Finite Group Databasebeta

← #14412217

Subgroups — #14412217

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92000C211yesmaximal, characteristic
2C3×#66079C211yesmaximal, characteristic, complemented
3#11754120C211yesmaximal, characteristic, complemented
4#11751233C211yesmaximal, characteristic, complemented
5C2×C5×#824C211yesmaximal, characteristic, complemented
6C2×#90962C211yesmaximal, characteristic, complemented
7#11748357C211yesmaximal, characteristic, complemented
8#11748231C214yesmaximal, complemented
9D5×#824C214yesmaximal, complemented
10#10610437—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C2×#6779C414yes—
15C2×#6773C2212yes—
16C2×D15⋊Q8C412yes—
17#92000—22no—
18#92000—22no—
19#92000—22no—
20#92000—22no—
21C2×#6766C412yes—
22C2×D5×Dic6C2212yes—
23C2×C3×C5×M16C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25C2×C5×#208C2211yescharacteristic
26C2×C3×#681C2211yescharacteristic
27C3×#4053—22no—
28C3×D5×M16C2214yes—
29C3×#4047—22no—
30#91284—22no—
31#91283—22no—
32D5×#208C2214yes—
33#91108C2212yes—
34#91107C2212yes—
35C5×#824C2214yes—
36#90963C2212yes—
37#90962C2214yes—
38#90960C2212yes—
39#83815—51nomaximal, Hall
40C2×#4147—31no—
41#66079—31no—
42#66079D311yescharacteristic, complemented
43C2×C5×#101—31no—
44C2×#3968—31no—
45#65421—31no—
46#65421—31no—
47#65040—34no—
48D5×#101—34no—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220C2×C412yes—
51#6817—21no—
52#6817—21no—
53#6817—21no—
54#6817—21no—
55C2×D60C2311yescharacteristic
56C2×C4×D15C2×C412yes—
57C2×Dic30C2311yescharacteristic
58C22×C5×Dic3C2×C412yes—
59C2×C5×Dic6—21no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6—21no—
62C2×C5×Dic6—21no—
63C2×C5×Dic6C2×C412yes—
64C2×C5×Dic6C2312yes—
65C2×C3×C22⋊D5C2×C412yes—
66C3×#709D412yes—
67C3×#709D412yes—
68C3×#709D412yes—
69C3×#709D412yes—
70C2×C3×D20C2×C411yescharacteristic
71C2×C3×C4×D5C2312yes—
72C2×C3×Dic10C2×C411yescharacteristic
73C2×#1204C2×C414yes—
74C2×#1202C2×C414yes—
75C2×#1200C2×C414yes—
76#6779—28no—
77#6779—28no—
78C2×D5×Dic3C2×C414yes—
79#6773—24no—
80#6773—24no—
81D15⋊Q8—24no—
82D15⋊Q8—24no—
83#6766—24no—
84#6766—24no—
85D5×Dic6—24no—
86D5×Dic6—24no—
87C3×C5×M16—21no—
88C3×C5×M16C2312yes—
89C2×C3×C5×C8—21no—
90#6710—21no—
91#6710C2312yes—
92C2×C3⋊#168—21no—
93C5×#208—21no—
94C5×#208C2312yes—
95C2×C5×C3⋊C8—21no—
96C3×#681—21no—
97C3×#681C2312yes—
98C2×C3×#168—21no—
99C3×#676—24no—
100C3×C8×D5—24no—
101#6649—24no—
102D5×C3⋊C8—24no—
103C2×#1010—51no—
104C3×#568—51no—
105#5819—51no—
106C2×#824—51no—
107C2×#824—54no—
108C2×#824D511yescharacteristic, complemented
109#5132—51no—
110#5132—51no—
111#5132—54no—
112C22×C5×Q8—31no—
113#4147—62no—
114#4147—62no—
115#4147—62no—
116#4147—62no—
117C2×#713—32no—
118C2×#713—32no—
119C2×Q8×D5—32no—
120C2×Q8×D5—32no—
121C2×#709—31no—
122C2×#709—34no—
123C2×#709C2×D311yescharacteristic
124C2×C5×M16—31no—
125C2×C5×M16C2×D311yescharacteristic
126C2×#681—31no—
127C2×#681C2×D311yescharacteristic
128#4053—22no—
129#4053—62no—
130D5×M16—34no—
131D5×M16C2×D314yes—
132#4047—22no—
133#4047—62no—
134C5×#101—34no—
135#3968—34no—
136#3956—32no—
137#3956—32no—
138#3955—32no—
139#3955—32no—
140#2889—151noSylow
141C23×C3×C5C22×C411yescharacteristic
142C22×D15C22×C412yes—
143C22×C3×D5C22×C412yes—
144C2×C3×C4×C5C22×C411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150#1220—22no—
151#1220—22no—
152C2×Dic15C22×C412yes—
153D60—21no—
154D60—21no—
155C4×D15—22no—
156C4×D15—22no—
157Dic30—21no—
158Dic30—21no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3C22×C414yes—
162C5×Dic6—22no—
163C5×Dic6—22no—
164C5×Dic6—22no—
165C5×Dic6—22no—
166C3×C22⋊D5C22⋊C414yes—
167C3×C22⋊D5C22⋊C414yes—
168C2×C3×Dic5C22×C412yes—
169C3×D20C22⋊C412yes—
170C3×D20C22⋊C412yes—
171C3×C4×D5C2×D414yes—
172C3×C4×D5C2×D414yes—
173C3×Dic10C22⋊C412yes—
174C3×Dic10C22⋊C412yes—
175#1204—28no—
176#1202—28no—
177#1200—28no—
178D5×Dic3—28no—
179C3×C5×C8—22no—
180C3⋊#168—22no—
181C3×#168—22no—
182C5×C3⋊C8—22no—
183C2×C3×#41—51no—
184#1010—102no—
185#1010—102no—
186#1010—102no—
187#1010—102no—
188C2×D3×Q8—52no—
189C2×#237—54no—
190C2×#237—52no—
191C2×#235—51no—
192C2×#235—52no—
193C22×Dic6—52no—
194C22×Dic6C2×D511yescharacteristic
195C3×#131—102no—
196C3×#131—102no—
197C2×C3×M16—51no—
198C2×C3×M16—54no—
199C2×C3×M16C2×D511yescharacteristic
200#948—102no—
201#948—102no—
202C2×#208—51no—
203C2×#208—54no—
204C2×#208C2×D511yescharacteristic
205#824—54no—
206#824—52no—
207#824—52no—
208#824C2×D514yes—
209#823—52no—
210#823—52no—
211C2×C5×Q8—32no—
212C2×C5×Q8—32no—
213C2×C5×Q8—61no—
214C2×C5×Q8—61no—
215C2×C5×Q8—61no—
216C2×C5×Q8—61no—
217C22×C4×C5—32no—
218C22×C4×C5C22×D311yescharacteristic
219C2×C22⋊D5—32no—
220C2×C22⋊D5C4×D312yes—
221#713—64no—
222#713—64no—
223#713—64no—
224#713—64no—
225Q8×D5—64no—
226Q8×D5—64no—
227Q8×D5—64no—
228Q8×D5—64no—
229#709—61no—
230#709—61no—
231#709—61no—
232#709—61no—
233#709—68no—
234#709—68no—
235#709D1212yes—
236#709D1212yes—
237#709#6712yes—
238#709#6712yes—
239C2×D20—34no—
240C2×D20—31no—
241C2×D20C4×D311yescharacteristic
242C2×C4×D5—34no—
243C2×C4×D5—32no—
244C2×C4×D5—34no—
245C2×C4×D5C22×D312yes—
246C2×Dic10—31no—
247C2×Dic10—34no—
248C2×Dic10C4×D311yescharacteristic
249C5×M16—21no—
250C5×M16—32no—
251C5×M16—61no—
252C5×M16C22×D312yes—
253C2×C5×C8—21no—
254C2×C5×C8—61no—
255#681—21no—
256#681—32no—
257#681—61no—
258#681C22×D312yes—
259C2×#168—21no—
260C2×#168—61no—
261#676—24no—
262#676—64no—
263C8×D5—24no—
264C8×D5—64no—
265C2×2−1+4—151no—
266#568—51no—
267#568—151no—
268#413—154no—
269#413—151no—
270#413—151no—
271C2×#101—31no—
272C2×#101—154no—
273C2×#101—151no—
274C22×C3×C5—41no—
275C22×C3×C5C2×C22⋊C411yescharacteristic
276C22×C3×C5C2×C22⋊C411yescharacteristic
277C22×C3×C5C23×C411yescharacteristic
278C2×D15—22no—
279C2×D15—42no—
280C2×C3×D5—42no—
281C2×C3×D5C2×C22⋊C414yes—
282C3×C4×C5C2×C22⋊C411yescharacteristic
283C3×C4×C5C2×C22⋊C411yescharacteristic
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286Dic15—22no—
287C3×Dic5C2×C22⋊C414yes—
288C5×Dic3—24no—
289C3×#41—52no—
290C3×#41—52no—
291C3×#41—52no—
292C3×#41—52no—
293C2×C3×Q8—51no—
294C2×C3×D4—52no—
295C2×C3×D4—51no—
296C22×C3×C4—52no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—52no—
299C2×#67—54no—
300C22×Dic3—54no—
301C22×Dic3C4×D512yes—
302D3×Q8—104no—
303D3×Q8—104no—
304#237—104no—
305#237—104no—
306#237—108no—
307#237—108no—
308#235—104no—
309#235—104no—
310#235—101no—
311#235—101no—
312#235—101no—
313#235—101no—
314C2×D12—51no—
315C2×C4×D3—52no—
316C2×C4×D3—54no—
317C2×Dic6—21no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—51no—
322C2×Dic6—54no—
323C2×Dic6—104no—
324C2×Dic6—104no—
325C2×Dic6C4×D512yes—
326C2×Dic6C22×D512yes—
327C3×M16—21no—
328C3×M16—52no—
329C3×M16—104no—
330C3×M16—101no—
331C3×M16C22×D512yes—
332C2×C3×C8—21no—
333C2×C3×C8—104no—
334C2×C3×C8—101no—
335#208—21no—
336#208—52no—
337#208—104no—
338#208—101no—
339#208C22×D512yes—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—104no—
342C2×C3⋊C8—101no—
343C23×C5C2×C4×D311yescharacteristic
344C22×D5—32no—
345C22×D5C2×C4×D312yes—
346C5×Q8—62no—
347C5×Q8—62no—
348C5×Q8—62no—
349C5×Q8—62no—
350C2×C4×C5—34no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5C2×C4×D311yescharacteristic
354C2×C4×C5C2×D1211yescharacteristic
355C2×C4×C5C2×D1211yescharacteristic
356C2×C4×C5C2×#6711yescharacteristic
357C2×C4×C5C2×#6711yescharacteristic
358C2×C4×C5C23×D311yescharacteristic
359C22⋊D5—62no—
360C22⋊D5—62no—
361C22⋊D5(C2×D3)⋊C414yes—
362C22⋊D5(C2×D3)⋊C414yes—
363C2×Dic5—32no—
364C2×Dic5C2×C4×D312yes—
365D20—68no—
366D20—61no—
367D20—61no—
368D20(C2×D3)⋊C412yes—
369D20(C2×D3)⋊C412yes—
370C4×D5—68no—
371C4×D5—62no—
372C4×D5—62no—
373C4×D5—68no—
374C4×D5C2×D1214yes—
375C4×D5C2×#6714yes—
376Dic10—61no—
377Dic10—61no—
378Dic10—68no—
379Dic10(C2×D3)⋊C412yes—
380Dic10(C2×D3)⋊C412yes—
381C5×C8—22no—
382C5×C8—62no—
383#168—22no—
384#168—62no—
3852−1+4—302no—
3862−1+4—302no—
3872−1+4—302no—
3882−1+4—302no—
389C2×#41—51no—
390C2×#41—154no—
391C2×#41—152no—
392C2×#41—152no—
393C2×#41—151no—
394C22×Q8—31no—
395C22×Q8—152no—
396C22×Q8—152no—
397#131—102no—
398#131—102no—
399#131—302no—
400#131—302no—
401C2×M16—31no—
402C2×M16—51no—
403C2×M16—54no—
404C2×M16—154no—
405C2×M16—151no—
406C2×M16D3×D511yescharacteristic
407#101—34no—
408#101—152no—
409#101—154no—
410#101—152no—
411#100—152no—
412#100—152no—
413C2×C3×C5—21no—
414C2×C3×C5—21no—
415C2×C3×C5—21no—
416C2×C3×C5C22×C22⋊C411yescharacteristic
417D15—42no—
418C3×D5—24no—
419C23×C3—52no—
420C23×C3C2×C4×D511yescharacteristic
421C22×D3—52no—
422C3×Q8—52no—
423C3×Q8—52no—
424C3×D4—54no—
425C3×D4—54no—
426C3×D4—52no—
427C3×D4—52no—
428C2×C3×C4—52no—
429C2×C3×C4—54no—
430C2×C3×C4—54no—
431C2×C3×C4C2×C4×D511yescharacteristic
432C2×C3×C4D4×D511yescharacteristic
433C2×C3×C4D4×D511yescharacteristic
434C2×C3×C4D4×D511yescharacteristic
435C2×C3×C4D4×D511yescharacteristic
436C2×C3×C4C23×D511yescharacteristic
437#67—108no—
438#67—102no—
439#67—102no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—52no—
443C2×Dic3—108no—
444C2×Dic3C2×C4×D514yes—
445D12—101no—
446D12—101no—
447C4×D3—108no—
448C4×D3—102no—
449C4×D3—102no—
450Dic6—22no—
451Dic6—22no—
452Dic6—22no—
453Dic6—22no—
454Dic6—108no—
455Dic6—101no—
456Dic6—101no—
457C3×C8—22no—
458C3×C8—102no—
459C3⋊C8—22no—
460C3⋊C8—102no—
461C22×C5—41no—
462C22×C5C2×(C2×D3)⋊C411yescharacteristic
463C22×C5C2×(C2×D3)⋊C411yescharacteristic
464C22×C5C22×C4×D311yescharacteristic
465C2×D5—42no—
466C2×D5—62no—
467C2×D5—122no—
468C2×D5C2×(C2×D3)⋊C414yes—
469C4×C5—64no—
470C4×C5C2×(C2×D3)⋊C411yescharacteristic
471C4×C5C2×(C2×D3)⋊C411yescharacteristic
472C4×C5C22×D1211yescharacteristic
473C4×C5C22×#6711yescharacteristic
474Dic5—62no—
475Dic5C2×(C2×D3)⋊C414yes—
476#41—52no—
477#41—52no—
478#41—52no—
479#41—52no—
480#41—304no—
481#41—304no—
482#41—308no—
483#41—308no—
484#41—304no—
485#41—304no—
486#41—301no—
487#41—301no—
488#41—301no—
489#41—301no—
490C2×Q8—32no—
491C2×Q8—32no—
492C2×Q8—51no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—154no—
498C2×Q8—151no—
499C2×Q8—304no—
500C2×Q8—304no—
501C2×Q8—304no—
502C2×Q8—304no—
503C2×D4—52no—
504C2×D4—51no—
505C2×D4—154no—
506C2×D4—152no—
507C2×D4—151no—
508C22×C4—32no—
509C22×C4—52no—
510C22×C4—154no—
511C22×C4—154no—
512C22×C4—152no—
513C22×C4C2×D3×D511yescharacteristic
514M16—21no—
515M16—32no—
516M16—52no—
517M16—61no—
518M16—104no—
519M16—101no—
520M16—152no—
521M16—304no—
522M16—301no—
523M16C2×D3×D512yes—
524C2×C8—21no—
525C2×C8—61no—
526C2×C8—104no—
527C2×C8—101no—
528C2×C8—304no—
529C2×C8—301no—
530C3×C5#288911yescharacteristic, complemented, Hall
531C22×C3—41no—
532C22×C3—54no—
533C22×C3—202no—
534C22×C3D5×C22⋊C411yescharacteristic
535C22×C3D5×C22⋊C411yescharacteristic
536C22×C3C22×C4×D511yescharacteristic
537C2×D3—102no—
538C2×D3—202no—
539C3×C4—54no—
540C3×C4D5×C22⋊C411yescharacteristic
541C3×C4D5×C22⋊C411yescharacteristic
542C3×C4C2×D4×D511yescharacteristic
543C3×C4C2×D4×D511yescharacteristic
544Dic3—24no—
545Dic3—102no—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5—21no—
549C2×C5C22×(C2×D3)⋊C411yescharacteristic
550D5—24no—
551D5—122no—
552C23—52no—
553C23—152no—
554C23C4×D3×D511yescharacteristic
555Q8—52no—
556Q8—52no—
557Q8—62no—
558Q8—62no—
559Q8—62no—
560Q8—62no—
561Q8—308no—
562Q8—301no—
563Q8—301no—
564D4—54no—
565D4—54no—
566D4—52no—
567D4—52no—
568D4—308no—
569D4—302no—
570D4—302no—
571D4—301no—
572D4—301no—
573C2×C4—34no—
574C2×C4—52no—
575C2×C4—54no—
576C2×C4—54no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—152no—
580C2×C4—308no—
581C2×C4—308no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4C4×D3×D511yescharacteristic
585C2×C4D5×D1211yescharacteristic
586C2×C4D5×D1211yescharacteristic
587C2×C4D5×#6711yescharacteristic
588C2×C4D5×#6711yescharacteristic
589C2×C4C22×D3×D511yescharacteristic
590C8—22no—
591C8—62no—
592C8—102no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—104no—
598C2×C3C2×D5×C22⋊C411yescharacteristic
599D3—202no—
600C5#8381511yescharacteristic, complemented, Sylow
601C22—41no—
602C22—54no—
603C22—202no—
604C22—302no—
605C22—602no—
606C22D5×(C2×D3)⋊C411yescharacteristic
607C22D5×(C2×D3)⋊C411yescharacteristic
608C22C2×C4×D3×D511yescharacteristic
609C4—54no—
610C4—64no—
611C4—302no—
612C4D5×(C2×D3)⋊C411yescharacteristic
613C4D5×(C2×D3)⋊C411yescharacteristic
614C4C2×D5×D1211yescharacteristic
615C4C2×D5×#6711yescharacteristic
616C3#1061043711yescharacteristic, complemented, Sylow
617C2—21no—
618C2—21no—
619C2—21no—
620C2—104no—
621C2—602no—
622C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2C2×D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92000C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2889
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#66079C2semidirect
3. #11754120C2semidirect
4. #11751233C2semidirect
5. C2×C5×#824C2semidirect
6. C2×#90962C2semidirect
7. #11748357C2semidirect
8. #11748231C2semidirect
9. D5×#824C2semidirect
42. #66079D3semidirect
108. C2×#824D5semidirect
530. C3×C5#2889semidirect
600. C5#83815semidirect
616. C3#10610437semidirect

Maximal subgroups

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

subgroupindex
C2×#920002
C3×#660792
#117541202
#117512332
C2×C5×#8242
C2×#909622
#117483572
#117482312
D5×#8242
#106104373
#838155