414412yes—
447C22×C3D5×#4111yescharacteristic
448C22×C3D5×#4111yescharacteristic
449C22×C3D5×#4112yes—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—54no—
455C3×C4—102no—
456C3×C4—102no—
457C3×C4—104no—
458C3×C4—202no—
459C2×C5—42no—
460C2×C5C2×C3×#11711yescharacteristic
461C2×C5C3×C4×#4111yescharacteristic
462C2×C5C3×#51811yescharacteristic
463C2×C5C3×#55312yes—
464C2×C5C3×#55912yes—
465D5—42no—
466C23—22no—
467C23—22no—
468C23—21no—
469C23—21no—
470C23—52no—
471C23—102no—
472C23—102no—
473C23—101no—
474C23—101no—
475C23C2×C3×C4×D512yes—
476C23C23×C3×D511yescharacteristic
477D4—108no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—44no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—52no—
492C2×C4—54no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—204no—
501C2×C4C2×C3×C4×D512yes—
502C2×C4C2×C3×C4×D512yes—
503C2×C3—42no—
504C2×C3—202no—
505C2×C3#6582011yescharacteristic
506C2×C3D5×#11711yescharacteristic
507C2×C3#6585611yescharacteristic
508C2×C3#6599512yes—
509C2×C3#6599812yes—
510C5C3×#235711yescharacteristic, complemented, Sylow
511C22—22no—
512C22—22no—
513C22—22no—
514C22—42no—
515C22—42no—
516C22—102no—
517C22—102no—
518C22—102no—
519C22—202no—
520C22—202no—
521C22C22×C3×C4×D511yescharacteristic
522C22C3×#414412yes—
523C22C3×D5×#4111yescharacteristic
524C22C3×D5×#4111yescharacteristic
525C22C3×D5×#4112yes—
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—54no—
531C4—102no—
532C4—104no—
533C4—102no—
534C4—202no—
535C3#1060579211yescharacteristic, direct product factor, Sylow
536C2—42no—
537C2—202no—
538C2C3×#6582011yescharacteristic
539C2C3×D5×#11711yescharacteristic
540C2C3×#6585611yescharacteristic
541C2C3×#6599512yes—
542C2C3×#6599812yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#381D5
hypocenterC5C3×#2357
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#381

Complements

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

NH ≅ G/Ntype
2. C3×C5×#381C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
5. C3×#65233C2semidirect
6. C3×#64958C2semidirect
7. C3×#64955C2semidirect
8. C3×#64953C2semidirect
9. C3×#64939C2semidirect
10. C3×#64938C2semidirect
11. C3×#64938C2semidirect
12. #10605792C3direct (N × H)
19. C3×C4×C22⋊D5C4semidirect
39. C5×#381C2×C3semidirect
40. C4×C22⋊Dic5C2×C3semidirect
42. #65233C2×C3semidirect
43. #64958C2×C3semidirect
44. #64955C2×C3semidirect
45. #64953C2×C3semidirect
46. #64939C2×C3semidirect
47. #64938C2×C3semidirect
48. #64938C2×C3semidirect
86. C3×#381D5semidirect
97. C4×C22⋊D5C3×C4semidirect
214. #381C3×D5semidirect
434. C3×C5#2357semidirect
510. C5C3×#2357semidirect
535. C3#10605792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C3×C5×#3812
C3×C4×C22⋊Dic52
C3×#652462
C3×#652332
C3×#649582
C3×#649552
C3×#649532
C3×#649392
C3×#649382
#106057923
C3×#23575