Finite Group Databasebeta

← #14328951

Subgroups — #14328951

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91360C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C2×#91333C211yesmaximal, characteristic, complemented
4#11751030C211yesmaximal, characteristic, complemented
5C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic
7#11748842C211yesmaximal, characteristic, complemented
8#11748712C212yesmaximal
9#11748705C212yesmaximal
10#11748667C212yesmaximal, complemented
11#11748659C212yesmaximal, complemented
12#10605378—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C2×C3×C42×C5C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C4×C5×Dic3C2212yes—
20C2×C3×#685C2211yescharacteristic
21C2×C3×#685C2211yescharacteristic
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×Dic3⋊Dic5C2212yes—
24C2×Dic3⋊Dic5C2212yes—
25C2×#6669C2212yes—
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30#91360C418yescomplemented
31#91358—24no—
32#91333—24no—
33#91115C2212yes—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#3963C2211yescharacteristic
38#90994C2212yes—
39#73468—51nomaximal, Hall
40C2×#4043—31no—
41C2×#4038—31no—
42C2×#4033—31no—
43C4×C5×C4⋊C4—31no—
44#65274—31no—
45#65229—32no—
46C4×#685D311yescharacteristic
47C4×C4⋊Dic5—32no—
48#65218—31no—
49#64959—32no—
50#64942—32no—
51C23×C3×D5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C2×Dic30—22no—
58C2×Dic30—22no—
59C2×Dic30C2×C414yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yes—
68C3×C42×C5—22no—
69C4⋊Dic15—22no—
70C5×C4⋊Dic3C2×C414yes—
71C5×C4⋊Dic3D414yes—
72C4×C5×Dic3—24no—
73C3×#685—22no—
74C3×#685—22no—
75C3×C4×Dic5—22no—
76Dic3⋊Dic5—24no—
77Dic3⋊Dic5C2×C418yes—
78#6669—24no—
79#6665—24no—
80#6665C2×C418yes—
81Dic3×Dic5—24no—
82Dic3×Dic5—24no—
83C2×#926—51no—
84C2×#924—51no—
85C2×C4×Dic6—51no—
86C3×C4×C22⋊C4—51no—
87#4945—52no—
88#4944—52no—
89C4×C4⋊Dic3D511yescharacteristic, complemented
90#4929—51no—
91#4928—51no—
92#4652—52no—
93#4649—52no—
94C22×C4×D5C2×D311yescharacteristic
95C22×Dic10—31no—
96C2×C5×C4⋊C4—31no—
97C2×C5×C4⋊C4—31no—
98C2×C42×C5—32no—
99C2×C42×C5C2×D311yescharacteristic
100C2×#685—32no—
101C2×#685—32no—
102C2×#685C2×D311yescharacteristic
103C2×#685C2×D311yescharacteristic
104C2×C4⋊Dic5—32no—
105C2×C4⋊Dic5—31no—
106C2×C4⋊Dic5—32no—
107C2×#683—32no—
108C2×C4×Dic5—32no—
109C2×C4×Dic5—32no—
110C2×C4×Dic5C2×D311yescharacteristic
111#4043—38no—
112#4038—64no—
113#4033—64no—
114C5×#95—32no—
115#3963—32no—
116#3963—32no—
117#3963—32no—
118#3963C2×D311yescharacteristic
119#3963C2×D311yescharacteristic
120#2362—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—21no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5—21no—
126C22×C3×D5—21no—
127C22×C3×D5—21no—
128C22×C3×D5C22×C412yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5#4112yes—
137C2×C3×C4×C5#4112yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15C22×C414yes—
144Dic30—28no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C22×C414yes—
150C2×C5×Dic3C2×D414yes—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5C22×C412yes—
159C2×C3×Dic5#4112yes—
160C3×C4×D5—28no—
161C23×C3×C4—51no—
162C22×Dic6—51no—
163C2×C3×C22⋊C4—51no—
164C2×C3×C22⋊C4—51no—
165C2×C3×C42—51no—
166C2×C3×C42C2×D511yescharacteristic
167C2×#217—52no—
168C2×#217—52no—
169#926—104no—
170C2×C4⋊Dic3—51no—
171C2×C4⋊Dic3C2×D511yescharacteristic
172C2×C4⋊Dic3C2×D511yescharacteristic
173#924—58no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—52no—
179C2×C4×Dic3C2×D512yes—
180C4×Dic6—104no—
181C3×#95—51no—
182C3×#95—51no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C3⋊#95C2×D512yes—
187C23×D5C22×D311yescharacteristic
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5C22×D311yescharacteristic
196C22×Dic5C22×D311yescharacteristic
197C22×Dic5C22×D311yescharacteristic
198C2×C4×D5—22no—
199C2×C4×D5—22no—
200C2×C4×D5C4×D314yes—
201C2×Dic10—34no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C5×C4⋊C4—34no—
205C5×C4⋊C4—34no—
206C42×C5—22no—
207C42×C5—64no—
208#685—22no—
209#685—22no—
210#685—38no—
211#685—64no—
212C4⋊Dic5—38no—
213C4⋊Dic5—62no—
214C4⋊Dic5—64no—
215#683—64no—
216C4×Dic5—22no—
217C4×Dic5—64no—
218C4×Dic5—64no—
219C2×C22⋊Q8—151no—
220C2×C4×Q8—151no—
221C2×#117—151no—
222#391—151no—
223#389—151no—
224#388—152no—
225#388—152no—
226#387—152no—
227C4×C4⋊C4—31no—
228C4×C4⋊C4—152no—
229C4×C22⋊C4—51no—
230C22×C3×C5C23×C411yescharacteristic
231C22×C3×C5C22×D411yescharacteristic
232C22×C3×C5C2×#4111yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C52−1+411yescharacteristic
236C22×C3×C52−1+411yescharacteristic
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—41no—
241C2×C3×D5—41no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—22no—
245C3×C4×C5—41no—
246C3×C4×C5C4×D414yes—
247Dic15—24no—
248Dic15—42no—
249C3×Dic5—22no—
250C3×Dic5—22no—
251C3×Dic5—41no—
252C5×Dic3—24no—
253C5×Dic3—24no—
254C24×C3—51no—
255C22×C3×C4—51no—
256C22×C3×C4—51no—
257C22×C3×C4—54no—
258C22×C3×C4—51no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D511yescharacteristic
264C22×Dic3—52no—
265C22×Dic3—52no—
266C22×Dic3C22×D512yes—
267C22×Dic3C22×D512yes—
268C2×Dic6—54no—
269C2×Dic6—102no—
270C2×Dic6—102no—
271C3×C22⋊C4—102no—
272C3×C22⋊C4—102no—
273C3×C42—22no—
274C3×C42—102no—
275#217—58no—
276#217—104no—
277C4⋊Dic3—102no—
278C4⋊Dic3C4×D514yes—
279C4⋊Dic3D2014yes—
280Dic3⋊C4—58no—
281Dic3⋊C4—104no—
282Dic3⋊C4—104no—
283C4×Dic3—24no—
284C4×Dic3—104no—
285C4×Dic3—104no—
286C23×C5C23×D311yescharacteristic
287C22×D5—21no—
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—21no—
293C22×D5C2×C4×D312yes—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—34no—
300C2×C4×C5—34no—
301C2×C4×C5—62no—
302C2×C4×C5—62no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5C2×C4×D312yes—
306C2×C4×C5#23512yes—
307C2×C4×C5D3×D412yes—
308C2×C4×C5#23712yes—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—34no—
317C2×Dic5—62no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5C2×C4×D312yes—
323C2×Dic5#23512yes—
324C4×D5—28no—
325Dic10—68no—
326C22×Q8—151no—
327C23×C4—51no—
328C22⋊Q8—158no—
329C4×Q8—304no—
330#117—304no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—152no—
334C2×C4⋊C4—152no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—151no—
337C2×C22⋊C4—51no—
338C2×C22⋊C4—51no—
339C2×C22⋊C4—152no—
340C2×C22⋊C4—152no—
341C2×C42—32no—
342C2×C42—51no—
343C2×C42—152no—
344C2×C42—152no—
345C2×C42D3×D511yescharacteristic
346#95—32no—
347#95—51no—
348#95—51no—
349#95—152no—
350#95—152no—
351#95—152no—
352C2×C3×C5C2×C4×D411yescharacteristic
353C2×C3×C5C4×#4111yescharacteristic
354C2×C3×C5#51911yescharacteristic
355C2×C3×C5#54711yescharacteristic
356C2×C3×C5#54811yescharacteristic
357C2×C3×C5#55211yescharacteristic
358C2×C3×C5#55611yescharacteristic
359C3×D5—42no—
360C23×C3—52no—
361C23×C3—101no—
362C23×C3—101no—
363C23×C3—101no—
364C23×C3—101no—
365C23×C3—101no—
366C23×C3—101no—
367C23×C3C23×D511yescharacteristic
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—52no—
374C2×C3×C4—52no—
375C2×C3×C4—101no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4—101no—
379C2×C3×C4—108no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—101no—
383C2×C3×C4C2×C4×D512yes—
384C2×C3×C4C2×D2012yes—
385C2×C3×C4#70912yes—
386C2×C3×C4#71112yes—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—54no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3C2×C4×D514yes—
398C2×Dic3C2×D2014yes—
399Dic6—108no—
400C22×C5C22×C4×D311yescharacteristic
401C22×C5C2×#23511yescharacteristic
402C22×C5C2×#23511yescharacteristic
403C22×C5C2×D3×D411yescharacteristic
404C22×C5C2×#23711yescharacteristic
405C22×C5#101011yescharacteristic
406C22×C5#101011yescharacteristic
407C2×D5—22no—
408C2×D5—22no—
409C2×D5—22no—
410C2×D5—41no—
411C2×D5—41no—
412C2×D5—41no—
413C2×D5—41no—
414C4×C5—22no—
415C4×C5—41no—
416C4×C5—64no—
417C4×C5—64no—
418C4×C5#67⋊C414yes—
419Dic5—22no—
420Dic5—22no—
421Dic5—41no—
422Dic5—64no—
423Dic5—122no—
424C24—51no—
425C2×Q8—154no—
426C2×Q8—302no—
427C2×Q8—302no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—54no—
433C22×C4—51no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4C2×D3×D511yescharacteristic
439C22×C4C2×D3×D511yescharacteristic
440C22×C4C2×D3×D511yescharacteristic
441C4⋊C4—34no—
442C4⋊C4—34no—
443C4⋊C4—158no—
444C4⋊C4—304no—
445C4⋊C4—304no—
446C4⋊C4—302no—
447C22⋊C4—102no—
448C22⋊C4—102no—
449C22⋊C4—158no—
450C22⋊C4—304no—
451C42—22no—
452C42—64no—
453C42—102no—
454C42—304no—
455C42—304no—
456C3×C5#236211yescharacteristic, complemented, Hall
457C22×C3—102no—
458C22×C3—102no—
459C22×C3—102no—
460C22×C3—201no—
461C22×C3—201no—
462C22×C3—201no—
463C22×C3—201no—
464C22×C3C22×C4×D511yescharacteristic
465C22×C3C22×D2011yescharacteristic
466C22×C3C2×#70911yescharacteristic
467C22×C3C2×#71111yescharacteristic
468C22×C3#414711yescharacteristic
469C22×C3D5×#4111yescharacteristic
470C22×C3#415011yescharacteristic
471C3×C4—22no—
472C3×C4—41no—
473C3×C4—102no—
474C3×C4—102no—
475C3×C4—201no—
476C3×C4C4×D2014yes—
477Dic3—24no—
478Dic3—24no—
479Dic3—104no—
480Dic3—202no—
481C2×C5C4×#23511yescharacteristic
482C2×C5C2×#67⋊C411yescharacteristic
483C2×C5#551611yescharacteristic
484C2×C5#554111yescharacteristic
485C2×C5#554211yescharacteristic
486C2×C5#555111yescharacteristic
487C2×C5#555211yescharacteristic
488D5—42no—
489C23—52no—
490C23—101no—
491C23—101no—
492C23—101no—
493C23—101no—
494C23—101no—
495C23—101no—
496C23C22×D3×D511yescharacteristic
497Q8—308no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—52no—
506C2×C4—52no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—101no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—108no—
516C2×C4—101no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—154no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4#677212yes—
526C2×C4C4×D3×D512yes—
527C2×C4D3×D2012yes—
528C2×C4#677912yes—
529C2×C3—202no—
530C2×C3C2×C4×D2011yescharacteristic
531C2×C3#6584711yescharacteristic
532C2×C3#6586711yescharacteristic
533C2×C3C4×#71111yescharacteristic
534C2×C3#6588911yescharacteristic
535C2×C3#6590611yescharacteristic
536C2×C3#6591011yescharacteristic
537C5#7346811yescharacteristic, complemented, Sylow
538C22—102no—
539C22—102no—
540C22—102no—
541C22—201no—
542C22—201no—
543C22—201no—
544C22—201no—
545C22#9200011yescharacteristic
546C22#9200111yescharacteristic
547C22C2×#677211yescharacteristic
548C22C2×C4×D3×D511yescharacteristic
549C22C2×D3×D2011yescharacteristic
550C22D5×#23511yescharacteristic
551C22C2×#677911yescharacteristic
552C4—22no—
553C4—41no—
554C4—64no—
555C4—64no—
556C4—102no—
557C4—102no—
558C4—201no—
559C4—304no—
560C4—602no—
561C4#9139514yes—
562C3#1060537811yescharacteristic, complemented, Sylow
563C2—202no—
564C2#1175251611yescharacteristic
565C2#1175254111yescharacteristic
566C2C4×#677211yescharacteristic
567C2#1175267611yescharacteristic
568C2#1175423011yescharacteristic
569C2#1175424411yescharacteristic
570C2C2×#9139511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2362
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#91333C2semidirect
4. #11751030C2semidirect
5. C4×C5×C4⋊Dic3C2semidirect
7. #11748842C2semidirect
10. #11748667C2semidirect
11. #11748659C2semidirect
30. #91360C4semidirect
89. C4×C4⋊Dic3D5semidirect
456. C3×C5#2362semidirect
537. C5#73468semidirect
562. C3#10605378semidirect

Maximal subgroups

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

subgroupindex
C2×#913602
C2×#913582
C2×#913332
#117510302
C4×C5×C4⋊Dic32
C3×C4×#6852
#117488422
#117487122
#117487052
#117486672
#117486592
#106053783
#734685