Finite Group Databasebeta

← C3×#10605370 #14327664

Subgroups — C3×#10605370 #14327664

Order 1920.

1264 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×#4039C211yesmaximal, characteristic
2C2×C3×#4018C212yesmaximal, complemented
3C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#65277C211yesmaximal, characteristic
5C3×#65265C211yesmaximal, characteristic, complemented
6C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
7C3×#65229C212yesmaximal, complemented
8C3×#65228C211yesmaximal, characteristic
9C3×C4×#683C211yesmaximal, characteristic, complemented
10C3×#64958C212yesmaximal, complemented
11C3×#64956C212yesmaximal, complemented
12#10605370C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C3×C42×C5C2212yes—
19C2×C3×#685C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×#685C2212yes—
23C2×C3×#685C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×#683C2211yescharacteristic
26C2×C3×#683C2212yes—
27C2×C3×#683C2212yes—
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2212yes—
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C3×#4039C418yescomplemented
33C3×#4018—28no—
34C3×C5×#95C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#3963C2211yescharacteristic
38C3×#2354—51nomaximal, Hall
39C2×#4039C2×C311yescharacteristic
40C2×#4018C2×C312yescomplemented
41C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
42#65277C2×C311yescharacteristic
43#65265C2×C311yescharacteristic, complemented
44C4⋊C4×Dic5C2×C311yescharacteristic, complemented
45#65229C2×C312yescomplemented
46#65228C2×C311yescharacteristic
47C4×#683C2×C311yescharacteristic, complemented
48#64958C2×C312yescomplemented
49#64956C2×C312yescomplemented
50C23×C3×D5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C2×C3×D20—22no—
62C2×C3×D20—22no—
63C2×C3×D20C2×C414yes—
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5C2×C418yes—
67C3×C5×C4⋊C4—22no—
68C3×C5×C4⋊C4C2×C414yes—
69C3×C42×C5—24no—
70C3×C42×C5—22no—
71C3×#685—24no—
72C3×#685—24no—
73C3×#685—42no—
74C3×#685—42no—
75C3×#685C2×C418yes—
76C3×C4⋊Dic5—22no—
77C3×#683—24no—
78C3×#683—22no—
79C3×#683—42no—
80C3×#683D414yescomplemented
81C3×C4×Dic5—22no—
82C3×C4×Dic5—24no—
83C3×C4×Dic5C2×C414yes—
84C2×C3×C4×D4—51no—
85C2×C3×#117—52no—
86C3×#390—51no—
87C3×#390—51no—
88C3×#388—52no—
89C3×#388—52no—
90C3×#384—51no—
91C3×#380—52no—
92C3×C4×C4⋊C4—51no—
93C3×C4×C4⋊C4—51no—
94C3×C4×C4⋊C4D511yescharacteristic, complemented
95C22×D20C22×C311yescharacteristic
96C22×C4×D5C22×C312yes—
97C2×C5×C4⋊C4C22×C311yescharacteristic
98C2×C5×C4⋊C4C22×C311yescharacteristic
99C2×C42×C5C22×C312yes—
100C2×C42×C5C22×C311yescharacteristic
101C2×#685C22×C312yes—
102C2×#685C22×C312yes—
103C2×#685C22×C312yes—
104C2×#685C22×C312yes—
105C2×#685C22×C312yes—
106C2×C4⋊Dic5C22×C311yescharacteristic
107C2×#683C22×C312yes—
108C2×#683C22×C311yescharacteristic
109C2×#683C22×C312yes—
110C2×#683C22×C311yescharacteristic
111C2×C4×Dic5C22×C312yes—
112C2×C4×Dic5C22×C311yescharacteristic
113C2×C4×Dic5C22×C311yescharacteristic
114#4039C3×C418yescomplemented
115#4018—28no—
116C5×#95C22×C312yes—
117#3963C22×C312yes—
118#3963C22×C311yescharacteristic
119#3963C22×C311yescharacteristic
120#2354—51noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5C22×C414yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C414yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5#4112yes—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C22×C412yes—
156C2×C3×Dic5C2×D412yes—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5#4112yes—
159C3×D20—28no—
160C3×C4×D5—216no—
161C22×C3×D4—51no—
162C23×C3×C4—52no—
163C3×C4×D4—58no—
164C3×#117—108no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—51no—
167C2×C3×C4⋊C4—51no—
168C2×C3×C4⋊C4—52no—
169C2×C3×C4⋊C4—52no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C4⋊C4C2×D511yescharacteristic
172C2×C3×C22⋊C4—52no—
173C2×C3×C22⋊C4—52no—
174C2×C3×C22⋊C4—52no—
175C2×C3×C22⋊C4—52no—
176C2×C3×C22⋊C4—52no—
177C2×C3×C42—51no—
178C2×C3×C42—51no—
179C2×C3×C42—52no—
180C2×C3×C42C2×D511yescharacteristic
181C2×C3×C42C2×D512yes—
182C3×#95—52no—
183C3×#95—51no—
184C3×#95—51no—
185C3×#95C2×D512yes—
186C23×D5C23×C312yes—
187C22×C4×C5C23×C312yes—
188C22×C4×C5C23×C311yescharacteristic
189C22×C4×C5C23×C312yes—
190C22×C4×C5C23×C311yescharacteristic
191C22×C4×C5C23×C311yescharacteristic
192C22×Dic5C23×C311yescharacteristic
193C22×Dic5C23×C312yes—
194C22×Dic5C23×C311yescharacteristic
195C22×Dic5C23×C311yescharacteristic
196C22×Dic5C23×C311yescharacteristic
197C2×D20—22no—
198C2×D20—22no—
199C2×D20C2×C3×C414yes—
200C2×C4×D5—24no—
201C2×C4×D5—24no—
202C2×C4×D5C2×C3×C418yes—
203C5×C4⋊C4—22no—
204C5×C4⋊C4C2×C3×C414yes—
205C42×C5—24no—
206C42×C5—22no—
207#685—24no—
208#685—24no—
209#685—42no—
210#685—42no—
211#685C2×C3×C418yes—
212C4⋊Dic5—22no—
213#683—24no—
214#683—22no—
215#683—42no—
216#683C3×D414yescomplemented
217C4×Dic5—22no—
218C4×Dic5—24no—
219C4×Dic5C2×C3×C414yes—
220C2×C4×D4—51no—
221C2×#117—52no—
222#390—51no—
223#390—51no—
224#388—52no—
225#388—52no—
226#384—51no—
227#380—52no—
228C4×C4⋊C4—51no—
229C4×C4⋊C4—51no—
230C4×C4⋊C4C3×D511yescharacteristic, complemented
231C22×C3×C5C23×C411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5H(5,𝔽2)11yescharacteristic
237C22×C3×C52−1+411yescharacteristic
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—24no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C3×C4×C5—24no—
246C3×C4×C5—22no—
247C3×C4×C5—42no—
248C3×C4×C5—41no—
249C3×C4×C5#11714yescomplemented
250C3×Dic5—22no—
251C3×Dic5—22no—
252C3×Dic5—42no—
253C3×Dic5—41no—
254C3×Dic5C4×D414yes—
255C24×C3—52no—
256C2×C3×D4—54no—
257C2×C3×D4—102no—
258C2×C3×D4—102no—
259C22×C3×C4—51no—
260C22×C3×C4—51no—
261C22×C3×C4—51no—
262C22×C3×C4—58no—
263C22×C3×C4—51no—
264C22×C3×C4—52no—
265C22×C3×C4—104no—
266C22×C3×C4—104no—
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D512yes—
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C22×C3×C4C22×D511yescharacteristic
272C3×C4⋊C4—22no—
273C3×C4⋊C4—54no—
274C3×C4⋊C4—102no—
275C3×C4⋊C4—104no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4—202no—
278C3×C4⋊C4C4×D514yes—
279C3×C22⋊C4—58no—
280C3×C22⋊C4—104no—
281C3×C22⋊C4—104no—
282C3×C22⋊C4—202no—
283C3×C22⋊C4—202no—
284C3×C42—22no—
285C3×C42—24no—
286C3×C42—54no—
287C3×C42—104no—
288C3×C42—102no—
289C23×C5C24×C311yescharacteristic
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5C22×C3×C414yes—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5C22×C3×C414yes—
308C2×C4×C5C22×C3×C412yes—
309C2×C4×C5C2×C3×D412yes—
310C2×C4×C5C3×#4112yes—
311C2×C4×C5C3×#4112yes—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—22no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—21no—
322C2×Dic5C22×C3×C412yes—
323C2×Dic5C22×C3×C412yes—
324C2×Dic5C2×C3×D412yes—
325C2×Dic5C2×C3×D412yes—
326C2×Dic5C3×#4112yes—
327D20—28no—
328C4×D5—216no—
329C22×D4—51no—
330C23×C4—52no—
331C4×D4—58no—
332#117—108no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—52no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—52no—
338C2×C4⋊C4C2×C3×D511yescharacteristic
339C2×C4⋊C4C2×C3×D511yescharacteristic
340C2×C22⋊C4—52no—
341C2×C22⋊C4—52no—
342C2×C22⋊C4—52no—
343C2×C22⋊C4—52no—
344C2×C22⋊C4—52no—
345C2×C42—51no—
346C2×C42—52no—
347C2×C42—51no—
348C2×C42C2×C3×D512yes—
349C2×C42C2×C3×D511yescharacteristic
350#95—52no—
351#95—51no—
352#95—51no—
353#95C2×C3×D512yes—
354C2×C3×C5C2×#11711yescharacteristic
355C2×C3×C5C2×C4×D411yescharacteristic
356C2×C3×C5#52011yescharacteristic
357C2×C3×C5#54711yescharacteristic
358C2×C3×C5#55011yescharacteristic
359C2×C3×C5#55511yescharacteristic
360C2×C3×C5#55611yescharacteristic
361C3×D5—44no—
362C23×C3—54no—
363C23×C3—102no—
364C23×C3—102no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3C23×D511yescharacteristic
370C3×D4—108no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—52no—
382C2×C3×C4—52no—
383C2×C3×C4—52no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—1016no—
387C2×C3×C4—101no—
388C2×C3×C4—101no—
389C2×C3×C4—101no—
390C2×C3×C4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4—102no—
397C2×C3×C4C2×C4×D514yes—
398C2×C3×C4C2×C4×D512yes—
399C2×C3×C4#70912yes—
400C2×C3×C4#70912yes—
401C2×C3×C4D4×D512yes—
402C22×C5C23×C3×C411yescharacteristic
403C22×C5C22×C3×D411yescharacteristic
404C22×C5C2×C3×#4111yescharacteristic
405C22×C5C2×C3×#4111yescharacteristic
406C22×C5C2×C3×#4111yescharacteristic
407C22×C5C3×H(5,𝔽2)11yescharacteristic
408C22×C5C3×2−1+411yescharacteristic
409C2×D5—24no—
410C2×D5—24no—
411C2×D5—24no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—42no—
416C4×C5—24no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—41no—
420C4×C5C3×#11714yescomplemented
421Dic5—22no—
422Dic5—22no—
423Dic5—42no—
424Dic5—41no—
425Dic5C3×C4×D414yes—
426C24—52no—
427C2×D4—54no—
428C2×D4—102no—
429C2×D4—102no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—58no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—104no—
437C22×C4—104no—
438C22×C4C22×C3×D511yescharacteristic
439C22×C4C22×C3×D512yes—
440C22×C4C22×C3×D512yes—
441C22×C4C22×C3×D511yescharacteristic
442C22×C4C22×C3×D511yescharacteristic
443C4⋊C4—22no—
444C4⋊C4—54no—
445C4⋊C4—104no—
446C4⋊C4—102no—
447C4⋊C4—102no—
448C4⋊C4—202no—
449C4⋊C4C3×C4×D514yes—
450C22⋊C4—58no—
451C22⋊C4—104no—
452C22⋊C4—104no—
453C22⋊C4—202no—
454C22⋊C4—202no—
455C42—22no—
456C42—24no—
457C42—54no—
458C42—104no—
459C42—102no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3—104no—
462C22×C3—104no—
463C22×C3—104no—
464C22×C3—202no—
465C22×C3—202no—
466C22×C3—202no—
467C22×C3—202no—
468C22×C3C22×C4×D511yescharacteristic
469C22×C3C2×#70911yescharacteristic
470C22×C3C2×#70911yescharacteristic
471C22×C3C2×D4×D511yescharacteristic
472C22×C3#414711yescharacteristic
473C22×C3D5×#4111yescharacteristic
474C22×C3#414911yescharacteristic
475C3×C4—22no—
476C3×C4—24no—
477C3×C4—41no—
478C3×C4—42no—
479C3×C4—54no—
480C3×C4—102no—
481C3×C4—102no—
482C3×C4—201no—
483C3×C4—202no—
484C3×C4#401814yescomplemented
485C2×C5C2×C3×#11711yescharacteristic
486C2×C5C2×C3×C4×D411yescharacteristic
487C2×C5C3×#52011yescharacteristic
488C2×C5C3×#54711yescharacteristic
489C2×C5C3×#55011yescharacteristic
490C2×C5C3×#55511yescharacteristic
491C2×C5C3×#55611yescharacteristic
492D5—44no—
493C23—54no—
494C23—102no—
495C23—102no—
496C23—102no—
497C23—102no—
498C23—102no—
499C23—102no—
500C23C23×C3×D511yescharacteristic
501D4—108no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—52no—
515C2×C4—52no—
516C2×C4—52no—
517C2×C4—1016no—
518C2×C4—101no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—101no—
526C2×C4—101no—
527C2×C4—102no—
528C2×C4C2×C3×C4×D514yes—
529C2×C4C2×C3×C4×D512yes—
530C2×C4C3×#70912yes—
531C2×C4C3×#70912yes—
532C2×C4C3×D4×D512yes—
533C2×C3—204no—
534C2×C3C2×#401811yescharacteristic
535C2×C3#6584111yescharacteristic
536C2×C3#6586611yescharacteristic
537C2×C3C4×D4×D511yescharacteristic
538C2×C3#6588711yescharacteristic
539C2×C3#6590211yescharacteristic
540C2×C3#6590811yescharacteristic
541C5C3×#235411yescharacteristic, complemented, Sylow
542C22—104no—
543C22—104no—
544C22—104no—
545C22—202no—
546C22—202no—
547C22—202no—
548C22—202no—
549C22C22×C3×C4×D511yescharacteristic
550C22C2×C3×#70911yescharacteristic
551C22C2×C3×#70911yescharacteristic
552C22C2×C3×D4×D511yescharacteristic
553C22C3×#414711yescharacteristic
554C22C3×D5×#4111yescharacteristic
555C22C3×#414911yescharacteristic
556C4—24no—
557C4—22no—
558C4—41no—
559C4—42no—
560C4—54no—
561C4—102no—
562C4—102no—
563C4—201no—
564C4—202no—
565C4C3×#401814yescomplemented
566C3#1060537011yescharacteristic, direct product factor, Sylow
567C2—204no—
568C2C2×C3×#401811yescharacteristic
569C2C3×#6584111yescharacteristic
570C2C3×#6586611yescharacteristic
571C2C3×C4×D4×D511yescharacteristic
572C2C3×#6588711yescharacteristic
573C2C3×#6590211yescharacteristic
574C2C3×#6590811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2354
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4018C2semidirect
3. C3×C4×C5×C4⋊C4C2semidirect
5. C3×#65265C2semidirect
6. C3×C4⋊C4×Dic5C2semidirect
7. C3×#65229C2semidirect
9. C3×C4×#683C2semidirect
10. C3×#64958C2semidirect
11. C3×#64956C2semidirect
12. #10605370C3direct (N × H)
32. C3×#4039C4semidirect
40. C2×#4018C2×C3semidirect
41. C4×C5×C4⋊C4C2×C3semidirect
43. #65265C2×C3semidirect
44. C4⋊C4×Dic5C2×C3semidirect
45. #65229C2×C3semidirect
47. C4×#683C2×C3semidirect
48. #64958C2×C3semidirect
49. #64956C2×C3semidirect
80. C3×#683D4semidirect
94. C3×C4×C4⋊C4D5semidirect
114. #4039C3×C4semidirect
216. #683C3×D4semidirect
230. C4×C4⋊C4C3×D5semidirect
249. C3×C4×C5#117semidirect
420. C4×C5C3×#117semidirect
460. C3×C5#2354semidirect
484. C3×C4#4018semidirect
541. C5C3×#2354semidirect
565. C4C3×#4018semidirect
566. C3#10605370direct (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
C2×C3×#40182
C3×C4×C5×C4⋊C42
C3×#652772
C3×#652652
C3×C4⋊C4×Dic52
C3×#652292
C3×#652282
C3×C4×#6832
C3×#649582
C3×#649562
#106053703
C3×#23545