Finite Group Databasebeta

← #14439264

Subgroups — #14439264

Order 1920.

1104 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
1C3×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#91515C212yesmaximal, complemented
3C2×#91513C212yesmaximal, complemented
4#11752673C211yesmaximal, characteristic
5#11751187C211yesmaximal, characteristic, complemented
6C5×#5086C211yesmaximal, characteristic, complemented
7#11749347C212yesmaximal, complemented
8#11749339C212yesmaximal, complemented
9#11747082C211yesmaximal, characteristic, complemented
10#11747076C211yesmaximal, characteristic, complemented
11#11747003C211yesmaximal, characteristic, complemented
12#10613601—31nomaximal, Hall
13C2×C3×Q8×D5C2212yes—
14C2×#6773C2211yescharacteristic
15C2×#6772C2211yescharacteristic
16C3×C5×C4⋊Q8C2211yescharacteristic
17C2×#6718C2212yes—
18C2×#6717C2212yes—
19#91764C2211yescharacteristic
20C2×C5×#216C2212yes—
21C2×C5×#215C2212yes—
22C5×#875C2211yescharacteristic
23C3×#4090C2212yes—
24C3×D5×C4⋊C4—22no—
25C3×#4034—22no—
26C3×C42×D5C2211yescharacteristic
27C3×#4015C2211yescharacteristic
28#91515—28no—
29#91513—28no—
30#91451C2211yescharacteristic
31#91448—22no—
32#91405—22no—
33#91376C2211yescharacteristic
34C2×#6662C2212yes—
35C2×#6661C2212yes—
36C2×#6658C2212yes—
37C2×#6656C2212yes—
38C2×#6649C2212yes—
39#91087C2211yescharacteristic
40C5×#803C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83203—51nomaximal, Hall
43C2×#4064—32no—
44C2×#4061—32no—
45D5×C4⋊Q8D311yescharacteristic, complemented
46#66002—31no—
47C5×#497—31no—
48#65470—32no—
49#65464—32no—
50#65375—31no—
51#65349—31no—
52#65004—31no—
53#64996—31no—
54C2×C3×C5×Q8C2312yes—
55C2×D60C2311yescharacteristic
56C2×Dic30C2311yescharacteristic
57C2×C5×D12C2311yescharacteristic
58C2×C5×Dic6C2311yescharacteristic
59C3×Q8×D5—24no—
60C3×Q8×D5—24no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5D412yes—
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×Dic10—22no—
65C2×C3×Dic10C2312yes—
66C2×#1203—22no—
67C2×#1202—21no—
68C2×#1201—21no—
69C2×#1200—21no—
70C2×D3×Dic5—21no—
71#6773—24no—
72#6772—24no—
73C3×C5×C4⋊C4—22no—
74C3×C42×C5C2311yescharacteristic
75#6718—24no—
76#6717—24no—
77#6714—22no—
78C2×C3⋊#168C2312yes—
79C5×#216—24no—
80C5×#215—24no—
81C5×(C2×D3)⋊C4—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C4⋊Dic5—22no—
84C3×#683—24no—
85C3×C4×Dic5D412yes—
86C3×C4×Dic5C2311yescharacteristic
87#6668—22no—
88#6662—24no—
89#6661—24no—
90#6658—24no—
91#6656—24no—
92#6649D418yescomplemented
93C2×C3×C4⋊Q8—51no—
94C2×#942—52no—
95C2×#942—52no—
96#5477—51no—
97#5092—52no—
98#5086—51no—
99#5086—51no—
100#5086—51no—
101#5086D511yescharacteristic, complemented
102#5085—52no—
103C4×#208—51no—
104C2×#713—31no—
105C2×Q8×D5C2×D312yes—
106C2×#711—31no—
107C2×C5×Q16—32no—
108C2×C5×SD16—32no—
109C5×C4⋊Q8C2×D311yescharacteristic
110C5×#124—31no—
111#4090—31no—
112#4090C2×D312yes—
113C2×#689—32no—
114C2×#689—32no—
115C2×#688—32no—
116#4086—31no—
117C2×#687—32no—
118#4064—68no—
119#4061—68no—
120C2×Dic20—32no—
121C2×#677—32no—
122C2×#676—32no—
123D5×C4⋊C4—22no—
124#4034—22no—
125#4030—62no—
126#4027—62no—
127#4021—31no—
128C42×D5C2×D311yescharacteristic
129#4015C2×D311yescharacteristic
130C5×#97—31no—
131C8×Dic5—32no—
132#3935—31no—
133#3152—151noSylow
134C22×D15—21no—
135C22×C5×D3—21no—
136C22×C3×D5C2×D411yescharacteristic
137C3×C5×Q8—22no—
138C3×C5×Q8—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143D60—22no—
144Dic30—22no—
145C2×C5×Dic3—21no—
146C5×D12—22no—
147C5×Dic6—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C2×D411yescharacteristic
150C2×C3×Dic5C2×D412yes—
151C3×C4×D5—24no—
152C3×C4×D5—44no—
153C3×C4×D5C2×D414yes—
154C3×Dic10—22no—
155C3×Dic10—22no—
156C3×Dic10—44no—
157#1203—44no—
158#1202—42no—
159#1201—42no—
160#1200—42no—
161D3×Dic5—42no—
162C3⋊#168C2×D414yes—
163C5×C3⋊C8C2×D414yes—
164C22×C3×Q8—52no—
165C2×#235—51no—
166C2×#235—51no—
167C3×C4⋊Q8—52no—
168C3×C4⋊Q8—51no—
169C3×C4⋊Q8—102no—
170C3×C4⋊Q8C2×D511yescharacteristic
171C2×C3×C4⋊C4—102no—
172C2×C3×C42—51no—
173C2×#216—52no—
174C2×#216—52no—
175C2×#216—52no—
176C2×#216C2×D512yes—
177#942—108no—
178#942—108no—
179C2×#215—52no—
180C2×#215—52no—
181C2×#215—52no—
182C2×#215C2×D512yes—
183#930—102no—
184C2×#208—52no—
185#875—51no—
186#875C2×D511yescharacteristic
187#874—51no—
188C4×D12—102no—
189#869—51no—
190#803—51no—
191#803C2×D511yescharacteristic
192C4×C3⋊C8—52no—
193C2×C5×Q8—31no—
194C2×C5×Q8C22×D312yes—
195C2×C5×D4—31no—
196C2×C22⋊D5—61no—
197C2×C22⋊D5—62no—
198C22×Dic5—61no—
199#713—64no—
200Q8×D5—24no—
201Q8×D5—24no—
202#711—64no—
203C2×D20—31no—
204C2×D20—61no—
205C2×C4×D5—22no—
206C2×C4×D5—61no—
207C2×C4×D5#6712yes—
208C2×C4×D5C22×D311yescharacteristic
209C2×Dic10—22no—
210C2×Dic10—31no—
211C2×Dic10C22×D312yes—
212C5×Q16—64no—
213C5×SD16—64no—
214C2×C5×C8—32no—
215C5×C4⋊C4—22no—
216C5×C22⋊C4—62no—
217C42×C5C22×D311yescharacteristic
218#689—64no—
219#689—64no—
220#688—64no—
221#687—64no—
222#685—62no—
223C4⋊Dic5—22no—
224#683—24no—
225#683—62no—
226C4×Dic5#6712yes—
227C4×Dic5C22×D311yescharacteristic
228C2×#168—32no—
229Dic20—64no—
230#677—64no—
231#676—38no—
232C2×#137—152no—
233C2×#137—152no—
234#532—151no—
235C2×C4⋊Q8—51no—
236#497—31no—
237#497—151no—
238#497—151no—
239#497—151no—
240#494—152no—
241#492—152no—
242C4×M16—151no—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—41no—
245C2×D15—42no—
246C2×C5×D3—41no—
247C2×C5×D3—42no—
248C2×C3×D5—22no—
249C2×C3×D5#12712yes—
250C3×C4×C5—22no—
251C3×C4×C5—42no—
252C3×C4×C5C22×D412yes—
253Dic15—41no—
254C3×Dic5—42no—
255C3×Dic5#12712yes—
256C3×Dic5#13714yescomplemented
257C5×Dic3—41no—
258C2×C3×Q8—52no—
259C2×C3×Q8—102no—
260C2×C3×Q8—104no—
261C2×C3×Q8—104no—
262C2×C3×Q8C22×D512yes—
263C22×C3×C4—51no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C2×#67—101no—
267C2×#67—101no—
268#235—104no—
269#235—104no—
270C2×D12—51no—
271C2×D12—102no—
272C2×D12C22×D511yescharacteristic
273C2×C4×D3—101no—
274C2×C4×D3—101no—
275C2×Dic6—51no—
276C2×Dic6C22×D511yescharacteristic
277C3×C4⋊C4—22no—
278C3×C4⋊C4—104no—
279C3×C4⋊C4—102no—
280C3×C42—52no—
281C3×C42—51no—
282C3×C42C22×D511yescharacteristic
283#216—24no—
284#216—104no—
285#216—104no—
286#216—104no—
287#215—24no—
288#215—104no—
289#215—104no—
290#215—104no—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—102no—
294#208—58no—
295C2×C3⋊C8—52no—
296C2×C3⋊C8C22×D512yes—
297C23×C5—61no—
298C22×D5—61no—
299C22×D5C2×#6711yescharacteristic
300C5×Q8—22no—
301C5×Q8—22no—
302C5×Q8—62no—
303C5×D4—62no—
304C2×C4×C5—22no—
305C2×C4×C5—61no—
306C2×C4×C5C2×#6712yes—
307C2×C4×C5C23×D311yescharacteristic
308C22⋊D5—122no—
309C22⋊D5—124no—
310C2×Dic5—22no—
311C2×Dic5—61no—
312C2×Dic5—122no—
313C2×Dic5C2×#6711yescharacteristic
314C2×Dic5C2×#6712yes—
315D20—62no—
316D20—122no—
317C4×D5—24no—
318C4×D5—44no—
319C4×D5—122no—
320C4×D5D3×D414yes—
321Dic10—22no—
322Dic10—22no—
323Dic10—44no—
324Dic10—62no—
325C5×C8—34no—
326#168—34no—
327C2×#41—151no—
328C2×#41—151no—
329C22×Q8—52no—
330#137—308no—
331#137—308no—
332C2×Q16—32no—
333C2×Q16—152no—
334C2×Q16—152no—
335C2×Q16—152no—
336C2×SD16—32no—
337C2×SD16—152no—
338C2×SD16—152no—
339C2×SD16—152no—
340C2×M16—152no—
341C4⋊Q8—52no—
342C4⋊Q8—51no—
343C4⋊Q8—102no—
344C4⋊Q8—151no—
345C4⋊Q8D3×D511yescharacteristic
346#127—151no—
347#124—31no—
348#124—151no—
349#121—302no—
350C4×D4—302no—
351C2×C4⋊C4—102no—
352C2×C42—51no—
353#97—31no—
354#97—151no—
355C4×C8—152no—
356C2×C3×C5C2×#12711yescharacteristic
357C2×C3×C5C2×#13712yes—
358D15—81no—
359C3×D5—22no—
360C5×D3—81no—
361C23×C3—51no—
362C22×D3—21no—
363C22×D3—101no—
364C3×Q8—22no—
365C3×Q8—22no—
366C3×Q8—102no—
367C3×Q8—102no—
368C3×Q8—204no—
369C2×C3×C4—22no—
370C2×C3×C4—52no—
371C2×C3×C4—51no—
372C2×C3×C4—54no—
373C2×C3×C4—104no—
374C2×C3×C4—102no—
375C2×C3×C4—204no—
376C2×C3×C4D4×D512yes—
377C2×C3×C4C23×D511yescharacteristic
378#67—202no—
379#67—202no—
380C2×Dic3—21no—
381C2×Dic3—101no—
382D12—22no—
383D12—102no—
384D12—204no—
385C4×D3—202no—
386C4×D3—202no—
387Dic6—22no—
388Dic6—102no—
389C3⋊C8—54no—
390C3⋊C8D4×D514yes—
391C22×C5—121no—
392C22×C5—122no—
393C22×C5C22×#6711yescharacteristic
394C2×D5—22no—
395C2×D5—121no—
396C2×D5—122no—
397C2×D5#94012yes—
398C4×C5—22no—
399C4×C5—42no—
400C4×C5—121no—
401C4×C5C2×D3×D412yes—
402Dic5—42no—
403Dic5—121no—
404Dic5#94012yes—
405Dic5#94214yescomplemented
406#41—304no—
407#41—304no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—102no—
411C2×Q8—104no—
412C2×Q8—104no—
413C2×Q8—151no—
414C2×Q8C2×D3×D512yes—
415C2×D4—31no—
416C2×D4—151no—
417C2×D4—302no—
418C2×D4—301no—
419C2×D4—301no—
420C22×C4—51no—
421C22×C4—52no—
422C22×C4—102no—
423C22×C4—301no—
424C22×C4—301no—
425Q16—64no—
426Q16—304no—
427Q16—304no—
428Q16—304no—
429SD16—64no—
430SD16—304no—
431SD16—304no—
432SD16—304no—
433M16—158no—
434C2×C8—32no—
435C2×C8—152no—
436C4⋊C4—22no—
437C4⋊C4—104no—
438C4⋊C4—102no—
439C4⋊C4—302no—
440C22⋊C4—62no—
441C22⋊C4—302no—
442C42—52no—
443C42—51no—
444C42C2×D3×D511yescharacteristic
445C3×C5#315211yescharacteristic, complemented, Hall
446C22×C3—52no—
447C22×C3—102no—
448C22×C3C2×D4×D511yescharacteristic
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—201no—
452C2×D3—202no—
453C3×C4—22no—
454C3×C4—42no—
455C3×C4—52no—
456C3×C4—54no—
457C3×C4—202no—
458C3×C4C2×D4×D512yes—
459Dic3—41no—
460Dic3—201no—
461C2×C5—241no—
462C2×C5C2×#94011yescharacteristic
463C2×C5C2×#94212yes—
464D5—22no—
465D5—241no—
466C23—51no—
467C23—61no—
468C23—301no—
469Q8—22no—
470Q8—22no—
471Q8—62no—
472Q8—102no—
473Q8—102no—
474Q8—204no—
475Q8—302no—
476D4—62no—
477D4—302no—
478D4—604no—
479D4—602no—
480D4—602no—
481C2×C4—22no—
482C2×C4—52no—
483C2×C4—51no—
484C2×C4—54no—
485C2×C4—61no—
486C2×C4—104no—
487C2×C4—102no—
488C2×C4—204no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4—602no—
492C2×C4D5×#6712yes—
493C2×C4C22×D3×D511yescharacteristic
494C8—34no—
495C8—154no—
496C2×C3—102no—
497C2×C3D5×#12711yescharacteristic
498C2×C3D5×#13712yes—
499D3—81no—
500D3—401no—
501C5#8320311yescharacteristic, complemented, Sylow
502C22—52no—
503C22—102no—
504C22—121no—
505C22—122no—
506C22—601no—
507C22—602no—
508C22C2×D5×#6711yescharacteristic
509C4—22no—
510C4—42no—
511C4—52no—
512C4—54no—
513C4—121no—
514C4—202no—
515C4—601no—
516C4D3×D4×D512yes—
517C3#1061360111yescharacteristic, complemented, Sylow
518C2—102no—
519C2—241no—
520C2—1201no—
521C2D5×#94011yescharacteristic
522C2D5×#94212yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752673C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3152
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D5×C4⋊Q8C2semidirect
2. C2×#91515C2semidirect
3. C2×#91513C2semidirect
5. #11751187C2semidirect
6. C5×#5086C2semidirect
7. #11749347C2semidirect
8. #11749339C2semidirect
9. #11747082C2semidirect
10. #11747076C2semidirect
11. #11747003C2semidirect
45. D5×C4⋊Q8D3semidirect
92. #6649D4semidirect
101. #5086D5semidirect
256. C3×Dic5#137semidirect
405. Dic5#942semidirect
445. C3×C5#3152semidirect
501. C5#83203semidirect
517. C3#10613601semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
C2×#915152
C2×#915132
#117526732
#117511872
C5×#50862
#117493472
#117493392
#117470822
#117470762
#117470032
#106136013
#832035