Finite Group Databasebeta

← #14301116

Subgroups — #14301116

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6716C211yesmaximal, characteristic
2C2×#91333C211yesmaximal, characteristic, complemented
3C2×C5×#832C211yesmaximal, characteristic
4C3×#65510C211yesmaximal, characteristic
5C2×#90974C211yesmaximal, characteristic, complemented
6#11745979C211yesmaximal, characteristic, complemented
7#11745966C211yesmaximal, characteristic, complemented
8#10601006—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C2×#6716—22no—
12C2×#6716—22no—
13C2×#6716C414yescomplemented
14C22×C3⋊#168C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×C22⋊Dic5—21no—
18C2×C3×C22⋊Dic5—21no—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×#6669—21no—
22C2×Dic3×Dic5—21no—
23#91333—22no—
24#91333—22no—
25C5×#832—22no—
26#90974—22no—
27#69660—51nomaximal, Hall
28C22×#687—31no—
29C2×#4033—31no—
30C2×C5×#102—31no—
31#65510D311yescharacteristic
32C2×#3948—31no—
33#64770—31no—
34#64749—31no—
35C24×C3×C5—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C412yes—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30C2×C412yes—
48C2×Dic30D412yes—
49C2×Dic30D412yes—
50C22×C5×Dic3—21no—
51C22×C3×Dic5—21no—
52C22×C3×Dic5D411yescharacteristic
53C22×C3×Dic5D411yescharacteristic
54#6716—28no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168C2×C412yes—
58C5×C4⋊Dic3—21no—
59C5×C4⋊Dic3D412yes—
60C2×C5×C3⋊C8—21no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C3×C22⋊Dic5—42no—
64C3×C22⋊Dic5—42no—
65C3×C4⋊Dic5—21no—
66C3×C4⋊Dic5—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5—21no—
69#6669—24no—
70Dic3×Dic5—24no—
71C22×#214—51no—
72C2×C4×Dic6—51no—
73C3×#390—51no—
74C2×#832D511yescharacteristic
75C2×#810—51no—
76#4529—51no—
77#4524—51no—
78C22×C5×D4C2×D311yescharacteristic
79C22×Dic10—31no—
80C22×C5×C8—31no—
81C2×C5×C4⋊C4—31no—
82C2×C22⋊Dic5—21no—
83C2×C22⋊Dic5—21no—
84C2×#687—34no—
85C2×#687—62no—
86C2×#687—62no—
87C2×C4⋊Dic5C2×D311yescharacteristic
88C2×#683—61no—
89C2×C4×Dic5—61no—
90C2×C4×Dic5C2×D311yescharacteristic
91C22×#168—31no—
92#4033—62no—
93#4033—62no—
94C5×#102—62no—
95#3948—62no—
96#1880—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C3×C5×D4—22no—
106C3×C5×D4—22no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—22no—
117C2×Dic15—22no—
118Dic30—22no—
119Dic30—22no—
120Dic30—22no—
121Dic30C22⋊C414yescomplemented
122C2×C5×Dic3—22no—
123C2×C5×Dic3—41no—
124C2×C5×Dic3—41no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5SD1612yescomplemented
134C3⋊#168—22no—
135C5×C3⋊C8—41no—
136C22×C3×D4C2×D511yescharacteristic
137C22×Dic6—51no—
138C2×C3×C4⋊C4—51no—
139C2×C3×C22⋊C4—101no—
140C2×C3×C22⋊C4—101no—
141C2×C3×C42—51no—
142C2×#214—54no—
143C2×#214—102no—
144C2×#214—102no—
145C2×C4⋊Dic3C2×D511yescharacteristic
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—101no—
148C22×C3⋊C8—51no—
149C22×C3⋊C8C2×D511yescharacteristic
150C4×Dic6—102no—
151C4×Dic6—102no—
152#832—22no—
153#810—102no—
154C24×C5—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4C4×D312yes—
161C22×C4×C5—61no—
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—21no—
164C22×Dic5—61no—
165C22×Dic5#6711yescharacteristic
166C22×Dic5#6711yescharacteristic
167C2×Dic10—32no—
168C2×Dic10—32no—
169C2×Dic10—32no—
170C2×Dic10—61no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C2×C5×C8—61no—
174C2×C5×C8—61no—
175C2×C5×C8—61no—
176C5×C4⋊C4—32no—
177C5×C4⋊C4—61no—
178C22⋊Dic5—42no—
179C22⋊Dic5—42no—
180#687—68no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183#683—64no—
184C4×Dic5—21no—
185C4×Dic5—21no—
186C4×Dic5—64no—
187C2×#168—32no—
188C2×#168—61no—
189C2×#168—61no—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—31no—
194#390—51no—
195#340—151no—
196#336—151no—
197C22×C3×C5—42no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—81no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5C2×SD1611yescharacteristic
208C22×C3×C5#13511yescharacteristic
209C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
210C22×C3×C5#13711yescharacteristic
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—24no—
216C3×Dic5—22no—
217C3×Dic5—41no—
218C3×Dic5—81no—
219C5×Dic3—42no—
220C24×C3—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C4×D512yes—
227C22×C3×C4—51no—
228C22×C3×C4—51no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—101no—
233C2×Dic6—52no—
234C2×Dic6—52no—
235C2×Dic6—52no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6—101no—
239C3×C4⋊C4—101no—
240C3×C4⋊C4—101no—
241C3×C22⋊C4—202no—
242C3×C22⋊C4—202no—
243C3×C42—101no—
244C3×C42—101no—
245#214—108no—
246C4⋊Dic3—21no—
247C4⋊Dic3C22⋊D512yes—
248Dic3⋊C4—104no—
249C4×Dic3—104no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—52no—
254C2×C3⋊C8—101no—
255C2×C3⋊C8—101no—
256C23×C5—22no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5C2×#6711yescharacteristic
264C5×D4—22no—
265C5×D4—22no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—62no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23711yescharacteristic
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—41no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5#21412yescomplemented
289Dic10—34no—
290Dic10—62no—
291Dic10—62no—
292Dic10—62no—
293C5×C8—121no—
294#168—62no—
295C22×Q8—151no—
296C22×D4D3×D511yescharacteristic
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—31no—
301C22×C8—151no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—51no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—101no—
308C2×C22⋊C4—101no—
309C2×C42—51no—
310C2×C42—301no—
311#103—302no—
312#102—62no—
313C2×C3×C5—82no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5C4×SD1611yescharacteristic
316C2×C3×C5#44011yescharacteristic
317C2×C3×C5#44811yescharacteristic
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#46011yescharacteristic
320C2×C3×C5#46411yescharacteristic
321C23×C3—22no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3D4×D511yescharacteristic
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—41no—
332C3×D4—41no—
333C2×C3×C4—52no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—201no—
340C2×C3×C4—201no—
341C2×C3×C4—201no—
342C2×C3×C4C2×C4×D511yescharacteristic
343C2×C3×C4#70911yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4#71111yescharacteristic
347C2×C3×C4C2×C22⋊D511yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—102no—
352C2×Dic3—102no—
353C2×Dic3—102no—
354Dic6—54no—
355Dic6—102no—
356Dic6—102no—
357Dic6—102no—
358C3⋊C8—41no—
359C3⋊C8—102no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—42no—
363C22×C5—81no—
364C22×C5—81no—
365C22×C5—81no—
366C22×C5—81no—
367C22×C5C4×#6711yescharacteristic
368C22×C5#93211yescharacteristic
369C22×C5C2×#21411yescharacteristic
370C22×C5#93711yescharacteristic
371C22×C5#93811yescharacteristic
372C22×C5#95011yescharacteristic
373C22×C5#95111yescharacteristic
374C4×C5—122no—
375C4×C5D3×C22⋊C411yescharacteristic
376C4×C5#67⋊C411yescharacteristic
377C4×C5#88311yescharacteristic
378C4×C5#88411yescharacteristic
379Dic5—22no—
380Dic5—41no—
381Dic5—64no—
382Dic5—81no—
383C24—21no—
384C2×Q8—152no—
385C2×Q8—152no—
386C2×Q8—152no—
387C2×Q8—301no—
388C2×Q8—301no—
389C2×Q8—301no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4#120012yes—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—61no—
399C22×C4—101no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—152no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—32no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—101no—
413C4⋊C4—304no—
414C22⋊C4—202no—
415C22⋊C4—202no—
416C42—101no—
417C42—101no—
418C42—304no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3#402711yescharacteristic
428C22×C3#403011yescharacteristic
429C22×C3#405711yescharacteristic
430C22×C3#405811yescharacteristic
431C22×C3D5×SD1611yescharacteristic
432C22×C3#406111yescharacteristic
433C22×C3#408311yescharacteristic
434C3×C4—102no—
435C3×C4—201no—
436C3×C4—401no—
437C3×C4D5×C22⋊C411yescharacteristic
438C3×C4#402911yescharacteristic
439C3×C4C4×C22⋊D511yescharacteristic
440C3×C4#408411yescharacteristic
441Dic3—42no—
442Dic3—104no—
443C2×C5—82no—
444C2×C5#495611yescharacteristic
445C2×C5C4×#21411yescharacteristic
446C2×C5#501811yescharacteristic
447C2×C5#503711yescharacteristic
448C2×C5#504011yescharacteristic
449C2×C5#505411yescharacteristic
450C2×C5#507511yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23D5×#6711yescharacteristic
459Q8—154no—
460Q8—302no—
461Q8—302no—
462Q8—302no—
463D4—22no—
464D4—22no—
465D4—41no—
466D4—41no—
467C2×C4—52no—
468C2×C4—62no—
469C2×C4—101no—
470C2×C4—101no—
471C2×C4—101no—
472C2×C4—101no—
473C2×C4—101no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—201no—
477C2×C4—201no—
478C2×C4—201no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4#677911yescharacteristic
483C2×C4#678211yescharacteristic
484C2×C4C2×#120011yescharacteristic
485C2×C4D3×C22⋊D511yescharacteristic
486C2×C4#679011yescharacteristic
487C2×C4#679011yescharacteristic
488C8—121no—
489C8—302no—
490C2×C3—82no—
491C2×C3#6504611yescharacteristic
492C2×C3#6504711yescharacteristic
493C2×C3#6505111yescharacteristic
494C2×C3#6505611yescharacteristic
495C2×C3#6524511yescharacteristic
496C2×C3#6544711yescharacteristic
497C2×C3#6545911yescharacteristic
498C5#6966011yescharacteristic, complemented, Sylow
499C22—42no—
500C22—42no—
501C22—42no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22D5×#21411yescharacteristic
507C22#9148411yescharacteristic
508C22#9148911yescharacteristic
509C22#9149011yescharacteristic
510C22#9153311yescharacteristic
511C22#9155211yescharacteristic
512C22#9157711yescharacteristic
513C4—102no—
514C4—122no—
515C4—201no—
516C4—304no—
517C4—401no—
518C4#9155611yescharacteristic
519C4#9155711yescharacteristic
520C4#9156111yescharacteristic
521C4#9156211yescharacteristic
522C3#1060100611yescharacteristic, complemented, Sylow
523C2—82no—
524C2#1174899811yescharacteristic
525C2#1174900011yescharacteristic
526C2#1174900211yescharacteristic
527C2#1174900411yescharacteristic
528C2#1174915411yescharacteristic
529C2#1174915911yescharacteristic
530C2#1174952011yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91333C2semidirect
5. C2×#90974C2semidirect
6. #11745979C2semidirect
7. #11745966C2semidirect
13. C2×#6716C4semidirect
121. Dic30C22⋊C4semidirect
133. C2×C3×Dic5SD16semidirect
288. C2×Dic5#214semidirect
419. C3×C5#1880semidirect
498. C5#69660semidirect
522. C3#10601006semidirect

Maximal subgroups

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

subgroupindex
C22×#67162
C2×#913332
C2×C5×#8322
C3×#655102
C2×#909742
#117459792
#117459662
#106010063
#696605