Finite Group Databasebeta

← #14307966

Subgroups — #14307966

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756285C211yesmaximal, characteristic
2C2×#91389C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic
4C3×#65293C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic
6C2×#90963C211yesmaximal, characteristic, complemented
7C5×#4532C211yesmaximal, characteristic, complemented
8#10599561—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91786—22no—
14#91775—22no—
15#91764—21no—
16#91758—21no—
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C2×Dic3⋊Dic5—22no—
21#91389—22no—
22#91389—22no—
23C2×#6662—21no—
24#91315—22no—
25#91315—22no—
26C2×#6658—21no—
27C3×#3942—22no—
28#90980—22no—
29#90963—22no—
30#70346—51nomaximal, Hall
31C2×#4055—31no—
32#65860—31no—
33C2×#4015—31no—
34C2×#3956—31no—
35#65293D311yescharacteristic, complemented
36C2×#3937—31no—
37C5×#339—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15D412yes—
41#6817—21no—
42#6817—21no—
43#6817—21no—
44#6817—21no—
45C2×D60D411yescharacteristic
46C2×C4×D15—21no—
47C2×Dic30—21no—
48C2×Dic30—21no—
49C2×Dic30—21no—
50C2×Dic30—21no—
51C2×Dic30—21no—
52C2×Dic30—21no—
53C2×Dic30D411yescharacteristic
54C22×C5×Dic3—21no—
55C22×C3×Dic5—21no—
56C2×C3×Dic10—21no—
57C2×C3×Dic10—21no—
58C2×C3×Dic10—21no—
59C2×C3×Dic10—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10D412yes—
62C3×C5×C4⋊C4D412yes—
63C3×C5×C22⋊C4—21no—
64C3×C42×C5—21no—
65#6714—24no—
66C4⋊Dic15—24no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3D412yes—
69C5×#208—21no—
70C5×#208D412yes—
71C2×C5×C3⋊C8—21no—
72C3×#681—21no—
73C3×#681—21no—
74C2×C3×#168—21no—
75Dic3⋊Dic5—28no—
76#6662—24no—
77#6658—24no—
78C2×#944—51no—
79C2×#942—51no—
80#5526—51no—
81C3×#419—51no—
82C2×#825—51no—
83C2×#824—51no—
84#4532D511yescharacteristic, complemented
85C2×#709—31no—
86C22×Dic10—31no—
87C22×Dic10C2×D311yescharacteristic
88C2×C5×M16—31no—
89C5×#117C2×D311yescharacteristic
90C2×C42×C5—31no—
91C2×C4⋊Dic5—62no—
92C2×#681C2×D311yescharacteristic
93#4055—62no—
94#4055—62no—
95C2×Dic20—61no—
96C2×#677—61no—
97#4043—62no—
98#4032—62no—
99#4021—61no—
100#4015—61no—
101#4015—62no—
102#4015—62no—
103#3956—62no—
104#3942—22no—
105#3937—62no—
106#2005—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116#1220—41no—
117#1220—41no—
118C2×Dic15—22no—
119C2×Dic15—21no—
120C2×Dic15—22no—
121C2×Dic15—22no—
122D60—21no—
123D60—21no—
124C4×D15—41no—
125C4×D15—41no—
126Dic30—21no—
127Dic30—21no—
128Dic30—41no—
129Dic30—41no—
130Dic30—41no—
131Dic30—41no—
132C2×C5×Dic3—24no—
133C2×C5×Dic3—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C3×Dic10—22no—
138C3×Dic10—22no—
139C3×Dic10—41no—
140C3×Dic10—41no—
141C3×#168—41no—
142C5×C3⋊C8—22no—
143C22×C3×Q8—51no—
144C2×#235—51no—
145C22×Dic6—51no—
146C2×C3×M16—51no—
147C3×#117C2×D511yescharacteristic
148#944—102no—
149#944—102no—
150C2×#216—101no—
151#942—102no—
152#942—102no—
153C2×#215—101no—
154C2×Dic3⋊C4—102no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208C2×D511yescharacteristic
157#897—102no—
158#886—102no—
159#875—101no—
160#869—101no—
161C3×#103—102no—
162#825—102no—
163#824—102no—
164C22×C4×C5—61no—
165C22×C4×C5C22×D311yescharacteristic
166C2×C22⋊D5—61no—
167C22×Dic5—21no—
168C22×Dic5—32no—
169#709—61no—
170#709—61no—
171#709—61no—
172#709—61no—
173C2×D20—31no—
174C2×C4×D5—61no—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10—31no—
181C2×Dic10—61no—
182C2×Dic10—61no—
183C2×Dic10—61no—
184C2×Dic10—61no—
185C2×Dic10—61no—
186C2×Dic10—61no—
187C2×Dic10D1212yes—
188C5×M16—32no—
189C5×M16—61no—
190C2×C5×C8—61no—
191C5×C4⋊C4#6712yes—
192C5×C22⋊C4—21no—
193C42×C5—21no—
194C42×C5—32no—
195C42×C5—61no—
196#685—64no—
197C4⋊Dic5—68no—
198C4⋊Dic5—64no—
199#681—21no—
200#681—21no—
201C2×#168—21no—
202Dic20—64no—
203#677—64no—
204C2×#137—151no—
205#536—151no—
206C2×C4⋊Q8—151no—
207C2×#104—151no—
208#419—51no—
209C2×#101—151no—
210#339—31no—
211C22×C3×C5—22no—
212C22×C3×C5#12011yescharacteristic
213C22×C3×C5#12011yescharacteristic
214C22×C3×C5#12111yescharacteristic
215C2×D15—41no—
216C2×D15—42no—
217C3×C4×C5—42no—
218C3×C4×C5#12011yescharacteristic
219C3×C4×C5#12111yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5#12711yescharacteristic
222Dic15—41no—
223Dic15—42no—
224C3×Dic5—42no—
225C5×Dic3—24no—
226C2×C3×Q8—52no—
227C2×C3×Q8—101no—
228C2×C3×Q8—101no—
229C2×C3×Q8—101no—
230C2×C3×Q8—101no—
231C2×C3×Q8—101no—
232C22×C3×C4—101no—
233C22×C3×C4C22×D511yescharacteristic
234C2×#67—101no—
235C22×Dic3—21no—
236C22×Dic3—52no—
237#235—101no—
238#235—101no—
239#235—101no—
240#235—101no—
241C2×D12—51no—
242C2×C4×D3—101no—
243C2×Dic6—51no—
244C2×Dic6—101no—
245C2×Dic6—101no—
246C2×Dic6—101no—
247C2×Dic6—101no—
248C2×Dic6—101no—
249C2×Dic6—101no—
250C3×M16—101no—
251C3×M16—101no—
252C2×C3×C8—101no—
253C3×C4⋊C4D2012yes—
254C3×C22⋊C4—21no—
255C3×C42—21no—
256#216—104no—
257#215—104no—
258(C2×D3)⋊C4—104no—
259C4⋊Dic3—104no—
260Dic3⋊C4—108no—
261C4×Dic3—21no—
262C4×Dic3D2012yes—
263#208—21no—
264#208D2012yes—
265C2×C3⋊C8—21no—
266C23×C5D3×D411yescharacteristic
267C22×D5—61no—
268C2×C4×C5—22no—
269C2×C4×C5—64no—
270C2×C4×C5—62no—
271C2×C4×C5C2×D1211yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C22⋊D5—121no—
278C22⋊D5—121no—
279C2×Dic5—22no—
280C2×Dic5—41no—
281C2×Dic5—41no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—61no—
285C2×Dic5—62no—
286D20—61no—
287D20—61no—
288C4×D5—121no—
289C4×D5—121no—
290Dic10—22no—
291Dic10—22no—
292Dic10—41no—
293Dic10—41no—
294Dic10—61no—
295Dic10—61no—
296Dic10—121no—
297Dic10—121no—
298Dic10—121no—
299Dic10—121no—
300C5×C8—62no—
301#168—41no—
302C2×#41—151no—
303C22×Q8—51no—
304C22×Q8—151no—
305#137—302no—
306#137—302no—
307C2×Q16—301no—
308C2×SD16—301no—
309C2×M16—31no—
310C2×M16—51no—
311C4⋊Q8—301no—
312C4⋊Q8—302no—
313C4⋊Q8—302no—
314#124—301no—
315#123—302no—
316C22⋊Q8—302no—
317#117D3×D511yescharacteristic
318C2×C4⋊C4—302no—
319C2×C42—31no—
320#104—302no—
321#103—102no—
322#101—302no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#39211yescharacteristic
326C2×C3×C5#45612yes—
327D15—81no—
328C23×C3D4×D511yescharacteristic
329C22×D3—101no—
330C3×Q8—102no—
331C3×Q8—102no—
332C3×Q8—201no—
333C3×Q8—201no—
334C2×C3×C4—22no—
335C2×C3×C4—102no—
336C2×C3×C4—201no—
337C2×C3×C4—201no—
338C2×C3×C4C2×D2011yescharacteristic
339C2×C3×C4C2×D2011yescharacteristic
340C2×C3×C4C2×D2011yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4#71311yescharacteristic
344#67—201no—
345#67—201no—
346C2×Dic3—24no—
347C2×Dic3—22no—
348C2×Dic3—102no—
349C2×Dic3—101no—
350C2×Dic3—102no—
351C2×Dic3—102no—
352D12—101no—
353D12—101no—
354C4×D3—201no—
355C4×D3—201no—
356Dic6—101no—
357Dic6—101no—
358Dic6—201no—
359Dic6—201no—
360Dic6—201no—
361Dic6—201no—
362C3×C8—201no—
363C3⋊C8—22no—
364C22×C5—22no—
365C22×C5#88211yescharacteristic
366C22×C5#88411yescharacteristic
367C22×C5#93711yescharacteristic
368C2×D5—122no—
369C2×D5—121no—
370C4×C5—42no—
371C4×C5—64no—
372C4×C5#88211yescharacteristic
373C4×C5#88411yescharacteristic
374C4×C5#93011yescharacteristic
375C4×C5#94011yescharacteristic
376Dic5—42no—
377Dic5—121no—
378Dic5—122no—
379#41—301no—
380#41—301no—
381#41—301no—
382#41—301no—
383C2×Q8—52no—
384C2×Q8—101no—
385C2×Q8—101no—
386C2×Q8—101no—
387C2×Q8—101no—
388C2×Q8—101no—
389C2×Q8—151no—
390C2×Q8—301no—
391C2×Q8—301no—
392C2×Q8—301no—
393C2×Q8—301no—
394C2×Q8—301no—
395C2×Q8—301no—
396C2×D4—151no—
397C2×D4—301no—
398C22×C4—61no—
399C22×C4—101no—
400C22×C4—152no—
401C22×C4—301no—
402C22×C4C2×D3×D511yescharacteristic
403Q16—304no—
404SD16—304no—
405M16—32no—
406M16—61no—
407M16—101no—
408M16—101no—
409C2×C8—61no—
410C2×C8—101no—
411C4⋊C4—304no—
412C4⋊C4—308no—
413C4⋊C4#120212yes—
414C22⋊C4—21no—
415C22⋊C4—304no—
416C42—21no—
417C42—32no—
418C42—61no—
419C3×C5#200511yescharacteristic, complemented, Hall
420C22×C3—22no—
421C22×C3#402811yescharacteristic
422C22×C3#402811yescharacteristic
423C22×C3#404111yescharacteristic
424C2×D3—202no—
425C2×D3—201no—
426C3×C4—42no—
427C3×C4—202no—
428C3×C4#402011yescharacteristic
429C3×C4#402811yescharacteristic
430C3×C4#404111yescharacteristic
431C3×C4#404111yescharacteristic
432Dic3—24no—
433Dic3—201no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5#496011yescharacteristic
438C2×C5#520512yes—
439D5—241no—
440C23—301no—
441C23#679011yescharacteristic
442Q8—102no—
443Q8—102no—
444Q8—201no—
445Q8—201no—
446Q8—301no—
447Q8—301no—
448Q8—601no—
449Q8—601no—
450Q8—601no—
451Q8—601no—
452D4—301no—
453D4—301no—
454D4—601no—
455D4—601no—
456C2×C4—22no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—102no—
460C2×C4—201no—
461C2×C4—201no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4#677311yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4D3×D2011yescharacteristic
471C2×C4D3×D2011yescharacteristic
472C2×C4C2×#120211yescharacteristic
473C2×C4#679011yescharacteristic
474C8—62no—
475C8—201no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3#6496011yescharacteristic
479C2×C3#6511512yes—
480D3—401no—
481C5#7034611yescharacteristic, complemented, Sylow
482C22—22no—
483C22—602no—
484C22—601no—
485C22#9145911yescharacteristic
486C22#9147611yescharacteristic
487C22#9157211yescharacteristic
488C4—42no—
489C4—64no—
490C4—202no—
491C4—602no—
492C4—601no—
493C4#9145011yescharacteristic
494C4#9145811yescharacteristic
495C4#9145911yescharacteristic
496C4#9147611yescharacteristic
497C3#1059956111yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—1201no—
501C2#1174893111yescharacteristic
502C2#1174942412yes—
subgroupG/H
centerC22#91572
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5#120
prime radicalC2×#6817C22
hypercenter#117D3×D5
hypocenterC3×C5#2005
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#91389C2semidirect
4. C3×#65293C2semidirect
6. C2×#90963C2semidirect
7. C5×#4532C2semidirect
35. #65293D3semidirect
84. #4532D5semidirect
419. C3×C5#2005semidirect
481. C5#70346semidirect
497. C3#10599561semidirect

Maximal subgroups

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

subgroupindex
#117562852
C2×#913892
C2×#913152
C3×#652932
C2×#909802
C2×#909632
C5×#45322
#105995613
#703465