Finite Group Databasebeta

← C3×D5×#400 #14332023

Subgroups — C3×D5×#400 #14332023

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
3C3×C5×#400C211yesmaximal, characteristic, complemented
4C3×#65275C211yesmaximal, characteristic, complemented
5C3×#65271C211yesmaximal, characteristic, complemented
6C3×D5×#95C212yesmaximal
7C3×D5×#95C211yesmaximal, characteristic
8C3×D5×#95C212yesmaximal
9C3×#64949C212yesmaximal, complemented
10C3×#64948C211yesmaximal, characteristic, complemented
11C3×#64947C212yesmaximal, complemented
12D5×#400C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2212yes—
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C2×C3×#683C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×#683C2211yescharacteristic
25C3×D5×C4⋊C4—24no—
26C3×D5×C4⋊C4—24no—
27C3×C5×#95C2212yes—
28C3×C5×#95C2211yescharacteristic
29C3×C5×#95C2212yes—
30C3×#3963C2212yes—
31C3×#3963C2212yes—
32C3×#3963C2212yes—
33C3×#3963C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2211yescharacteristic
38C2×C3×#400—51nomaximal, Hall
39C2×D5×C4⋊C4C2×C311yescharacteristic
40C2×D5×C4⋊C4C2×C311yescharacteristic
41C5×#400C2×C311yescharacteristic, complemented
42#65275C2×C311yescharacteristic, complemented
43#65271C2×C311yescharacteristic, complemented
44D5×#95C2×C312yes—
45D5×#95C2×C312yes—
46D5×#95C2×C311yescharacteristic
47#64949C2×C312yescomplemented
48#64948C2×C311yescharacteristic, complemented
49#64947C2×C312yescomplemented
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—24no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5—28no—
68C2×C3×C4×D5—24no—
69C2×C3×C4×D5—24no—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5D414yes—
72C2×C3×C4×D5Q814yes—
73C3×C5×C4⋊C4—22no—
74C3×C5×C4⋊C4—22no—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5—22no—
77C3×#683—22no—
78C3×#683—22no—
79C3×#683—24no—
80C22×C3×C4⋊C4—51no—
81C22×C3×C4⋊C4—51no—
82C3×#400—51no—
83C3×#400—51no—
84C3×#400—52no—
85C3×#400—51no—
86C3×#400—52no—
87C3×#400D511yescharacteristic, direct product factor
88C2×C3×#95—52no—
89C2×C3×#95—51no—
90C2×C3×#95—52no—
91C22×C4×D5C22×C311yescharacteristic
92C22×C4×D5C22×C312yes—
93C22×C4×D5C22×C312yes—
94C22×C4×D5C22×C311yescharacteristic
95C22×C4×D5C22×C311yescharacteristic
96C2×C5×C4⋊C4C22×C311yescharacteristic
97C2×C5×C4⋊C4C22×C311yescharacteristic
98C2×C4⋊Dic5C22×C311yescharacteristic
99C2×C4⋊Dic5C22×C311yescharacteristic
100C2×#683C22×C311yescharacteristic
101C2×#683C22×C312yes—
102C2×#683C22×C311yescharacteristic
103D5×C4⋊C4—24no—
104D5×C4⋊C4—24no—
105C5×#95C22×C312yes—
106C5×#95C22×C311yescharacteristic
107C5×#95C22×C312yes—
108#3963C22×C312yes—
109#3963C22×C312yes—
110#3963C22×C312yes—
111#3963C22×C312yes—
112#3963C22×C312yes—
113#3963C22×C312yes—
114#3963C22×C312yes—
115#3963C22×C311yescharacteristic
116C2×#400—51noSylow
117C23×C3×C5C2411yescharacteristic
118C22×C3×D5C2×D412yes—
119C22×C3×D5C2×Q812yes—
120C22×C3×D5#4112yes—
121C22×C3×D5#4114yes—
122C22×C3×D5#4114yes—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×Q812yes—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—21no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—24no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×Q812yes—
147C3×C4×D5—28no—
148C3×C4×D5—28no—
149C3×C4×D5—44no—
150C3×C4×D5—48no—
151C3×C4×D5—48no—
152C23×C3×C4—51no—
153C23×C3×C4—51no—
154C23×C3×C4—52no—
155C23×C3×C4—52no—
156C23×C3×C4—51no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4—52no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C4⋊C4—51no—
161C2×C3×C4⋊C4—51no—
162C2×C3×C4⋊C4—104no—
163C2×C3×C4⋊C4—104no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C4⋊C4C2×D511yescharacteristic
166C3×#95—52no—
167C3×#95—52no—
168C3×#95—52no—
169C3×#95—51no—
170C3×#95—52no—
171C3×#95—52no—
172C3×#95—52no—
173C3×#95—52no—
174C3×#95C2×D511yescharacteristic
175C3×#95C2×D512yes—
176C3×#95C2×D512yes—
177C23×D5C23×C311yescharacteristic
178C22×C4×C5C23×C312yes—
179C22×C4×C5C23×C311yescharacteristic
180C22×C4×C5C23×C312yes—
181C22×C4×C5C23×C311yescharacteristic
182C22×C4×C5C23×C311yescharacteristic
183C22×Dic5C23×C312yes—
184C22×Dic5C23×C312yes—
185C22×Dic5C23×C311yescharacteristic
186C22×Dic5C23×C311yescharacteristic
187C22×Dic5C23×C311yescharacteristic
188C2×C4×D5—22no—
189C2×C4×D5—22no—
190C2×C4×D5—24no—
191C2×C4×D5—22no—
192C2×C4×D5—24no—
193C2×C4×D5—24no—
194C2×C4×D5—28no—
195C2×C4×D5—24no—
196C2×C4×D5—24no—
197C2×C4×D5—24no—
198C2×C4×D5C3×D414yes—
199C2×C4×D5C3×Q814yes—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C4⋊Dic5—22no—
203C4⋊Dic5—22no—
204#683—22no—
205#683—22no—
206#683—24no—
207C22×C4⋊C4—51no—
208C22×C4⋊C4—51no—
209#400—51no—
210#400—51no—
211#400—52no—
212#400—51no—
213#400—52no—
214#400C3×D511yescharacteristic, direct product factor
215C2×#95—51no—
216C2×#95—52no—
217C2×#95—52no—
218C22×C3×C5C22×D411yescharacteristic
219C22×C3×C5C22×Q811yescharacteristic
220C22×C3×C5C2×#4111yescharacteristic
221C22×C3×C5C2×#4112yes—
222C22×C3×C5C2×#4112yes—
223C2×C3×D5C22⋊Q814yes—
224C2×C3×D5#12314yes—
225C2×C3×D5#12414yes—
226C2×C3×D5#12518yes—
227C2×C3×D5#12618yes—
228C3×C4×C5—22no—
229C3×C4×C5—22no—
230C3×C4×C5—41no—
231C3×C4×C5—42no—
232C3×C4×C5—42no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C3×Dic5—41no—
236C3×Dic5—42no—
237C3×Dic5—42no—
238C24×C3—51no—
239C22×C3×C4—51no—
240C22×C3×C4—51no—
241C22×C3×C4—54no—
242C22×C3×C4—54no—
243C22×C3×C4—52no—
244C22×C3×C4—51no—
245C22×C3×C4—52no—
246C22×C3×C4—102no—
247C22×C3×C4—102no—
248C22×C3×C4—104no—
249C22×C3×C4—102no—
250C22×C3×C4—104no—
251C22×C3×C4—104no—
252C22×C3×C4—104no—
253C22×C3×C4—104no—
254C22×C3×C4—104no—
255C22×C3×C4—108no—
256C22×C3×C4C22×D512yes—
257C22×C3×C4C22×D511yescharacteristic
258C22×C3×C4C22×D512yes—
259C22×C3×C4C22×D511yescharacteristic
260C22×C3×C4C22×D511yescharacteristic
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—104no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—102no—
267C3×C4⋊C4—102no—
268C23×C5C24×C311yescharacteristic
269C22×D5C2×C3×D412yes—
270C22×D5C2×C3×Q812yes—
271C22×D5C3×#4112yes—
272C22×D5C3×#4114yes—
273C22×D5C3×#4114yes—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5C2×C3×D412yes—
285C2×C4×C5C2×C3×Q812yes—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—22no—
289C2×Dic5—21no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—24no—
293C2×Dic5—22no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5C2×C3×D412yes—
297C2×Dic5C2×C3×Q812yes—
298C4×D5—28no—
299C4×D5—28no—
300C4×D5—44no—
301C4×D5—48no—
302C4×D5—48no—
303C23×C4—51no—
304C23×C4—51no—
305C23×C4—51no—
306C23×C4—52no—
307C23×C4—52no—
308C2×C4⋊C4—51no—
309C2×C4⋊C4—52no—
310C2×C4⋊C4—51no—
311C2×C4⋊C4—51no—
312C2×C4⋊C4—51no—
313C2×C4⋊C4—104no—
314C2×C4⋊C4—104no—
315C2×C4⋊C4C2×C3×D511yescharacteristic
316C2×C4⋊C4C2×C3×D511yescharacteristic
317#95—52no—
318#95—52no—
319#95—52no—
320#95—51no—
321#95—52no—
322#95—52no—
323#95—52no—
324#95—52no—
325#95C2×C3×D511yescharacteristic
326#95C2×C3×D512yes—
327#95C2×C3×D512yes—
328C2×C3×C5C2×C22⋊Q811yescharacteristic
329C2×C3×C5C2×#12311yescharacteristic
330C2×C3×C5C2×#12411yescharacteristic
331C2×C3×C5C2×#12512yes—
332C2×C3×C5C2×#12612yes—
333C3×D5#40018yesdirect product factor
334C23×C3—52no—
335C23×C3—52no—
336C23×C3—52no—
337C23×C3—54no—
338C23×C3—54no—
339C23×C3C23×D511yescharacteristic
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—52no—
351C2×C3×C4—52no—
352C2×C3×C4—108no—
353C2×C3×C4—108no—
354C2×C3×C4—101no—
355C2×C3×C4—101no—
356C2×C3×C4—102no—
357C2×C3×C4—101no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—104no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—204no—
365C2×C3×C4—208no—
366C2×C3×C4—208no—
367C2×C3×C4D4×D512yes—
368C2×C3×C4Q8×D512yes—
369C22×C5C22×C3×D411yescharacteristic
370C22×C5C22×C3×Q811yescharacteristic
371C22×C5C2×C3×#4111yescharacteristic
372C22×C5C2×C3×#4112yes—
373C22×C5C2×C3×#4112yes—
374C2×D5C3×C22⋊Q814yes—
375C2×D5C3×#12314yes—
376C2×D5C3×#12414yes—
377C2×D5C3×#12518yes—
378C2×D5C3×#12618yes—
379C4×C5—22no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5—42no—
383C4×C5—42no—
384Dic5—22no—
385Dic5—22no—
386Dic5—41no—
387Dic5—42no—
388Dic5—42no—
389C24—51no—
390C22×C4—51no—
391C22×C4—51no—
392C22×C4—54no—
393C22×C4—54no—
394C22×C4—52no—
395C22×C4—51no—
396C22×C4—52no—
397C22×C4—102no—
398C22×C4—104no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—104no—
402C22×C4—104no—
403C22×C4—108no—
404C22×C4—104no—
405C22×C4—104no—
406C22×C4—104no—
407C22×C4C22×C3×D512yes—
408C22×C4C22×C3×D511yescharacteristic
409C22×C4C22×C3×D512yes—
410C22×C4C22×C3×D511yescharacteristic
411C22×C4C22×C3×D511yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—102no—
415C4⋊C4—104no—
416C4⋊C4—102no—
417C4⋊C4—102no—
418C4⋊C4—102no—
419C3×C5C2×#40011yescharacteristic, complemented, Hall
420C22×C3—54no—
421C22×C3—54no—
422C22×C3—54no—
423C22×C3—58no—
424C22×C3—58no—
425C22×C3C2×D4×D511yescharacteristic
426C22×C3C2×Q8×D511yescharacteristic
427C22×C3D5×#4111yescharacteristic
428C22×C3D5×#4112yes—
429C22×C3D5×#4112yes—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—102no—
436C3×C4—102no—
437C3×C4—201no—
438C3×C4—202no—
439C3×C4—202no—
440C2×C5C2×C3×C22⋊Q811yescharacteristic
441C2×C5C2×C3×#12311yescharacteristic
442C2×C5C2×C3×#12411yescharacteristic
443C2×C5C2×C3×#12512yes—
444C2×C5C2×C3×#12612yes—
445D5C3×#40018yesdirect product factor
446C23—52no—
447C23—52no—
448C23—52no—
449C23—54no—
450C23—54no—
451C23C23×C3×D511yescharacteristic
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—52no—
463C2×C4—52no—
464C2×C4—108no—
465C2×C4—108no—
466C2×C4—101no—
467C2×C4—101no—
468C2×C4—102no—
469C2×C4—101no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—104no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—204no—
477C2×C4—208no—
478C2×C4—208no—
479C2×C4C3×D4×D512yes—
480C2×C4C3×Q8×D512yes—
481C2×C3—58no—
482C2×C3D5×C22⋊Q811yescharacteristic
483C2×C3D5×#12311yescharacteristic
484C2×C3D5×#12411yescharacteristic
485C2×C3D5×#12512yes—
486C2×C3D5×#12612yes—
487C5C2×C3×#40011yescharacteristic, complemented, Sylow
488C22—54no—
489C22—54no—
490C22—54no—
491C22—58no—
492C22—58no—
493C22C2×C3×D4×D511yescharacteristic
494C22C2×C3×Q8×D511yescharacteristic
495C22C3×D5×#4111yescharacteristic
496C22C3×D5×#4112yes—
497C22C3×D5×#4112yes—
498C4—22no—
499C4—22no—
500C4—41no—
501C4—42no—
502C4—42no—
503C4—102no—
504C4—102no—
505C4—201no—
506C4—202no—
507C4—202no—
508C3D5×#40011yescharacteristic, direct product factor, Sylow
509C2—58no—
510C2C3×D5×C22⋊Q811yescharacteristic
511C2C3×D5×#12311yescharacteristic
512C2C3×D5×#12411yescharacteristic
513C2C3×D5×#12512yes—
514C2C3×D5×#12612yes—
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC3×C5×#400C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC3×#400D5
hypocenterC5C2×C3×#400
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
3. C3×C5×#400C2semidirect
4. C3×#65275C2semidirect
5. C3×#65271C2semidirect
9. C3×#64949C2semidirect
10. C3×#64948C2semidirect
11. C3×#64947C2semidirect
12. D5×#400C3direct (N × H)
41. C5×#400C2×C3semidirect
42. #65275C2×C3semidirect
43. #65271C2×C3semidirect
47. #64949C2×C3semidirect
48. #64948C2×C3semidirect
49. #64947C2×C3semidirect
87. C3×#400D5direct (N × H)
214. #400C3×D5direct (N × H)
333. C3×D5#400direct (N × H)
419. C3×C5C2×#400semidirect
445. D5C3×#400direct (N × H)
487. C5C2×C3×#400semidirect
508. C3D5×#400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C3×C5×#4002
C3×#652752
C3×#652712
C3×D5×#952
C3×#649492
C3×#649482
C3×#649472
D5×#4003
C2×C3×#4005