Finite Group Databasebeta

← #14424474

Subgroups — #14424474

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92001C211yesmaximal, characteristic, complemented
2C22×#6716C211yesmaximal, characteristic, complemented
3C5×#5805C211yesmaximal, characteristic, complemented
4C2×C3×#4078C211yesmaximal, characteristic, complemented
5#11749157C214yesmaximal, complemented
6#11749155C214yesmaximal, complemented
7#11748417C211yesmaximal, characteristic, complemented
8#11748364C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615121—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772—21no—
17C2×D3×Dic10C2212yescomplemented
18#92001—24no—
19#92001—24no—
20C2×#6765C2212yescomplemented
21C2×D5×Dic6—21no—
22C2×#6716—24no—
23C2×#6716C2214yes—
24C22×C3⋊#168C2211yescharacteristic
25C5×#953—22no—
26C5×#940—21no—
27C5×#938C2214yes—
28C5×#936—21no—
29C5×#926C2211yescharacteristic
30C2×C3×#687C2212yes—
31C3×#4078—24no—
32C2×C3×#686C2212yes—
33C2×C3×#681C2211yescharacteristic
34#90975C2214yescomplemented
35#90970C2212yescomplemented
36#90964C2212yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#83948—51nomaximal, Hall
39C2×#4150—31no—
40C5×#535—31no—
41C22×#687—31no—
42C2×#4078D311yescharacteristic, complemented
43#65523—31no—
44#65329—34no—
45#65326—34no—
46#65293—31no—
47#65291—31no—
48C24×C3×C5—21no—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—21no—
55C2×Dic30—21no—
56C2×Dic30—22no—
57C2×Dic30D414yescomplemented
58C2×Dic30C2312yes—
59C2×C5×#67—24no—
60C2×C5×#67D412yes—
61C5×#235—22no—
62C5×#235—22no—
63C2×C5×D12D411yescharacteristic
64C2×C4×C5×D3C2312yes—
65C2×C5×Dic6D411yescharacteristic
66C2×C3×C22⋊D5—21no—
67C3×#709—22no—
68C3×#709D414yescomplemented
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72C2×#1204—22no—
73C2×#1201—22no—
74C2×D3×Dic5—22no—
75#6780—216no—
76C2×D5×Dic3—22no—
77#6772—28no—
78D3×Dic10—24no—
79D3×Dic10—24no—
80#6765—24no—
81#6765—24no—
82D5×Dic6—28no—
83#6716—28no—
84C2×C3⋊#168—22no—
85C2×C3⋊#168C2312yes—
86C5×#217—21no—
87C5×#217—24no—
88C5×C4⋊Dic3C2312yes—
89C4×C5×Dic3—21no—
90C3×#687—24no—
91C3×#686—24no—
92C3×#681—22no—
93C2×C3×#168C2312yes—
94C2×#1010—51no—
95C2×C3×AGL(1,ℤ/8)—51no—
96#5805D511yescharacteristic, complemented
97C22×#214—51no—
98#5233—51no—
99#5170—54no—
100#5158—54no—
101#5129—51no—
102#5120—51no—
103C2×C5×#41—31no—
104C22×C5×D4C2×D311yescharacteristic
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—61no—
108C2×#711—61no—
109C2×#711—62no—
110C2×#709—32no—
111C2×#709C2×D311yescharacteristic
112C22×Dic10—31no—
113C22×Dic10—32no—
114C5×#127—61no—
115C5×#124—61no—
116C5×#121—34no—
117C5×#120—62no—
118C5×#117—31no—
119C2×#687—34no—
120C2×#687—64no—
121C2×#687C2×D312yes—
122#4078—24no—
123C2×#686C2×D312yes—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126C22⋊#168—34no—
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3010—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×C5×D3C2×D412yes—
136C22×C3×D5—21no—
137C3×C5×D4—22no—
138C3×C5×D4—22no—
139C3×C5×D4—42no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—24no—
145C2×Dic15—22no—
146Dic30—24no—
147Dic30—22no—
148Dic30C2×D414yes—
149C5×#67—24no—
150C5×#67—84no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3C2×D412yes—
153C5×D12—22no—
154C4×C5×D3—22no—
155C4×C5×D3—22no—
156C5×Dic6—22no—
157C3×C22⋊D5—24no—
158C2×C3×Dic5—21no—
159C3×D20—21no—
160C3×D20C2×D412yes—
161C3×C4×D5—24no—
162C3×Dic10—21no—
163C3×Dic10C2×D412yes—
164#1204—28no—
165#1201—28no—
166D3×Dic5—28no—
167D5×Dic3—28no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×C3×#41—51no—
171C22×C3×D4C2×D511yescharacteristic
172#1010—104no—
173#1010—104no—
174C2×D3×Q8—52no—
175C2×#237—52no—
176C2×#237—102no—
177C2×#235—101no—
178C2×#235C2×D511yescharacteristic
179C22×Dic6—51no—
180C22×Dic6—101no—
181C3×AGL(1,ℤ/8)—104no—
182C2×C3×SD16—52no—
183C2×C3×D8—52no—
184C2×C3×M16—51no—
185#953—22no—
186#940—21no—
187#938C2×D514yes—
188#936—21no—
189C2×#214—54no—
190C2×#214—104no—
191#926C2×D511yescharacteristic
192C22×C3⋊C8—51no—
193#835—52no—
194#832—52no—
195(C2×D3)⋊C8—54no—
196#816—54no—
197C24×C5—21no—
198C5×#41—62no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—22no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—32no—
205C2×C5×D4—31no—
206C2×C5×D4—64no—
207C2×C5×D4C22×D312yes—
208C22×C4×C5—32no—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—21no—
211C2×C22⋊D5—62no—
212C22×Dic5—62no—
213C22×Dic5—61no—
214Q8×D5—68no—
215#711—68no—
216#711—616no—
217#709—22no—
218#709—64no—
219#709—64no—
220#709#6714yescomplemented
221C2×D20C22×D311yescharacteristic
222C2×C4×D5—21no—
223C2×C4×D5—62no—
224C2×Dic10—34no—
225C2×Dic10—32no—
226C2×Dic10—64no—
227C2×Dic10—62no—
228C2×Dic10—61no—
229C2×Dic10—62no—
230C2×Dic10—64no—
231C2×Dic10C22×D311yescharacteristic
232C5×C4⋊C4—32no—
233C5×C22⋊C4—64no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236#687—24no—
237#687—68no—
238#686—24no—
239#681—22no—
240C2×#168—32no—
241C2×#168—62no—
242C2×#168C22×D312yes—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—51no—
245C22×SD16—151no—
246#535—31no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—42no—
254C22×C3×C5—44no—
255C22×C3×C5—84no—
256C22×C3×C5#12012yes—
257C22×C3×C5C22×D411yescharacteristic
258C2×C5×D3—22no—
259C2×C5×D3—24no—
260C2×C3×D5—22no—
261C2×C3×D5—42no—
262C3×C4×C5#12012yes—
263C3×C4×C5C22×D411yescharacteristic
264C3×C4×C5C22×D411yescharacteristic
265Dic15—24no—
266C3×Dic5—22no—
267C5×Dic3—22no—
268C5×Dic3—42no—
269C24×C3—21no—
270C3×#41—54no—
271C3×#41—102no—
272C2×C3×Q8—51no—
273C2×C3×D4—22no—
274C2×C3×D4—22no—
275C2×C3×D4—21no—
276C2×C3×D4—51no—
277C2×C3×D4—101no—
278C2×C3×D4C22×D512yes—
279C22×C3×C4—101no—
280C22×C3×C4C22×D511yescharacteristic
281C2×#67—24no—
282C2×#67—102no—
283C2×#67C22⋊D512yes—
284C22×Dic3—101no—
285C22×Dic3—102no—
286D3×Q8—104no—
287D3×Q8—104no—
288#237—104no—
289#237—104no—
290#237—1016no—
291#235—22no—
292#235—22no—
293#235—108no—
294C2×D12C22⋊D511yescharacteristic
295C2×C4×D3—102no—
296C2×C4×D3C22×D512yes—
297C2×Dic6—54no—
298C2×Dic6—52no—
299C2×Dic6—108no—
300C2×Dic6—102no—
301C2×Dic6—101no—
302C2×Dic6—102no—
303C2×Dic6C22⋊D511yescharacteristic
304C3×SD16—104no—
305C3×D8—104no—
306C3×M16—102no—
307C2×C3×C8—52no—
308#217—21no—
309#217—24no—
310#214—108no—
311C4⋊Dic3C22×D512yes—
312C4×Dic3—21no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8—102no—
315C23×C5—22no—
316C23×C5—32no—
317C23×C5—42no—
318C23×C5—82no—
319C23×C5D3×D411yescharacteristic
320C22×D5—21no—
321C5×Q8—62no—
322C5×D4—22no—
323C5×D4—22no—
324C5×D4—42no—
325C5×D4—64no—
326C5×D4—62no—
327C5×D4—244no—
328C2×C4×C5—32no—
329C2×C4×C5—62no—
330C2×C4×C5—62no—
331C2×C4×C5—62no—
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5D3×D412yes—
334C2×C4×C5C2×#6712yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—24no—
337C22⋊D5—68no—
338C2×Dic5—21no—
339C2×Dic5—68no—
340C2×Dic5—64no—
341C2×Dic5—62no—
342D20—21no—
343D20C2×#6712yes—
344C4×D5—24no—
345C4×D5—68no—
346Dic10—21no—
347Dic10—34no—
348Dic10—68no—
349Dic10—64no—
350Dic10—62no—
351Dic10C2×#6712yes—
352#168—22no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—51no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4D3×D511yescharacteristic
365AGL(1,ℤ/8)—104no—
366C2×SD16—52no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—52no—
370C2×M16—51no—
371C22×C8—151no—
372#127—61no—
373#124—61no—
374#121—34no—
375#120—62no—
376#117—31no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—82no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385C3×D5—42no—
386C5×D3—42no—
387C23×C3—22no—
388C23×C3—42no—
389C23×C3—82no—
390C23×C3—101no—
391C23×C3C2×C22⋊D511yescharacteristic
392C22×D3C2×C22⋊D512yes—
393C3×Q8—52no—
394C3×Q8—101no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—42no—
398C3×D4—52no—
399C3×D4—104no—
400C3×D4—101no—
401C2×C3×C4—101no—
402C2×C3×C4—104no—
403C2×C3×C4D4×D512yes—
404C2×C3×C4D4×D512yes—
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C23×D511yescharacteristic
407#67—24no—
408#67—84no—
409#67—108no—
410C2×Dic3—22no—
411C2×Dic3—108no—
412C2×Dic3—102no—
413C2×Dic3—104no—
414C2×Dic3C2×C22⋊D512yes—
415D12—22no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—108no—
419Dic6—22no—
420Dic6—54no—
421Dic6—108no—
422Dic6—102no—
423Dic6—104no—
424C3×C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—44no—
428C22×C5—42no—
429C22×C5—64no—
430C22×C5—62no—
431C22×C5—84no—
432C22×C5#93712yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—22no—
435C2×D5—42no—
436C4×C5—62no—
437C4×C5—122no—
438C4×C5#93712yes—
439C4×C5C2×D3×D411yescharacteristic
440C4×C5C22×#6711yescharacteristic
441Dic5—22no—
442Dic5—64no—
443C24—21no—
444#41—54no—
445#41—62no—
446#41—62no—
447#41—102no—
448#41—304no—
449#41—304no—
450#41—308no—
451#41—3016no—
452C2×Q8—31no—
453C2×Q8—51no—
454C2×Q8—154no—
455C2×Q8—152no—
456C2×Q8—302no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—308no—
460C2×Q8—302no—
461C2×Q8—301no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—32no—
466C2×D4—31no—
467C2×D4—51no—
468C2×D4—64no—
469C2×D4—101no—
470C2×D4—302no—
471C2×D4C2×D3×D512yes—
472C22×C4—32no—
473C22×C4—101no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—104no—
479SD16—308no—
480D8—104no—
481M16—102no—
482C2×C8—52no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4—32no—
486C22⋊C4—64no—
487C22⋊C4—61no—
488C42—61no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—42no—
492C22×C3—44no—
493C22×C3—84no—
494C22×C3—102no—
495C22×C3—202no—
496C22×C3#408312yes—
497C22×C3C22×C22⋊D511yescharacteristic
498C2×D3—22no—
499C2×D3—24no—
500C3×C4—102no—
501C3×C4#408312yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—22no—
505Dic3—42no—
506Dic3—104no—
507C2×C5—22no—
508C2×C5—82no—
509C2×C5—122no—
510C2×C5#577512yes—
511C2×C5C2×#93711yescharacteristic
512D5—42no—
513C23—22no—
514C23—32no—
515C23—42no—
516C23—82no—
517C23—101no—
518C23D3×C22⋊D511yescharacteristic
519Q8—52no—
520Q8—62no—
521Q8—101no—
522Q8—154no—
523Q8—308no—
524Q8—302no—
525Q8—304no—
526D4—22no—
527D4—22no—
528D4—42no—
529D4—52no—
530D4—64no—
531D4—62no—
532D4—104no—
533D4—101no—
534D4—244no—
535D4—308no—
536C2×C4—32no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—101no—
541C2×C4—104no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—302no—
545C2×C4—304no—
546C2×C4D5×#6712yes—
547C2×C4D3×C22⋊D511yescharacteristic
548C2×C4#679012yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—302no—
552C2×C3—22no—
553C2×C3—82no—
554C2×C3—202no—
555C2×C3C2×#408311yescharacteristic
556C2×C3#6617012yes—
557D3—42no—
558C5#8394811yescharacteristic, complemented, Sylow
559C22—22no—
560C22—42no—
561C22—44no—
562C22—62no—
563C22—64no—
564C22—84no—
565C22—102no—
566C22—202no—
567C22#9157712yes—
568C22C2×D3×C22⋊D511yescharacteristic
569C4—62no—
570C4—102no—
571C4—122no—
572C4—304no—
573C4#9157712yes—
574C4C2×D5×#6711yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061512111yescharacteristic, complemented, Sylow
577C2—22no—
578C2—82no—
579C2—122no—
580C2—202no—
581C2#1175472012yes—
582C2C2×#9157711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#92001C2semidirect
2. C22×#6716C2semidirect
3. C5×#5805C2semidirect
4. C2×C3×#4078C2semidirect
5. #11749157C2semidirect
6. #11749155C2semidirect
7. #11748417C2semidirect
8. #11748364C2semidirect
9. #11748347C2semidirect
17. C2×D3×Dic10C22semidirect
20. C2×#6765C22semidirect
34. #90975C22semidirect
35. #90970C22semidirect
36. #90964C22semidirect
37. (C2×D3)⋊#168C22semidirect
42. C2×#4078D3semidirect
57. C2×Dic30D4semidirect
68. C3×#709D4semidirect
96. #5805D5semidirect
220. #709#67semidirect
489. C3×C5#3010semidirect
558. C5#83948semidirect
576. C3#10615121semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C22×#67162
C5×#58052
C2×C3×#40782
#117491572
#117491552
#117484172
#117483642
#117483472
#106151213
#839485