Finite Group Databasebeta

← #14417787

Subgroups — #14417787

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
1C5×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic
3#11754509C211yesmaximal, characteristic, complemented
4#11751333C211yesmaximal, characteristic, complemented
5#11749256C212yesmaximal, complemented
6Dic3×#688C212yesmaximal, complemented
7Dic3×#687C212yesmaximal, complemented
8#11748988C212yesmaximal, complemented
9C2×#90985C211yesmaximal, characteristic, complemented
10#11748368C211yesmaximal, characteristic, complemented
11#11748323C211yesmaximal, characteristic, complemented
12#10614289—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C5×Q8×Dic3C2212yes—
18C5×D4×Dic3—22no—
19C5×D4×Dic3C2212yes—
20C5×#926—21no—
21C5×#926C2211yescharacteristic
22C2×C5×C4⋊Dic3—21no—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C3×#4096C418yescomplemented
25C2×C3×#689C2211yescharacteristic
26C2×C3×#688C2211yescharacteristic
27C2×C3×#687C2211yescharacteristic
28C2×C3×#686C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30#91559—22no—
31Dic3×D20C2212yes—
32D5×C4⋊Dic3—21no—
33#91358—21no—
34Dic3×Dic10C2212yes—
35#91119C2212yes—
36#91116C2212yes—
37#90985C2212yes—
38#90985C2212yes—
39#90970C2212yes—
40#90964C2212yes—
41#90953C2212yes—
42Dic3×#168C2212yes—
43#83899—51nomaximal, Hall
44C5×#520—31no—
45C2×#4096D311yescharacteristic
46#65857—31no—
47#65521—31no—
48#65319—32no—
49C4×#688—32no—
50C4×#687—32no—
51#65303—32no—
52#65286—31no—
53#65255—31no—
54C2×#3940—31no—
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
62C22×Dic15—21no—
63C22×C5×Dic3—21no—
64C22×C5×Dic3—22no—
65C2×C3×C22⋊D5—21no—
66C3×#709—22no—
67C3×#709C2×C414yescomplemented
68C2×C3×D20C2311yescharacteristic
69C2×C3×C4×D5—21no—
70C2×C3×Dic10C2311yescharacteristic
71C2×D5×Dic3—22no—
72C4⋊Dic15—21no—
73C4⋊Dic15C2312yes—
74#6710—22no—
75C2×C3⋊#168C2312yes—
76C5×#217—22no—
77C5×#217D412yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3—22no—
80C5×C4⋊Dic3D411yescharacteristic
81C5×C4⋊Dic3D411yescharacteristic
82C5×C4⋊Dic3C2312yes—
83C4×C5×Dic3—22no—
84C4×C5×Dic3C2312yes—
85C3×#689C2×C414yescomplemented
86C3×#688C2×C414yescomplemented
87C3×#687C2×C414yescomplemented
88C3×#686C2×C414yescomplemented
89C2×C3×#168C2×C414yescomplemented
90C2×C3×#168C2311yescharacteristic
91C2×C3×#168C2311yescharacteristic
92#6668—22no—
93#6665—22no—
94Dic3×Dic5—22no—
95C2×C3×#135—51no—
96#5827—51no—
97#5827D511yescharacteristic, complemented
98#5232—51no—
99#5232—51no—
100#5184—52no—
101Dic3×SD16—52no—
102Dic3×SD16—52no—
103#5152—52no—
104C2×#817—51no—
105#5101—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709C2×D311yescharacteristic
108C4×C5×Q8—32no—
109C4×C5×D4—32no—
110C4×C5×D4—62no—
111C5×#117—31no—
112C5×#117—61no—
113C2×C5×C4⋊C4—31no—
114C2×C5×C4⋊C4—61no—
115#4096Dic318yescomplemented
116C2×#689C2×D311yescharacteristic
117C2×#688C2×D311yescharacteristic
118C2×#687C2×D311yescharacteristic
119C2×#686C2×D311yescharacteristic
120C2×C4⋊Dic5—31no—
121C2×#681—31no—
122C22×#168C2×D311yescharacteristic
123#4038—61no—
124D5×C4⋊C4—61no—
125#4027—62no—
126C4×D20—32no—
127C4×Dic10—32no—
128#3967—32no—
129#3964—32no—
130#3942—32no—
131#3941—32no—
132#3940—32no—
133#3940—32no—
134#3935—32no—
135C4×#168—32no—
136#2952—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×C3×D5—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
151C2×Dic15—22no—
152C2×Dic15—81no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—82no—
155C2×C5×Dic3—81no—
156C2×C5×Dic3C2×D412yes—
157C2×C5×Dic3C2×D412yes—
158C3×C22⋊D5—24no—
159C2×C3×Dic5—21no—
160C3×D20—21no—
161C3×D20C22×C412yes—
162C3×C4×D5—24no—
163C3×Dic10—21no—
164C3×Dic10C22×C412yes—
165D5×Dic3—82no—
166C3⋊#168—22no—
167C3×#168C22×C412yes—
168C3×#168C22×C412yes—
169C2×C3×#41—51no—
170C2×C3×#41C2×D511yescharacteristic
171C3×#135—58no—
172C2×C3×Q16—51no—
173C2×C3×SD16—51no—
174C2×C3×SD16—51no—
175C2×C3×D8—51no—
176C22×C3×C8—51no—
177Q8×Dic3—52no—
178Q8×Dic3C2×D512yes—
179D4×Dic3—22no—
180D4×Dic3—52no—
181D4×Dic3—102no—
182D4×Dic3C2×D512yes—
183#926—21no—
184#926—101no—
185#926C2×D511yescharacteristic
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×C4⋊Dic3C2×D511yescharacteristic
190C2×#208—51no—
191#835—52no—
192#835—52no—
193#832—52no—
194#832—52no—
195#817—52no—
196#817—52no—
197#815—52no—
198C8×Dic3—52no—
199C5×#41—22no—
200C5×#41C2×Dic314yescomplemented
201C2×C5×Q8C22×D311yescharacteristic
202C2×C5×D4—21no—
203C2×C5×D4C22×D311yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5—62no—
206C22×C4×C5—61no—
207C22×C4×C5C22×D311yescharacteristic
208C2×C22⋊D5—21no—
209C22×Dic5—61no—
210#709—22no—
211#709C2×Dic314yescomplemented
212C2×D20C22×D311yescharacteristic
213C2×C4×D5—21no—
214C2×C4×D5—62no—
215C2×Dic10C22×D311yescharacteristic
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C4⋊C4—32no—
219C5×C4⋊C4—62no—
220C5×C4⋊C4—61no—
221C5×C22⋊C4—32no—
222C5×C22⋊C4—62no—
223C42×C5—32no—
224C42×C5—62no—
225#689C2×Dic314yescomplemented
226#688C2×Dic314yescomplemented
227#687C2×Dic314yescomplemented
228#686C2×Dic314yescomplemented
229#685—62no—
230C4⋊Dic5—32no—
231C4⋊Dic5—61no—
232#683—62no—
233C4×Dic5—62no—
234#681—62no—
235C2×#168—32no—
236C2×#168C2×Dic314yescomplemented
237C2×#168C22×D311yescharacteristic
238C2×#168C22×D311yescharacteristic
239C2×#135—51no—
240#520—31no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—151no—
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×C3×D5—22no—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C3×C4×C5—22no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—42no—
265C3×Dic5—22no—
266C5×Dic3—22no—
267C5×Dic3—22no—
268C5×Dic3—42no—
269C3×#41—22no—
270C3×#41—54no—
271C3×#41—102no—
272C3×#41C4×D514yescomplemented
273C2×C3×Q8—51no—
274C2×C3×Q8C22×D511yescharacteristic
275C2×C3×D4—21no—
276C2×C3×D4—51no—
277C2×C3×D4—101no—
278C2×C3×D4C22×D511yescharacteristic
279C22×C3×C4—21no—
280C22×C3×C4—101no—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—21no—
283C22×Dic3—22no—
284C22×Dic3—101no—
285C22×Dic3—102no—
286C3×Q16—54no—
287C3×SD16—54no—
288C3×SD16—54no—
289C3×D8—54no—
290C2×C3×C8—54no—
291C2×C3×C8—51no—
292C2×C3×C8—51no—
293#217—22no—
294#217—102no—
295#217C22⋊D512yes—
296C4⋊Dic3—21no—
297C4⋊Dic3—22no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300C4⋊Dic3—102no—
301C4⋊Dic3C22⋊D511yescharacteristic
302C4⋊Dic3C22⋊D511yescharacteristic
303C4⋊Dic3C22×D512yes—
304C4×Dic3—22no—
305C4×Dic3—102no—
306C4×Dic3C22×D512yes—
307#208—102no—
308C2×C3⋊C8—52no—
309C23×C5—21no—
310C23×C5D3×D411yescharacteristic
311C22×D5—21no—
312C5×Q8—21no—
313C5×Q8C22×Dic312yes—
314C5×D4—24no—
315C5×D4—21no—
316C5×D4C22×Dic312yes—
317C2×C4×C5—21no—
318C2×C4×C5—24no—
319C2×C4×C5—32no—
320C2×C4×C5—32no—
321C2×C4×C5—62no—
322C2×C4×C5—242no—
323C2×C4×C5—241no—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5#23712yes—
326C2×C4×C5C22×Dic312yes—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—24no—
329C2×Dic5—21no—
330C2×Dic5—62no—
331C2×Dic5—241no—
332D20—21no—
333D20C22×Dic312yes—
334C4×D5—24no—
335C4×D5—242no—
336Dic10—21no—
337Dic10C22×Dic312yes—
338#168—62no—
339#168C22×Dic312yes—
340#168C22×Dic312yes—
341C2×#41—51no—
342C2×#41D3×D511yescharacteristic
343#135—58no—
344C2×Q16—51no—
345C2×SD16—51no—
346C2×SD16—51no—
347C2×D8—51no—
348C2×M16—151no—
349C22×C8—51no—
350C4×Q8—32no—
351C4×Q8—152no—
352C4×D4—32no—
353C4×D4—62no—
354C4×D4—152no—
355C4×D4—302no—
356#117—31no—
357#117—61no—
358#117—301no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—151no—
362C2×C4⋊C4—301no—
363#106—152no—
364#106—152no—
365#103—152no—
366#103—152no—
367#102—152no—
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
376C3×D5—42no—
377C23×C3—21no—
378C23×C3—101no—
379C23×C3C2×C22⋊D511yescharacteristic
380C3×Q8—21no—
381C3×Q8—52no—
382C3×Q8—101no—
383C3×Q8C2×C4×D512yes—
384C3×D4—24no—
385C3×D4—21no—
386C3×D4—52no—
387C3×D4—104no—
388C3×D4—101no—
389C3×D4C2×C4×D512yes—
390C2×C3×C4—21no—
391C2×C3×C4—24no—
392C2×C3×C4—101no—
393C2×C3×C4—104no—
394C2×C3×C4C2×C4×D512yes—
395C2×C3×C4#70912yes—
396C2×C3×C4C2×C22⋊D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398C2×Dic3—22no—
399C2×Dic3—82no—
400C2×Dic3—81no—
401C2×Dic3—102no—
402C2×Dic3—402no—
403C2×Dic3—401no—
404C2×Dic3C2×C22⋊D512yes—
405C2×Dic3C2×C22⋊D512yes—
406C3×C8—52no—
407C3×C8—52no—
408C3⋊C8—102no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—22no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5D4×Dic312yes—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—22no—
417C2×D5—41no—
418C2×D5—41no—
419C4×C5—22no—
420C4×C5—62no—
421C4×C5—62no—
422C4×C5—122no—
423C4×C5D4×Dic312yes—
424C4×C5C2×#23711yescharacteristic
425C4×C5C23×Dic311yescharacteristic
426Dic5—22no—
427Dic5—122no—
428#41—22no—
429#41—54no—
430#41—102no—
431#41D5×Dic314yescomplemented
432C2×Q8—51no—
433C2×Q8C2×D3×D511yescharacteristic
434C2×D4—21no—
435C2×D4—51no—
436C2×D4—101no—
437C2×D4C2×D3×D511yescharacteristic
438C22×C4—21no—
439C22×C4—62no—
440C22×C4—61no—
441C22×C4—101no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—54no—
446SD16—54no—
447SD16—54no—
448D8—54no—
449M16—302no—
450C2×C8—54no—
451C2×C8—51no—
452C2×C8—51no—
453C2×C8—152no—
454C4⋊C4—31no—
455C4⋊C4—31no—
456C4⋊C4—32no—
457C4⋊C4—62no—
458C4⋊C4—61no—
459C4⋊C4—152no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—32no—
463C22⋊C4—62no—
464C22⋊C4—302no—
465C42—32no—
466C42—62no—
467C42—302no—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—102no—
475C22×C3—201no—
476C22×C3—201no—
477C22×C3C4×C22⋊D512yes—
478C22×C3C22×C22⋊D511yescharacteristic
479C3×C4—22no—
480C3×C4—102no—
481C3×C4C4×C22⋊D512yes—
482C3×C4C22×C4×D511yescharacteristic
483C3×C4C2×#70911yescharacteristic
484Dic3—22no—
485Dic3—22no—
486Dic3—42no—
487Dic3—202no—
488C2×C5—22no—
489C2×C5—42no—
490C2×C5#577011yescharacteristic
491C2×C5#577011yescharacteristic
492C2×C5C2×D4×Dic311yescharacteristic
493D5—42no—
494C23—21no—
495C23—101no—
496C23D3×C22⋊D511yescharacteristic
497Q8—21no—
498Q8—52no—
499Q8—101no—
500Q8C2×D5×Dic312yes—
501D4—24no—
502D4—21no—
503D4—52no—
504D4—104no—
505D4—101no—
506D4C2×D5×Dic312yes—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—62no—
512C2×C4—101no—
513C2×C4—104no—
514C2×C4—242no—
515C2×C4—241no—
516C2×C4—302no—
517C2×C4—1202no—
518C2×C4—1201no—
519C2×C4C2×D5×Dic312yes—
520C2×C4#677912yes—
521C2×C4D3×C22⋊D511yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—52no—
524C8—52no—
525C8—302no—
526C2×C3—22no—
527C2×C3—42no—
528C2×C3—202no—
529C2×C3C2×C4×C22⋊D511yescharacteristic
530C2×C3#6617011yescharacteristic
531C2×C3#6617111yescharacteristic
532C5#8389911yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—22no—
536C22—41no—
537C22—41no—
538C22—102no—
539C22—201no—
540C22—201no—
541C22Dic3×C22⋊D512yes—
542C22C2×D3×C22⋊D511yescharacteristic
543C4—22no—
544C4—62no—
545C4—62no—
546C4—102no—
547C4—122no—
548C4—602no—
549C4Dic3×C22⋊D512yes—
550C4C22×D5×Dic311yescharacteristic
551C4C2×#677911yescharacteristic
552C3#1061428911yescharacteristic, complemented, Sylow
553C2—22no—
554C2—42no—
555C2—202no—
556C2#1175532611yescharacteristic
557C2#1175534711yescharacteristic
558C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4096C2
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
1. C5×#5827C2semidirect
3. #11754509C2semidirect
4. #11751333C2semidirect
5. #11749256C2semidirect
6. Dic3×#688C2semidirect
7. Dic3×#687C2semidirect
8. #11748988C2semidirect
9. C2×#90985C2semidirect
10. #11748368C2semidirect
11. #11748323C2semidirect
24. C3×#4096C4semidirect
56. C3×C5×#41C2×C4semidirect
67. C3×#709C2×C4semidirect
85. C3×#689C2×C4semidirect
86. C3×#688C2×C4semidirect
87. C3×#687C2×C4semidirect
88. C3×#686C2×C4semidirect
89. C2×C3×#168C2×C4semidirect
97. #5827D5semidirect
115. #4096Dic3semidirect
200. C5×#41C2×Dic3semidirect
211. #709C2×Dic3semidirect
225. #689C2×Dic3semidirect
226. #688C2×Dic3semidirect
227. #687C2×Dic3semidirect
228. #686C2×Dic3semidirect
236. C2×#168C2×Dic3semidirect
272. C3×#41C4×D5semidirect
431. #41D5×Dic3semidirect
468. C3×C5#2952semidirect
532. C5#83899semidirect
552. C3#10614289semidirect

Maximal subgroups

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

subgroupindex
C5×#58272
C2×C3×#40962
#117545092
#117513332
#117492562
Dic3×#6882
Dic3×#6872
#117489882
C2×#909852
#117483682
#117483232
#106142893
#838995