Finite Group Databasebeta

← #14328030

Subgroups — #14328030

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic, complemented
3C4×C5×#217C211yesmaximal, characteristic, complemented
4#11749489C212yesmaximal
5#11749486C212yesmaximal, complemented
6#11748770C212yesmaximal, complemented
7#11748737C211yesmaximal, characteristic, complemented
8#11748702C211yesmaximal, characteristic, complemented
9#11748638C211yesmaximal, characteristic, complemented
10Dic3×#683C212yesmaximal, complemented
11#11748580C211yesmaximal, characteristic, complemented
12#10605194—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×#6719C2212yes—
17C2×C5×#217C2212yes—
18C2×C4×C5×Dic3C2212yes—
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C3×C4×C22⋊D5C418yescomplemented
21C2×C3×#685C2211yescharacteristic
22C2×C3×#683C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×#6668C2212yes—
25C2×#6668C2212yes—
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30#91115C2212yes—
31#91115C2211yescharacteristic
32#91115C2211yescharacteristic
33C5×C3⋊#95C2211yescharacteristic
34C5×C3⋊#95C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#82338—51nomaximal, Hall
38C2×C4×C22⋊D5D311yescharacteristic
39C4×C5×C22⋊C4—31no—
40#65500—31no—
41#65246—32no—
42#65234—32no—
43#65229—32no—
44C4×#683—32no—
45#64955—31no—
46#64953—31no—
47#64939—31no—
48#64938—31no—
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2312yes—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5C2×C414yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—42no—
66C2×C3×C4×D5C2×C414yes—
67#6719—42no—
68C5×#217—24no—
69C4×C5×Dic3—42no—
70C3×C22⋊Dic5C2×C414yes—
71C3×#685C2×C414yes—
72C3×#683C2×C414yes—
73C3×C4×Dic5C2×C414yes—
74#6668—24no—
75#6668—24no—
76#6665—24no—
77#6665—42no—
78Dic3×Dic5—24no—
79Dic3×Dic5—42no—
80C2×C3×C4×D4—51no—
81#5221—52no—
82#5211—51no—
83#5211—51no—
84C4×#217—51no—
85C4×#217D511yescharacteristic, complemented
86Dic3×C4⋊C4—52no—
87#4951—52no—
88#4951—52no—
89#4936—51no—
90C4×C4⋊Dic3—51no—
91C23×C4×C5C2×D311yescharacteristic
92C22×C22⋊D5C2×D311yescharacteristic
93C22×C4×D5C2×D311yescharacteristic
94C2×C5×C22⋊C4—32no—
95C2×C42×C5—32no—
96C2×C22⋊Dic5—32no—
97C2×C22⋊Dic5C2×D311yescharacteristic
98C4×C22⋊D5Dic318yescomplemented
99C2×#685—32no—
100C2×#685—32no—
101C2×#685C2×D311yescharacteristic
102C2×#683—32no—
103C2×#683—32no—
104C2×#683C2×D311yescharacteristic
105C2×C4×Dic5—32no—
106C2×C4×Dic5—32no—
107C2×C4×Dic5C2×D311yescharacteristic
108C5×#95—31no—
109C5×#95—31no—
110#3963—31no—
111#3963—31no—
112#3963—32no—
113#3963—32no—
114#3963—32no—
115#2357—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—22no—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3#4114yes—
144C3×C22⋊D5—28no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5#4112yes—
151C2×C3×Dic5#4112yes—
152C3×C4×D5—44no—
153C22×C3×D4—51no—
154C23×C3×C4—51no—
155C23×C3×C4C2×D511yescharacteristic
156C3×C4×D4—58no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C22⋊C4—51no—
159C2×C3×C22⋊C4—51no—
160C2×C3×C42—51no—
161C2×#217—52no—
162C2×#217—52no—
163C2×#217—52no—
164C2×#217C2×D512yes—
165C2×C4⋊Dic3—52no—
166C2×C4⋊Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C2×C4×Dic3C2×D512yes—
170C3⋊#95—51no—
171C3⋊#95—51no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95C2×D511yescharacteristic
176C3⋊#95C2×D511yescharacteristic
177C24×C5C22×D311yescharacteristic
178C23×D5C22×D311yescharacteristic
179C22×C4×C5—32no—
180C22×C4×C5—32no—
181C22×C4×C5—42no—
182C22×C4×C5C2×Dic314yes—
183C22×C4×C5C22×D311yescharacteristic
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—22no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5C2×Dic314yes—
188C22×Dic5—32no—
189C22×Dic5—32no—
190C22×Dic5C22×D311yescharacteristic
191C22×Dic5C22×D311yescharacteristic
192C22×Dic5C22×D311yescharacteristic
193C2×C4×D5—42no—
194C2×C4×D5C2×Dic314yes—
195C5×C22⋊C4—64no—
196C42×C5—122no—
197C22⋊Dic5—122no—
198C22⋊Dic5C2×Dic314yes—
199#685—64no—
200#685—122no—
201#685C2×Dic314yes—
202#683—64no—
203#683—64no—
204#683C2×Dic314yes—
205C4×Dic5—64no—
206C4×Dic5—122no—
207C4×Dic5C2×Dic314yes—
208C2×C4×D4—51no—
209#390—152no—
210#388—152no—
211#388—152no—
212#382—151no—
213#381—151no—
214#381—151no—
215C4×C4⋊C4—151no—
216C4×C4⋊C4—152no—
217C4×C22⋊C4—31no—
218C4×C22⋊C4—151no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—42no—
223C22×C3×C5—42no—
224C22×C3×C5C23×C411yescharacteristic
225C22×C3×C5C2×#4112yes—
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5H(5,𝔽2)12yes—
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C3×C4×C5—22no—
235C3×C4×C5—22no—
236Dic15—42no—
237Dic15—42no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C3×Dic5#11714yes—
241C5×Dic3—24no—
242C5×Dic3—42no—
243C24×C3—51no—
244C24×C3C22×D511yescharacteristic
245C2×C3×D4—54no—
246C2×C3×D4—102no—
247C2×C3×D4—102no—
248C22×C3×C4—42no—
249C22×C3×C4—51no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—54no—
253C22×C3×C4—202no—
254C22×C3×C4C4×D514yes—
255C22×C3×C4C22×D511yescharacteristic
256C22×C3×C4C22×D511yescharacteristic
257C22×Dic3—52no—
258C22×Dic3—52no—
259C22×Dic3C22×D512yes—
260C22×Dic3C22×D512yes—
261C3×C4⋊C4—54no—
262C3×C22⋊C4—54no—
263C3×C22⋊C4—54no—
264C3×C42—54no—
265#217—24no—
266#217—104no—
267#217—202no—
268#217—202no—
269C4⋊Dic3—104no—
270C4⋊Dic3—104no—
271C4×Dic3—42no—
272C4×Dic3—104no—
273C4×Dic3—202no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—22no—
277C23×C5—22no—
278C23×C5C22×Dic312yes—
279C23×C5C23×D311yescharacteristic
280C22×D5—21no—
281C22×D5—21no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5C22×Dic312yes—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—34no—
288C2×C4×C5—44no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5C22×Dic312yes—
295C2×C4×C5C22×Dic312yes—
296C22⋊D5—28no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—62no—
300C2×Dic5—62no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5#23512yes—
306C2×Dic5#23512yes—
307C2×Dic5C22×Dic312yes—
308C2×Dic5C22×Dic312yes—
309C2×Dic5C22×Dic312yes—
310C4×D5—44no—
311C22×D4—51no—
312C23×C4—51no—
313C23×C4D3×D511yescharacteristic
314C4×D4—58no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—152no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—51no—
320C2×C22⋊C4—51no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C42—32no—
325C2×C42—51no—
326C2×C42—152no—
327C2×C42—152no—
328#95—31no—
329#95—31no—
330#95—152no—
331#95—152no—
332#95—151no—
333#95—151no—
334#95—152no—
335C2×C3×C5—42no—
336C2×C3×C5C2×#11711yescharacteristic
337C2×C3×C5C4×#4111yescharacteristic
338C2×C3×C5#51811yescharacteristic
339C2×C3×C5#55312yes—
340C2×C3×C5#55912yes—
341C3×D5—42no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—52no—
347C23×C3—102no—
348C23×C3—102no—
349C23×C3—101no—
350C23×C3—101no—
351C23×C3C2×C4×D512yes—
352C23×C3C23×D511yescharacteristic
353C3×D4—108no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—44no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4—52no—
360C2×C3×C4—52no—
361C2×C3×C4—52no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—204no—
365C2×C3×C4C2×C4×D512yes—
366C2×C3×C4C2×C4×D512yes—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3#70914yes—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5C2×#23511yescharacteristic
385C22×C5C2×#23511yescharacteristic
386C22×C5#100412yes—
387C22×C5D3×#4112yes—
388C22×C5C23×Dic311yescharacteristic
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—22no—
392C2×D5—42no—
393C2×D5—42no—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—64no—
397C4×C5—122no—
398Dic5—22no—
399Dic5—22no—
400Dic5—122no—
401Dic5—122no—
402Dic5#92614yes—
403C24—51no—
404C24C2×D3×D511yescharacteristic
405C2×D4—54no—
406C2×D4—102no—
407C2×D4—102no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—42no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—54no—
415C22×C4—152no—
416C22×C4—152no—
417C22×C4—202no—
418C22×C4D5×Dic314yes—
419C22×C4C2×D3×D511yescharacteristic
420C22×C4C2×D3×D511yescharacteristic
421C4⋊C4—54no—
422C4⋊C4—304no—
423C4⋊C4—304no—
424C22⋊C4—54no—
425C22⋊C4—54no—
426C22⋊C4—64no—
427C22⋊C4—304no—
428C22⋊C4—602no—
429C22⋊C4—602no—
430C42—54no—
431C42—122no—
432C42—304no—
433C42—602no—
434C3×C5#235711yescharacteristic, complemented, Hall
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3—102no—
443C22×C3—202no—
444C22×C3—202no—
445C22×C3C22×C4×D511yescharacteristic
446C22×C3C2×#70912yes—
447C22×C3#414412yes—
448C22×C3D5×#4111yescharacteristic
449C22×C3D5×#4111yescharacteristic
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—54no—
453C3×C4—102no—
454C3×C4—102no—
455Dic3—24no—
456Dic3—42no—
457Dic3—202no—
458Dic3—202no—
459C2×C5—42no—
460C2×C5#555812yes—
461C2×C5#555912yes—
462C2×C5C2×#92611yescharacteristic
463C2×C5#579811yescharacteristic
464C2×C5Dic3×#4111yescharacteristic
465D5—42no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—52no—
471C23—101no—
472C23—101no—
473C23—102no—
474C23—102no—
475C23C2×D5×Dic312yes—
476C23C22×D3×D511yescharacteristic
477D4—108no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—34no—
481C2×C4—44no—
482C2×C4—52no—
483C2×C4—52no—
484C2×C4—52no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—204no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4C2×D5×Dic312yes—
502C2×C4C2×D5×Dic312yes—
503C2×C3—42no—
504C2×C3—202no—
505C2×C3C4×#70911yescharacteristic
506C2×C3#6582011yescharacteristic
507C2×C3D5×#11711yescharacteristic
508C2×C3#6587412yes—
509C2×C3#6589312yes—
510C5#8233811yescharacteristic, complemented, Sylow
511C22—22no—
512C22—22no—
513C22—22no—
514C22—42no—
515C22—42no—
516C22—102no—
517C22—102no—
518C22—102no—
519C22—202no—
520C22—202no—
521C22D5×#23511yescharacteristic
522C22D5×#23511yescharacteristic
523C22D3×#70912yes—
524C22C22×D5×Dic311yescharacteristic
525C22#9204912yes—
526C4—22no—
527C4—22no—
528C4—54no—
529C4—64no—
530C4—102no—
531C4—102no—
532C4—122no—
533C4—602no—
534C4—602no—
535C3#1060519411yescharacteristic, complemented, Sylow
536C2—42no—
537C2—202no—
538C2D5×#92611yescharacteristic
539C2Dic3×#70911yescharacteristic
540C2#1175456812yes—
541C2#1175457312yes—
542C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2357
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751312C2semidirect
3. C4×C5×#217C2semidirect
5. #11749486C2semidirect
6. #11748770C2semidirect
7. #11748737C2semidirect
8. #11748702C2semidirect
9. #11748638C2semidirect
10. Dic3×#683C2semidirect
11. #11748580C2semidirect
20. C3×C4×C22⋊D5C4semidirect
85. C4×#217D5semidirect
98. C4×C22⋊D5Dic3semidirect
434. C3×C5#2357semidirect
510. C5#82338semidirect
535. C3#10605194semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
#117513122
C4×C5×#2172
#117494892
#117494862
#117487702
#117487372
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Dic3×#6832
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