Finite Group Databasebeta

← C3×#10602342 #14280094

Subgroups — C3×#10602342 #14280094

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C22×C3×C22⋊Dic5C211yesmaximal, characteristic
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic
4C2×C3×#3963C212yesmaximal, complemented
5C2×C3×#3963C212yesmaximal, complemented
6#10602342C311yesmaximal, characteristic, direct product factor, Hall
7C25×C3×C5C2211yescharacteristic
8C23×C3×C4×C5C2212yes—
9C23×C3×Dic5C2211yescharacteristic
10C23×C3×Dic5C2211yescharacteristic
11C23×C3×Dic5C2212yes—
12C2×C3×C5×C22⋊C4—22no—
13C2×C3×C5×C22⋊C4—24no—
14C2×C3×C22⋊Dic5—22no—
15C2×C3×C22⋊Dic5—22no—
16C2×C3×C22⋊Dic5—22no—
17C2×C3×C22⋊Dic5—24no—
18C2×C3×C22⋊Dic5C414yescomplemented
19C3×#3963—24no—
20C3×#3963—24no—
21C3×#1440—51nomaximal, Hall
22C22×C5×C22⋊C4C2×C311yescharacteristic
23C22×C22⋊Dic5C2×C311yescharacteristic
24C22×C22⋊Dic5C2×C311yescharacteristic
25C2×#3963C2×C312yescomplemented
26C2×#3963C2×C312yescomplemented
27C24×C3×C5—22no—
28C24×C3×C5—22no—
29C24×C3×C5—22no—
30C24×C3×C5—22no—
31C24×C3×C5—22no—
32C24×C3×C5—22no—
33C24×C3×C5C2×C412yes—
34C24×C3×C5D412yes—
35C24×C3×C5D412yes—
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—22no—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—22no—
43C22×C3×C4×C5D414yes—
44C22×C3×Dic5—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5—21no—
48C22×C3×Dic5—22no—
49C22×C3×Dic5—22no—
50C22×C3×Dic5—22no—
51C22×C3×Dic5—22no—
52C22×C3×Dic5—22no—
53C22×C3×Dic5—22no—
54C22×C3×Dic5—22no—
55C22×C3×Dic5—22no—
56C22×C3×Dic5—22no—
57C22×C3×Dic5—22no—
58C22×C3×Dic5C2×C412yes—
59C22×C3×Dic5C2×C412yes—
60C22×C3×Dic5D414yes—
61C3×C5×C22⋊C4—28no—
62C3×C22⋊Dic5—28no—
63C3×C22⋊Dic5—28no—
64C22×C3×C22⋊C4—51no—
65C22×C3×C22⋊C4—51no—
66C22×C3×C22⋊C4D511yescharacteristic
67C2×C3×#95—52no—
68C2×C3×#95—52no—
69C25×C5C22×C311yescharacteristic
70C23×C4×C5C22×C312yes—
71C23×Dic5C22×C311yescharacteristic
72C23×Dic5C22×C311yescharacteristic
73C23×Dic5C22×C312yes—
74C2×C5×C22⋊C4—22no—
75C2×C5×C22⋊C4—24no—
76C2×C22⋊Dic5—22no—
77C2×C22⋊Dic5—22no—
78C2×C22⋊Dic5—22no—
79C2×C22⋊Dic5—24no—
80C2×C22⋊Dic5C3×C414yescomplemented
81#3963—24no—
82#3963—24no—
83#1440—51noSylow
84C23×C3×C5—22no—
85C23×C3×C5—22no—
86C23×C3×C5—24no—
87C23×C3×C5—24no—
88C23×C3×C5—22no—
89C23×C3×C5—22no—
90C23×C3×C5—24no—
91C23×C3×C5—24no—
92C23×C3×C5—24no—
93C23×C3×C5—24no—
94C23×C3×C5—22no—
95C23×C3×C5—22no—
96C23×C3×C5—42no—
97C23×C3×C5—42no—
98C23×C3×C5—42no—
99C23×C3×C5—42no—
100C23×C3×C5—42no—
101C23×C3×C5—42no—
102C23×C3×C5—42no—
103C23×C3×C5—42no—
104C23×C3×C5C22⋊C414yes—
105C23×C3×C5C22×C411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D412yes—
109C23×C3×C5C2×D412yes—
110C23×C3×C5#4112yes—
111C23×C3×C5#4112yes—
112C23×C3×C5#4112yes—
113C23×C3×C5#4112yes—
114C2×C3×C4×C5—24no—
115C2×C3×C4×C5—24no—
116C2×C3×C4×C5—24no—
117C2×C3×C4×C5—42no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5—42no—
120C2×C3×C4×C5—42no—
121C2×C3×Dic5—22no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5—24no—
124C2×C3×Dic5—24no—
125C2×C3×Dic5—24no—
126C2×C3×Dic5—24no—
127C2×C3×Dic5—24no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5—42no—
131C2×C3×Dic5—42no—
132C2×C3×Dic5—42no—
133C2×C3×Dic5—42no—
134C2×C3×Dic5—41no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—42no—
137C2×C3×Dic5—42no—
138C25×C3C2×D511yescharacteristic
139C23×C3×C4—51no—
140C23×C3×C4—51no—
141C23×C3×C4—52no—
142C23×C3×C4C2×D512yes—
143C2×C3×C22⋊C4—22no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—54no—
146C2×C3×C22⋊C4—104no—
147C2×C3×C22⋊C4—102no—
148C2×C3×C22⋊C4—102no—
149C2×C3×C22⋊C4—102no—
150C3×#95—104no—
151C3×#95—104no—
152C24×C5—22no—
153C24×C5—22no—
154C24×C5—22no—
155C24×C5—22no—
156C24×C5—22no—
157C24×C5—22no—
158C24×C5C2×C3×C412yes—
159C24×C5C3×D412yes—
160C24×C5C3×D412yes—
161C24×C5C23×C311yescharacteristic
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5C3×D414yes—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5C2×C3×C412yes—
184C22×Dic5C2×C3×C412yes—
185C22×Dic5C3×D414yes—
186C5×C22⋊C4—28no—
187C22⋊Dic5—28no—
188C22⋊Dic5—28no—
189C22×C22⋊C4—51no—
190C22×C22⋊C4—51no—
191C22×C22⋊C4C3×D511yescharacteristic
192C2×#95—52no—
193C2×#95—52no—
194C22×C3×C5—24no—
195C22×C3×C5—24no—
196C22×C3×C5—24no—
197C22×C3×C5—44no—
198C22×C3×C5—44no—
199C22×C3×C5—44no—
200C22×C3×C5—44no—
201C22×C3×C5—44no—
202C22×C3×C5—44no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#11711yescharacteristic
205C22×C3×C5#11711yescharacteristic
206C22×C3×C5C4×D412yes—
207C22×C3×C5C4×D412yes—
208C22×C3×C5#12011yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12112yes—
211C22×C3×C5#12112yes—
212C22×C3×C5#12112yes—
213C22×C3×C5#12112yes—
214C22×C3×C5#12312yes—
215C22×C3×C5#12312yes—
216C22×C3×C5#12311yescharacteristic
217C22×C3×C5#12311yescharacteristic
218C22×C3×C5#12312yes—
219C22×C3×C5#12312yes—
220C22×C3×C5#12412yes—
221C22×C3×C5#12412yes—
222C22×C3×C5#12612yes—
223C22×C3×C5#12612yes—
224C3×C4×C5—44no—
225C3×Dic5—42no—
226C3×Dic5—42no—
227C3×Dic5—44no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3C4×D512yes—
235C24×C3D2012yes—
236C24×C3C22⋊D512yes—
237C24×C3C22×D511yescharacteristic
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—52no—
245C22×C3×C4—52no—
246C22×C3×C4—54no—
247C22×C3×C4—102no—
248C22×C3×C4—101no—
249C22×C3×C4—101no—
250C22×C3×C4—102no—
251C22×C3×C4—102no—
252C22×C3×C4—102no—
253C22×C3×C4—102no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C22×C3×C4—102no—
257C22×C3×C4—102no—
258C22×C3×C4—102no—
259C22×C3×C4—101no—
260C22×C3×C4—101no—
261C22×C3×C4C22⋊D514yes—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—108no—
264C3×C22⋊C4—108no—
265C23×C5—22no—
266C23×C5—22no—
267C23×C5—24no—
268C23×C5—24no—
269C23×C5—22no—
270C23×C5—22no—
271C23×C5—24no—
272C23×C5—24no—
273C23×C5—24no—
274C23×C5—24no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—42no—
278C23×C5—42no—
279C23×C5—42no—
280C23×C5—42no—
281C23×C5—42no—
282C23×C5—42no—
283C23×C5—42no—
284C23×C5—42no—
285C23×C5C3×C22⋊C414yes—
286C23×C5C22×C3×C411yescharacteristic
287C23×C5C2×C3×D411yescharacteristic
288C23×C5C2×C3×D412yes—
289C23×C5C2×C3×D411yescharacteristic
290C23×C5C2×C3×D412yes—
291C23×C5C3×#4112yes—
292C23×C5C3×#4112yes—
293C23×C5C3×#4112yes—
294C23×C5C3×#4112yes—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—24no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—24no—
305C2×Dic5—24no—
306C2×Dic5—24no—
307C2×Dic5—24no—
308C2×Dic5—24no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—42no—
312C2×Dic5—42no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—41no—
316C2×Dic5—42no—
317C2×Dic5—41no—
318C2×Dic5—42no—
319C25C2×C3×D511yescharacteristic
320C23×C4—51no—
321C23×C4—51no—
322C23×C4—52no—
323C23×C4C2×C3×D512yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—54no—
327C2×C22⋊C4—104no—
328C2×C22⋊C4—102no—
329C2×C22⋊C4—102no—
330C2×C22⋊C4—102no—
331#95—104no—
332#95—104no—
333C2×C3×C5—44no—
334C2×C3×C5#38111yescharacteristic
335C2×C3×C5#38611yescharacteristic
336C2×C3×C5#38611yescharacteristic
337C2×C3×C5#38812yes—
338C2×C3×C5#38812yes—
339C2×C3×C5#39412yes—
340C2×C3×C5#39412yes—
341C2×C3×C5#39712yes—
342C2×C3×C5#39712yes—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—24no—
347C23×C3—22no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3#68514yes—
364C23×C3C2×C4×D511yescharacteristic
365C23×C3C2×D2011yescharacteristic
366C23×C3#70912yes—
367C23×C3D4×D512yes—
368C23×C3#71112yes—
369C23×C3#71112yes—
370C23×C3#71112yes—
371C23×C3C2×C22⋊D511yescharacteristic
372C23×C3C2×C22⋊D512yes—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—104no—
381C2×C3×C4—104no—
382C2×C3×C4—104no—
383C2×C3×C4—102no—
384C2×C3×C4—102no—
385C2×C3×C4—104no—
386C2×C3×C4—104no—
387C2×C3×C4—201no—
388C2×C3×C4—201no—
389C2×C3×C4—202no—
390C2×C3×C4—201no—
391C2×C3×C4—202no—
392C2×C3×C4—201no—
393C2×C3×C4—202no—
394C2×C3×C4—202no—
395C2×C3×C4—202no—
396C2×C3×C4—202no—
397C22×C5—24no—
398C22×C5—24no—
399C22×C5—24no—
400C22×C5—44no—
401C22×C5—44no—
402C22×C5—44no—
403C22×C5—44no—
404C22×C5—44no—
405C22×C5—44no—
406C22×C5C2×C3×C22⋊C411yescharacteristic
407C22×C5C3×#11711yescharacteristic
408C22×C5C3×#11711yescharacteristic
409C22×C5C3×C4×D412yes—
410C22×C5C3×C4×D412yes—
411C22×C5C3×#12011yescharacteristic
412C22×C5C3×#12011yescharacteristic
413C22×C5C3×#12112yes—
414C22×C5C3×#12112yes—
415C22×C5C3×#12112yes—
416C22×C5C3×#12112yes—
417C22×C5C3×#12312yes—
418C22×C5C3×#12312yes—
419C22×C5C3×#12312yes—
420C22×C5C3×#12312yes—
421C22×C5C3×#12311yescharacteristic
422C22×C5C3×#12311yescharacteristic
423C22×C5C3×#12412yes—
424C22×C5C3×#12412yes—
425C22×C5C3×#12612yes—
426C22×C5C3×#12612yes—
427C4×C5—44no—
428Dic5—42no—
429Dic5—42no—
430Dic5—44no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24C3×C4×D512yes—
438C24C3×D2012yes—
439C24C3×C22⋊D512yes—
440C24C22×C3×D511yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—54no—
450C22×C4—102no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4C3×C22⋊D514yes—
465C22⋊C4—28no—
466C22⋊C4—108no—
467C22⋊C4—108no—
468C3×C5#144011yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—44no—
473C22×C3—44no—
474C22×C3—44no—
475C22×C3—44no—
476C22×C3—44no—
477C22×C3—44no—
478C22×C3#402311yescharacteristic
479C22×C3#402311yescharacteristic
480C22×C3#402512yes—
481C22×C3#402512yes—
482C22×C3#402712yes—
483C22×C3#402811yescharacteristic
484C22×C3#402912yes—
485C22×C3#403112yes—
486C22×C3#403212yes—
487C22×C3#403211yescharacteristic
488C22×C3C2×#68511yescharacteristic
489C22×C3C4×C22⋊D512yes—
490C22×C3#407511yescharacteristic
491C22×C3#407612yes—
492C22×C3#408112yes—
493C22×C3#408112yes—
494C22×C3#408212yes—
495C22×C3#408412yes—
496C22×C3#408512yes—
497C22×C3#408512yes—
498C22×C3#409911yescharacteristic
499C3×C4—44no—
500C3×C4—202no—
501C3×C4—202no—
502C3×C4—204no—
503C2×C5—44no—
504C2×C5C3×#38111yescharacteristic
505C2×C5C3×#38611yescharacteristic
506C2×C5C3×#38611yescharacteristic
507C2×C5C3×#38812yes—
508C2×C5C3×#38812yes—
509C2×C5C3×#39412yes—
510C2×C5C3×#39412yes—
511C2×C5C3×#39712yes—
512C2×C5C3×#39712yes—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—24no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23C3×#68514yes—
534C23C2×C3×C4×D511yescharacteristic
535C23C2×C3×D2011yescharacteristic
536C23C3×#70912yes—
537C23C3×D4×D512yes—
538C23C3×#71112yes—
539C23C3×#71112yes—
540C23C3×#71112yes—
541C23C2×C3×C22⋊D511yescharacteristic
542C23C2×C3×C22⋊D512yes—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—104no—
551C2×C4—104no—
552C2×C4—104no—
553C2×C4—104no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—104no—
557C2×C4—202no—
558C2×C4—202no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—202no—
562C2×C4—201no—
563C2×C4—202no—
564C2×C4—201no—
565C2×C4—202no—
566C2×C4—202no—
567C2×C3—44no—
568C2×C3#6523211yescharacteristic
569C2×C3#6523312yes—
570C2×C3#6523412yes—
571C2×C3#6524112yes—
572C2×C3#6524212yes—
573C2×C3#6524711yescharacteristic
574C2×C3#6525012yes—
575C2×C3#6550211yescharacteristic
576C2×C3#6551112yes—
577C5C3×#144011yescharacteristic, complemented, Sylow
578C22—24no—
579C22—24no—
580C22—24no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—44no—
586C22—44no—
587C22C3×#402311yescharacteristic
588C22C3×#402311yescharacteristic
589C22C3×#402512yes—
590C22C3×#402512yes—
591C22C3×#402712yes—
592C22C3×#402811yescharacteristic
593C22C3×#402912yes—
594C22C3×#403112yes—
595C22C3×#403212yes—
596C22C3×#403211yescharacteristic
597C22C2×C3×#68511yescharacteristic
598C22C3×C4×C22⋊D512yes—
599C22C3×#407511yescharacteristic
600C22C3×#407612yes—
601C22C3×#408112yes—
602C22C3×#408112yes—
603C22C3×#408212yes—
604C22C3×#408412yes—
605C22C3×#408512yes—
606C22C3×#408512yes—
607C22C3×#409911yescharacteristic
608C4—44no—
609C4—202no—
610C4—202no—
611C4—204no—
612C3#1060234211yescharacteristic, direct product factor, Sylow
613C2—44no—
614C2C3×#6523211yescharacteristic
615C2C3×#6523312yes—
616C2C3×#6523412yes—
617C2C3×#6524112yes—
618C2C3×#6524212yes—
619C2C3×#6524711yescharacteristic
620C2C3×#6525012yes—
621C2C3×#6550211yescharacteristic
622C2C3×#6551112yes—
subgroupG/H
centerC24×C3C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
cosocleC24×C5C23×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#1440
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C3×#3963C2semidirect
5. C2×C3×#3963C2semidirect
6. #10602342C3direct (N × H)
18. C2×C3×C22⋊Dic5C4semidirect
25. C2×#3963C2×C3semidirect
26. C2×#3963C2×C3semidirect
80. C2×C22⋊Dic5C3×C4semidirect
468. C3×C5#1440semidirect
577. C5C3×#1440semidirect
612. C3#10602342direct (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
C22×C3×C22⋊Dic52
C2×C3×#39632
#106023423
C3×#14405