Finite Group Databasebeta

← #14283431

Subgroups — #14283431

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754352C211yesmaximal, characteristic
2C5×#4667C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746272C211yesmaximal, characteristic, complemented
5C3×#64672C211yesmaximal, characteristic, complemented
6#11745961C211yesmaximal, characteristic, complemented
7#11745959C211yesmaximal, characteristic, complemented
8#10600301—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×#6769C411yescharacteristic, complemented
11#91819C2211yescharacteristic
12C2×C5×(C2×D3)⋊C4—21no—
13C2×C5×Dic3⋊C4—21no—
14C3×#4070C2211yescharacteristic
15#91570—21no—
16#91556—21no—
17#91460C411yescharacteristic, complemented
18#91446—21no—
19#91369C411yescharacteristic, complemented
20#91351—21no—
21#91338C411yescharacteristic, complemented
22C2×#6650—21no—
23C3×C5×#95C2211yescharacteristic
24#91114C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27(C2×D3)⋊#168—21no—
28#68337—51nomaximal, Hall
29#66125—31no—
30C5×#380—31no—
31#65496—31no—
32#64672—31no—
33#64672D311yescharacteristic, complemented
34#64671—31no—
35#64671—31no—
36C23×C5×D3D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C2×D60C2×C411yescharacteristic
41C22×C5×Dic3—21no—
42C22×C5×Dic3D411yescharacteristic
43C2×C4×C5×D3—42no—
44C2×C4×C5×D3C2×C411yescharacteristic
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C2×C4×C5×D3D411yescharacteristic
48C2×C3×Dic10C2×C411yescharacteristic
49C2×#1203—21no—
50C2×#1203—21no—
51C2×#1200—21no—
52#6769—42no—
53#6714—21no—
54C4⋊Dic15C2×C411yescharacteristic
55C2×C3⋊#168—21no—
56C5×(C2×D3)⋊C4—42no—
57C5×Dic3⋊C4—42no—
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5C2×C411yescharacteristic
60C3×#683—21no—
61C2×C3×#168—21no—
62#6669—21no—
63#6667—21no—
64(C2×D3)⋊Dic5—21no—
65(C2×D3)⋊Dic5—21no—
66Dic3×Dic5—21no—
67#6650—42no—
68#5627—51no—
69#4726—51no—
70#4667D511yescharacteristic, complemented
71C3×#328—51no—
72#4538—51no—
73#4470—51no—
74#4451—51no—
75C23×C4×C5—31no—
76C2×#709—31no—
77C2×C5×C4⋊C4—61no—
78C2×C5×C22⋊C4—61no—
79#4099—61no—
80#4076—31no—
81#4076—31no—
82#4075—61no—
83C4×C22⋊D5—61no—
84C4×C22⋊D5—61no—
85#4072—31no—
86#4070—31no—
87#4070C2×D311yescharacteristic
88C2×#681—61no—
89C5×#95—31no—
90C5×#95C2×D311yescharacteristic
91C22⋊#168—31no—
92C22⋊#168—61no—
93C22⋊#168C2×D311yescharacteristic
94#1513—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—21no—
97C22×C5×D3—21no—
98C22×C5×D3—21no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3C22⋊C411yescharacteristic
102C22×C5×D3C22⋊C411yescharacteristic
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109#1220—41no—
110#1220—41no—
111C2×Dic15—21no—
112D60—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C4×C5×D3—22no—
120C4×C5×D3—22no—
121C4×C5×D3—41no—
122C4×C5×D3—41no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C3×Dic10—41no—
126#1203—42no—
127#1203—42no—
128#1200—42no—
129C3⋊#168—41no—
130C3×#168—41no—
131C2×#239—51no—
132C22×C4×D3C2×D511yescharacteristic
133C3×C22⋊Q8—51no—
134#946—51no—
135#930—51no—
136C2×(C2×D3)⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×ΓL(1,𝔽25)—101no—
139#895—51no—
140#894—101no—
141#893—101no—
142#892—51no—
143#882—101no—
144#67⋊C4—101no—
145C3×C22⋊C8—51no—
146C3×#95C2×D511yescharacteristic
147C3⋊#95C2×D511yescharacteristic
148#830—51no—
149(C2×D3)⋊C8—101no—
150C24×C5—31no—
151C22×C4×C5—21no—
152C22×C4×C5—31no—
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—61no—
158C22×C4×C5—122no—
159C22×C4×C5C22×D311yescharacteristic
160C2×C22⋊D5—61no—
161C2×C22⋊D5—61no—
162C2×C22⋊D5—61no—
163#709—122no—
164C2×D20—31no—
165C2×C4×D5—61no—
166C2×Dic10C4×D311yescharacteristic
167C5×C4⋊C4—122no—
168C5×C22⋊C4—122no—
169C22⋊Dic5—21no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172#685—61no—
173#685—61no—
174C4⋊Dic5—31no—
175C4⋊Dic5C4×D311yescharacteristic
176#683—21no—
177#683—61no—
178C4×Dic5—61no—
179#681—122no—
180C2×#168—21no—
181C2×#168—61no—
182#525—151no—
183#407—151no—
184#380—31no—
185#328—51no—
186#328—151no—
187#327—151no—
188#327—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
193C22×C3×C5#13711yescharacteristic
194C2×D15—41no—
195C2×D15—41no—
196C2×D15—41no—
197C2×C5×D3—21no—
198C2×C5×D3—21no—
199C2×C5×D3—21no—
200C2×C5×D3—21no—
201C2×C5×D3—21no—
202C2×C5×D3—21no—
203C2×C5×D3—42no—
204C2×C5×D3—42no—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—81no—
208Dic15—41no—
209C3×Dic5—41no—
210C3×Dic5—41no—
211C5×Dic3—21no—
212C5×Dic3—81no—
213C5×Dic3#9912yes—
214C23×D3C22⋊D511yescharacteristic
215C2×C3×Q8—51no—
216C22×C3×C4—21no—
217C22×C3×C4C22×D511yescharacteristic
218C2×#67—101no—
219C22×Dic3—21no—
220C22×Dic3C22⋊D511yescharacteristic
221#239—202no—
222C2×D12—51no—
223C2×D12—101no—
224C2×D12—101no—
225C2×C4×D3—42no—
226C2×C4×D3—101no—
227C2×C4×D3C4×D511yescharacteristic
228C2×C4×D3C4×D511yescharacteristic
229C2×C4×D3D2011yescharacteristic
230C2×C4×D3D2011yescharacteristic
231C2×C3×C8—101no—
232C3×C4⋊C4—51no—
233C3×C4⋊C4—101no—
234C3×C22⋊C4—101no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—101no—
237(C2×D3)⋊C4—101no—
238(C2×D3)⋊C4—101no—
239(C2×D3)⋊C4—101no—
240C4⋊Dic3—51no—
241Dic3⋊C4—42no—
242Dic3⋊C4—101no—
243C4×Dic3—101no—
244C2×C3⋊C8—101no—
245ΓL(1,𝔽25)—202no—
246C23×C5—31no—
247C23×C5—31no—
248C23×C5—61no—
249C23×C5—61no—
250C23×C5—121no—
251C23×C5—121no—
252C23×C5D3×D411yescharacteristic
253C22×D5—61no—
254C2×C4×C5—31no—
255C2×C4×C5—31no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—62no—
261C2×C4×C5—62no—
262C2×C4×C5—62no—
263C2×C4×C5—121no—
264C2×C4×C5—121no—
265C2×C4×C5—121no—
266C2×C4×C5—121no—
267C2×C4×C5—121no—
268C2×C4×C5C2×C4×D311yescharacteristic
269C2×C4×C5D3×D411yescharacteristic
270C22⋊D5—122no—
271C22⋊D5—122no—
272C22⋊D5—121no—
273C22⋊D5—121no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—61no—
277D20—121no—
278C4×D5—122no—
279Dic10—41no—
280#168—41no—
281#168—121no—
282C2×#41—151no—
283C23×C4—31no—
284C2×M16—301no—
285#123—301no—
286C22⋊Q8—51no—
287C22⋊Q8—151no—
288#121—151no—
289#121—151no—
290#120—301no—
291C4×D4—301no—
292C4×D4—301no—
293#117—151no—
294C2×C4⋊C4—61no—
295C2×C22⋊C4—61no—
296C22⋊C8—51no—
297C22⋊C8—151no—
298C22⋊C8—301no—
299#95—31no—
300#95D3×D511yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5C2×#9911yescharacteristic
304C2×C3×C5#41711yescharacteristic
305C2×C3×C5#42111yescharacteristic
306D15—81no—
307C5×D3—41no—
308C5×D3—41no—
309C23×C3C2×C22⋊D511yescharacteristic
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—101no—
315C22×D3#68511yescharacteristic
316C22×D3#68511yescharacteristic
317C3×Q8—201no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4C2×D2011yescharacteristic
326#67—201no—
327#67—201no—
328C2×Dic3—22no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—101no—
333C2×Dic3#68511yescharacteristic
334C2×Dic3#68511yescharacteristic
335D12—201no—
336D12—202no—
337D12—202no—
338C4×D3—22no—
339C4×D3—22no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—202no—
343C3×C8—201no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—61no—
348C22×C5—61no—
349C22×C5—61no—
350C22×C5—61no—
351C22×C5—61no—
352C22×C5—61no—
353C22×C5—122no—
354C22×C5—122no—
355C22×C5D3×C22⋊C411yescharacteristic
356C22×C5#91411yescharacteristic
357C22×C5#91811yescharacteristic
358C2×D5—121no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—32no—
364C4×C5—61no—
365C4×C5—81no—
366C4×C5—241no—
367Dic5—41no—
368Dic5—41no—
369Dic5—121no—
370C24—31no—
371#41—602no—
372C2×Q8—51no—
373C2×D4—151no—
374C2×D4—301no—
375C2×D4—301no—
376C2×D4—301no—
377C22×C4—21no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4—122no—
385C22×C4—301no—
386C22×C4C2×D3×D511yescharacteristic
387M16—602no—
388C2×C8—101no—
389C2×C8—301no—
390C4⋊C4—51no—
391C4⋊C4—101no—
392C4⋊C4—122no—
393C4⋊C4—151no—
394C4⋊C4—301no—
395C22⋊C4—101no—
396C22⋊C4—122no—
397C22⋊C4—301no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C22⋊C4—301no—
401C42—301no—
402C3×C5#151311yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3C2×#68511yescharacteristic
406C22×C3#407811yescharacteristic
407C22×C3#408811yescharacteristic
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—201no—
417C2×D3—201no—
418C2×D3—201no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—81no—
422C3×C4—201no—
423C3×C4—201no—
424Dic3—21no—
425Dic3—81no—
426Dic3—201no—
427Dic3#393812yes—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—121no—
431C2×C5—121no—
432C2×C5D3×#9911yescharacteristic
433C2×C5#480311yescharacteristic
434C2×C5#482111yescharacteristic
435D5—241no—
436C23—31no—
437C23—31no—
438C23—61no—
439C23—61no—
440C23—121no—
441C23—121no—
442C23—301no—
443C23D3×C22⋊D511yescharacteristic
444Q8—201no—
445D4—601no—
446D4—602no—
447D4—602no—
448D4—601no—
449D4—601no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—101no—
460C2×C4—101no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—301no—
467C2×C4—602no—
468C2×C4C4×D3×D511yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C8—201no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3C2×#393811yescharacteristic
475C2×C3#6525511yescharacteristic
476C2×C3#6529411yescharacteristic
477D3—41no—
478D3—41no—
479D3—401no—
480C5#6833711yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—61no—
484C22—61no—
485C22—61no—
486C22—61no—
487C22—61no—
488C22—61no—
489C22—122no—
490C22—122no—
491C22—601no—
492C22—601no—
493C22—601no—
494C22D3×#68511yescharacteristic
495C22#9149611yescharacteristic
496C22#9152011yescharacteristic
497C4—21no—
498C4—21no—
499C4—32no—
500C4—61no—
501C4—81no—
502C4—201no—
503C4—201no—
504C4—241no—
505C4—601no—
506C3#1060030111yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—121no—
510C2—121no—
511C2—1201no—
512C2#1174711111yescharacteristic
513C2D3×#393811yescharacteristic
514C2#1174750511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754352C2
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1513
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C5×#4667C2semidirect
3. #11748505C2semidirect
4. #11746272C2semidirect
5. C3×#64672C2semidirect
6. #11745961C2semidirect
7. #11745959C2semidirect
10. C2×#6769C4semidirect
17. #91460C4semidirect
19. #91369C4semidirect
21. #91338C4semidirect
33. #64672D3semidirect
70. #4667D5semidirect
402. C3×C5#1513semidirect
480. C5#68337semidirect
506. C3#10600301semidirect

Maximal subgroups

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

subgroupindex
#117543522
C5×#46672
#117485052
#117462722
C3×#646722
#117459612
#117459592
#106003013
#683375