Finite Group Databasebeta

← C3×#10601208 #14297373

Subgroups — C3×#10601208 #14297373

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic
2C3×C5×#421C211yesmaximal, characteristic, complemented
3C3×#65525C211yesmaximal, characteristic, complemented
4C3×#65421C211yesmaximal, characteristic, complemented
5C3×#65409C211yesmaximal, characteristic, complemented
6C3×#65295C211yesmaximal, characteristic, complemented
7C3×#65293C211yesmaximal, characteristic, complemented
8#10601208C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4150—22no—
11C3×#4150—22no—
12C3×#4150—22no—
13C3×#4150—22no—
14C2×C3×Q8×D5C412yescomplemented
15C2×C3×#711—22no—
16C2×C3×#711C412yescomplemented
17C2×C3×#709—21no—
18C2×C3×#709C2211yescharacteristic
19C22×C3×Dic10—21no—
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C3×C5×#117C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25C3×C5×#104—22no—
26C3×#3969—22no—
27C3×#3956—21no—
28C3×#3955—21no—
29C3×#3948—22no—
30C3×#3942—22no—
31C3×#3938—22no—
32C3×#1796—51nomaximal, Hall
33C2×#4150C2×C311yescharacteristic
34C5×#421C2×C311yescharacteristic, complemented
35#65525C2×C311yescharacteristic, complemented
36#65421C2×C311yescharacteristic, complemented
37#65409C2×C311yescharacteristic, complemented
38#65295C2×C311yescharacteristic, complemented
39#65293C2×C311yescharacteristic, complemented
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C3×C5×#41D412yes—
43C3×C5×#41D412yes—
44C2×C3×C5×Q8C2×C411yescharacteristic
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4C2×C411yescharacteristic
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C3×C22⋊D5—22no—
50C2×C3×C22⋊D5D412yes—
51C22×C3×Dic5—21no—
52C22×C3×Dic5—22no—
53C3×Q8×D5—24no—
54C3×Q8×D5—24no—
55C3×#711—28no—
56C3×#711—28no—
57C3×#711—24no—
58C3×#711—24no—
59C3×#709—24no—
60C3×#709—24no—
61C3×#709—21no—
62C3×#709—21no—
63C3×#709—21no—
64C3×#709—21no—
65C2×C3×D20D411yescharacteristic
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C412yes—
68C2×C3×Dic10—24no—
69C2×C3×Dic10—24no—
70C2×C3×Dic10—21no—
71C2×C3×Dic10—21no—
72C2×C3×Dic10—21no—
73C2×C3×Dic10—22no—
74C2×C3×Dic10C2×C412yes—
75C2×C3×Dic10D411yescharacteristic
76C2×C3×Dic10D412yes—
77C2×C3×Dic10D412yes—
78C3×C5×M16—21no—
79C3×C5×M16—21no—
80C2×C3×C5×C8—21no—
81C3×C5×C4⋊C4—21no—
82C3×C5×C22⋊C4—21no—
83C3×C42×C5—21no—
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5—21no—
86C3×C4×Dic5—21no—
87C3×#681—21no—
88C3×#681—21no—
89C2×C3×#168—21no—
90C2×C3×2−1+4—51no—
91C3×#421—51no—
92C3×#421D511yescharacteristic, complemented
93C3×#419—51no—
94C3×#419—51no—
95C3×#413—51no—
96C3×#410—51no—
97C2×C5×#41C22×C311yescharacteristic
98#4150—22no—
99#4150—22no—
100#4150—22no—
101#4150—22no—
102C2×Q8×D5C3×C412yescomplemented
103C2×#711—22no—
104C2×#711C3×C412yescomplemented
105C2×#709—21no—
106C2×#709C22×C311yescharacteristic
107C22×Dic10—21no—
108C22×Dic10C22×C311yescharacteristic
109C2×C5×M16C22×C311yescharacteristic
110C5×#117C22×C311yescharacteristic
111#4072C22×C311yescharacteristic
112C2×#681C22×C311yescharacteristic
113C5×#104—22no—
114#3969—22no—
115#3956—21no—
116#3955—21no—
117#3948—22no—
118#3942—22no—
119#3938—22no—
120#1796—51noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×C3×D5C22⋊C412yes—
124C3×C5×Q8—21no—
125C3×C5×Q8C22⋊C412yes—
126C3×C5×D4—22no—
127C3×C5×D4—22no—
128C3×C5×D4—21no—
129C3×C5×D4C22⋊C412yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C3×C22⋊D5—28no—
141C3×C22⋊D5—22no—
142C3×C22⋊D5—22no—
143C2×C3×Dic5—28no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—41no—
148C2×C3×Dic5C22⋊C412yes—
149C3×D20—21no—
150C3×D20—21no—
151C3×C4×D5—28no—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×Dic10—28no—
155C3×Dic10—22no—
156C3×Dic10—21no—
157C3×Dic10—21no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160C3×Dic10C22⋊C414yes—
161C3×C5×C8—41no—
162C3×#168—41no—
163C3×2−1+4—102no—
164C3×2−1+4—102no—
165C3×2−1+4—102no—
166C3×2−1+4—102no—
167C2×C3×#41—51no—
168C2×C3×#41—52no—
169C2×C3×#41—101no—
170C2×C3×#41—102no—
171C2×C3×#41C2×D511yescharacteristic
172C22×C3×Q8—52no—
173C22×C3×Q8—51no—
174C22×C3×Q8—101no—
175C2×C3×M16—51no—
176C2×C3×M16C2×D511yescharacteristic
177C3×#117—51no—
178C3×#117C2×D511yescharacteristic
179C3×#104—22no—
180C3×#104—102no—
181C3×#103—102no—
182C3×#103—102no—
183C3×#101—101no—
184C3×#100—101no—
185C3×#99—102no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41C3×D412yes—
189C5×#41C3×D412yes—
190C2×C5×Q8C2×C3×C411yescharacteristic
191C2×C5×D4—21no—
192C2×C5×D4C2×C3×C411yescharacteristic
193C22×C4×C5—21no—
194C22×C4×C5C23×C311yescharacteristic
195C2×C22⋊D5—22no—
196C2×C22⋊D5C3×D412yes—
197C22×Dic5—21no—
198C22×Dic5—22no—
199Q8×D5—24no—
200Q8×D5—24no—
201#711—28no—
202#711—28no—
203#711—24no—
204#711—24no—
205#709—24no—
206#709—24no—
207#709—21no—
208#709—21no—
209#709—21no—
210#709—21no—
211C2×D20C3×D411yescharacteristic
212C2×C4×D5—22no—
213C2×C4×D5C2×C3×C412yes—
214C2×Dic10—24no—
215C2×Dic10—24no—
216C2×Dic10—21no—
217C2×Dic10—21no—
218C2×Dic10—21no—
219C2×Dic10—22no—
220C2×Dic10C2×C3×C412yes—
221C2×Dic10C3×D411yescharacteristic
222C2×Dic10C3×D412yes—
223C2×Dic10C3×D412yes—
224C5×M16—21no—
225C5×M16—21no—
226C2×C5×C8—21no—
227C5×C4⋊C4—21no—
228C5×C22⋊C4—21no—
229C42×C5—21no—
230C22⋊Dic5—21no—
231C4⋊Dic5—21no—
232C4×Dic5—21no—
233#681—21no—
234#681—21no—
235C2×#168—21no—
236C2×2−1+4—51no—
237#421—51no—
238#421C3×D511yescharacteristic, complemented
239#419—51no—
240#419—51no—
241#413—51no—
242#410—51no—
243C22×C3×C5—22no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5#12011yescharacteristic
248C22×C3×C5#12011yescharacteristic
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C3×C4×C5—22no—
252C3×C4×C5—81no—
253C3×C4×C5C2×C22⋊C411yescharacteristic
254C3×C4×C5C2×C22⋊C411yescharacteristic
255C3×C4×C5#12011yescharacteristic
256C3×C4×C5#12011yescharacteristic
257C3×Dic5—22no—
258C3×Dic5—24no—
259C3×Dic5—81no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—104no—
263C3×#41—104no—
264C3×#41—104no—
265C3×#41—108no—
266C3×#41—108no—
267C3×#41—104no—
268C3×#41—101no—
269C3×#41—101no—
270C3×#41—101no—
271C3×#41—101no—
272C3×#41D2012yes—
273C3×#41C22⋊D512yes—
274C2×C3×Q8—51no—
275C2×C3×Q8—52no—
276C2×C3×Q8—52no—
277C2×C3×Q8—52no—
278C2×C3×Q8—102no—
279C2×C3×Q8—104no—
280C2×C3×Q8—104no—
281C2×C3×Q8—104no—
282C2×C3×Q8—104no—
283C2×C3×Q8—101no—
284C2×C3×Q8—101no—
285C2×C3×Q8—101no—
286C2×C3×Q8C4×D511yescharacteristic
287C2×C3×D4—21no—
288C2×C3×D4—52no—
289C2×C3×D4—51no—
290C2×C3×D4—102no—
291C2×C3×D4C4×D511yescharacteristic
292C22×C3×C4—21no—
293C22×C3×C4—52no—
294C22×C3×C4—102no—
295C22×C3×C4—102no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C3×M16—21no—
299C3×M16—21no—
300C3×M16—101no—
301C3×M16—101no—
302C2×C3×C8—21no—
303C2×C3×C8—101no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—101no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—101no—
308C3×C42—21no—
309C3×C42—101no—
310C23×C5—21no—
311C23×C5C2×C3×D411yescharacteristic
312C22×D5C3×C22⋊C412yes—
313C5×Q8—21no—
314C5×Q8C3×C22⋊C412yes—
315C5×D4—22no—
316C5×D4—22no—
317C5×D4—21no—
318C5×D4C3×C22⋊C412yes—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—41no—
323C2×C4×C5C22×C3×C411yescharacteristic
324C2×C4×C5C2×C3×D411yescharacteristic
325C2×C4×C5C2×C3×D411yescharacteristic
326C2×C4×C5C2×C3×D411yescharacteristic
327C2×C4×C5C2×C3×D411yescharacteristic
328C2×C4×C5C2×C3×D411yescharacteristic
329C22⋊D5—28no—
330C22⋊D5—22no—
331C22⋊D5—22no—
332C2×Dic5—28no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—41no—
337C2×Dic5C3×C22⋊C412yes—
338D20—21no—
339D20—21no—
340C4×D5—28no—
341C4×D5—22no—
342C4×D5—22no—
343Dic10—28no—
344Dic10—22no—
345Dic10—21no—
346Dic10—22no—
347Dic10—21no—
348Dic10—22no—
349Dic10C3×C22⋊C414yes—
350C5×C8—41no—
351#168—41no—
3522−1+4—102no—
3532−1+4—102no—
3542−1+4—102no—
3552−1+4—102no—
356C2×#41—51no—
357C2×#41—52no—
358C2×#41—101no—
359C2×#41—102no—
360C2×#41C2×C3×D511yescharacteristic
361C22×Q8—52no—
362C22×Q8—51no—
363C22×Q8—101no—
364C2×M16—51no—
365C2×M16C2×C3×D511yescharacteristic
366#117—51no—
367#117C2×C3×D511yescharacteristic
368#104—22no—
369#104—102no—
370#103—102no—
371#103—102no—
372#101—101no—
373#100—101no—
374#99—102no—
375C2×C3×C5—21no—
376C2×C3×C5—21no—
377C2×C3×C5—21no—
378C2×C3×C5—42no—
379C2×C3×C5#37911yescharacteristic
380C3×D5—42no—
381C23×C3—21no—
382C23×C3—52no—
383C23×C3D4×D511yescharacteristic
384C3×Q8—21no—
385C3×Q8—54no—
386C3×Q8—108no—
387C3×Q8—101no—
388C3×Q8—102no—
389C3×Q8—102no—
390C3×Q8—101no—
391C3×Q8—102no—
392C3×Q8#68512yes—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—21no—
396C3×D4—108no—
397C3×D4—102no—
398C3×D4—102no—
399C3×D4—101no—
400C3×D4—101no—
401C3×D4#68512yes—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—41no—
406C2×C3×C4—52no—
407C2×C3×C4—108no—
408C2×C3×C4—108no—
409C2×C3×C4—102no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—201no—
415C2×C3×C4C2×C4×D511yescharacteristic
416C2×C3×C4C2×D2011yescharacteristic
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4D4×D511yescharacteristic
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D511yescharacteristic
421C3×C8—41no—
422C3×C8—201no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5C2×C3×C22⋊C411yescharacteristic
427C22×C5C3×#12011yescharacteristic
428C22×C5C3×#12011yescharacteristic
429C2×D5—22no—
430C2×D5—42no—
431C4×C5—22no—
432C4×C5—81no—
433C4×C5C2×C3×C22⋊C411yescharacteristic
434C4×C5C2×C3×C22⋊C411yescharacteristic
435C4×C5C3×#12011yescharacteristic
436C4×C5C3×#12011yescharacteristic
437Dic5—22no—
438Dic5—24no—
439Dic5—81no—
440#41—21no—
441#41—21no—
442#41—104no—
443#41—104no—
444#41—104no—
445#41—108no—
446#41—108no—
447#41—104no—
448#41—101no—
449#41—101no—
450#41—101no—
451#41—101no—
452#41C3×D2012yes—
453#41C3×C22⋊D512yes—
454C2×Q8—51no—
455C2×Q8—52no—
456C2×Q8—52no—
457C2×Q8—52no—
458C2×Q8—102no—
459C2×Q8—104no—
460C2×Q8—104no—
461C2×Q8—104no—
462C2×Q8—104no—
463C2×Q8—101no—
464C2×Q8—101no—
465C2×Q8—101no—
466C2×Q8C3×C4×D511yescharacteristic
467C2×D4—21no—
468C2×D4—52no—
469C2×D4—51no—
470C2×D4—102no—
471C2×D4C3×C4×D511yescharacteristic
472C22×C4—21no—
473C22×C4—52no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—101no—
477C22×C4C22×C3×D511yescharacteristic
478M16—21no—
479M16—21no—
480M16—101no—
481M16—101no—
482C2×C8—21no—
483C2×C8—101no—
484C4⋊C4—21no—
485C4⋊C4—101no—
486C22⋊C4—21no—
487C22⋊C4—101no—
488C42—21no—
489C42—101no—
490C3×C5#179611yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—102no—
495C22×C3—202no—
496C22×C3D5×C22⋊C411yescharacteristic
497C22×C3#402811yescharacteristic
498C22×C3#408311yescharacteristic
499C3×C4—22no—
500C3×C4—81no—
501C3×C4—102no—
502C3×C4—104no—
503C3×C4—401no—
504C3×C4D5×C22⋊C411yescharacteristic
505C3×C4#402811yescharacteristic
506C3×C4C2×#68511yescharacteristic
507C3×C4#408311yescharacteristic
508C2×C5—21no—
509C2×C5—21no—
510C2×C5—21no—
511C2×C5—42no—
512C2×C5C3×#37911yescharacteristic
513D5—42no—
514C23—21no—
515C23—52no—
516C23C3×D4×D511yescharacteristic
517Q8—21no—
518Q8—54no—
519Q8—108no—
520Q8—101no—
521Q8—102no—
522Q8—101no—
523Q8—102no—
524Q8—102no—
525Q8C3×#68512yes—
526D4—22no—
527D4—22no—
528D4—21no—
529D4—108no—
530D4—102no—
531D4—102no—
532D4—101no—
533D4—101no—
534D4C3×#68512yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—52no—
540C2×C4—108no—
541C2×C4—108no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—201no—
548C2×C4C2×C3×C4×D511yescharacteristic
549C2×C4C2×C3×D2011yescharacteristic
550C2×C4C3×D4×D511yescharacteristic
551C2×C4C3×D4×D511yescharacteristic
552C2×C4C3×D4×D511yescharacteristic
553C2×C4C2×C3×C22⋊D511yescharacteristic
554C8—41no—
555C8—201no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—202no—
561C2×C3#6524411yescharacteristic
562C5C3×#179611yescharacteristic, complemented, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—102no—
567C22—202no—
568C22C3×D5×C22⋊C411yescharacteristic
569C22C3×#402811yescharacteristic
570C22C3×#408311yescharacteristic
571C4—22no—
572C4—81no—
573C4—102no—
574C4—104no—
575C4—401no—
576C4C3×D5×C22⋊C411yescharacteristic
577C4C3×#402811yescharacteristic
578C4C2×C3×#68511yescharacteristic
579C4C3×#408311yescharacteristic
580C3#1060120811yescharacteristic, direct product factor, Sylow
581C2—21no—
582C2—21no—
583C2—21no—
584C2—42no—
585C2—202no—
586C2C3×#6524411yescharacteristic
subgroupG/H
centerC2×C3#65244
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5#379
prime radicalC2×C3×#4150C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#421D5
hypocenterC5C3×#1796
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C3×C5×#421C2semidirect
3. C3×#65525C2semidirect
4. C3×#65421C2semidirect
5. C3×#65409C2semidirect
6. C3×#65295C2semidirect
7. C3×#65293C2semidirect
8. #10601208C3direct (N × H)
14. C2×C3×Q8×D5C4semidirect
16. C2×C3×#711C4semidirect
34. C5×#421C2×C3semidirect
35. #65525C2×C3semidirect
36. #65421C2×C3semidirect
37. #65409C2×C3semidirect
38. #65295C2×C3semidirect
39. #65293C2×C3semidirect
92. C3×#421D5semidirect
102. C2×Q8×D5C3×C4semidirect
104. C2×#711C3×C4semidirect
238. #421C3×D5semidirect
490. C3×C5#1796semidirect
562. C5C3×#1796semidirect
580. C3#10601208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C3×C5×#4212
C3×#655252
C3×#654212
C3×#654092
C3×#652952
C3×#652932
#106012083
C3×#17965