Finite Group Databasebeta

← #14417784

Subgroups — #14417784

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91839C211yesmaximal, characteristic
2C3×#66161C211yesmaximal, characteristic, complemented
3#11754506C211yesmaximal, characteristic, complemented
4C5×#5232C211yesmaximal, characteristic, complemented
5#11749250C212yesmaximal, complemented
6#11749221C212yesmaximal, complemented
7#11748998C212yesmaximal, complemented
8#11748979C212yesmaximal, complemented
9C2×#90986C211yesmaximal, characteristic, complemented
10#11748413C211yesmaximal, characteristic, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10610600—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15#91839C418yescomplemented
16C2×#6718C2211yescharacteristic
17C2×#6717C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C3×Q8×Dic5C2212yes—
24C3×D4×Dic5—22no—
25C3×D4×Dic5C2212yes—
26C3×#4072—21no—
27C3×#4072C2211yescharacteristic
28C2×C3×C4⋊Dic5—21no—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30#91556—22no—
31#91437—21no—
32#91418C2212yes—
33#91347—21no—
34#91333C2212yes—
35C5×#835C2212yes—
36C5×#832C2212yes—
37#90986C2212yes—
38#90986C2212yes—
39#90974C2212yes—
40#90968C2212yes—
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82558—51nomaximal, Hall
44#66161D311yescharacteristic, complemented
45C2×#4096—31no—
46#65838—31no—
47C5×#417—31no—
48#65422—31no—
49#65411—31no—
50C2×#3940—31no—
51#65078—32no—
52#65077—32no—
53#65074—32no—
54#65047—32no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817C2×C414yescomplemented
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C22×C5×Dic3—21no—
69C22×C3×Dic5—21no—
70C22×C3×Dic5—22no—
71C2×#1200—22no—
72#6718C2×C414yescomplemented
73#6717C2×C414yescomplemented
74#6716C2×C414yescomplemented
75#6715C2×C414yescomplemented
76C2×C3⋊#168C2×C414yescomplemented
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C5×C4⋊Dic3—21no—
80C5×C4⋊Dic3C2312yes—
81C5×#208—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C22⋊Dic5—22no—
84C3×C22⋊Dic5D412yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5—22no—
87C3×C4⋊Dic5D411yescharacteristic
88C3×C4⋊Dic5D411yescharacteristic
89C3×C4⋊Dic5C2312yes—
90C3×C4×Dic5—22no—
91C3×C4×Dic5C2312yes—
92#6669—22no—
93#6667—22no—
94Dic3×Dic5—22no—
95C3×#520—51no—
96C2×#950—51no—
97#5523—51no—
98#5232D511yescharacteristic, complemented
99#5030—52no—
100C4×#215—52no—
101C4×#214—52no—
102#5014—52no—
103#4997—51no—
104#4966—51no—
105C2×#808—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C2×C5×M16—31no—
109C2×C5×C4⋊C4—31no—
110#4096—38no—
111Q8×Dic5C2×D312yes—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—22no—
115D4×Dic5C2×D312yes—
116C2×#687—31no—
117C2×#686—31no—
118C4×C22⋊D5—62no—
119#4072—21no—
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168—31no—
124#4039—32no—
125#4038—61no—
126D5×C4⋊C4—61no—
127#4033—32no—
128C5×#103—32no—
129C5×#102—32no—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133C8×Dic5—32no—
134#3940—32no—
135#3940—32no—
136#2952—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—24no—
152C2×Dic15—21no—
153D60—21no—
154D60C22×C412yes—
155C4×D15—24no—
156Dic30—21no—
157Dic30C22×C412yes—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—81no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—82no—
162C2×C3×Dic5—81no—
163C2×C3×Dic5C2×D412yes—
164C2×C3×Dic5C2×D412yes—
165#1200—82no—
166C3⋊#168C22×C412yes—
167C3⋊#168C22×C412yes—
168C5×C3⋊C8—22no—
169C2×C3×#41C2×D511yescharacteristic
170C2×#235—51no—
171C3×C4×Q8—52no—
172C3×C4×D4—52no—
173C3×C4×D4—102no—
174C3×#117—51no—
175C3×#117—101no—
176C2×C3×C4⋊C4—51no—
177C2×C3×C4⋊C4—101no—
178#950—58no—
179C2×#216—51no—
180C2×#215—51no—
181C2×#214—51no—
182C2×#213—51no—
183C2×C4⋊Dic3C2×D511yescharacteristic
184C2×#208C2×D511yescharacteristic
185C22×C3⋊C8—51no—
186#892—101no—
187D3×C4⋊C4—101no—
188#67⋊C4—102no—
189C4×D12—52no—
190C4×Dic6—52no—
191#835C2×D512yes—
192#832C2×D512yes—
193#810—52no—
194#809—52no—
195#808—52no—
196#808—52no—
197#803—52no—
198C4×C3⋊C8—52no—
199C5×#41—22no—
200C5×#41C4×D314yescomplemented
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4—21no—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—61no—
208C22×Dic5—21no—
209C22×Dic5—22no—
210#709—34no—
211#709—62no—
212C2×D20—31no—
213C2×C4×D5—61no—
214C2×C4×D5—62no—
215C2×Dic10—31no—
216C5×M16—62no—
217C2×C5×C8—32no—
218C5×C4⋊C4—32no—
219C5×C4⋊C4—61no—
220C22⋊Dic5—22no—
221C22⋊Dic5#6712yes—
222#689—34no—
223#688—34no—
224#687—34no—
225#686—34no—
226#685—62no—
227C4⋊Dic5—21no—
228C4⋊Dic5—22no—
229C4⋊Dic5#6711yescharacteristic
230C4⋊Dic5#6711yescharacteristic
231C4⋊Dic5C22×D312yes—
232#683—62no—
233C4×Dic5—22no—
234C4×Dic5—62no—
235C4×Dic5C22×D312yes—
236C2×#168—34no—
237C2×#168—31no—
238C2×#168—31no—
239C2×#135—151no—
240#520—51no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—31no—
248#417—151no—
249#405—151no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5C4×D412yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—41no—
259C2×D15—41no—
260C3×C4×C5—22no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—22no—
265C3×Dic5—22no—
266C3×Dic5—22no—
267C3×Dic5—42no—
268C5×Dic3—42no—
269C3×#41—22no—
270C3×#41C4×D514yescomplemented
271C2×C3×Q8C22×D511yescharacteristic
272C2×C3×D4—21no—
273C2×C3×D4C22×D511yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—102no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C22×Dic3—21no—
280#235—54no—
281#235—102no—
282C2×D12—51no—
283C2×C4×D3—101no—
284C2×C4×D3—102no—
285C2×Dic6—51no—
286C3×C4⋊C4—51no—
287C3×C4⋊C4—51no—
288C3×C4⋊C4—52no—
289C3×C4⋊C4—102no—
290C3×C4⋊C4—101no—
291C3×C22⋊C4—52no—
292C3×C22⋊C4—102no—
293C3×C42—52no—
294C3×C42—102no—
295#216—54no—
296#215—54no—
297#214—54no—
298#213—54no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—21no—
301C4⋊Dic3C22×D512yes—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304#208—22no—
305C2×C3⋊C8—54no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8C22×D512yes—
309C23×C5—21no—
310C23×C5C2×#6711yescharacteristic
311C22×D5—61no—
312C5×Q8—21no—
313C5×Q8C2×C4×D312yes—
314C5×D4—24no—
315C5×D4—21no—
316C5×D4C2×C4×D312yes—
317C2×C4×C5—21no—
318C2×C4×C5—24no—
319C2×C4×C5—62no—
320C2×C4×C5—241no—
321C2×C4×C5C2×C4×D312yes—
322C2×C4×C5#23512yes—
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—64no—
326C2×Dic5—22no—
327C2×Dic5—61no—
328C2×Dic5—82no—
329C2×Dic5—81no—
330C2×Dic5C2×#6712yes—
331C2×Dic5C2×#6712yes—
332D20—32no—
333D20—61no—
334C4×D5—64no—
335C4×D5—242no—
336Dic10—32no—
337Dic10—61no—
338C5×C8—62no—
339#168—32no—
340#168—32no—
341C2×#41—151no—
342C2×#41D3×D511yescharacteristic
343#135—158no—
344C2×Q16—151no—
345C2×SD16—151no—
346C2×SD16—151no—
347C2×D8—151no—
348C2×M16—31no—
349C22×C8—151no—
350C4×Q8—52no—
351C4×Q8—152no—
352C4×D4—52no—
353C4×D4—102no—
354C4×D4—152no—
355C4×D4—302no—
356#117—51no—
357#117—101no—
358#117—301no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—301no—
363#106—152no—
364#106—152no—
365#103—32no—
366#103—152no—
367#102—32no—
368#102—152no—
369#97—152no—
370C4×C8—152no—
371C2×C3×C5—22no—
372C2×C3×C5—42no—
373C2×C3×C5C2×C4×D411yescharacteristic
374C2×C3×C5#57711yescharacteristic
375C2×C3×C5#57711yescharacteristic
376D15—42no—
377C23×C3—21no—
378C23×C3D4×D511yescharacteristic
379C22×D3—101no—
380C3×Q8—21no—
381C3×Q8C2×C4×D512yes—
382C3×D4—24no—
383C3×D4—21no—
384C3×D4C2×C4×D512yes—
385C2×C3×C4—21no—
386C2×C3×C4—24no—
387C2×C3×C4—52no—
388C2×C3×C4—52no—
389C2×C3×C4—102no—
390C2×C3×C4—402no—
391C2×C3×C4—401no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4D4×D511yescharacteristic
394C2×C3×C4#71112yes—
395C2×C3×C4C23×D511yescharacteristic
396#67—104no—
397C2×Dic3—22no—
398C2×Dic3—81no—
399C2×Dic3—101no—
400D12—52no—
401D12—101no—
402C4×D3—104no—
403C4×D3—402no—
404Dic6—52no—
405Dic6—101no—
406C3⋊C8—22no—
407C3⋊C8—52no—
408C3⋊C8—52no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—22no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5C4×#6712yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—62no—
417C2×D5—121no—
418C2×D5—121no—
419C4×C5—22no—
420C4×C5—122no—
421C4×C5C4×#6712yes—
422C4×C5C22×C4×D311yescharacteristic
423C4×C5C2×#23511yescharacteristic
424Dic5—22no—
425Dic5—22no—
426Dic5—42no—
427Dic5—62no—
428#41—22no—
429#41—154no—
430#41—302no—
431#41#120014yescomplemented
432C2×Q8—151no—
433C2×Q8C2×D3×D511yescharacteristic
434C2×D4—21no—
435C2×D4—151no—
436C2×D4—301no—
437C2×D4C2×D3×D511yescharacteristic
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—102no—
441C22×C4—101no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—154no—
446SD16—154no—
447SD16—154no—
448D8—154no—
449M16—62no—
450C2×C8—32no—
451C2×C8—154no—
452C2×C8—151no—
453C2×C8—151no—
454C4⋊C4—32no—
455C4⋊C4—51no—
456C4⋊C4—51no—
457C4⋊C4—52no—
458C4⋊C4—61no—
459C4⋊C4—102no—
460C4⋊C4—101no—
461C4⋊C4—302no—
462C22⋊C4—52no—
463C22⋊C4—102no—
464C22⋊C4—302no—
465C42—52no—
466C42—102no—
467C42—302no—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3#402712yes—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—102no—
477C2×D3—201no—
478C2×D3—201no—
479C3×C4—22no—
480C3×C4—102no—
481C3×C4—102no—
482C3×C4—202no—
483C3×C4#402712yes—
484C3×C4C22×C4×D511yescharacteristic
485C3×C4C2×#71111yescharacteristic
486Dic3—42no—
487Dic3—102no—
488C2×C5—22no—
489C2×C5—42no—
490C2×C5C2×C4×#6711yescharacteristic
491C2×C5#583611yescharacteristic
492C2×C5#583711yescharacteristic
493D5—122no—
494C23—21no—
495C23—301no—
496C23D5×#6711yescharacteristic
497Q8—21no—
498Q8—152no—
499Q8—301no—
500Q8C2×#120012yes—
501D4—24no—
502D4—21no—
503D4—152no—
504D4—304no—
505D4—301no—
506D4C2×#120012yes—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—52no—
510C2×C4—52no—
511C2×C4—62no—
512C2×C4—102no—
513C2×C4—241no—
514C2×C4—301no—
515C2×C4—304no—
516C2×C4—402no—
517C2×C4—401no—
518C2×C4—1202no—
519C2×C4#678212yes—
520C2×C4C2×#120012yes—
521C2×C4D5×#6711yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—62no—
524C8—152no—
525C8—152no—
526C2×C3—22no—
527C2×C3—42no—
528C2×C3C2×#402711yescharacteristic
529C2×C3#6610911yescharacteristic
530C2×C3#6611211yescharacteristic
531D3—202no—
532C5#8255811yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22—302no—
539C22—601no—
540C22—601no—
541C22#9155212yes—
542C22C2×D5×#6711yescharacteristic
543C4—22no—
544C4—102no—
545C4—102no—
546C4—122no—
547C4—202no—
548C4—302no—
549C4#9155212yes—
550C4C2×#678211yescharacteristic
551C4C22×#120011yescharacteristic
552C3#1061060011yescharacteristic, complemented, Sylow
553C2—22no—
554C2—42no—
555C2—602no—
556C2#1175531711yescharacteristic
557C2#1175533511yescharacteristic
558C2C2×#9155211yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66161C2semidirect
3. #11754506C2semidirect
4. C5×#5232C2semidirect
5. #11749250C2semidirect
6. #11749221C2semidirect
7. #11748998C2semidirect
8. #11748979C2semidirect
9. C2×#90986C2semidirect
10. #11748413C2semidirect
11. #11748320C2semidirect
15. #91839C4semidirect
44. #66161D3semidirect
56. C3×C5×#41C2×C4semidirect
64. #6817C2×C4semidirect
72. #6718C2×C4semidirect
73. #6717C2×C4semidirect
74. #6716C2×C4semidirect
75. #6715C2×C4semidirect
76. C2×C3⋊#168C2×C4semidirect
98. #5232D5semidirect
200. C5×#41C4×D3semidirect
270. C3×#41C4×D5semidirect
431. #41#1200semidirect
468. C3×C5#2952semidirect
532. C5#82558semidirect
552. C3#10610600semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C3×#661612
#117545062
C5×#52322
#117492502
#117492212
#117489982
#117489792
C2×#909862
#117484132
#117483202
#106106003
#825585