Finite Group Databasebeta

← C2×C3×#64935 #14320923

Subgroups — C2×C3×#64935 #14320923

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic10C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic
3C22×C3×C4×Dic5C211yesmaximal, characteristic
4C2×C3×C5×#95C211yesmaximal, characteristic
5C2×C3×#3963C211yesmaximal, characteristic
6C2×C3×#3963C211yesmaximal, characteristic
7C2×C3×#3963C211yesmaximal, characteristic
8C3×#64935C218yesmaximal, direct product factor
9C2×#64935C311yesmaximal, characteristic, direct product factor, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×C3×Dic10—24no—
18C22×C3×Dic10—24no—
19C22×C3×Dic10C418yescomplemented
20C22×C3×Dic10C2214yes—
21C2×C3×#683—24no—
22C2×C3×#683C2214yes—
23C2×C3×C4×Dic5—24no—
24C2×C3×C4×Dic5C2214yes—
25C3×C5×#95C2214yes—
26C3×#3963C2214yes—
27C3×#3963C2214yes—
28C3×#3963C2214yes—
29C2×C3×#391—51nomaximal, Hall
30C23×Dic10C2×C311yescharacteristic
31C22×#683C2×C311yescharacteristic
32C22×C4×Dic5C2×C311yescharacteristic
33C2×C5×#95C2×C311yescharacteristic
34C2×#3963C2×C311yescharacteristic
35C2×#3963C2×C311yescharacteristic
36C2×#3963C2×C311yescharacteristic
37#64935C2×C318yesdirect product factor
38C24×C3×C5C2311yescharacteristic
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5—22no—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—22no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5C2×C414yes—
47C22×C3×C4×C5Q814yescomplemented
48C22×C3×C4×C5C2312yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2312yes—
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×C414yes—
59C22×C3×Dic5C2×C414yes—
60C22×C3×Dic5D414yes—
61C22×C3×Dic5D414yes—
62C22×C3×Dic5Q814yescomplemented
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2312yes—
67C2×C3×Dic10—232no—
68C2×C3×Dic10—28no—
69C2×C3×Dic10—28no—
70C2×C3×Dic10C2×C4116yescomplemented
71C3×#683—28no—
72C3×C4×Dic5—28no—
73C23×C3×Q8—51no—
74C22×C3×C4⋊C4—51no—
75C22×C3×C42—51no—
76C3×#391—58no—
77C2×C3×#95—51no—
78C2×C3×#95—51no—
79C2×C3×#95—51no—
80C2×C3×#95D511yescharacteristic
81C23×C4×C5C22×C311yescharacteristic
82C23×C4×C5C22×C311yescharacteristic
83C23×C4×C5C22×C311yescharacteristic
84C23×Dic5C22×C311yescharacteristic
85C23×Dic5C22×C311yescharacteristic
86C23×Dic5C22×C311yescharacteristic
87C23×Dic5C22×C311yescharacteristic
88C22×Dic10—24no—
89C22×Dic10—24no—
90C22×Dic10C3×C418yescomplemented
91C22×Dic10C22×C314yes—
92C2×#683—24no—
93C2×#683C22×C314yes—
94C2×C4×Dic5—24no—
95C2×C4×Dic5C22×C314yes—
96C5×#95C22×C314yes—
97#3963C22×C314yes—
98#3963C22×C314yes—
99#3963C22×C314yes—
100C2×#391—51noSylow
101C23×C3×C5C22×C412yes—
102C23×C3×C5C2×D412yes—
103C23×C3×C5C2×D412yes—
104C23×C3×C5C2×Q812yes—
105C23×C3×C5C2×Q812yes—
106C23×C3×C5#4112yes—
107C23×C3×C5#4112yes—
108C23×C3×C5C2411yescharacteristic
109C2×C3×C4×C5—28no—
110C2×C3×C4×C5—28no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—44no—
119C2×C3×C4×C5C22×C414yes—
120C2×C3×C4×C5C2×Q814yescomplemented
121C2×C3×Dic5—28no—
122C2×C3×Dic5—28no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—22no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—44no—
131C2×C3×Dic5C22⋊C4116yes—
132C2×C3×Dic5C22×C414yes—
133C2×C3×Dic5C22×C414yes—
134C2×C3×Dic5C2×D414yes—
135C2×C3×Dic5C2×D414yes—
136C2×C3×Dic5C2×Q814yescomplemented
137C3×Dic10—232no—
138C22×C3×Q8—58no—
139C22×C3×Q8—54no—
140C22×C3×Q8—104no—
141C22×C3×Q8—104no—
142C23×C3×C4—51no—
143C23×C3×C4—51no—
144C23×C3×C4—51no—
145C23×C3×C4—51no—
146C23×C3×C4C2×D511yescharacteristic
147C23×C3×C4C2×D511yescharacteristic
148C23×C3×C4C2×D511yescharacteristic
149C2×C3×C4⋊C4—54no—
150C2×C3×C4⋊C4—104no—
151C2×C3×C42—54no—
152C2×C3×C42—104no—
153C3×#95—54no—
154C3×#95—54no—
155C3×#95—54no—
156C3×#95C2×D514yes—
157C24×C5C23×C311yescharacteristic
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5C2×C3×C414yes—
166C22×C4×C5C3×Q814yescomplemented
167C22×C4×C5C23×C312yes—
168C22×C4×C5C23×C312yes—
169C22×C4×C5C23×C312yes—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5C2×C3×C414yes—
178C22×Dic5C2×C3×C414yes—
179C22×Dic5C3×D414yes—
180C22×Dic5C3×D414yes—
181C22×Dic5C3×Q814yescomplemented
182C22×Dic5C23×C312yes—
183C22×Dic5C23×C312yes—
184C22×Dic5C23×C312yes—
185C22×Dic5C23×C312yes—
186C2×Dic10—232no—
187C2×Dic10—28no—
188C2×Dic10—28no—
189C2×Dic10C2×C3×C4116yescomplemented
190#683—28no—
191C4×Dic5—28no—
192C23×Q8—51no—
193C22×C4⋊C4—51no—
194C22×C42—51no—
195#391—58no—
196C2×#95—51no—
197C2×#95—51no—
198C2×#95—51no—
199C2×#95C3×D511yescharacteristic
200C22×C3×C5C2×C22⋊C414yes—
201C22×C3×C5C4×Q814yes—
202C22×C3×C5C4×Q814yes—
203C22×C3×C5C22⋊Q814yes—
204C22×C3×C5C22⋊Q814yes—
205C22×C3×C5#12414yes—
206C22×C3×C5C4⋊Q814yes—
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5C22×D411yescharacteristic
209C22×C3×C5C22×D411yescharacteristic
210C22×C3×C5C22×Q811yescharacteristic
211C22×C3×C5C22×Q811yescharacteristic
212C22×C3×C5C2×#4111yescharacteristic
213C22×C3×C5C2×#4111yescharacteristic
214C3×C4×C5—24no—
215C3×C4×C5—24no—
216C3×C4×C5—42no—
217C3×Dic5—24no—
218C3×Dic5—24no—
219C3×Dic5—42no—
220C3×Dic5C2×C22⋊C418yes—
221C24×C3C22×D511yescharacteristic
222C2×C3×Q8—516no—
223C2×C3×Q8—108no—
224C2×C3×Q8—108no—
225C2×C3×Q8—1032no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—54no—
234C22×C3×C4—54no—
235C22×C3×C4—54no—
236C22×C3×C4—52no—
237C22×C3×C4—54no—
238C22×C3×C4—54no—
239C22×C3×C4—52no—
240C22×C3×C4—52no—
241C22×C3×C4—52no—
242C22×C3×C4—102no—
243C22×C3×C4—102no—
244C22×C3×C4—102no—
245C22×C3×C4—102no—
246C22×C3×C4—102no—
247C22×C3×C4—102no—
248C22×C3×C4—102no—
249C22×C3×C4Dic1014yescomplemented
250C22×C3×C4C4×D514yes—
251C22×C3×C4C22×D512yes—
252C22×C3×C4C22×D512yes—
253C22×C3×C4C22×D512yes—
254C3×C4⋊C4—108no—
255C3×C42—108no—
256C23×C5C22×C3×C412yes—
257C23×C5C2×C3×D412yes—
258C23×C5C2×C3×D412yes—
259C23×C5C2×C3×Q812yes—
260C23×C5C2×C3×Q812yes—
261C23×C5C3×#4112yes—
262C23×C5C3×#4112yes—
263C23×C5C24×C311yescharacteristic
264C2×C4×C5—28no—
265C2×C4×C5—28no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—44no—
274C2×C4×C5C22×C3×C414yes—
275C2×C4×C5C2×C3×Q814yescomplemented
276C2×Dic5—28no—
277C2×Dic5—28no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—44no—
286C2×Dic5C3×C22⋊C4116yes—
287C2×Dic5C22×C3×C414yes—
288C2×Dic5C22×C3×C414yes—
289C2×Dic5C2×C3×D414yes—
290C2×Dic5C2×C3×D414yes—
291C2×Dic5C2×C3×Q814yescomplemented
292Dic10—232no—
293C22×Q8—58no—
294C22×Q8—54no—
295C22×Q8—104no—
296C22×Q8—104no—
297C23×C4—51no—
298C23×C4—51no—
299C23×C4—51no—
300C23×C4—51no—
301C23×C4C2×C3×D511yescharacteristic
302C23×C4C2×C3×D511yescharacteristic
303C23×C4C2×C3×D511yescharacteristic
304C2×C4⋊C4—54no—
305C2×C4⋊C4—104no—
306C2×C42—54no—
307C2×C42—104no—
308#95—54no—
309#95—54no—
310#95—54no—
311#95C2×C3×D514yes—
312C2×C3×C5#39118yescomplemented
313C2×C3×C5C22×C22⋊C411yescharacteristic
314C2×C3×C5C2×C4×Q811yescharacteristic
315C2×C3×C5C2×C4×Q811yescharacteristic
316C2×C3×C5C2×C22⋊Q811yescharacteristic
317C2×C3×C5C2×C22⋊Q811yescharacteristic
318C2×C3×C5C2×#12411yescharacteristic
319C2×C3×C5C2×C4⋊Q811yescharacteristic
320C23×C3C2×Dic1012yes—
321C23×C3C2×C4×D512yes—
322C23×C3#70912yes—
323C23×C3D4×D512yes—
324C23×C3D4×D512yes—
325C23×C3#71112yes—
326C23×C3Q8×D512yes—
327C23×C3C23×D511yescharacteristic
328C3×Q8—1032no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—28no—
334C2×C3×C4—28no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—44no—
339C2×C3×C4—54no—
340C2×C3×C4—54no—
341C2×C3×C4—54no—
342C2×C3×C4—516no—
343C2×C3×C4—54no—
344C2×C3×C4—54no—
345C2×C3×C4—102no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—102no—
349C2×C3×C4—108no—
350C2×C3×C4—108no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—102no—
354C2×C3×C4—204no—
355C2×C3×C4C2×Dic1014yescomplemented
356C2×C3×C4C2×C4×D514yes—
357C22×C5C2×C3×C22⋊C414yes—
358C22×C5C3×C4×Q814yes—
359C22×C5C3×C4×Q814yes—
360C22×C5C3×C22⋊Q814yes—
361C22×C5C3×C22⋊Q814yes—
362C22×C5C3×#12414yes—
363C22×C5C3×C4⋊Q814yes—
364C22×C5C23×C3×C411yescharacteristic
365C22×C5C22×C3×D411yescharacteristic
366C22×C5C22×C3×D411yescharacteristic
367C22×C5C22×C3×Q811yescharacteristic
368C22×C5C22×C3×Q811yescharacteristic
369C22×C5C2×C3×#4111yescharacteristic
370C22×C5C2×C3×#4111yescharacteristic
371C4×C5—24no—
372C4×C5—24no—
373C4×C5—42no—
374Dic5—24no—
375Dic5—24no—
376Dic5—42no—
377Dic5C2×C3×C22⋊C418yes—
378C24C22×C3×D511yescharacteristic
379C2×Q8—516no—
380C2×Q8—108no—
381C2×Q8—108no—
382C2×Q8—1032no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—54no—
391C22×C4—54no—
392C22×C4—54no—
393C22×C4—52no—
394C22×C4—54no—
395C22×C4—54no—
396C22×C4—52no—
397C22×C4—52no—
398C22×C4—52no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4—102no—
403C22×C4—102no—
404C22×C4—102no—
405C22×C4—102no—
406C22×C4C3×Dic1014yescomplemented
407C22×C4C3×C4×D514yes—
408C22×C4C22×C3×D512yes—
409C22×C4C22×C3×D512yes—
410C22×C4C22×C3×D512yes—
411C4⋊C4—108no—
412C42—108no—
413C3×C5C2×#39111yescharacteristic, complemented, Hall
414C22×C3C4×Dic1014yes—
415C22×C3#402414yes—
416C22×C3D5×C22⋊C414yes—
417C22×C3#403114yes—
418C22×C3#403314yes—
419C22×C3#403414yes—
420C22×C3#404214yes—
421C22×C3C22×Dic1011yescharacteristic
422C22×C3C22×C4×D511yescharacteristic
423C22×C3C2×#70911yescharacteristic
424C22×C3C2×D4×D511yescharacteristic
425C22×C3C2×D4×D511yescharacteristic
426C22×C3C2×#71111yescharacteristic
427C22×C3C2×Q8×D511yescharacteristic
428C3×C4—24no—
429C3×C4—24no—
430C3×C4—42no—
431C3×C4—58no—
432C3×C4—104no—
433C3×C4—104no—
434C3×C4—202no—
435C2×C5C3×#39118yescomplemented
436C2×C5C22×C3×C22⋊C411yescharacteristic
437C2×C5C2×C3×C4×Q811yescharacteristic
438C2×C5C2×C3×C4×Q811yescharacteristic
439C2×C5C2×C3×C22⋊Q811yescharacteristic
440C2×C5C2×C3×C22⋊Q811yescharacteristic
441C2×C5C2×C3×#12411yescharacteristic
442C2×C5C2×C3×C4⋊Q811yescharacteristic
443C23C2×C3×Dic1012yes—
444C23C2×C3×C4×D512yes—
445C23C3×#70912yes—
446C23C3×D4×D512yes—
447C23C3×D4×D512yes—
448C23C3×#71112yes—
449C23C3×Q8×D512yes—
450C23C23×C3×D511yescharacteristic
451Q8—1032no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—28no—
457C2×C4—28no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—44no—
462C2×C4—54no—
463C2×C4—54no—
464C2×C4—54no—
465C2×C4—516no—
466C2×C4—54no—
467C2×C4—54no—
468C2×C4—102no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—108no—
473C2×C4—108no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—102no—
477C2×C4—204no—
478C2×C4C2×C3×Dic1014yescomplemented
479C2×C4C2×C3×C4×D514yes—
480C2×C3#6493518yesdirect product factor
481C2×C3C2×C4×Dic1011yescharacteristic
482C2×C3C2×#402411yescharacteristic
483C2×C3C2×D5×C22⋊C411yescharacteristic
484C2×C3C2×#403111yescharacteristic
485C2×C3C2×#403311yescharacteristic
486C2×C3C2×#403411yescharacteristic
487C2×C3C2×#404211yescharacteristic
488C5C2×C3×#39111yescharacteristic, complemented, Sylow
489C22C3×C4×Dic1014yes—
490C22C3×#402414yes—
491C22C3×D5×C22⋊C414yes—
492C22C3×#403114yes—
493C22C3×#403314yes—
494C22C3×#403414yes—
495C22C3×#404214yes—
496C22C22×C3×Dic1011yescharacteristic
497C22C22×C3×C4×D511yescharacteristic
498C22C2×C3×#70911yescharacteristic
499C22C2×C3×D4×D511yescharacteristic
500C22C2×C3×D4×D511yescharacteristic
501C22C2×C3×#71111yescharacteristic
502C22C2×C3×Q8×D511yescharacteristic
503C4—24no—
504C4—24no—
505C4—42no—
506C4—58no—
507C4—104no—
508C4—104no—
509C4—202no—
510C3C2×#6493511yescharacteristic, direct product factor, Sylow
511C2C3×#6493518yesdirect product factor
512C2C2×C3×C4×Dic1011yescharacteristic
513C2C2×C3×#402411yescharacteristic
514C2C2×C3×D5×C22⋊C411yescharacteristic
515C2C2×C3×#403111yescharacteristic
516C2C2×C3×#403311yescharacteristic
517C2C2×C3×#403411yescharacteristic
518C2C2×C3×#404211yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC2×C3×#95D5
hypocenterC5C2×C3×#391
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. C3×#64935C2direct (N × H)
9. C2×#64935C3direct (N × H)
19. C22×C3×Dic10C4semidirect
37. #64935C2×C3direct (N × H)
47. C22×C3×C4×C5Q8semidirect
62. C22×C3×Dic5Q8semidirect
70. C2×C3×Dic10C2×C4semidirect
90. C22×Dic10C3×C4semidirect
120. C2×C3×C4×C5C2×Q8semidirect
136. C2×C3×Dic5C2×Q8semidirect
166. C22×C4×C5C3×Q8semidirect
181. C22×Dic5C3×Q8semidirect
189. C2×Dic10C2×C3×C4semidirect
249. C22×C3×C4Dic10semidirect
275. C2×C4×C5C2×C3×Q8semidirect
291. C2×Dic5C2×C3×Q8semidirect
312. C2×C3×C5#391semidirect
355. C2×C3×C4C2×Dic10semidirect
406. C22×C4C3×Dic10semidirect
413. C3×C5C2×#391semidirect
435. C2×C5C3×#391semidirect
478. C2×C4C2×C3×Dic10semidirect
480. C2×C3#64935direct (N × H)
488. C5C2×C3×#391semidirect
510. C3C2×#64935direct (N × H)
511. C2C3×#64935direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic102
C22×C3×#6832
C22×C3×C4×Dic52
C2×C3×C5×#952
C2×C3×#39632
C3×#649352
C2×#649353
C2×C3×#3915