Finite Group Databasebeta

← C3×#10607700 #14323136

Subgroups — C3×#10607700 #14323136

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic
2C3×C5×#389C211yesmaximal, characteristic, complemented
3C3×#65279C212yesmaximal, complemented
4C3×#65277C211yesmaximal, characteristic
5C3×#65276C212yesmaximal, complemented
6C3×#65274C211yesmaximal, characteristic, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65228C211yesmaximal, characteristic
9C3×#65221C211yesmaximal, characteristic, complemented
10C3×#64959C212yesmaximal, complemented
11C3×#64953C212yesmaximal, complemented
12#10607700C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2212yes—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C2×C3×#685C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2212yes—
23C2×C3×#685C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4⋊Dic5C2212yes—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C3×#4039C418yescomplemented
30C3×C5×#95C2212yes—
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36C3×#3963C2211yescharacteristic
37C3×#2319—51nomaximal, Hall
38C2×#4039C2×C311yescharacteristic
39C5×#389C2×C311yescharacteristic, complemented
40#65279C2×C312yescomplemented
41#65277C2×C311yescharacteristic
42#65276C2×C312yescomplemented
43#65274C2×C311yescharacteristic, complemented
44C4⋊C4×Dic5C2×C311yescharacteristic, complemented
45#65228C2×C311yescharacteristic
46#65221C2×C311yescharacteristic, complemented
47#64959C2×C312yescomplemented
48#64953C2×C312yescomplemented
49C23×C3×D5C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×Dic5C2311yescharacteristic
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×D20—22no—
61C2×C3×D20—22no—
62C2×C3×D20C2×C414yes—
63C2×C3×C4×D5—42no—
64C2×C3×C4×D5—42no—
65C2×C3×C4×D5C2×C418yes—
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4—42no—
68C3×C5×C4⋊C4C2×C414yes—
69C3×C42×C5—22no—
70C3×#685—42no—
71C3×#685—42no—
72C3×#685—42no—
73C3×#685—42no—
74C3×#685C2×C418yes—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5—42no—
77C3×C4×Dic5—22no—
78C3×C4×Dic5—42no—
79C3×C4×Dic5C2×C414yes—
80C2×C3×C4×D4—51no—
81C3×#390—51no—
82C3×#390—51no—
83C3×#389—51no—
84C3×#389D511yescharacteristic, complemented
85C3×#388—52no—
86C3×#388—52no—
87C3×#381—52no—
88C3×#380—52no—
89C3×C4×C4⋊C4—51no—
90C3×#376—51no—
91C22×D20C22×C311yescharacteristic
92C22×C4×D5C22×C312yes—
93C2×C5×C4⋊C4C22×C311yescharacteristic
94C2×C5×C4⋊C4C22×C312yes—
95C2×C5×C4⋊C4C22×C311yescharacteristic
96C2×C42×C5C22×C311yescharacteristic
97C2×#685C22×C312yes—
98C2×#685C22×C312yes—
99C2×#685C22×C312yes—
100C2×#685C22×C312yes—
101C2×#685C22×C312yes—
102C2×C4⋊Dic5C22×C311yescharacteristic
103C2×C4⋊Dic5C22×C312yes—
104C2×C4×Dic5C22×C311yescharacteristic
105C2×C4×Dic5C22×C312yes—
106C2×C4×Dic5C22×C311yescharacteristic
107#4039C3×C418yescomplemented
108C5×#95C22×C312yes—
109#3963C22×C311yescharacteristic
110#3963C22×C312yes—
111#3963C22×C312yes—
112#3963C22×C311yescharacteristic
113#3963C22×C311yescharacteristic
114#3963C22×C311yescharacteristic
115#2319—51noSylow
116C23×C3×C5C2411yescharacteristic
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5C22×C414yes—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5C22×C414yes—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5#4112yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5C22×C412yes—
153C2×C3×Dic5C22×C412yes—
154C3×D20—28no—
155C3×C4×D5—48no—
156C22×C3×D4—51no—
157C23×C3×C4—52no—
158C3×C4×D4—58no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—52no—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C2×C3×C4⋊C4C2×D512yes—
163C2×C3×C4⋊C4C2×D511yescharacteristic
164C2×C3×C22⋊C4—52no—
165C2×C3×C22⋊C4—52no—
166C2×C3×C22⋊C4—52no—
167C2×C3×C22⋊C4—52no—
168C2×C3×C22⋊C4—52no—
169C2×C3×C42—51no—
170C2×C3×C42—51no—
171C2×C3×C42—52no—
172C2×C3×C42C2×D511yescharacteristic
173C3×#95—51no—
174C3×#95—51no—
175C3×#95—51no—
176C3×#95—51no—
177C3×#95—52no—
178C3×#95—52no—
179C3×#95C2×D512yes—
180C23×D5C23×C312yes—
181C22×C4×C5C23×C311yescharacteristic
182C22×C4×C5C23×C311yescharacteristic
183C22×C4×C5C23×C312yes—
184C22×C4×C5C23×C312yes—
185C22×C4×C5C23×C311yescharacteristic
186C22×Dic5C23×C311yescharacteristic
187C22×Dic5C23×C311yescharacteristic
188C22×Dic5C23×C312yes—
189C22×Dic5C23×C311yescharacteristic
190C22×Dic5C23×C311yescharacteristic
191C2×D20—22no—
192C2×D20—22no—
193C2×D20C2×C3×C414yes—
194C2×C4×D5—42no—
195C2×C4×D5—42no—
196C2×C4×D5C2×C3×C418yes—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—42no—
199C5×C4⋊C4C2×C3×C414yes—
200C42×C5—22no—
201#685—42no—
202#685—42no—
203#685—42no—
204#685—42no—
205#685C2×C3×C418yes—
206C4⋊Dic5—22no—
207C4⋊Dic5—42no—
208C4×Dic5—22no—
209C4×Dic5—42no—
210C4×Dic5C2×C3×C414yes—
211C2×C4×D4—51no—
212#390—51no—
213#390—51no—
214#389—51no—
215#389C3×D511yescharacteristic, complemented
216#388—52no—
217#388—52no—
218#381—52no—
219#380—52no—
220C4×C4⋊C4—51no—
221#376—51no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C2×#4111yescharacteristic
224C22×C3×C5C2×#4111yescharacteristic
225C22×C3×C5H(5,𝔽2)11yescharacteristic
226C22×C3×C5H(5,𝔽2)11yescharacteristic
227C22×C3×C5H(5,𝔽2)11yescharacteristic
228C22×C3×C52−1+411yescharacteristic
229C2×C3×D5—24no—
230C2×C3×D5—24no—
231C2×C3×D5—24no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C3×C4×C5—24no—
237C3×C4×C5—41no—
238C3×C4×C5—42no—
239C3×C4×C5—41no—
240C3×C4×C5#11714yes—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—41no—
244C3×Dic5—42no—
245C3×Dic5—41no—
246C24×C3—52no—
247C2×C3×D4—54no—
248C2×C3×D4—102no—
249C2×C3×D4—102no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—58no—
253C22×C3×C4—51no—
254C22×C3×C4—51no—
255C22×C3×C4—52no—
256C22×C3×C4—202no—
257C22×C3×C4—202no—
258C22×C3×C4C22×D511yescharacteristic
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D512yes—
261C22×C3×C4C22×D512yes—
262C22×C3×C4C22×D511yescharacteristic
263C3×C4⋊C4—22no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—202no—
267C3×C4⋊C4C4×D514yes—
268C3×C22⋊C4—58no—
269C3×C22⋊C4—202no—
270C3×C22⋊C4—202no—
271C3×C22⋊C4—202no—
272C3×C22⋊C4—202no—
273C3×C42—22no—
274C3×C42—54no—
275C3×C42—102no—
276C3×C42—202no—
277C23×C5C24×C311yescharacteristic
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5C22×C3×C414yes—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—22no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5C22×C3×C414yes—
297C2×C4×C5C22×C3×C412yes—
298C2×C4×C5C3×#4112yes—
299C2×C4×C5C3×#4112yes—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—21no—
309C2×Dic5—22no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5C22×C3×C412yes—
314C2×Dic5C22×C3×C412yes—
315D20—28no—
316C4×D5—48no—
317C22×D4—51no—
318C23×C4—52no—
319C4×D4—58no—
320C2×C4⋊C4—51no—
321C2×C4⋊C4—52no—
322C2×C4⋊C4C2×C3×D511yescharacteristic
323C2×C4⋊C4C2×C3×D512yes—
324C2×C4⋊C4C2×C3×D511yescharacteristic
325C2×C22⋊C4—52no—
326C2×C22⋊C4—52no—
327C2×C22⋊C4—52no—
328C2×C22⋊C4—52no—
329C2×C22⋊C4—52no—
330C2×C42—51no—
331C2×C42—51no—
332C2×C42—52no—
333C2×C42C2×C3×D511yescharacteristic
334#95—51no—
335#95—51no—
336#95—51no—
337#95—51no—
338#95—52no—
339#95—52no—
340#95C2×C3×D512yes—
341C2×C3×C5C2×#11711yescharacteristic
342C2×C3×C5#51811yescharacteristic
343C2×C3×C5#52011yescharacteristic
344C2×C3×C5#54011yescharacteristic
345C2×C3×C5#54011yescharacteristic
346C2×C3×C5#54211yescharacteristic
347C2×C3×C5#54211yescharacteristic
348C3×D5—44no—
349C23×C3—54no—
350C23×C3—102no—
351C23×C3—102no—
352C23×C3—102no—
353C23×C3—102no—
354C23×C3—102no—
355C23×C3—102no—
356C23×C3C23×D511yescharacteristic
357C3×D4—108no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—52no—
370C2×C3×C4—52no—
371C2×C3×C4—101no—
372C2×C3×C4—101no—
373C2×C3×C4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—102no—
379C2×C3×C4—101no—
380C2×C3×C4—102no—
381C2×C3×C4—101no—
382C2×C3×C4—102no—
383C2×C3×C4—101no—
384C2×C3×C4—208no—
385C2×C3×C4C2×C4×D514yes—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4#71112yes—
388C2×C3×C4#71312yes—
389C22×C5C23×C3×C411yescharacteristic
390C22×C5C2×C3×#4111yescharacteristic
391C22×C5C2×C3×#4111yescharacteristic
392C22×C5C3×H(5,𝔽2)11yescharacteristic
393C22×C5C3×H(5,𝔽2)11yescharacteristic
394C22×C5C3×H(5,𝔽2)11yescharacteristic
395C22×C5C3×2−1+411yescharacteristic
396C2×D5—24no—
397C2×D5—24no—
398C2×D5—24no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C4×C5—24no—
404C4×C5—41no—
405C4×C5—42no—
406C4×C5—41no—
407C4×C5C3×#11714yes—
408Dic5—22no—
409Dic5—22no—
410Dic5—41no—
411Dic5—42no—
412Dic5—41no—
413C24—52no—
414C2×D4—54no—
415C2×D4—102no—
416C2×D4—102no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—58no—
420C22×C4—51no—
421C22×C4—51no—
422C22×C4—52no—
423C22×C4—202no—
424C22×C4—202no—
425C22×C4C22×C3×D511yescharacteristic
426C22×C4C22×C3×D511yescharacteristic
427C22×C4C22×C3×D512yes—
428C22×C4C22×C3×D512yes—
429C22×C4C22×C3×D511yescharacteristic
430C4⋊C4—22no—
431C4⋊C4—42no—
432C4⋊C4—102no—
433C4⋊C4—202no—
434C4⋊C4C3×C4×D514yes—
435C22⋊C4—58no—
436C22⋊C4—202no—
437C22⋊C4—202no—
438C22⋊C4—202no—
439C22⋊C4—202no—
440C42—22no—
441C42—54no—
442C42—102no—
443C42—202no—
444C3×C5#231911yescharacteristic, complemented, Hall
445C22×C3—104no—
446C22×C3—104no—
447C22×C3—104no—
448C22×C3—202no—
449C22×C3—202no—
450C22×C3—202no—
451C22×C3—202no—
452C22×C3C22×C4×D511yescharacteristic
453C22×C3C2×#71111yescharacteristic
454C22×C3#414411yescharacteristic
455C22×C3C2×#71311yescharacteristic
456C22×C3#414711yescharacteristic
457C22×C3#414911yescharacteristic
458C22×C3#414911yescharacteristic
459C3×C4—24no—
460C3×C4—41no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—102no—
464C3×C4—102no—
465C3×C4—201no—
466C3×C4—201no—
467C3×C4—202no—
468C3×C4#403814yes—
469C2×C5C2×C3×#11711yescharacteristic
470C2×C5C3×#51811yescharacteristic
471C2×C5C3×#52011yescharacteristic
472C2×C5C3×#54011yescharacteristic
473C2×C5C3×#54011yescharacteristic
474C2×C5C3×#54211yescharacteristic
475C2×C5C3×#54211yescharacteristic
476D5—44no—
477C23—54no—
478C23—102no—
479C23—102no—
480C23—102no—
481C23—102no—
482C23—102no—
483C23—102no—
484C23C23×C3×D511yescharacteristic
485D4—108no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—52no—
498C2×C4—52no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—101no—
502C2×C4—101no—
503C2×C4—101no—
504C2×C4—101no—
505C2×C4—101no—
506C2×C4—102no—
507C2×C4—101no—
508C2×C4—102no—
509C2×C4—101no—
510C2×C4—102no—
511C2×C4—101no—
512C2×C4—208no—
513C2×C4C2×C3×C4×D514yes—
514C2×C4C2×C3×C4×D512yes—
515C2×C4C3×#71112yes—
516C2×C4C3×#71312yes—
517C2×C3—204no—
518C2×C3C2×#403811yescharacteristic
519C2×C3#6587911yescharacteristic
520C2×C3#6590811yescharacteristic
521C2×C3#6595311yescharacteristic
522C2×C3#6597711yescharacteristic
523C2×C3#6603211yescharacteristic
524C2×C3#6606711yescharacteristic
525C5C3×#231911yescharacteristic, complemented, Sylow
526C22—104no—
527C22—104no—
528C22—104no—
529C22—202no—
530C22—202no—
531C22—202no—
532C22—202no—
533C22C22×C3×C4×D511yescharacteristic
534C22C2×C3×#71111yescharacteristic
535C22C3×#414411yescharacteristic
536C22C2×C3×#71311yescharacteristic
537C22C3×#414711yescharacteristic
538C22C3×#414911yescharacteristic
539C22C3×#414911yescharacteristic
540C4—24no—
541C4—41no—
542C4—42no—
543C4—41no—
544C4—102no—
545C4—102no—
546C4—201no—
547C4—202no—
548C4—201no—
549C4C3×#403814yes—
550C3#1060770011yescharacteristic, direct product factor, Sylow
551C2—204no—
552C2C2×C3×#403811yescharacteristic
553C2C3×#6587911yescharacteristic
554C2C3×#6590811yescharacteristic
555C2C3×#6595311yescharacteristic
556C2C3×#6597711yescharacteristic
557C2C3×#6603211yescharacteristic
558C2C3×#6606711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#389C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×#389D5
hypocenterC5C3×#2319
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
2. C3×C5×#389C2semidirect
3. C3×#65279C2semidirect
5. C3×#65276C2semidirect
6. C3×#65274C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
9. C3×#65221C2semidirect
10. C3×#64959C2semidirect
11. C3×#64953C2semidirect
12. #10607700C3direct (N × H)
29. C3×#4039C4semidirect
39. C5×#389C2×C3semidirect
40. #65279C2×C3semidirect
42. #65276C2×C3semidirect
43. #65274C2×C3semidirect
44. C4⋊C4×Dic5C2×C3semidirect
46. #65221C2×C3semidirect
47. #64959C2×C3semidirect
48. #64953C2×C3semidirect
84. C3×#389D5semidirect
107. #4039C3×C4semidirect
215. #389C3×D5semidirect
444. C3×C5#2319semidirect
525. C5C3×#2319semidirect
550. C3#10607700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C3×C5×#3892
C3×#652792
C3×#652772
C3×#652762
C3×#652742
C3×C4⋊C4×Dic52
C3×#652282
C3×#652212
C3×#649592
C3×#649532
#106077003
C3×#23195