Finite Group Databasebeta

← #14299482

Subgroups — #14299482

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91358C211yesmaximal, characteristic
2C2×#91102C211yesmaximal, characteristic, complemented
3C2×C3×#3952C211yesmaximal, characteristic
4#11748759C211yesmaximal, characteristic
5C2×#90985C211yesmaximal, characteristic, complemented
6C5×#4551C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10599670—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6665—21no—
17C2×#6665—21no—
18C2×Dic3×Dic5—21no—
19#91358—22no—
20#91358—22no—
21#91102—22no—
22C3×#3952C414yescomplemented
23#90994—21no—
24#90985—22no—
25#69929—51nomaximal, Hall
26C2×#4038—31no—
27C2×#3952D311yescharacteristic
28C2×#3950—31no—
29#65276—31no—
30C2×#3940—31no—
31C5×#340—31no—
32#64749—31no—
33C23×C3×D5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C22×Dic15—21no—
37C22×C5×Dic3—21no—
38C22×C5×Dic3—21no—
39C22×C3×Dic5D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C412yes—
45C2×C3×C4×D5Q812yes—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8C2×C412yes—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D412yes—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3D412yes—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168C2×C412yes—
60#6665—24no—
61#6665—42no—
62Dic3×Dic5—24no—
63C2×#926—51no—
64C2×C3×C22⋊C8—51no—
65#5212—51no—
66C2×#818—51no—
67C2×#817—51no—
68#4551—51no—
69#4551D511yescharacteristic, complemented
70C22×C4×D5C2×D311yescharacteristic
71C22×C5×C8C2×D311yescharacteristic
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4—31no—
74C2×#685—61no—
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—31no—
78C2×C4×Dic5—61no—
79C22×#168C2×D311yescharacteristic
80#4038—62no—
81#4038—62no—
82#3963—61no—
83#3952Dic314yescomplemented
84#3950—62no—
85#3940—62no—
86#1854—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5—21no—
89C22×C3×D5—21no—
90C22×C3×D5—21no—
91C22×C3×D5—21no—
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5C4⋊C412yes—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×Q811yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×Dic15—22no—
102C2×Dic15—41no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5C4⋊C412yes—
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×C5×C8—22no—
121C3×#168—22no—
122C23×C3×C4—51no—
123C22×C3×C8—51no—
124C22×C3×C8C2×D511yescharacteristic
125C2×#217—101no—
126C2×#217—101no—
127#926—102no—
128#926—102no—
129C2×C4⋊Dic3—51no—
130C2×C4⋊Dic3—51no—
131C2×C4⋊Dic3C2×D511yescharacteristic
132C2×C4⋊Dic3C2×D511yescharacteristic
133C2×C4×Dic3—101no—
134C3×C22⋊C8—54no—
135C3⋊#95—101no—
136#818—102no—
137#817—102no—
138C23×D5D1211yescharacteristic
139C22×C4×C5—61no—
140C22×C4×C5—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—61no—
143C22×Dic5—61no—
144C22×Dic5D1211yescharacteristic
145C2×C4×D5—21no—
146C2×C4×D5—21no—
147C2×C4×D5—21no—
148C2×C4×D5—21no—
149C2×C4×D5Dic612yes—
150C2×C4×D5C2×Dic312yes—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8C2×Dic312yes—
154C5×C4⋊C4—32no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4—61no—
157C5×C4⋊C4—61no—
158#685—64no—
159#685—122no—
160C4⋊Dic5—32no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163C4⋊Dic5—61no—
164C4×Dic5—64no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168C2×Dic312yes—
168C2×#117—151no—
169C2×#107—151no—
170C2×#106—151no—
171C2×C22⋊C8—51no—
172#380—151no—
173#340—31no—
174#340—151no—
175C22×C3×C5C2×C4⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5#13711yescharacteristic
182C2×C3×D5—22no—
183C2×C3×D5—22no—
184C2×C3×D5—22no—
185C2×C3×D5—41no—
186C2×C3×D5—41no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193Dic15—42no—
194Dic15—81no—
195C3×Dic5—22no—
196C5×Dic3—42no—
197C5×Dic3—81no—
198C24×C3—51no—
199C22×C3×C4—51no—
200C22×C3×C4—52no—
201C22×C3×C4—52no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4C22×D511yescharacteristic
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—101no—
210C22×Dic3—101no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—52no—
214C2×C3×C8—101no—
215C2×C3×C8—101no—
216C2×C3×C8C4×D512yes—
217#217—104no—
218#217—202no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—52no—
223C4⋊Dic3—101no—
224C4⋊Dic3—101no—
225C4⋊Dic3—101no—
226C4⋊Dic3D2012yes—
227C4×Dic3—104no—
228C23×C5C2×D1211yescharacteristic
229C22×D5—21no—
230C22×D5—21no—
231C22×D5—21no—
232C22×D5—21no—
233C22×D5—21no—
234C22×D5—21no—
235C22×D5C4⋊Dic312yes—
236C2×C4×C5—62no—
237C2×C4×C5—121no—
238C2×C4×C5—121no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×Dic611yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C22×Dic311yescharacteristic
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—62no—
251C2×Dic5—121no—
252C2×Dic5—121no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C2×Dic5—121no—
256C2×Dic5C4⋊Dic312yes—
257C4×D5—22no—
258C4×D5—22no—
259C4×D5—22no—
260C4×D5—22no—
261C5×C8—22no—
262#168—22no—
263C23×C4—51no—
264C22×C8—51no—
265C22×C8D3×D511yescharacteristic
266#117—302no—
267#117—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—151no—
272C2×C22⋊C4—301no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—302no—
276#106—302no—
277C22⋊C8—54no—
278#95—301no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#42711yescharacteristic
281C2×C3×C5#42811yescharacteristic
282C2×C3×C5#44911yescharacteristic
283C2×C3×C5#45211yescharacteristic
284C2×C3×C5#48211yescharacteristic
285C2×C3×C5#48511yescharacteristic
286C3×D5—42no—
287C23×C3—52no—
288C23×C3—101no—
289C23×C3—101no—
290C23×C3—101no—
291C23×C3—101no—
292C23×C3—101no—
293C23×C3—101no—
294C23×C3D4×D511yescharacteristic
295C2×C3×C4—52no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—102no—
299C2×C3×C4—102no—
300C2×C3×C4—102no—
301C2×C3×C4—102no—
302C2×C3×C4C2×C4×D511yescharacteristic
303C2×C3×C4C2×D2011yescharacteristic
304C2×C3×C4#70911yescharacteristic
305C2×C3×C4D4×D511yescharacteristic
306C2×C3×C4#71111yescharacteristic
307C2×C3×C4Q8×D511yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—102no—
315C2×Dic3—201no—
316C2×Dic3—201no—
317C2×Dic3—201no—
318C2×Dic3—201no—
319C2×Dic3—201no—
320C3×C8—22no—
321C3×C8—102no—
322C22×C5#88211yescharacteristic
323C22×C5#88611yescharacteristic
324C22×C5#90411yescharacteristic
325C22×C5#90411yescharacteristic
326C22×C5#90811yescharacteristic
327C22×C5#90911yescharacteristic
328C22×C5C2×C4⋊Dic311yescharacteristic
329C2×D5—22no—
330C2×D5—22no—
331C2×D5—22no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5—41no—
336C4×C5—122no—
337C4×C5—241no—
338C4×C5#87811yescharacteristic
339C4×C5#87811yescharacteristic
340C4×C5D4×Dic311yescharacteristic
341C4×C5D4×Dic311yescharacteristic
342Dic5—22no—
343Dic5—122no—
344Dic5—241no—
345C24—51no—
346C22×C4—51no—
347C22×C4—52no—
348C22×C4—52no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—101no—
355C22×C4—301no—
356C22×C4—301no—
357C22×C4C2×D3×D511yescharacteristic
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—52no—
361C2×C8—101no—
362C2×C8—101no—
363C2×C8D5×Dic312yes—
364C4⋊C4—32no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—152no—
369C4⋊C4—301no—
370C4⋊C4—301no—
371C4⋊C4—301no—
372C22⋊C4—304no—
373C22⋊C4—602no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3—102no—
377C22×C3—102no—
378C22×C3—102no—
379C22×C3—201no—
380C22×C3—201no—
381C22×C3—201no—
382C22×C3—201no—
383C22×C3#402811yescharacteristic
384C22×C3#402911yescharacteristic
385C22×C3D5×C4⋊C411yescharacteristic
386C22×C3#405811yescharacteristic
387C22×C3#406011yescharacteristic
388C22×C3#406111yescharacteristic
389C22×C3#406511yescharacteristic
390C3×C4—102no—
391C3×C4C4×D2011yescharacteristic
392C3×C4#402711yescharacteristic
393C3×C4#404211yescharacteristic
394C3×C4#404311yescharacteristic
395Dic3—42no—
396Dic3—81no—
397Dic3—202no—
398Dic3—401no—
399C2×C5#472311yescharacteristic
400C2×C5#473311yescharacteristic
401C2×C5#473411yescharacteristic
402C2×C5#473711yescharacteristic
403C2×C5#495011yescharacteristic
404C2×C5#510611yescharacteristic
405C2×C5#512111yescharacteristic
406D5—42no—
407C23—52no—
408C23—101no—
409C23—101no—
410C23—101no—
411C23—101no—
412C23—101no—
413C23—101no—
414C23D5×D1211yescharacteristic
415C2×C4—52no—
416C2×C4—62no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—102no—
420C2×C4—102no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—302no—
429C2×C4—601no—
430C2×C4—601no—
431C2×C4—601no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4D5×Dic611yescharacteristic
435C2×C4#676511yescharacteristic
436C2×C4D3×D2011yescharacteristic
437C2×C4C2×D5×Dic311yescharacteristic
438C2×C4#678011yescharacteristic
439C2×C4#679011yescharacteristic
440C8—22no—
441C8—102no—
442C2×C3—202no—
443C2×C3#6495711yescharacteristic
444C2×C3#6507211yescharacteristic
445C2×C3#6507311yescharacteristic
446C2×C3#6510011yescharacteristic
447C2×C3#6510311yescharacteristic
448C2×C3#6515011yescharacteristic
449C2×C3#6516911yescharacteristic
450C5#6992911yescharacteristic, complemented, Sylow
451C22—102no—
452C22—102no—
453C22—102no—
454C22—201no—
455C22—201no—
456C22—201no—
457C22—201no—
458C22#9124911yescharacteristic
459C22#9126011yescharacteristic
460C22#9127011yescharacteristic
461C22#9127111yescharacteristic
462C22D5×C4⋊Dic311yescharacteristic
463C22#9141411yescharacteristic
464C22#9147611yescharacteristic
465C4—102no—
466C4—122no—
467C4—241no—
468C4—602no—
469C4—1201no—
470C4#9142211yescharacteristic
471C4Dic3×D2011yescharacteristic
472C4#9143111yescharacteristic
473C4#9155911yescharacteristic
474C3#1059967011yescharacteristic, complemented, Sylow
475C2—202no—
476C2#1174761811yescharacteristic
477C2#1174767211yescharacteristic
478C2#1174767411yescharacteristic
479C2#1174790311yescharacteristic
480C2#1174816011yescharacteristic
481C2#1174816411yescharacteristic
482C2#1174890011yescharacteristic
subgroupG/H
centerC23D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1854
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#91102C2semidirect
5. C2×#90985C2semidirect
6. C5×#4551C2semidirect
7. #11745981C2semidirect
22. C3×#3952C4semidirect
69. #4551D5semidirect
83. #3952Dic3semidirect
375. C3×C5#1854semidirect
450. C5#69929semidirect
474. C3#10599670semidirect

Maximal subgroups

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

subgroupindex
C2×#913582
C2×#911022
C2×C3×#39522
#117487592
C2×#909852
C5×#45512
#117459812
#105996703
#699295