Finite Group Databasebeta

← C3×#10610677 #14416815

Subgroups — C3×#10610677 #14416815

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic
3C3×#65856C211yesmaximal, characteristic
4C3×C5×#419C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic
6C3×M16×Dic5C211yesmaximal, characteristic, complemented
7C3×#65284C211yesmaximal, characteristic, complemented
8C3×#65106C212yesmaximal, complemented
9C3×#65079C212yesmaximal, complemented
10C3×#65078C212yesmaximal, complemented
11C3×#65077C212yesmaximal, complemented
12#10610677C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C3×Q8×Dic5—21no—
18C3×Q8×Dic5—21no—
19C3×Q8×Dic5C2212yes—
20C3×Q8×Dic5C2212yes—
21C2×C3×#689C2212yes—
22C3×#4088C418yescomplemented
23C2×C3×#688C2212yes—
24C2×C3×C4⋊Dic5—21no—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5—21no—
27C2×C3×C4×Dic5C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29C3×#4039C2211yescharacteristic
30C3×#4039C2211yescharacteristic
31C3×#4033C2211yescharacteristic
32C3×#4033C2211yescharacteristic
33C3×#4027—21no—
34C3×#4027—21no—
35C3×#4018—21no—
36C3×C42×D5—21no—
37C3×C5×#103C2212yes—
38C3×C5×#103C2212yes—
39C3×#3953C2212yes—
40C3×#3948C2212yes—
41C3×#3947C2212yes—
42C3×C8×Dic5C2212yes—
43C3×#3940C2212yes—
44C3×#3939C2212yes—
45C3×C4×#137—51nomaximal, Hall
46C2×Q8×Dic5C2×C311yescharacteristic, complemented
47C2×#4088C2×C311yescharacteristic
48#65856C2×C311yescharacteristic
49C5×#419C2×C311yescharacteristic, complemented
50#65422C2×C311yescharacteristic
51M16×Dic5C2×C311yescharacteristic, complemented
52#65284C2×C311yescharacteristic, complemented
53#65106C2×C312yescomplemented
54#65079C2×C312yescomplemented
55#65078C2×C312yescomplemented
56#65077C2×C312yescomplemented
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2×C414yescomplemented
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×C3×C22⋊D5—21no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C3×#709—22no—
68C3×#709C2×C414yes—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—21no—
73C2×C3×Dic10C2311yescharacteristic
74C3×C5×M16—22no—
75C2×C3×C5×C8C2312yes—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C22⋊C4—21no—
79C3×C42×C5—21no—
80C3×#689C2×C418yescomplemented
81C3×#688C2×C418yescomplemented
82C3×#685—21no—
83C3×#685—21no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5—22no—
87C3×C4⋊Dic5C2312yes—
88C3×#683—21no—
89C3×#683—21no—
90C3×C4×Dic5—22no—
91C3×C4×Dic5—22no—
92C3×C4×Dic5—21no—
93C3×C4×Dic5—21no—
94C3×C4×Dic5D411yescharacteristic
95C3×C4×Dic5D411yescharacteristic
96C3×C4×Dic5C2311yescharacteristic
97C3×C4×Dic5C2311yescharacteristic
98C3×#681C2×C414yescomplemented
99C2×C3×#168C2312yes—
100C2×C3×#137—51no—
101C3×C4×#41—51no—
102C2×C3×C4×Q8—51no—
103C3×#441—52no—
104C3×#440—52no—
105C3×C4×Q16—52no—
106C3×C4×SD16—52no—
107C3×#428—51no—
108C3×#419D511yescharacteristic, complemented
109C3×#417—51no—
110C3×C4×M16—51no—
111C22×C5×Q8C22×C311yescharacteristic
112C2×#709C22×C311yescharacteristic
113C2×C5×M16C22×C311yescharacteristic
114C5×#117C22×C311yescharacteristic
115Q8×Dic5—21no—
116Q8×Dic5—21no—
117Q8×Dic5C22×C312yes—
118Q8×Dic5C22×C312yes—
119C2×#689C22×C312yes—
120#4088C3×C418yescomplemented
121C2×#688C22×C312yes—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5C22×C311yescharacteristic
124C2×C4×Dic5—21no—
125C2×C4×Dic5C22×C311yescharacteristic
126C2×#681C22×C311yescharacteristic
127#4039C22×C311yescharacteristic
128#4039C22×C311yescharacteristic
129#4033C22×C311yescharacteristic
130#4033C22×C311yescharacteristic
131#4027—21no—
132#4027—21no—
133#4018—21no—
134C42×D5—21no—
135C5×#103C22×C312yes—
136C5×#103C22×C312yes—
137#3953C22×C312yes—
138#3948C22×C312yes—
139#3947C22×C312yes—
140C8×Dic5C22×C312yes—
141#3940C22×C312yes—
142#3939C22×C312yes—
143C4×#137—51noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×C3×D5—21no—
146C3×C5×Q8—24no—
147C3×C5×Q8—22no—
148C3×C5×Q8C22×C414yes—
149C2×C3×C4×C5—24no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5#4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C3×C22⋊D5—24no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—41no—
162C2×C3×Dic5—42no—
163C2×C3×Dic5C2×D411yescharacteristic
164C2×C3×Dic5C2×D411yescharacteristic
165C2×C3×Dic5C2×D411yescharacteristic
166C2×C3×Dic5C2×D411yescharacteristic
167C3×D20—21no—
168C3×D20C22×C412yes—
169C3×C4×D5—24no—
170C3×C4×D5—42no—
171C3×C4×D5—42no—
172C3×Dic10—21no—
173C3×Dic10C22×C412yes—
174C3×C5×C8—22no—
175C3×#168C22×C414yes—
176C2×C3×#41—51no—
177C22×C3×Q8C2×D511yescharacteristic
178C3×#137—58no—
179C2×C3×Q16—52no—
180C2×C3×SD16—52no—
181C2×C3×M16—51no—
182C2×C3×M16C2×D511yescharacteristic
183C3×C4×Q8—52no—
184C3×C4×Q8—52no—
185C3×C4×Q8—51no—
186C3×C4×Q8—51no—
187C3×C4×Q8—101no—
188C3×C4×Q8—101no—
189C3×C4×D4—51no—
190C3×C4×D4—51no—
191C3×C4×D4—101no—
192C3×C4×D4—101no—
193C3×#117—101no—
194C3×#117C2×D511yescharacteristic
195C2×C3×C4⋊C4—51no—
196C2×C3×C4⋊C4—101no—
197C2×C3×C42—51no—
198C2×C3×C42—101no—
199C2×C3×C42—101no—
200C3×#107—52no—
201C3×#106—52no—
202C3×#103—52no—
203C3×#103C2×D512yes—
204C3×#103C2×D512yes—
205C3×#102—52no—
206C3×#97—52no—
207C3×C4×C8—52no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8C2×C3×C414yescomplemented
211C2×C5×Q8C23×C312yes—
212C22×C4×C5—21no—
213C22×C4×C5C23×C311yescharacteristic
214C2×C22⋊D5—21no—
215C22×Dic5—21no—
216C22×Dic5C3×D411yescharacteristic
217C22×Dic5C3×D411yescharacteristic
218#709—22no—
219#709C2×C3×C414yes—
220C2×D20C23×C311yescharacteristic
221C2×C4×D5—21no—
222C2×C4×D5—21no—
223C2×C4×D5—21no—
224C2×Dic10C23×C311yescharacteristic
225C5×M16—22no—
226C2×C5×C8C23×C312yes—
227C5×C4⋊C4C23×C311yescharacteristic
228C5×C4⋊C4C23×C311yescharacteristic
229C5×C22⋊C4—21no—
230C42×C5—21no—
231#689C2×C3×C418yescomplemented
232#688C2×C3×C418yescomplemented
233#685—21no—
234#685—21no—
235C4⋊Dic5—21no—
236C4⋊Dic5—22no—
237C4⋊Dic5—22no—
238C4⋊Dic5C23×C312yes—
239#683—21no—
240#683—21no—
241C4×Dic5—21no—
242C4×Dic5—21no—
243C4×Dic5—22no—
244C4×Dic5—22no—
245C4×Dic5C3×D411yescharacteristic
246C4×Dic5C3×D411yescharacteristic
247C4×Dic5C23×C311yescharacteristic
248C4×Dic5C23×C311yescharacteristic
249#681C2×C3×C414yescomplemented
250C2×#168C23×C312yes—
251C2×#137—51no—
252C4×#41—51no—
253C2×C4×Q8—51no—
254#441—52no—
255#440—52no—
256C4×Q16—52no—
257C4×SD16—52no—
258#428—51no—
259#419C3×D511yescharacteristic, complemented
260#417—51no—
261C4×M16—51no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×C3×D5—22no—
267C2×C3×D5—41no—
268C2×C3×D5—41no—
269C3×C4×C5—24no—
270C3×C4×C5—41no—
271C3×C4×C5—41no—
272C3×C4×C5C4×D412yes—
273C3×C4×C5C23×C411yescharacteristic
274C3×C4×C5C2×#4111yescharacteristic
275C3×Dic5—22no—
276C3×Dic5—21no—
277C3×Dic5—21no—
278C3×Dic5—21no—
279C3×Dic5—42no—
280C3×Dic5#13712yescomplemented
281C3×#41—54no—
282C3×#41—102no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—51no—
286C2×C3×Q8C4×D514yescomplemented
287C2×C3×Q8C22×D512yes—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—21no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—101no—
294C22×C3×C4—101no—
295C22×C3×C4—101no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C3×Q16—58no—
299C3×SD16—58no—
300C3×M16—22no—
301C3×M16—54no—
302C2×C3×C8—52no—
303C2×C3×C8C22×D512yes—
304C3×C4⋊C4—52no—
305C3×C4⋊C4—101no—
306C3×C4⋊C4—101no—
307C3×C4⋊C4—102no—
308C3×C4⋊C4—102no—
309C3×C4⋊C4—101no—
310C3×C4⋊C4C22×D511yescharacteristic
311C3×C4⋊C4C22×D511yescharacteristic
312C3×C22⋊C4—21no—
313C3×C22⋊C4—101no—
314C3×C22⋊C4—101no—
315C3×C42—21no—
316C3×C42—51no—
317C3×C42—51no—
318C3×C42—51no—
319C3×C42—51no—
320C3×C42—101no—
321C3×C42—101no—
322C3×C42—102no—
323C3×C42—102no—
324C23×C5C2×C3×D411yescharacteristic
325C22×D5—21no—
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8C22×C3×C414yes—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5C22×C3×C412yes—
334C2×C4×C5C2×C3×D411yescharacteristic
335C2×C4×C5C3×#4112yes—
336C2×C4×C5C24×C311yescharacteristic
337C22⋊D5—24no—
338C2×Dic5—21no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—41no—
342C2×Dic5—42no—
343C2×Dic5C2×C3×D411yescharacteristic
344C2×Dic5C2×C3×D411yescharacteristic
345C2×Dic5C2×C3×D411yescharacteristic
346C2×Dic5C2×C3×D411yescharacteristic
347D20—21no—
348D20C22×C3×C412yes—
349C4×D5—24no—
350C4×D5—42no—
351C4×D5—42no—
352Dic10—21no—
353Dic10C22×C3×C412yes—
354C5×C8—22no—
355#168C22×C3×C414yes—
356C2×#41—51no—
357C22×Q8C2×C3×D511yescharacteristic
358#137—58no—
359C2×Q16—52no—
360C2×SD16—52no—
361C2×M16—51no—
362C2×M16C2×C3×D511yescharacteristic
363C4×Q8—52no—
364C4×Q8—52no—
365C4×Q8—51no—
366C4×Q8—51no—
367C4×Q8—101no—
368C4×Q8—101no—
369C4×D4—51no—
370C4×D4—51no—
371C4×D4—101no—
372C4×D4—101no—
373#117—101no—
374#117C2×C3×D511yescharacteristic
375C2×C4⋊C4—51no—
376C2×C4⋊C4—101no—
377C2×C42—51no—
378C2×C42—101no—
379C2×C42—101no—
380#107—52no—
381#106—52no—
382#103—52no—
383#103C2×C3×D512yes—
384#103C2×C3×D512yes—
385#102—52no—
386#97—52no—
387C4×C8—52no—
388C2×C3×C5—22no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×#13711yescharacteristic
391C2×C3×C5#57511yescharacteristic
392C3×D5—42no—
393C23×C3—101no—
394C23×C3D4×D511yescharacteristic
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8—52no—
398C3×Q8—101no—
399C3×Q8C2×C4×D514yes—
400C3×D4—52no—
401C3×D4—104no—
402C3×D4—101no—
403C2×C3×C4—22no—
404C2×C3×C4—24no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—51no—
408C2×C3×C4—51no—
409C2×C3×C4—51no—
410C2×C3×C4—51no—
411C2×C3×C4—102no—
412C2×C3×C4—101no—
413C2×C3×C4—104no—
414C2×C3×C4—102no—
415C2×C3×C4—202no—
416C2×C3×C4—202no—
417C2×C3×C4—201no—
418C2×C3×C4—202no—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4#71112yes—
422C2×C3×C4C23×D511yescharacteristic
423C3×C8—22no—
424C3×C8—54no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5C3×C4×D412yes—
428C22×C5C22×C3×D411yescharacteristic
429C2×D5—22no—
430C2×D5—41no—
431C2×D5—41no—
432C4×C5—24no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5C3×C4×D412yes—
436C4×C5C23×C3×C411yescharacteristic
437C4×C5C2×C3×#4111yescharacteristic
438Dic5—21no—
439Dic5—21no—
440Dic5—21no—
441Dic5—22no—
442Dic5—42no—
443Dic5C3×#13712yescomplemented
444#41—54no—
445#41—102no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—51no—
449C2×Q8C3×C4×D514yescomplemented
450C2×Q8C22×C3×D512yes—
451C2×D4—51no—
452C2×D4—101no—
453C22×C4—21no—
454C22×C4—51no—
455C22×C4—51no—
456C22×C4—101no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4C22×C3×D511yescharacteristic
461Q16—58no—
462SD16—58no—
463M16—22no—
464M16—54no—
465C2×C8—52no—
466C2×C8C22×C3×D512yes—
467C4⋊C4—52no—
468C4⋊C4—102no—
469C4⋊C4—102no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—101no—
473C4⋊C4C22×C3×D511yescharacteristic
474C4⋊C4C22×C3×D511yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—101no—
477C22⋊C4—101no—
478C42—21no—
479C42—51no—
480C42—51no—
481C42—51no—
482C42—51no—
483C42—101no—
484C42—101no—
485C42—102no—
486C42—102no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—102no—
491C22×C3—201no—
492C22×C3—201no—
493C22×C3#402712yes—
494C22×C3C2×D4×D511yescharacteristic
495C3×C4—24no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—52no—
499C3×C4—102no—
500C3×C4—101no—
501C3×C4—101no—
502C3×C4—101no—
503C3×C4—202no—
504C3×C4#402712yes—
505C3×C4C22×C4×D511yescharacteristic
506C3×C4C2×#71111yescharacteristic
507C2×C5—22no—
508C2×C5C2×C3×C4×D411yescharacteristic
509C2×C5C2×C3×#13711yescharacteristic
510C2×C5C3×#57511yescharacteristic
511D5—42no—
512C23—101no—
513C23C3×D4×D511yescharacteristic
514Q8—22no—
515Q8—24no—
516Q8—52no—
517Q8—101no—
518Q8C2×C3×C4×D514yes—
519D4—52no—
520D4—104no—
521D4—101no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—51no—
527C2×C4—51no—
528C2×C4—51no—
529C2×C4—51no—
530C2×C4—102no—
531C2×C4—101no—
532C2×C4—104no—
533C2×C4—102no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4—201no—
537C2×C4—202no—
538C2×C4C2×C3×C4×D512yes—
539C2×C4C3×D4×D511yescharacteristic
540C2×C4C3×#71112yes—
541C2×C4C23×C3×D511yescharacteristic
542C8—22no—
543C8—54no—
544C2×C3—22no—
545C2×C3—202no—
546C2×C3C2×#402711yescharacteristic
547C2×C3D5×#13711yescharacteristic
548C2×C3#6611111yescharacteristic
549C5C3×C4×#13711yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—102no—
553C22—201no—
554C22—201no—
555C22C3×#402712yes—
556C22C2×C3×D4×D511yescharacteristic
557C4—24no—
558C4—41no—
559C4—41no—
560C4—52no—
561C4—101no—
562C4—101no—
563C4—101no—
564C4—102no—
565C4—202no—
566C4C3×#402712yes—
567C4C22×C3×C4×D511yescharacteristic
568C4C2×C3×#71111yescharacteristic
569C3#1061067711yescharacteristic, direct product factor, Sylow
570C2—22no—
571C2—202no—
572C2C2×C3×#402711yescharacteristic
573C2C3×D5×#13711yescharacteristic
574C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#419C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C4×C5C24×C3
hypercenterC3×#419D5
hypocenterC5C3×C4×#137
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic5C2semidirect
4. C3×C5×#419C2semidirect
6. C3×M16×Dic5C2semidirect
7. C3×#65284C2semidirect
8. C3×#65106C2semidirect
9. C3×#65079C2semidirect
10. C3×#65078C2semidirect
11. C3×#65077C2semidirect
12. #10610677C3direct (N × H)
22. C3×#4088C4semidirect
46. C2×Q8×Dic5C2×C3semidirect
49. C5×#419C2×C3semidirect
51. M16×Dic5C2×C3semidirect
52. #65284C2×C3semidirect
53. #65106C2×C3semidirect
54. #65079C2×C3semidirect
55. #65078C2×C3semidirect
56. #65077C2×C3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
80. C3×#689C2×C4semidirect
81. C3×#688C2×C4semidirect
98. C3×#681C2×C4semidirect
108. C3×#419D5semidirect
120. #4088C3×C4semidirect
210. C2×C5×Q8C2×C3×C4semidirect
231. #689C2×C3×C4semidirect
232. #688C2×C3×C4semidirect
249. #681C2×C3×C4semidirect
259. #419C3×D5semidirect
280. C3×Dic5#137semidirect
286. C2×C3×Q8C4×D5semidirect
443. Dic5C3×#137semidirect
449. C2×Q8C3×C4×D5semidirect
487. C3×C5C4×#137semidirect
549. C5C3×C4×#137semidirect
569. C3#10610677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic52
C2×C3×#40882
C3×#658562
C3×C5×#4192
C3×#654222
C3×M16×Dic52
C3×#652842
C3×#651062
C3×#650792
C3×#650782
C3×#650772
#106106773
C3×C4×#1375