Finite Group Databasebeta

← C3×#10610932 #14416998

Subgroups — C3×#10610932 #14416998

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4054C211yesmaximal, characteristic
2C3×#65855C211yesmaximal, characteristic, complemented
3C3×#65838C211yesmaximal, characteristic, complemented
4C3×C5×#428C211yesmaximal, characteristic, complemented
5C3×#65411C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7C2×C3×#3941C211yesmaximal, characteristic, complemented
8C3×#65178C212yesmaximal, complemented
9C3×#65161C212yesmaximal, complemented
10C3×#65158C212yesmaximal, complemented
11C3×#65141C212yesmaximal, complemented
12#10610932C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×#709C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C3×C4×C22⋊D5—22no—
19C3×#4072C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21C3×#4054C418yescomplemented
22C2×C3×D40C2212yes—
23C2×C3×#677C2212yes—
24C3×#4039C2212yes—
25C3×#4039C2212yes—
26C3×#4039C2212yescomplemented
27C3×#4038—21no—
28C3×D5×C4⋊C4—21no—
29C3×#4033C2212yescomplemented
30C3×D5×C22⋊C4—22no—
31C3×C4×D20—21no—
32C3×C4×D20—21no—
33C3×C5×#107C2212yescomplemented
34C3×C5×#106C2212yescomplemented
35C3×#3947C2212yescomplemented
36C3×C8×Dic5C2212yescomplemented
37C3×#3942C2211yescharacteristic, complemented
38C3×#3942C2211yescharacteristic, complemented
39C3×#3941C2212yes—
40C3×#3941C2212yes—
41C3×#3941C2211yescharacteristic, complemented
42C3×#3941C2211yescharacteristic, complemented
43C3×#2946—51nomaximal, Hall
44C2×#4054C2×C311yescharacteristic
45#65855C2×C311yescharacteristic, complemented
46#65838C2×C311yescharacteristic, complemented
47C5×#428C2×C311yescharacteristic, complemented
48#65411C2×C311yescharacteristic, complemented
49#65291C2×C311yescharacteristic, complemented
50C2×#3941C2×C311yescharacteristic, complemented
51#65178C2×C312yescomplemented
52#65161C2×C312yescomplemented
53#65158C2×C312yescomplemented
54#65141C2×C312yescomplemented
55C23×C3×D5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×C3×C22⋊D5—21no—
59C3×#709—22no—
60C3×#709C2×C414yescomplemented
61C2×C3×D20—21no—
62C2×C3×D20—22no—
63C2×C3×D20C2×C414yescomplemented
64C2×C3×D20C2312yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×Dic10C2311yescharacteristic
71C3×C5×M16C2×C414yescomplemented
72C2×C3×C5×C8C2312yes—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5—21no—
79C3×C22⋊Dic5D412yes—
80C3×#685—22no—
81C3×#685—22no—
82C3×#685—22no—
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5D411yescharacteristic
85C3×#683—22no—
86C3×C4×Dic5—22no—
87C3×C4×Dic5C2312yes—
88C2×C3×#168—22no—
89C2×C3×#168C2311yescharacteristic
90C2×C3×#168C2311yescharacteristic
91C3×D40C2×C418yescomplemented
92C3×#677C2×C418yescomplemented
93C2×C3×AGL(1,ℤ/8)—51no—
94C3×#520—51no—
95C3×#518—51no—
96C3×#442—52no—
97C3×#440—52no—
98C3×C4×SD16—52no—
99C3×C4×D8—52no—
100C3×#428D511yescharacteristic, complemented
101C3×#416—51no—
102C2×C3×#102—51no—
103C3×#405—51no—
104C2×#709C22×C311yescharacteristic
105C22×D20C22×C311yescharacteristic
106C2×C5×M16C22×C311yescharacteristic
107C5×#117C22×C311yescharacteristic
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C4×C22⋊D5—22no—
110#4072C22×C311yescharacteristic
111C22×#168C22×C311yescharacteristic
112#4054C3×C418yescomplemented
113C2×D40C22×C312yes—
114C2×#677C22×C312yes—
115#4039C22×C312yes—
116#4039C22×C312yes—
117#4039C22×C312yescomplemented
118#4038—21no—
119D5×C4⋊C4—21no—
120#4033C22×C312yescomplemented
121D5×C22⋊C4—22no—
122C4×D20—21no—
123C4×D20—21no—
124C5×#107C22×C312yescomplemented
125C5×#106C22×C312yescomplemented
126#3947C22×C312yescomplemented
127C8×Dic5C22×C312yescomplemented
128#3942C22×C311yescharacteristic, complemented
129#3942C22×C311yescharacteristic, complemented
130#3941C22×C312yes—
131#3941C22×C312yes—
132#3941C22×C311yescharacteristic, complemented
133#3941C22×C311yescharacteristic, complemented
134#2946—51noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—21no—
137C22×C3×D5—22no—
138C22×C3×D5—24no—
139C22×C3×D5—81no—
140C22×C3×D5—81no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—81no—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5#4112yes—
148C2×C3×C4×C5C2411yescharacteristic
149C3×C22⋊D5—24no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5C2×D412yes—
152C2×C3×Dic5C2×D412yes—
153C3×D20—24no—
154C3×D20—22no—
155C3×D20—21no—
156C3×D20C22×C414yes—
157C3×D20C22×C412yes—
158C3×C4×D5—24no—
159C3×C4×D5—82no—
160C3×C4×D5—82no—
161C3×C4×D5—82no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164C3×C5×C8C22×C414yes—
165C3×#168—21no—
166C3×#168—21no—
167C2×C3×#41—51no—
168C22×C3×D4—51no—
169C3×AGL(1,ℤ/8)—58no—
170C2×C3×SD16—52no—
171C2×C3×D8—52no—
172C2×C3×M16C2×D511yescharacteristic
173C22×C3×C8—51no—
174C3×C4×Q8—52no—
175C3×C4×D4—52no—
176C3×C4×D4—52no—
177C3×C4×D4—52no—
178C3×C4×D4—101no—
179C3×C4×D4—101no—
180C3×C4×D4—102no—
181C3×#117—51no—
182C3×#117—101no—
183C3×#117C2×D511yescharacteristic
184C2×C3×C4⋊C4—101no—
185C2×C3×C4⋊C4C2×D511yescharacteristic
186C2×C3×C22⋊C4—102no—
187C3×#107C2×D512yescomplemented
188C3×#106C2×D512yescomplemented
189C3×#103—51no—
190C3×#103—51no—
191C3×#102—52no—
192C3×#102—52no—
193C3×#102—51no—
194C3×#102—51no—
195C3×#97—52no—
196C3×C4×C8—52no—
197C23×D5—21no—
198C22×C4×C5—21no—
199C22×C4×C5C23×C311yescharacteristic
200C2×C22⋊D5—21no—
201#709—22no—
202#709C2×C3×C414yescomplemented
203C2×D20—21no—
204C2×D20—22no—
205C2×D20C2×C3×C414yescomplemented
206C2×D20C23×C312yes—
207C2×D20C23×C311yescharacteristic
208C2×C4×D5—21no—
209C2×C4×D5—22no—
210C2×C4×D5—22no—
211C2×C4×D5—22no—
212C2×Dic10C23×C311yescharacteristic
213C5×M16C2×C3×C414yescomplemented
214C2×C5×C8C23×C312yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C23×C312yes—
217C5×C4⋊C4C23×C311yescharacteristic
218C5×C4⋊C4C23×C311yescharacteristic
219C5×C22⋊C4—21no—
220C42×C5—21no—
221C22⋊Dic5C3×D412yes—
222#685—22no—
223#685—22no—
224#685—22no—
225C4⋊Dic5C3×D411yescharacteristic
226C4⋊Dic5C3×D411yescharacteristic
227#683—22no—
228C4×Dic5—22no—
229C4×Dic5C23×C312yes—
230C2×#168—22no—
231C2×#168C23×C311yescharacteristic
232C2×#168C23×C311yescharacteristic
233D40C2×C3×C418yescomplemented
234#677C2×C3×C418yescomplemented
235C2×AGL(1,ℤ/8)—51no—
236#520—51no—
237#518—51no—
238#442—52no—
239#440—52no—
240C4×SD16—52no—
241C4×D8—52no—
242#428C3×D511yescharacteristic, complemented
243#416—51no—
244C2×#102—51no—
245#405—51no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5—22no—
251C2×C3×D5—24no—
252C2×C3×D5—41no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—41no—
256C2×C3×D5—84no—
257C3×C4×C5—41no—
258C3×C4×C5—42no—
259C3×C4×C5—41no—
260C3×C4×C5C4×D412yes—
261C3×C4×C5C23×C411yescharacteristic
262C3×C4×C5C2×#4111yescharacteristic
263C3×Dic5—22no—
264C3×Dic5—22no—
265C3×Dic5—22no—
266C24×C3—101no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—54no—
271C2×C3×D4—51no—
272C2×C3×D4—52no—
273C2×C3×D4—101no—
274C2×C3×D4—101no—
275C2×C3×D4—102no—
276C22×C3×C4—21no—
277C22×C3×C4—102no—
278C22×C3×C4—102no—
279C22×C3×C4—102no—
280C22×C3×C4—101no—
281C22×C3×C4C22×D511yescharacteristic
282C3×SD16—58no—
283C3×D8—58no—
284C3×M16C4×D514yescomplemented
285C2×C3×C8—51no—
286C2×C3×C8—51no—
287C2×C3×C8—102no—
288C2×C3×C8C22×D512yes—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—51no—
291C3×C4⋊C4—51no—
292C3×C4⋊C4—102no—
293C3×C4⋊C4C22×D512yes—
294C3×C4⋊C4C22×D511yescharacteristic
295C3×C4⋊C4C22×D511yescharacteristic
296C3×C22⋊C4—21no—
297C3×C22⋊C4—52no—
298C3×C22⋊C4—102no—
299C3×C22⋊C4—102no—
300C3×C22⋊C4—102no—
301C3×C42—21no—
302C3×C42—52no—
303C3×C42—102no—
304C23×C5C2×C3×D411yescharacteristic
305C22×D5—21no—
306C22×D5—22no—
307C22×D5—24no—
308C22×D5—81no—
309C22×D5—81no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—81no—
314C2×C4×C5C22×C3×C412yes—
315C2×C4×C5C2×C3×D411yescharacteristic
316C2×C4×C5C3×#4112yes—
317C2×C4×C5C24×C311yescharacteristic
318C22⋊D5—24no—
319C2×Dic5—21no—
320C2×Dic5C2×C3×D412yes—
321C2×Dic5C2×C3×D412yes—
322D20—24no—
323D20—22no—
324D20—21no—
325D20C22×C3×C414yes—
326D20C22×C3×C412yes—
327C4×D5—24no—
328C4×D5—82no—
329C4×D5—82no—
330C4×D5—82no—
331Dic10—21no—
332Dic10C22×C3×C412yes—
333C5×C8C22×C3×C414yes—
334#168—21no—
335#168—21no—
336C2×#41—51no—
337C22×D4—51no—
338AGL(1,ℤ/8)—58no—
339C2×SD16—52no—
340C2×D8—52no—
341C2×M16C2×C3×D511yescharacteristic
342C22×C8—51no—
343C4×Q8—52no—
344C4×D4—52no—
345C4×D4—52no—
346C4×D4—52no—
347C4×D4—101no—
348C4×D4—101no—
349C4×D4—102no—
350#117—51no—
351#117—101no—
352#117C2×C3×D511yescharacteristic
353C2×C4⋊C4—101no—
354C2×C4⋊C4C2×C3×D511yescharacteristic
355C2×C22⋊C4—102no—
356#107C2×C3×D512yescomplemented
357#106C2×C3×D512yescomplemented
358#103—51no—
359#103—51no—
360#102—52no—
361#102—52no—
362#102—51no—
363#102—51no—
364#97—52no—
365C4×C8—52no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370C3×D5—42no—
371C3×D5—44no—
372C23×C3—101no—
373C23×C3—102no—
374C23×C3—104no—
375C23×C3—401no—
376C23×C3—401no—
377C23×C3D4×D511yescharacteristic
378C3×Q8—52no—
379C3×Q8—101no—
380C3×D4—52no—
381C3×D4—54no—
382C3×D4—104no—
383C3×D4—102no—
384C3×D4—101no—
385C3×D4—104no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—52no—
390C2×C3×C4—52no—
391C2×C3×C4—81no—
392C2×C3×C4—101no—
393C2×C3×C4—104no—
394C2×C3×C4—402no—
395C2×C3×C4—402no—
396C2×C3×C4—402no—
397C2×C3×C4C2×C4×D512yes—
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4#71312yes—
400C2×C3×C4C23×D511yescharacteristic
401C3×C8—101no—
402C3×C8—101no—
403C3×C8C2×C4×D514yes—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5C3×C4×D412yes—
407C22×C5C22×C3×D411yescharacteristic
408C2×D5—22no—
409C2×D5—24no—
410C2×D5—41no—
411C2×D5—42no—
412C2×D5—42no—
413C2×D5—41no—
414C2×D5—84no—
415C4×C5—41no—
416C4×C5—42no—
417C4×C5—41no—
418C4×C5C3×C4×D412yes—
419C4×C5C23×C3×C411yescharacteristic
420C4×C5C2×C3×#4111yescharacteristic
421Dic5—22no—
422Dic5—22no—
423Dic5—22no—
424C24—101no—
425#41—54no—
426#41—102no—
427C2×Q8—51no—
428C2×D4—54no—
429C2×D4—51no—
430C2×D4—52no—
431C2×D4—101no—
432C2×D4—101no—
433C2×D4—102no—
434C22×C4—21no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4—101no—
439C22×C4C22×C3×D511yescharacteristic
440SD16—58no—
441D8—58no—
442M16C3×C4×D514yescomplemented
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—102no—
446C2×C8C22×C3×D512yes—
447C4⋊C4—21no—
448C4⋊C4—51no—
449C4⋊C4—51no—
450C4⋊C4—102no—
451C4⋊C4C22×C3×D512yes—
452C4⋊C4C22×C3×D511yescharacteristic
453C4⋊C4C22×C3×D511yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—52no—
456C22⋊C4—102no—
457C22⋊C4—102no—
458C22⋊C4—102no—
459C42—21no—
460C42—52no—
461C42—102no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—102no—
466C22×C3—104no—
467C22×C3—201no—
468C22×C3—202no—
469C22×C3—202no—
470C22×C3—201no—
471C22×C3—404no—
472C22×C3#403912yes—
473C22×C3C2×D4×D511yescharacteristic
474C3×C4—42no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—102no—
478C3×C4—102no—
479C3×C4—102no—
480C3×C4#403912yes—
481C3×C4C22×C4×D511yescharacteristic
482C3×C4C2×#71311yescharacteristic
483C2×C5—22no—
484C2×C5C2×C3×C4×D411yescharacteristic
485C2×C5C3×#57611yescharacteristic
486C2×C5C3×#57711yescharacteristic
487D5—44no—
488D5—42no—
489C23—101no—
490C23—102no—
491C23—104no—
492C23—401no—
493C23—401no—
494C23C3×D4×D511yescharacteristic
495Q8—52no—
496Q8—101no—
497D4—52no—
498D4—54no—
499D4—104no—
500D4—102no—
501D4—101no—
502D4—104no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—52no—
507C2×C4—52no—
508C2×C4—81no—
509C2×C4—101no—
510C2×C4—104no—
511C2×C4—402no—
512C2×C4—402no—
513C2×C4—402no—
514C2×C4C2×C3×C4×D512yes—
515C2×C4C3×D4×D511yescharacteristic
516C2×C4C3×#71312yes—
517C2×C4C23×C3×D511yescharacteristic
518C8—101no—
519C8—101no—
520C8C2×C3×C4×D514yes—
521C2×C3—22no—
522C2×C3—204no—
523C2×C3—202no—
524C2×C3C2×#403911yescharacteristic
525C2×C3#6610811yescharacteristic
526C2×C3#6611211yescharacteristic
527C5C3×#294611yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—102no—
531C22—104no—
532C22—201no—
533C22—202no—
534C22—202no—
535C22—201no—
536C22—404no—
537C22C3×#403912yes—
538C22C2×C3×D4×D511yescharacteristic
539C4—42no—
540C4—41no—
541C4—41no—
542C4—102no—
543C4—102no—
544C4—102no—
545C4C3×#403912yes—
546C4C22×C3×C4×D511yescharacteristic
547C4C2×C3×#71311yescharacteristic
548C3#1061093211yescharacteristic, direct product factor, Sylow
549C2—22no—
550C2—204no—
551C2—202no—
552C2C2×C3×#403911yescharacteristic
553C2C3×#6610811yescharacteristic
554C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4054C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#428D5
hypocenterC5C3×#2946
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
2. C3×#65855C2semidirect
3. C3×#65838C2semidirect
4. C3×C5×#428C2semidirect
5. C3×#65411C2semidirect
6. C3×#65291C2semidirect
7. C2×C3×#3941C2semidirect
8. C3×#65178C2semidirect
9. C3×#65161C2semidirect
10. C3×#65158C2semidirect
11. C3×#65141C2semidirect
12. #10610932C3direct (N × H)
21. C3×#4054C4semidirect
26. C3×#4039C22semidirect
29. C3×#4033C22semidirect
33. C3×C5×#107C22semidirect
34. C3×C5×#106C22semidirect
35. C3×#3947C22semidirect
36. C3×C8×Dic5C22semidirect
37. C3×#3942C22semidirect
38. C3×#3942C22semidirect
41. C3×#3941C22semidirect
42. C3×#3941C22semidirect
45. #65855C2×C3semidirect
46. #65838C2×C3semidirect
47. C5×#428C2×C3semidirect
48. #65411C2×C3semidirect
49. #65291C2×C3semidirect
50. C2×#3941C2×C3semidirect
51. #65178C2×C3semidirect
52. #65161C2×C3semidirect
53. #65158C2×C3semidirect
54. #65141C2×C3semidirect
60. C3×#709C2×C4semidirect
63. C2×C3×D20C2×C4semidirect
71. C3×C5×M16C2×C4semidirect
91. C3×D40C2×C4semidirect
92. C3×#677C2×C4semidirect
100. C3×#428D5semidirect
112. #4054C3×C4semidirect
117. #4039C22×C3semidirect
120. #4033C22×C3semidirect
124. C5×#107C22×C3semidirect
125. C5×#106C22×C3semidirect
126. #3947C22×C3semidirect
127. C8×Dic5C22×C3semidirect
128. #3942C22×C3semidirect
129. #3942C22×C3semidirect
132. #3941C22×C3semidirect
133. #3941C22×C3semidirect
187. C3×#107C2×D5semidirect
188. C3×#106C2×D5semidirect
202. #709C2×C3×C4semidirect
205. C2×D20C2×C3×C4semidirect
213. C5×M16C2×C3×C4semidirect
233. D40C2×C3×C4semidirect
234. #677C2×C3×C4semidirect
242. #428C3×D5semidirect
284. C3×M16C4×D5semidirect
356. #107C2×C3×D5semidirect
357. #106C2×C3×D5semidirect
442. M16C3×C4×D5semidirect
462. C3×C5#2946semidirect
527. C5C3×#2946semidirect
548. C3#10610932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40542
C3×#658552
C3×#658382
C3×C5×#4282
C3×#654112
C3×#652912
C2×C3×#39412
C3×#651782
C3×#651612
C3×#651582
C3×#651412
#106109323
C3×#29465