Finite Group Databasebeta

← #14435466

Subgroups — #14435466

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
2#11754410C211yesmaximal, characteristic
3#11751329C211yesmaximal, characteristic, complemented
4C5×#5227C211yesmaximal, characteristic
5#11749329C212yesmaximal, complemented
6#11749311C212yesmaximal, complemented
7#11749250C212yesmaximal, complemented
8#11749223C212yesmaximal, complemented
9#11748414C211yesmaximal, characteristic, complemented
10#11748385C211yesmaximal, characteristic
11#11748333C211yesmaximal, characteristic, complemented
12#10611762—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6718C2212yes—
15#91813C2211yescharacteristic
16C2×C5×#215C2212yes—
17C5×#930C2211yescharacteristic
18C3×Q8×Dic5—21no—
19C3×Q8×Dic5—21no—
20C3×Q8×Dic5C2212yes—
21C3×Q8×Dic5C2212yes—
22C2×C3×C4⋊Dic5—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4×Dic5—21no—
25C2×C3×C4×Dic5C2211yescharacteristic
26Dic5×#67—21no—
27#91539—21no—
28Dic5×D12C2211yescharacteristic
29#91398—21no—
30#91388C2211yescharacteristic
31#91373C2211yescharacteristic
32#91372—21no—
33#91333C2211yescharacteristic
34#91119C2212yes—
35#91114C2211yescharacteristic
36C5×#835C2212yes—
37C5×#830C2211yescharacteristic
38#90990C2212yes—
39#90986C2212yes—
40#90982C2212yes—
41#90974C2212yes—
42#90966C2212yes—
43#90952C2212yes—
44#82445—51nomaximal, Hall
45C2×Q8×Dic5D311yescharacteristic, complemented
46#65934—31no—
47C5×#448—31no—
48#65517—31no—
49#65455—32no—
50#65453—32no—
51#65323—31no—
52#65085—32no—
53#65078—32no—
54#65011—31no—
55#65008—31no—
56C2×C3×C5×Q8—24no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×Dic30C2311yescharacteristic
62C2×C5×#67—21no—
63C2×C5×D12C2311yescharacteristic
64C22×C3×Dic5—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C2×D3×Dic5—21no—
68#6719—21no—
69#6718—24no—
70C4⋊Dic15C2311yescharacteristic
71#6712—21no—
72C2×C3⋊#168C2312yes—
73C5×#215—24no—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C2×C5×C3⋊C8C2312yes—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5—22no—
79C3×C4⋊Dic5—22no—
80C3×C4⋊Dic5C2312yes—
81C3×C4×Dic5—22no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5D411yescharacteristic
84C3×C4×Dic5D411yescharacteristic
85C3×C4×Dic5C2311yescharacteristic
86C3×C4×Dic5C2311yescharacteristic
87Dic3⋊Dic5—21no—
88#6669—21no—
89#6669—21no—
90(C2×D3)⋊Dic5—21no—
91(C2×D3)⋊Dic5—21no—
92(C2×D3)⋊Dic5—21no—
93Dic3×Dic5—21no—
94C2×C3×C4×Q8—51no—
95#5479—51no—
96#5228—51no—
97#5227D511yescharacteristic
98#5030—52no—
99#5028—52no—
100#5026—52no—
101#5022—52no—
102#4970—51no—
103#4968—51no—
104#4926—51no—
105C22×C5×Q8C2×D311yescharacteristic
106C2×C5×SD16—32no—
107C5×#121—31no—
108Q8×Dic5—21no—
109Q8×Dic5—21no—
110Q8×Dic5C2×D312yes—
111Q8×Dic5C2×D312yes—
112C2×#689—32no—
113#4082—31no—
114#4081—61no—
115D4×Dic5—31no—
116D4×Dic5—61no—
117C2×C4⋊Dic5—21no—
118C2×C4⋊Dic5C2×D311yescharacteristic
119#4070—31no—
120C2×C4×Dic5—21no—
121C2×C4×Dic5C2×D311yescharacteristic
122#4036—31no—
123#4033—31no—
124#4025—61no—
125#4023—61no—
126C5×#103—32no—
127C5×C22⋊C8—31no—
128#3967—32no—
129#3964—32no—
130C22⋊#168—31no—
131#3950—32no—
132#3948—32no—
133#3947—32no—
134#3946—32no—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C3×C5×Q8—24no—
140C3×C5×Q8—22no—
141C3×C5×Q8#4114yes—
142C2×C3×C4×C5—24no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—21no—
148C2×Dic15—21no—
149Dic30—22no—
150C5×#67—42no—
151C2×C5×Dic3—21no—
152C5×D12—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—41no—
156C2×C3×Dic5—42no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C2×C3×Dic5C2×D411yescharacteristic
161D3×Dic5—42no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C22×C3×Q8C2×D511yescharacteristic
165C3×C4×Q8—52no—
166C3×C4×Q8—52no—
167C3×C4×Q8—101no—
168C3×C4×Q8—101no—
169C2×C3×C4⋊C4—51no—
170C2×C3×C4⋊C4—101no—
171C2×C3×C42—51no—
172C2×C3×C42—101no—
173C2×#216—52no—
174C2×#215C2×D512yes—
175#930C2×D511yescharacteristic
176#929—101no—
177C4×#67—101no—
178#924—51no—
179#876—101no—
180#875—51no—
181C4×D12—51no—
182#872—101no—
183#870—51no—
184C4×Dic6—51no—
185#835—52no—
186#835C2×D512yes—
187#830—51no—
188#830C2×D511yescharacteristic
189#810—52no—
190#809—52no—
191#808—52no—
192#807—52no—
193C4⋊(C3⋊C8)—52no—
194#803—52no—
195C2×C5×Q8—24no—
196C2×C5×Q8—21no—
197C2×C5×Q8C22×D312yes—
198C2×C5×D4—31no—
199C2×C5×D4—61no—
200C22×C4×C5—21no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C22×Dic5—61no—
204C22×Dic5#6711yescharacteristic
205C22×Dic5#6711yescharacteristic
206C2×Dic10—31no—
207C5×SD16—64no—
208C2×C5×C8—32no—
209C5×C4⋊C4—31no—
210C5×C22⋊C4—61no—
211C22⋊Dic5—61no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214C22⋊Dic5—61no—
215#689—64no—
216C4⋊Dic5—21no—
217C4⋊Dic5—22no—
218C4⋊Dic5—22no—
219C4⋊Dic5—31no—
220C4⋊Dic5—61no—
221C4⋊Dic5C22×D312yes—
222#683—61no—
223#683—61no—
224#683—61no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5—61no—
228C4×Dic5#6711yescharacteristic
229C4×Dic5#6711yescharacteristic
230C4×Dic5C22×D311yescharacteristic
231C4×Dic5C22×D311yescharacteristic
232C2×#168—32no—
233#529—151no—
234C2×C4×Q8—51no—
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—31no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C3×C4×C5—24no—
252C3×C4×C5—21no—
253C3×C4×C5C2×#4112yes—
254Dic15—41no—
255Dic15—41no—
256C3×Dic5—21no—
257C3×Dic5—21no—
258C3×Dic5—21no—
259C3×Dic5—21no—
260C3×Dic5—42no—
261C5×Dic3—41no—
262C2×C3×Q8—24no—
263C2×C3×Q8—21no—
264C2×C3×Q8C22×D512yes—
265C22×C3×C4—21no—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271C2×D12C22×D511yescharacteristic
272C2×C4×D3—101no—
273C2×Dic6—51no—
274C3×C4⋊C4—52no—
275C3×C4⋊C4—102no—
276C3×C4⋊C4—102no—
277C3×C4⋊C4—101no—
278C3×C42—51no—
279C3×C42—51no—
280C3×C42—51no—
281C3×C42—51no—
282C3×C42—102no—
283C3×C42—102no—
284#217—101no—
285#216—104no—
286#215—24no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—101no—
289(C2×D3)⋊C4—101no—
290(C2×D3)⋊C4—101no—
291C4⋊Dic3—51no—
292C4⋊Dic3C22×D511yescharacteristic
293Dic3⋊C4—101no—
294Dic3⋊C4—101no—
295Dic3⋊C4—101no—
296Dic3⋊C4—101no—
297C4×Dic3—101no—
298C2×C3⋊C8—52no—
299C2×C3⋊C8C22×D512yes—
300C23×C5—61no—
301C23×C5C2×#6711yescharacteristic
302C5×Q8—24no—
303C5×Q8—22no—
304C5×Q8#23514yes—
305C5×D4—62no—
306C5×D4—122no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—61no—
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—41no—
316C2×Dic5—42no—
317C2×Dic5—61no—
318C2×Dic5—61no—
319C2×Dic5—122no—
320C2×Dic5C2×#6711yescharacteristic
321C2×Dic5C2×#6711yescharacteristic
322C2×Dic5C2×#6711yescharacteristic
323C2×Dic5C2×#6711yescharacteristic
324Dic10—62no—
325C5×C8—62no—
326#168—62no—
327C22×Q8D3×D511yescharacteristic
328C2×Q16—152no—
329C2×SD16—32no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—31no—
336C4×Q8—52no—
337C4×Q8—52no—
338C4×Q8—101no—
339C4×Q8—101no—
340C4×Q8—151no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C42—51no—
347C2×C42—101no—
348#107—152no—
349#106—152no—
350C4⋊C8—152no—
351#103—32no—
352#103—152no—
353#103—152no—
354#102—152no—
355C22⋊C8—31no—
356C22⋊C8—151no—
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C5×D3—81no—
363C23×C3D4×D511yescharacteristic
364C22×D3—21no—
365C3×Q8—24no—
366C3×Q8—22no—
367C3×Q8#71114yes—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—51no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—51no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—201no—
378C2×C3×C4—202no—
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—42no—
382C2×Dic3—21no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385D12—22no—
386C4×D3—202no—
387Dic6—102no—
388C3⋊C8—22no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—121no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5#94212yes—
396C22×C5C22×#6711yescharacteristic
397C4×C5—24no—
398C4×C5—21no—
399C4×C5—121no—
400C4×C5C2×#23512yes—
401Dic5—21no—
402Dic5—21no—
403Dic5—21no—
404Dic5—21no—
405Dic5—42no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8—151no—
411C2×Q8C2×D3×D512yes—
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—21no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—101no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—64no—
422C2×C8—32no—
423C2×C8—152no—
424C4⋊C4—31no—
425C4⋊C4—52no—
426C4⋊C4—102no—
427C4⋊C4—102no—
428C4⋊C4—101no—
429C4⋊C4—151no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—61no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—51no—
440C42—51no—
441C42—51no—
442C42—51no—
443C42—102no—
444C42—102no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#406112yes—
450C22×C3C2×D4×D511yescharacteristic
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—101no—
457C3×C4—101no—
458C3×C4—101no—
459C3×C4—101no—
460C3×C4—202no—
461C3×C4C2×#71112yes—
462Dic3—41no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#579111yescharacteristic
468C2×C5C2×#94211yescharacteristic
469C2×C5#582211yescharacteristic
470C23—61no—
471C23D5×#6711yescharacteristic
472Q8—24no—
473Q8—22no—
474Q8—302no—
475Q8#678214yes—
476D4—62no—
477D4—122no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—61no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—201no—
489C2×C4—202no—
490C2×C4—301no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D5×#6711yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—62no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6592011yescharacteristic
499C2×C3C2×#406111yescharacteristic
500C2×C3#6611111yescharacteristic
501D3—81no—
502C5#8244511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9151312yes—
509C22C2×D5×#6711yescharacteristic
510C4—24no—
511C4—21no—
512C4—101no—
513C4—101no—
514C4—101no—
515C4—101no—
516C4—121no—
517C4—202no—
518C4—601no—
519C4—601no—
520C4C2×#678212yes—
521C3#1061176211yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175508411yescharacteristic
525C2C2×#9151311yescharacteristic
526C2#1175538511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC5×#930C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic5C2semidirect
3. #11751329C2semidirect
5. #11749329C2semidirect
6. #11749311C2semidirect
7. #11749250C2semidirect
8. #11749223C2semidirect
9. #11748414C2semidirect
11. #11748333C2semidirect
45. C2×Q8×Dic5D3semidirect
446. C3×C5#3117semidirect
502. C5#82445semidirect
521. C3#10611762semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic52
#117544102
#117513292
C5×#52272
#117493292
#117493112
#117492502
#117492232
#117484142
#117483852
#117483332
#106117623
#824455