Finite Group Databasebeta

← C3×#10599096 #14283108

Subgroups — C3×#10599096 #14283108

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#121C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic, complemented
3C3×#64955C211yesmaximal, characteristic, complemented
4C3×C5×#327C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10599096C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×D4×D5—21no—
10C2×C3×D4×D5C411yescharacteristic, complemented
11C22×C3×C4×D5C2211yescharacteristic
12C3×C5×#121C2211yescharacteristic
13C3×#4085—21no—
14C3×#4084C411yescharacteristic, complemented
15C3×#4076C2211yescharacteristic
16C2×C3×#685—21no—
17C2×C3×C4×Dic5—21no—
18C2×C3×#676—21no—
19C3×#4041C411yescharacteristic, complemented
20C3×D5×C4⋊C4C411yescharacteristic, complemented
21C3×#4030—21no—
22C3×D5×C22⋊C4—21no—
23C3×C5×C22⋊C8C2211yescharacteristic, complemented
24C3×C5×#95C2211yescharacteristic, complemented
25C3×#3963C2211yescharacteristic, complemented
26C3×C22⋊#168C2211yescharacteristic, complemented
27C3×#3952—21no—
28C3×#1507—51nomaximal, Hall
29D5×#121C2×C311yescharacteristic
30#65015C2×C311yescharacteristic, complemented
31#64955C2×C311yescharacteristic, complemented
32C5×#327C2×C311yescharacteristic, complemented
33#64757C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C23×C3×D5D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—21no—
45C22×C3×Dic5—21no—
46C22×C3×Dic5D411yescharacteristic
47C3×D4×D5—42no—
48C3×D4×D5—42no—
49C3×D4×D5—42no—
50C2×C3×D20—21no—
51C2×C3×D20C2×C411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—42no—
54C2×C3×C4×D5C2×C411yescharacteristic
55C2×C3×C4×D5C2×C411yescharacteristic
56C2×C3×C4×D5D411yescharacteristic
57C2×C3×C4×D5D411yescharacteristic
58C2×C3×C5×C8—21no—
59C3×C5×C4⋊C4C2×C411yescharacteristic
60C3×C5×C22⋊C4—21no—
61C3×C22⋊Dic5—21no—
62C3×#685—24no—
63C3×#685—21no—
64C3×#685—21no—
65C3×C4⋊Dic5C2×C411yescharacteristic
66C3×#683—21no—
67C3×C4×Dic5—42no—
68C2×C3×#168—21no—
69C3×#676—42no—
70C2×C3×#121—51no—
71C3×#407—51no—
72C3×C4×C22⋊C4—51no—
73C3×#327—51no—
74C3×#327—51no—
75C3×#327—51no—
76C3×#327D511yescharacteristic, complemented
77C2×D4×D5—21no—
78C2×D4×D5C3×C411yescharacteristic, complemented
79C22×C4×D5C22×C311yescharacteristic
80C5×#121C22×C311yescharacteristic
81#4085—21no—
82#4084C3×C411yescharacteristic, complemented
83#4076C22×C311yescharacteristic
84C2×#685—21no—
85C2×C4×Dic5—21no—
86C2×#676—21no—
87#4041C3×C411yescharacteristic, complemented
88D5×C4⋊C4C3×C411yescharacteristic, complemented
89#4030—21no—
90D5×C22⋊C4—21no—
91C5×C22⋊C8C22×C311yescharacteristic, complemented
92C5×#95C22×C311yescharacteristic, complemented
93#3963C22×C311yescharacteristic, complemented
94C22⋊#168C22×C311yescharacteristic, complemented
95#3952—21no—
96#1507—51noSylow
97C23×C3×C5—21no—
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5—22no—
102C22×C3×D5—21no—
103C22×C3×D5—41no—
104C22×C3×D5—42no—
105C22×C3×D5—42no—
106C22×C3×D5—42no—
107C22×C3×D5C22⋊C411yescharacteristic
108C22×C3×D5C22⋊C411yescharacteristic
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C3×C5×D4—41no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C3×C22⋊D5—42no—
120C3×C22⋊D5—41no—
121C3×C22⋊D5—41no—
122C3×C22⋊D5—42no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5C22⋊C411yescharacteristic
129C2×C3×Dic5C22⋊C411yescharacteristic
130C3×D20—41no—
131C3×D20—42no—
132C3×C4×D5—22no—
133C3×C4×D5—22no—
134C3×C4×D5—41no—
135C3×C4×D5—41no—
136C3×C4×D5—42no—
137C3×C5×C8—41no—
138C3×#168—41no—
139C22×C3×D4—51no—
140C22×C3×D4—101no—
141C23×C3×C4—51no—
142C2×C3×M16—101no—
143C3×#121—51no—
144C3×#121—51no—
145C3×#121—51no—
146C3×#121—101no—
147C3×#121—101no—
148C3×#121C2×D511yescharacteristic
149C2×C3×C4⋊C4—51no—
150C2×C3×C22⋊C4—101no—
151C2×C3×C22⋊C4—101no—
152C2×C3×C42—101no—
153C3×C22⋊C8—51no—
154C3×C22⋊C8—101no—
155C3×C22⋊C8C2×D511yescharacteristic, complemented
156C3×#95—51no—
157C3×#95C2×D511yescharacteristic, complemented
158C23×D5—21no—
159C23×D5C3×D411yescharacteristic
160C2×C5×D4—21no—
161C2×C5×D4C2×C3×C411yescharacteristic
162C22×C4×C5—21no—
163C22×C4×C5C23×C311yescharacteristic
164C2×C22⋊D5—21no—
165C2×C22⋊D5—21no—
166C2×C22⋊D5—21no—
167C22×Dic5—21no—
168C22×Dic5C3×D411yescharacteristic
169D4×D5—42no—
170D4×D5—42no—
171D4×D5—42no—
172C2×D20—21no—
173C2×D20C2×C3×C411yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—42no—
176C2×C4×D5C2×C3×C411yescharacteristic
177C2×C4×D5C2×C3×C411yescharacteristic
178C2×C4×D5C3×D411yescharacteristic
179C2×C4×D5C3×D411yescharacteristic
180C2×C5×C8—21no—
181C5×C4⋊C4C2×C3×C411yescharacteristic
182C5×C22⋊C4—21no—
183C22⋊Dic5—21no—
184#685—24no—
185#685—21no—
186#685—21no—
187C4⋊Dic5C2×C3×C411yescharacteristic
188#683—21no—
189C4×Dic5—42no—
190C2×#168—21no—
191#676—42no—
192C2×#121—51no—
193#407—51no—
194C4×C22⋊C4—51no—
195#327—51no—
196#327—51no—
197#327—51no—
198#327C3×D511yescharacteristic, complemented
199C22×C3×C5—21no—
200C22×C3×C5—21no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
206C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
207C2×C3×D5—21no—
208C2×C3×D5—21no—
209C2×C3×D5—21no—
210C2×C3×D5—21no—
211C2×C3×D5—21no—
212C2×C3×D5—42no—
213C2×C3×D5—42no—
214C2×C3×D5—41no—
215C2×C3×D5—41no—
216C2×C3×D5—41no—
217C2×C3×D5—84no—
218C2×C3×D5#10412yes—
219C3×C4×C5—21no—
220C3×C4×C5—21no—
221C3×C4×C5—42no—
222C3×C4×C5—41no—
223C3×Dic5—21no—
224C3×Dic5—42no—
225C3×Dic5—41no—
226C3×Dic5#9912yes—
227C24×C3—51no—
228C24×C3—101no—
229C2×C3×D4—21no—
230C2×C3×D4—51no—
231C2×C3×D4—101no—
232C2×C3×D4—101no—
233C2×C3×D4—101no—
234C2×C3×D4—101no—
235C2×C3×D4—202no—
236C2×C3×D4—202no—
237C2×C3×D4—202no—
238C2×C3×D4C4×D511yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—51no—
241C22×C3×C4—51no—
242C22×C3×C4—51no—
243C22×C3×C4—51no—
244C22×C3×C4—51no—
245C22×C3×C4—101no—
246C22×C3×C4—101no—
247C22×C3×C4—202no—
248C22×C3×C4C22×D511yescharacteristic
249C3×M16—202no—
250C2×C3×C8—21no—
251C2×C3×C8—101no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4C4×D511yescharacteristic
255C3×C22⋊C4—21no—
256C3×C22⋊C4—101no—
257C3×C22⋊C4—104no—
258C3×C22⋊C4—101no—
259C3×C22⋊C4—101no—
260C3×C42—202no—
261C23×C5—21no—
262C23×C5C2×C3×D411yescharacteristic
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—22no—
266C22×D5—21no—
267C22×D5—41no—
268C22×D5—42no—
269C22×D5—42no—
270C22×D5—42no—
271C22×D5C3×C22⋊C411yescharacteristic
272C22×D5C3×C22⋊C411yescharacteristic
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—41no—
276C2×C4×C5—22no—
277C2×C4×C5—21no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5C22×C3×C411yescharacteristic
282C2×C4×C5C2×C3×D411yescharacteristic
283C22⋊D5—42no—
284C22⋊D5—41no—
285C22⋊D5—41no—
286C22⋊D5—42no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—21no—
290C2×Dic5—41no—
291C2×Dic5—41no—
292C2×Dic5C3×C22⋊C411yescharacteristic
293C2×Dic5C3×C22⋊C411yescharacteristic
294D20—41no—
295D20—42no—
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—41no—
299C4×D5—41no—
300C4×D5—42no—
301C5×C8—41no—
302#168—41no—
303C22×D4—51no—
304C22×D4—101no—
305C23×C4—51no—
306C2×M16—101no—
307#121—51no—
308#121—51no—
309#121—51no—
310#121—101no—
311#121—101no—
312#121C2×C3×D511yescharacteristic
313C2×C4⋊C4—51no—
314C2×C22⋊C4—101no—
315C2×C22⋊C4—101no—
316C2×C42—101no—
317C22⋊C8—51no—
318C22⋊C8—101no—
319C22⋊C8C2×C3×D511yescharacteristic, complemented
320#95—51no—
321#95C2×C3×D511yescharacteristic, complemented
322C2×C3×C5—21no—
323C2×C3×C5—21no—
324C2×C3×C5—81no—
325C2×C3×C5C2×#9911yescharacteristic
326C2×C3×C5#41811yescharacteristic
327C2×C3×C5C2×#10411yescharacteristic
328C3×D5—22no—
329C3×D5—41no—
330C3×D5—81no—
331C23×C3—21no—
332C23×C3—51no—
333C23×C3—51no—
334C23×C3—102no—
335C23×C3—101no—
336C23×C3—101no—
337C23×C3—101no—
338C23×C3—201no—
339C23×C3—202no—
340C23×C3—202no—
341C23×C3—202no—
342C23×C3D4×D511yescharacteristic
343C3×D4—41no—
344C3×D4—41no—
345C3×D4—41no—
346C3×D4—201no—
347C3×D4—202no—
348C3×D4—202no—
349C3×D4—202no—
350C3×D4—201no—
351C3×D4—201no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—51no—
358C2×C3×C4—51no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—101no—
364C2×C3×C4—201no—
365C2×C3×C4—201no—
366C2×C3×C4—202no—
367C2×C3×C4—201no—
368C2×C3×C4—201no—
369C2×C3×C4C2×C4×D511yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C3×C8—41no—
372C3×C8—201no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5C2×C3×C22⋊C411yescharacteristic
379C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
380C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—21no—
384C2×D5—21no—
385C2×D5—21no—
386C2×D5—42no—
387C2×D5—42no—
388C2×D5—41no—
389C2×D5—41no—
390C2×D5—41no—
391C2×D5—84no—
392C2×D5C3×#10412yes—
393C4×C5—21no—
394C4×C5—21no—
395C4×C5—42no—
396C4×C5—41no—
397Dic5—21no—
398Dic5—42no—
399Dic5—41no—
400Dic5C3×#9912yes—
401C24—51no—
402C24—101no—
403C2×D4—21no—
404C2×D4—51no—
405C2×D4—101no—
406C2×D4—101no—
407C2×D4—101no—
408C2×D4—101no—
409C2×D4—202no—
410C2×D4—202no—
411C2×D4—202no—
412C2×D4C3×C4×D511yescharacteristic
413C22×C4—21no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—51no—
419C22×C4—101no—
420C22×C4—101no—
421C22×C4—202no—
422C22×C4C22×C3×D511yescharacteristic
423M16—202no—
424C2×C8—21no—
425C2×C8—101no—
426C4⋊C4—51no—
427C4⋊C4—101no—
428C4⋊C4C3×C4×D511yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—101no—
431C22⋊C4—104no—
432C22⋊C4—101no—
433C22⋊C4—101no—
434C42—202no—
435C3×C5#150711yescharacteristic, complemented, Hall
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—52no—
442C22×C3—101no—
443C22×C3—101no—
444C22×C3—101no—
445C22×C3—101no—
446C22×C3—101no—
447C22×C3—202no—
448C22×C3—202no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3—404no—
453C22×C3D5×C22⋊C411yescharacteristic
454C22×C3#405711yescharacteristic
455C22×C3#406011yescharacteristic
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—52no—
461C3×C4—101no—
462C3×C4—202no—
463C3×C4—201no—
464C2×C5—21no—
465C2×C5—21no—
466C2×C5—81no—
467C2×C5C2×C3×#9911yescharacteristic
468C2×C5C3×#41811yescharacteristic
469C2×C5C2×C3×#10411yescharacteristic
470D5—22no—
471D5—41no—
472D5—81no—
473C23—21no—
474C23—51no—
475C23—51no—
476C23—102no—
477C23—101no—
478C23—101no—
479C23—101no—
480C23—201no—
481C23—202no—
482C23—202no—
483C23—202no—
484C23C3×D4×D511yescharacteristic
485D4—41no—
486D4—41no—
487D4—41no—
488D4—201no—
489D4—202no—
490D4—202no—
491D4—202no—
492D4—201no—
493D4—201no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—51no—
500C2×C4—51no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—102no—
505C2×C4—101no—
506C2×C4—201no—
507C2×C4—201no—
508C2×C4—202no—
509C2×C4—201no—
510C2×C4—201no—
511C2×C4C2×C3×C4×D511yescharacteristic
512C2×C4C3×D4×D511yescharacteristic
513C8—41no—
514C8—201no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—81no—
518C2×C3—102no—
519C2×C3—201no—
520C2×C3—401no—
521C2×C3D5×#9911yescharacteristic
522C2×C3#6505911yescharacteristic
523C2×C3D5×#10411yescharacteristic
524C5C3×#150711yescharacteristic, complemented, Sylow
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—52no—
531C22—101no—
532C22—101no—
533C22—101no—
534C22—101no—
535C22—101no—
536C22—202no—
537C22—202no—
538C22—201no—
539C22—201no—
540C22—201no—
541C22—404no—
542C22C3×D5×C22⋊C411yescharacteristic
543C22C3×#405711yescharacteristic
544C22C3×#406011yescharacteristic
545C4—21no—
546C4—21no—
547C4—42no—
548C4—41no—
549C4—52no—
550C4—101no—
551C4—202no—
552C4—201no—
553C3#1059909611yescharacteristic, direct product factor, Sylow
554C2—21no—
555C2—21no—
556C2—81no—
557C2—102no—
558C2—201no—
559C2—401no—
560C2C3×D5×#9911yescharacteristic
561C2C3×#6505911yescharacteristic
562C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#327C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#121C2
cosocleC22×C4×C5C23×C3
hypercenterC3×#327D5
hypocenterC5C3×#1507
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#65015C2semidirect
3. C3×#64955C2semidirect
4. C3×C5×#327C2semidirect
5. C3×#64757C2semidirect
6. C3×#64690C2semidirect
7. C3×#64671C2semidirect
8. #10599096C3direct (N × H)
10. C2×C3×D4×D5C4semidirect
14. C3×#4084C4semidirect
19. C3×#4041C4semidirect
20. C3×D5×C4⋊C4C4semidirect
23. C3×C5×C22⋊C8C22semidirect
24. C3×C5×#95C22semidirect
25. C3×#3963C22semidirect
26. C3×C22⋊#168C22semidirect
30. #65015C2×C3semidirect
31. #64955C2×C3semidirect
32. C5×#327C2×C3semidirect
33. #64757C2×C3semidirect
34. #64690C2×C3semidirect
35. #64671C2×C3semidirect
76. C3×#327D5semidirect
78. C2×D4×D5C3×C4semidirect
82. #4084C3×C4semidirect
87. #4041C3×C4semidirect
88. D5×C4⋊C4C3×C4semidirect
91. C5×C22⋊C8C22×C3semidirect
92. C5×#95C22×C3semidirect
93. #3963C22×C3semidirect
94. C22⋊#168C22×C3semidirect
155. C3×C22⋊C8C2×D5semidirect
157. C3×#95C2×D5semidirect
198. #327C3×D5semidirect
319. C22⋊C8C2×C3×D5semidirect
321. #95C2×C3×D5semidirect
435. C3×C5#1507semidirect
524. C5C3×#1507semidirect
553. C3#10599096direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×#1212
C3×#650152
C3×#649552
C3×C5×#3272
C3×#647572
C3×#646902
C3×#646712
#105990963
C3×#15075