Finite Group Databasebeta

← #14437816

Subgroups — #14437816

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2#11754615C211yesmaximal, characteristic, complemented
3#11751334C211yesmaximal, characteristic, complemented
4C5×#5233C211yesmaximal, characteristic, complemented
5#11749349C212yesmaximal, complemented
6#11749331C212yesmaximal, complemented
7#11749102C212yesmaximal, complemented
8#11749085C212yesmaximal, complemented
9#11748365C211yesmaximal, characteristic, complemented
10#11748364C211yesmaximal, characteristic, complemented
11C2×Dic5×C3⋊C8C211yesmaximal, characteristic, complemented
12#10610556—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C3×#4093C2211yescharacteristic
20C3×#4090C2211yescharacteristic
21C3×#4086C2211yescharacteristic
22C3×#4085—22no—
23C3×#4082C2211yescharacteristic
24C3×C4×C22⋊D5—22no—
25C2×C3×C4×Dic5C2211yescharacteristic
26#91574—22no—
27#91468C2212yes—
28C4×#1204—22no—
29#91388C2212yes—
30#91119C2212yes—
31#91116C2212yes—
32C5×#835C2212yes—
33C5×#832C2212yes—
34#90971C2212yes—
35#90970C2212yes—
36#90965C2212yes—
37#90964C2212yes—
38Dic5×C3⋊C8C2212yes—
39Dic5×C3⋊C8C2212yes—
40#83281—51nomaximal, Hall
41#66166D311yescharacteristic
42#65851—31no—
43C5×#416—31no—
44#65522—31no—
45#65402—31no—
46C2×C8×Dic5—31no—
47#65291—31no—
48#65089—32no—
49#65081—32no—
50#65057—32no—
51#65049—32no—
52C3×C5×#41—22no—
53C3×C5×#41—22no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×C3×C22⋊D5—21no—
60C2×C3×C22⋊D5—22no—
61C22×C3×Dic5D412yes—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10C2311yescharacteristic
67C2×#1204—22no—
68#6719—21no—
69C4⋊Dic15C2312yes—
70C4×Dic15—21no—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×C4⋊Dic3C2312yes—
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2312yes—
78C3×C22⋊Dic5—22no—
79C3×#685—22no—
80C3×#683—22no—
81C3×C4×Dic5D412yes—
82C3×C4×Dic5C2311yescharacteristic
83C3×C4×Dic5C2311yescharacteristic
84Dic3⋊Dic5—22no—
85#6669—22no—
86#6668—22no—
87C3×#532—51no—
88#5470—51no—
89#5233—51no—
90#5233—51no—
91#5233—51no—
92#5233D511yescharacteristic, complemented
93#5079—52no—
94#5070—52no—
95#5056—52no—
96#5056—52no—
97C2×C4×C3⋊C8—51no—
98C2×C5×#41C2×D311yescharacteristic
99C2×#709C2×D311yescharacteristic
100C22×C5×C8—31no—
101C5×#117—31no—
102#4093C2×D311yescharacteristic
103#4090C2×D311yescharacteristic
104#4086C2×D311yescharacteristic
105#4085—22no—
106#4082C2×D311yescharacteristic
107C4×C22⋊D5—22no—
108#4072—31no—
109C2×C4×Dic5C2×D311yescharacteristic
110C22×#168—31no—
111#4036—32no—
112#4034—32no—
113#4024—62no—
114C4×Dic10—62no—
115C5×#103—32no—
116C5×#102—32no—
117#3967—32no—
118#3964—32no—
119#3953—32no—
120#3948—32no—
121C8×Dic5—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3941—32no—
125#3131—151noSylow
126C23×C3×C5—21no—
127C23×C3×C5C2×D411yescharacteristic
128C22×C3×D5—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C3×C5×D4—21no—
132C3×C5×D4—21no—
133C3×C5×D4—42no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5#4112yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C2×C5×Dic3—22no—
142C3×C22⋊D5—42no—
143C3×C22⋊D5—44no—
144C2×C3×Dic5—24no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×D20—21no—
149C3×D20—21no—
150C3×C4×D5—42no—
151C3×Dic10—21no—
152C3×Dic10—21no—
153#1204—44no—
154C3⋊#168—22no—
155C5×C3⋊C8—22no—
156C2×C3×#41—51no—
157C2×C3×#41C2×D511yescharacteristic
158C3×C4⋊Q8—51no—
159C3×#127—51no—
160C3×#124—51no—
161C3×#124—51no—
162C3×#121—102no—
163C3×C4×D4—102no—
164C2×C3×C42—51no—
165#926—51no—
166#926C2×D511yescharacteristic
167#924—102no—
168C22×C3⋊C8—51no—
169C22×C3⋊C8C2×D511yescharacteristic
170#870—52no—
171#869—52no—
172C4×Dic6—102no—
173#835—52no—
174#835—52no—
175#835—52no—
176#835C2×D512yes—
177#832—52no—
178#832—52no—
179#832—52no—
180#832C2×D512yes—
181C4×C3⋊C8—52no—
182C4×C3⋊C8—52no—
183C5×#41—22no—
184C5×#41—22no—
185C2×C5×Q8C22×D311yescharacteristic
186C2×C5×D4—21no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—21no—
191C2×C22⋊D5—22no—
192C22×Dic5#6712yes—
193#709—22no—
194#709—22no—
195C2×D20C22×D311yescharacteristic
196C2×C4×D5—21no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—32no—
200C2×C5×C8—62no—
201C5×C4⋊C4—32no—
202C5×C22⋊C4—61no—
203C42×C5—61no—
204C22⋊Dic5—22no—
205C22⋊Dic5—61no—
206#685—22no—
207C4⋊Dic5—32no—
208C4⋊Dic5—62no—
209#683—22no—
210#683—62no—
211#683—62no—
212C4×Dic5—61no—
213C4×Dic5#6712yes—
214C4×Dic5C22×D311yescharacteristic
215C4×Dic5C22×D311yescharacteristic
216C2×#168—32no—
217C2×#168—62no—
218#533—151no—
219#532—51no—
220#488—152no—
221#488—152no—
222#487—152no—
223#486—152no—
224#416—31no—
225#416—151no—
226#416—151no—
227#416—151no—
228C2×C4×C8—151no—
229C22×C3×C5—22no—
230C22×C3×C5—41no—
231C22×C3×C5—42no—
232C22×C3×C5#12412yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×C3×D5—41no—
235C2×C3×D5—42no—
236C3×C4×C5—41no—
237C3×C4×C5#12412yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—42no—
241C3×Dic5—22no—
242C3×Dic5—41no—
243C3×Dic5#13514yes—
244C5×Dic3—42no—
245C3×#41—22no—
246C3×#41—22no—
247C3×#41—102no—
248C3×#41—102no—
249C2×C3×Q8—51no—
250C2×C3×Q8C22×D511yescharacteristic
251C2×C3×D4—21no—
252C2×C3×D4—51no—
253C2×C3×D4—102no—
254C2×C3×D4—101no—
255C2×C3×D4C22×D511yescharacteristic
256C22×C3×C4—21no—
257C22×C3×C4—52no—
258C22×C3×C4—101no—
259C22×C3×C4C22×D511yescharacteristic
260C2×Dic6—102no—
261C3×C4⋊C4—102no—
262C3×C22⋊C4—102no—
263C3×C22⋊C4—102no—
264C3×C42—52no—
265C3×C42—51no—
266C3×C42—51no—
267#217—21no—
268#217—101no—
269C4⋊Dic3—52no—
270C4⋊Dic3—102no—
271C4⋊Dic3C22×D512yes—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275C4×Dic3—101no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—102no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—21no—
281C23×C5C2×#6711yescharacteristic
282C22×D5—21no—
283C5×Q8—21no—
284C5×Q8—21no—
285C5×D4—21no—
286C5×D4—21no—
287C5×D4—42no—
288C2×C4×C5—21no—
289C2×C4×C5—42no—
290C2×C4×C5—62no—
291C2×C4×C5#23712yes—
292C2×C4×C5#23712yes—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—42no—
296C22⋊D5—44no—
297C2×Dic5—24no—
298C2×Dic5—21no—
299C2×Dic5—62no—
300C2×Dic5C2×#6712yes—
301C2×Dic5C2×#6712yes—
302D20—21no—
303D20—21no—
304C4×D5—42no—
305Dic10—21no—
306Dic10—21no—
307Dic10—124no—
308C5×C8—62no—
309#168—62no—
310C2×#41—51no—
311C2×#41D3×D511yescharacteristic
312C22×C8—31no—
313C22×C8—151no—
314C4⋊Q8—51no—
315C4⋊Q8—152no—
316#127—51no—
317#125—152no—
318#124—51no—
319#124—51no—
320C22⋊Q8—302no—
321#121—102no—
322C4×Q8—302no—
323C4×D4—102no—
324#117—31no—
325#117—151no—
326C2×C42—51no—
327#103—32no—
328#103—152no—
329#103—152no—
330#103—152no—
331#102—32no—
332#102—152no—
333#102—152no—
334#102—152no—
335C4×C8—152no—
336C4×C8—152no—
337C2×C3×C5—22no—
338C2×C3×C5—81no—
339C2×C3×C5C2×#12411yescharacteristic
340C2×C3×C5C2×#13512yes—
341C3×D5—81no—
342C23×C3—21no—
343C23×C3—101no—
344C23×C3D4×D511yescharacteristic
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—101no—
348C3×Q8—101no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—42no—
352C3×D4—101no—
353C3×D4—101no—
354C3×D4—204no—
355C3×D4—202no—
356C2×C3×C4—21no—
357C2×C3×C4—42no—
358C2×C3×C4—52no—
359C2×C3×C4—52no—
360C2×C3×C4—104no—
361C2×C3×C4—101no—
362C2×C3×C4—202no—
363C2×C3×C4#70912yes—
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4#71112yes—
366C2×C3×C4C23×D511yescharacteristic
367C2×Dic3—22no—
368C2×Dic3—102no—
369Dic6—204no—
370C3⋊C8—22no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—42no—
375C22×C5#93612yes—
376C22×C5C22×#6711yescharacteristic
377C2×D5—41no—
378C2×D5—42no—
379C4×C5—41no—
380C4×C5—122no—
381C4×C5#93612yes—
382C4×C5C2×#23711yescharacteristic
383C4×C5C2×#23711yescharacteristic
384Dic5—22no—
385Dic5—41no—
386Dic5—122no—
387Dic5#95014yes—
388#41—22no—
389#41—22no—
390#41—102no—
391#41—102no—
392C2×Q8—51no—
393C2×Q8—302no—
394C2×Q8C2×D3×D511yescharacteristic
395C2×D4—21no—
396C2×D4—51no—
397C2×D4—102no—
398C2×D4—101no—
399C2×D4C2×D3×D511yescharacteristic
400C22×C4—21no—
401C22×C4—52no—
402C22×C4—101no—
403C22×C4C2×D3×D511yescharacteristic
404C2×C8—32no—
405C2×C8—62no—
406C2×C8—152no—
407C2×C8—302no—
408C4⋊C4—32no—
409C4⋊C4—102no—
410C4⋊C4—152no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C22⋊C4—61no—
415C22⋊C4—102no—
416C22⋊C4—102no—
417C22⋊C4—301no—
418C42—52no—
419C42—51no—
420C42—51no—
421C42—61no—
422C42—301no—
423C3×C5#313111yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—41no—
426C22×C3—42no—
427C22×C3—201no—
428C22×C3—202no—
429C22×C3#403112yes—
430C22×C3C2×D4×D511yescharacteristic
431C3×C4—41no—
432C3×C4—54no—
433C3×C4—102no—
434C3×C4—201no—
435C3×C4#403112yes—
436C3×C4C2×#70911yescharacteristic
437C3×C4C2×#71111yescharacteristic
438Dic3—42no—
439Dic3—202no—
440C2×C5—22no—
441C2×C5—81no—
442C2×C5C2×#93611yescharacteristic
443C2×C5C2×#95012yes—
444D5—81no—
445C23—21no—
446C23—101no—
447C23D5×#6711yescharacteristic
448Q8—21no—
449Q8—21no—
450Q8—101no—
451Q8—101no—
452Q8—604no—
453D4—21no—
454D4—21no—
455D4—42no—
456D4—101no—
457D4—101no—
458D4—204no—
459D4—202no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—52no—
463C2×C4—52no—
464C2×C4—62no—
465C2×C4—104no—
466C2×C4—101no—
467C2×C4—202no—
468C2×C4—302no—
469C2×C4#677912yes—
470C2×C4#678012yes—
471C2×C4D5×#6711yescharacteristic
472C2×C4C22×D3×D511yescharacteristic
473C8—62no—
474C8—302no—
475C2×C3—22no—
476C2×C3—81no—
477C2×C3—401no—
478C2×C3C2×#403111yescharacteristic
479C2×C3D5×#13512yes—
480C5#8328111yescharacteristic, complemented, Sylow
481C22—22no—
482C22—42no—
483C22—41no—
484C22—202no—
485C22—201no—
486C22#9153412yes—
487C22C2×D5×#6711yescharacteristic
488C4—41no—
489C4—54no—
490C4—102no—
491C4—122no—
492C4—201no—
493C4—602no—
494C4#9153412yes—
495C4C2×#677911yescharacteristic
496C4C2×#678011yescharacteristic
497C3#1061055611yescharacteristic, complemented, Sylow
498C2—22no—
499C2—81no—
500C2—401no—
501C2D5×#95012yes—
502C2C2×#9153411yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC3×#66166C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754615C2semidirect
3. #11751334C2semidirect
4. C5×#5233C2semidirect
5. #11749349C2semidirect
6. #11749331C2semidirect
7. #11749102C2semidirect
8. #11749085C2semidirect
9. #11748365C2semidirect
10. #11748364C2semidirect
11. C2×Dic5×C3⋊C8C2semidirect
92. #5233D5semidirect
423. C3×C5#3131semidirect
480. C5#83281semidirect
497. C3#10610556semidirect

Maximal subgroups

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

subgroupindex
C3×#661662
#117546152
#117513342
C5×#52332
#117493492
#117493312
#117491022
#117490852
#117483652
#117483642
C2×Dic5×C3⋊C82
#106105563
#832815