Finite Group Databasebeta

← #14417267

Subgroups — #14417267

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754499C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3C2×#91307C211yesmaximal, characteristic
4#11751202C211yesmaximal, characteristic, complemented
5C2×C5×#816C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic
7#11748472C211yesmaximal, characteristic, complemented
8#11747829C212yesmaximal, complemented
9#11747828C212yesmaximal, complemented
10#11747736C212yesmaximal, complemented
11#11747735C212yesmaximal, complemented
12#10610505—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20Dic3×C22⋊D5—22no—
21#91529—22no—
22#91434C2212yes—
23D5×C4⋊Dic3—21no—
24#91358—21no—
25#91344C2212yes—
26#91344C2212yes—
27Dic5×Dic6—21no—
28Dic5×Dic6—21no—
29#91331C2212yes—
30C2×#6661C2212yes—
31#91307C418yescomplemented
32C2×#6655C2212yes—
33#91099C2212yes—
34C8×Dic15C2212yes—
35C5×#816C2212yes—
36C5×#816C2212yes—
37C3×#3953C2211yescharacteristic
38C3×#3953C2211yescharacteristic
39C3×#3948C2211yescharacteristic
40C3×#3948C2211yescharacteristic
41#90989C2212yes—
42#90986C2212yes—
43#78821—51nomaximal, Hall
44#66146—31no—
45C2×#4088—31no—
46#65838—31no—
47C2×C5×#103—31no—
48#65402D311yescharacteristic
49#65390—31no—
50#65253—31no—
51#65106—32no—
52#65079—32no—
53#65078—32no—
54#65077—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C5×Dic3—21no—
57C22×C5×Dic3—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—22no—
60C2×C5×Dic6C2×C414yescomplemented
61C2×C5×Dic6C2312yes—
62C2×C3×C22⋊D5—21no—
63C3×#709—22no—
64C3×#709C2×C414yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10C2311yescharacteristic
68C2×D5×Dic3—22no—
69C2×C3×C5×C8—22no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72#6719D412yes—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15D411yescharacteristic
75C4×Dic15C2312yes—
76#6710C2×C414yescomplemented
77C2×C3⋊#168C2312yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2312yes—
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4×Dic5—21no—
84Dic3⋊Dic5—22no—
85Dic3⋊Dic5—22no—
86#6668—22no—
87#6665—22no—
88Dic3×Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C418yescomplemented
92#6655C2×C418yescomplemented
93#5827—51no—
94C2×#951—51no—
95#5516—51no—
96C3×#416—51no—
97C2×#816D511yescharacteristic, complemented
98#5101—51no—
99#4995—51no—
100#4790—52no—
101#4789—52no—
102#4758—52no—
103#4757—52no—
104C22×C5×Q8—31no—
105C2×#709C2×D311yescharacteristic
106C22×C5×C8C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108Q8×Dic5—32no—
109Q8×Dic5—32no—
110Q8×Dic5—61no—
111Q8×Dic5—61no—
112C2×#689—32no—
113#4088—38no—
114C2×#688—32no—
115C4×C22⋊D5—62no—
116#4072—31no—
117#4072—62no—
118#4072C2×D311yescharacteristic
119C2×#681—31no—
120#4039—32no—
121#4038—61no—
122D5×C4⋊C4—61no—
123#4033—32no—
124C5×#103—32no—
125C5×#103—32no—
126#3953C2×D311yescharacteristic
127#3953C2×D311yescharacteristic
128#3948C2×D311yescharacteristic
129#3948C2×D311yescharacteristic
130#3947—32no—
131C8×Dic5—32no—
132#3940—32no—
133#3939—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143C2×C5×Dic3—24no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—81no—
147C5×Dic6—24no—
148C5×Dic6—22no—
149C5×Dic6C22×C414yes—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C3×D20—21no—
155C3×D20C22×C412yes—
156C3×C4×D5—24no—
157C3×Dic10—21no—
158C3×Dic10C22×C412yes—
159D5×Dic3—82no—
160C3×C5×C8—21no—
161C3×C5×C8—21no—
162C3⋊#168C22×C414yes—
163C2×C3×#41—51no—
164C22×Dic6C2×D511yescharacteristic
165C22×C3×C8C2×D511yescharacteristic
166C3×#117—51no—
167#951—58no—
168Q8×Dic3—52no—
169C2×#216—52no—
170D4×Dic3—52no—
171D4×Dic3—102no—
172C2×#214—52no—
173#926—51no—
174#926—101no—
175C2×C4⋊Dic3—101no—
176C2×C4⋊Dic3C2×D511yescharacteristic
177C2×#208—51no—
178#887—52no—
179#887—52no—
180#877—102no—
181C4×Dic6—101no—
182C4×Dic6—101no—
183C3×#103—51no—
184C3×#103—51no—
185C3×#102—51no—
186C3×#102—51no—
187#816C2×D512yes—
188#816C2×D512yes—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C2×C5×Q8—34no—
194C2×C5×Q8—32no—
195C2×C5×Q8—61no—
196C2×C5×Q8—62no—
197C22×C4×C5—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201#709—22no—
202#709C4×D314yes—
203C2×D20C22×D311yescharacteristic
204C2×C4×D5—21no—
205C2×C4×D5—62no—
206C2×Dic10C22×D311yescharacteristic
207C2×C5×C8—22no—
208C2×C5×C8C22×D311yescharacteristic
209C2×C5×C8C22×D311yescharacteristic
210C5×C4⋊C4—32no—
211C5×C4⋊C4—61no—
212C22⋊Dic5—21no—
213C22⋊Dic5—32no—
214#689—38no—
215#688—38no—
216#685—62no—
217C4⋊Dic5—31no—
218C4⋊Dic5—31no—
219C4⋊Dic5—62no—
220C4⋊Dic5—62no—
221C4⋊Dic5C22×D311yescharacteristic
222C4⋊Dic5C22×D311yescharacteristic
223#683—62no—
224C4×Dic5—21no—
225C4×Dic5—32no—
226C4×Dic5—62no—
227C4×Dic5—62no—
228C4×Dic5—62no—
229#681—34no—
230C2×#168—32no—
231C2×#137—151no—
232#520—151no—
233#519—151no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—51no—
240C2×#103—31no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C3×D5—22no—
247C2×C3×D5—41no—
248C2×C3×D5—41no—
249C3×C4×C5C4×D412yes—
250C3×C4×C5C23×C411yescharacteristic
251C3×C4×C5C2×#4111yescharacteristic
252Dic15—22no—
253Dic15—22no—
254C3×Dic5—22no—
255C3×Dic5—41no—
256C3×Dic5—41no—
257C5×Dic3—24no—
258C5×Dic3—42no—
259C3×#41—54no—
260C3×#41—102no—
261C2×C3×Q8—51no—
262C2×C3×D4—51no—
263C2×C3×D4—101no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—102no—
269C2×Dic6—21no—
270C2×Dic6—22no—
271C2×Dic6C4×D514yescomplemented
272C2×Dic6C22×D512yes—
273C2×C3×C8—22no—
274C2×C3×C8C22×D511yescharacteristic
275C2×C3×C8C22×D511yescharacteristic
276C3×C4⋊C4—51no—
277C3×C4⋊C4—51no—
278C3×C22⋊C4—101no—
279C3×C42—101no—
280#217—52no—
281#217—102no—
282#216—58no—
283#214—58no—
284C4⋊Dic3—21no—
285C4⋊Dic3—51no—
286C4⋊Dic3—51no—
287C4⋊Dic3—102no—
288C4⋊Dic3C22×D512yes—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—52no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295#208—54no—
296C2×C3⋊C8—52no—
297C23×C5D3×D411yescharacteristic
298C22×D5—21no—
299C5×Q8—34no—
300C5×Q8—64no—
301C5×Q8—62no—
302C2×C4×C5—64no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5—241no—
306C2×C4×C5C2×C4×D312yes—
307C2×C4×C5D3×D411yescharacteristic
308C2×C4×C5#23712yes—
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—24no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—32no—
315C2×Dic5—32no—
316D20—21no—
317D20C2×C4×D312yes—
318C4×D5—24no—
319C4×D5—242no—
320Dic10—21no—
321Dic10C2×C4×D312yes—
322C5×C8—21no—
323C5×C8—21no—
324#168—34no—
325C2×#41—51no—
326C22×Q8—31no—
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8D3×D511yescharacteristic
332C4×Q8—152no—
333C4×Q8—152no—
334C4×Q8—152no—
335C4×Q8—301no—
336C4×Q8—301no—
337C4×D4—152no—
338C4×D4—302no—
339#117—51no—
340#117—151no—
341#117—302no—
342#117—301no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—32no—
348#103—32no—
349#103—51no—
350#103—51no—
351#102—51no—
352#102—51no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C3×D5—42no—
360C23×C3—101no—
361C23×C3D4×D511yescharacteristic
362C3×Q8—52no—
363C3×Q8—101no—
364C3×D4—52no—
365C3×D4—104no—
366C3×D4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—104no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71112yes—
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—22no—
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3—52no—
379C2×Dic3—52no—
380C2×Dic3—81no—
381C2×Dic3—402no—
382Dic6—22no—
383Dic6—24no—
384Dic6C2×C4×D514yes—
385C3×C8—21no—
386C3×C8—21no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#67⋊C412yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—22no—
393C2×D5—41no—
394C2×D5—41no—
395C4×C5—64no—
396C4×C5—122no—
397C4×C5#67⋊C412yes—
398C4×C5C22×C4×D311yescharacteristic
399C4×C5C2×#23711yescharacteristic
400Dic5—22no—
401Dic5—41no—
402Dic5—41no—
403Dic5—62no—
404Dic5—62no—
405#41—54no—
406#41—102no—
407C2×Q8—34no—
408C2×Q8—32no—
409C2×Q8—51no—
410C2×Q8—61no—
411C2×Q8—62no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—22no—
423C2×C8—152no—
424C2×C8C2×D3×D511yescharacteristic
425C2×C8C2×D3×D511yescharacteristic
426C4⋊C4—32no—
427C4⋊C4—51no—
428C4⋊C4—51no—
429C4⋊C4—61no—
430C4⋊C4—151no—
431C4⋊C4—151no—
432C4⋊C4—302no—
433C4⋊C4—302no—
434C4⋊C4—302no—
435C22⋊C4—101no—
436C22⋊C4—152no—
437C22⋊C4—302no—
438C42—101no—
439C42—152no—
440C42—302no—
441C42—302no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—102no—
447C22×C3—201no—
448C22×C3—201no—
449C22×C3#402712yes—
450C22×C3C2×D4×D511yescharacteristic
451C3×C4—102no—
452C3×C4—201no—
453C3×C4—201no—
454C3×C4#402712yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#71111yescharacteristic
457Dic3—24no—
458Dic3—42no—
459Dic3—102no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#577011yescharacteristic
464C2×C5#577111yescharacteristic
465D5—42no—
466C23—101no—
467C23#677711yescharacteristic
468Q8—34no—
469Q8—52no—
470Q8—64no—
471Q8—62no—
472Q8—101no—
473D4—52no—
474D4—104no—
475D4—101no—
476C2×C4—64no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—101no—
480C2×C4—104no—
481C2×C4—101no—
482C2×C4—101no—
483C2×C4—152no—
484C2×C4—152no—
485C2×C4—241no—
486C2×C4—1202no—
487C2×C4C4×D3×D512yes—
488C2×C4#677711yescharacteristic
489C2×C4#678012yes—
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—154no—
494C2×C3—22no—
495C2×C3—202no—
496C2×C3C2×#402711yescharacteristic
497C2×C3#6609611yescharacteristic
498C2×C3#6610011yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—102no—
503C22—201no—
504C22—201no—
505C22#9144212yes—
506C22C2×#677711yescharacteristic
507C4—64no—
508C4—102no—
509C4—122no—
510C4—201no—
511C4—201no—
512C4—302no—
513C4—302no—
514C4#9144212yes—
515C4C2×C4×D3×D511yescharacteristic
516C4C2×#678011yescharacteristic
517C3#1061050511yescharacteristic, complemented, Sylow
518C2—22no—
519C2—202no—
520C2#1175398211yescharacteristic
521C2#1175400811yescharacteristic
522C2C2×#9144211yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754211C2semidirect
4. #11751202C2semidirect
5. C2×C5×#816C2semidirect
7. #11748472C2semidirect
8. #11747829C2semidirect
9. #11747828C2semidirect
10. #11747736C2semidirect
11. #11747735C2semidirect
31. #91307C4semidirect
60. C2×C5×Dic6C2×C4semidirect
76. #6710C2×C4semidirect
91. #6661C2×C4semidirect
92. #6655C2×C4semidirect
97. C2×#816D5semidirect
271. C2×Dic6C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10610505semidirect

Maximal subgroups

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

subgroupindex
#117544992
#117542112
C2×#913072
#117512022
C2×C5×#8162
C3×#654022
#117484722
#117478292
#117478282
#117477362
#117477352
#106105053
#788215