Finite Group Databasebeta

← #14320181

Subgroups — #14320181

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic
2C2×C4×#1200C211yesmaximal, characteristic
3C2×#91386C211yesmaximal, characteristic
4C4×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×C4×#683C211yesmaximal, characteristic, complemented
6#11748882C212yesmaximal
7#11748876C212yesmaximal
8C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
9C4×#6668C211yesmaximal, characteristic, complemented
10#11748644C212yesmaximal, complemented
11#11748641C212yesmaximal, complemented
12#10605484—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2211yescharacteristic
15C22×#1200C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6714C2212yes—
18C2×#6712C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20#91761—24no—
21C2×C5×Dic3⋊C4C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2212yes—
28C2×#6669C2212yes—
29C2×#6668C2212yes—
30C2×#6667C2212yes—
31C2×Dic3×Dic5C2211yescharacteristic
32C2×Dic3×Dic5C2211yescharacteristic
33C4×#1200C418yescomplemented
34#91386—24no—
35C5×C3⋊#95C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73753—51nomaximal, Hall
40C2×#4018—31no—
41C2×#4018—31no—
42C2×C42×D5—31no—
43C4×C5×C4⋊C4—31no—
44#65276—32no—
45#65265—32no—
46C4×C4⋊Dic5—31no—
47C4×#683—31no—
48C4×#683D311yescharacteristic, complemented
49#64956—32no—
50#64939—32no—
51C23×D15C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C2×C4×D15C2×C414yes—
57C2×C4×D15D414yes—
58C2×C4×D15Q814yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×#1200—24no—
66C2×#1200—24no—
67C2×#1200C2×C414yes—
68C2×#1200C2×C414yes—
69C3×C42×C5—22no—
70#6714—24no—
71#6712—24no—
72C4×Dic15—22no—
73C5×Dic3⋊C4—24no—
74C4×C5×Dic3—22no—
75C4×C5×Dic3C2×C414yes—
76C3×#683—24no—
77C3×C4×Dic5—22no—
78C3×C4×Dic5C2×C414yes—
79Dic3⋊Dic5—24no—
80#6669—24no—
81#6668—24no—
82#6667—24no—
83Dic3×Dic5C2×C414yes—
84Dic3×Dic5C2×C414yes—
85C2×#872—51no—
86C2×#872—51no—
87C2×C42×D3—51no—
88C3×C4×C4⋊C4—51no—
89#4987—52no—
90#4975—52no—
91C4×C4⋊Dic3—51no—
92C4×Dic3⋊C4—51no—
93C4×Dic3⋊C4D511yescharacteristic, complemented
94#4667—52no—
95#4650—52no—
96C22×C4×D5—31no—
97C22×C4×D5—31no—
98C22×C4×D5—31no—
99C2×C5×C4⋊C4—32no—
100C2×C42×C5—31no—
101C2×C42×C5—31no—
102C2×C42×C5C2×D311yescharacteristic
103C2×#685—32no—
104C2×#685—32no—
105C2×C4⋊Dic5—32no—
106C2×#683—32no—
107C2×#683—32no—
108C2×#683—32no—
109C2×#683C2×D312yes—
110C2×C4×Dic5—31no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5C2×D311yescharacteristic
114C2×C4×Dic5C2×D311yescharacteristic
115#4018—64no—
116#4018—64no—
117C42×D5—38no—
118C5×#95—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2285—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×D15—22no—
125C22×D15—22no—
126C22×D15C22×C412yes—
127C22×D15C2×D412yes—
128C22×D15C2×Q812yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×Q812yes—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15C22×C412yes—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×Q812yes—
141C4×D15C4⋊C4116yescomplemented
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3C22×C412yes—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3#4114yes—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22×C412yes—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5#4114yes—
156#1200—28no—
157#1200—28no—
158C22×C4×D3—51no—
159C22×C4×D3—51no—
160C22×C4×D3—51no—
161C2×C3×C4⋊C4—52no—
162C2×C3×C42—51no—
163C2×C3×C42—51no—
164C2×C3×C42C2×D511yescharacteristic
165C2×(C2×D3)⋊C4—52no—
166C2×(C2×D3)⋊C4—52no—
167C2×C4⋊Dic3—52no—
168C2×Dic3⋊C4—52no—
169C2×Dic3⋊C4—52no—
170C2×Dic3⋊C4—52no—
171C2×Dic3⋊C4C2×D512yes—
172C2×C4×Dic3—51no—
173C2×C4×Dic3—51no—
174C2×C4×Dic3—51no—
175C2×C4×Dic3C2×D511yescharacteristic
176C2×C4×Dic3C2×D511yescharacteristic
177#872—104no—
178#872—104no—
179C42×D3—58no—
180C3×#95—52no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95C2×D512yes—
184C23×D5—31no—
185C22×C4×C5—31no—
186C22×C4×C5—31no—
187C22×C4×C5—32no—
188C22×C4×C5C22×D312yes—
189C22×C4×C5C22×D311yescharacteristic
190C22×Dic5—31no—
191C22×Dic5—32no—
192C22×Dic5C22×D312yes—
193C22×Dic5C22×D311yescharacteristic
194C22×Dic5C22×D311yescharacteristic
195C2×C4×D5—34no—
196C2×C4×D5—34no—
197C2×C4×D5—34no—
198C2×C4×D5—34no—
199C2×C4×D5—34no—
200C2×C4×D5—64no—
201C2×C4×D5—64no—
202C5×C4⋊C4—64no—
203C42×C5—22no—
204C42×C5—34no—
205C42×C5—62no—
206#685—64no—
207#685—64no—
208C4⋊Dic5—64no—
209#683—24no—
210#683—64no—
211#683—64no—
212#683—64no—
213C4×Dic5—22no—
214C4×Dic5—34no—
215C4×Dic5—34no—
216C4×Dic5—62no—
217C4×Dic5C4×D314yes—
218C2×#117—151no—
219C2×#117—151no—
220C22×C42—151no—
221#384—152no—
222#382—152no—
223#380—152no—
224#380—152no—
225C4×C4⋊C4—31no—
226C4×C4⋊C4—51no—
227C4×C4⋊C4—151no—
228C4×C4⋊C4—151no—
229C22×C3×C5C23×C411yescharacteristic
230C22×C3×C5C22×D411yescharacteristic
231C22×C3×C5C22×Q811yescharacteristic
232C22×C3×C5C2×#4112yes—
233C22×C3×C5C2×#4112yes—
234C2×D15—22no—
235C2×D15—22no—
236C2×D15—24no—
237C2×D15—24no—
238C2×D15C2×C4⋊C414yes—
239C3×C4×C5—42no—
240C3×C4×C5C2×C4⋊C414yes—
241Dic15—42no—
242Dic15C2×C4⋊C414yes—
243C3×Dic5—22no—
244C3×Dic5—42no—
245C3×Dic5#11714yescomplemented
246C5×Dic3—22no—
247C5×Dic3—42no—
248C5×Dic3#11714yescomplemented
249C23×D3—51no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—52no—
253C22×C3×C4C22×D512yes—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—51no—
256C22×Dic3—52no—
257C22×Dic3C22×D512yes—
258C22×Dic3C22×D511yescharacteristic
259C22×Dic3C22×D511yescharacteristic
260C2×C4×D3—54no—
261C2×C4×D3—54no—
262C2×C4×D3—54no—
263C2×C4×D3—54no—
264C2×C4×D3—54no—
265C2×C4×D3—104no—
266C2×C4×D3—104no—
267C3×C4⋊C4—104no—
268C3×C42—22no—
269C3×C42—54no—
270C3×C42—102no—
271(C2×D3)⋊C4—104no—
272(C2×D3)⋊C4—104no—
273C4⋊Dic3—104no—
274Dic3⋊C4—24no—
275Dic3⋊C4—104no—
276Dic3⋊C4—104no—
277Dic3⋊C4—104no—
278C4×Dic3—22no—
279C4×Dic3—54no—
280C4×Dic3—54no—
281C4×Dic3—102no—
282C4×Dic3C4×D514yes—
283C23×C5C23×D311yescharacteristic
284C22×D5—32no—
285C22×D5—32no—
286C22×D5—32no—
287C22×D5—62no—
288C22×D5—62no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—32no—
293C2×C4×C5—34no—
294C2×C4×C5—32no—
295C2×C4×C5—62no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5C2×C4×D312yes—
300C2×C4×C5D3×D412yes—
301C2×C4×C5D3×Q812yes—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—32no—
307C2×Dic5—32no—
308C2×Dic5—32no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5C2×C4×D312yes—
313C2×Dic5C2×C4×D312yes—
314C2×Dic5#23514yes—
315C4×D5—316no—
316C4×D5—68no—
317C4×D5—68no—
318C23×C4—151no—
319C23×C4—151no—
320C23×C4—151no—
321#117—304no—
322#117—304no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—152no—
326C2×C4⋊C4—152no—
327C2×C4⋊C4—152no—
328C2×C4⋊C4—152no—
329C2×C22⋊C4—152no—
330C2×C22⋊C4—152no—
331C2×C42—31no—
332C2×C42—31no—
333C2×C42—51no—
334C2×C42—51no—
335C2×C42—158no—
336C2×C42—151no—
337C2×C42—151no—
338C2×C42—151no—
339C2×C42D3×D511yescharacteristic
340#95—32no—
341#95—52no—
342#95—152no—
343#95—152no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5C2×#11711yescharacteristic
346C2×C3×C5C2×#11711yescharacteristic
347C2×C3×C5#53212yes—
348C2×C3×C5#53312yes—
349D15—24no—
350C23×C3C23×D511yescharacteristic
351C22×D3—52no—
352C22×D3—52no—
353C22×D3—52no—
354C22×D3—102no—
355C22×D3—102no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—52no—
360C2×C3×C4—54no—
361C2×C3×C4—52no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—102no—
365C2×C3×C4—102no—
366C2×C3×C4C2×C4×D512yes—
367C2×C3×C4D4×D512yes—
368C2×C3×C4Q8×D512yes—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—52no—
374C2×Dic3—52no—
375C2×Dic3—52no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3—102no—
379C2×Dic3C2×C4×D512yes—
380C2×Dic3C2×C4×D512yes—
381C2×Dic3#70914yes—
382C4×D3—516no—
383C4×D3—108no—
384C4×D3—108no—
385C22×C5C22×C4×D311yescharacteristic
386C22×C5C2×#23512yes—
387C22×C5C2×D3×D411yescharacteristic
388C22×C5C2×D3×Q811yescharacteristic
389C22×C5D3×#4112yes—
390C2×D5—34no—
391C2×D5—62no—
392C2×D5—62no—
393C2×D5—64no—
394C2×D5—64no—
395C4×C5—34no—
396C4×C5—42no—
397C4×C5—62no—
398C4×C5—122no—
399C4×C5D3×C4⋊C414yes—
400Dic5—22no—
401Dic5—34no—
402Dic5—42no—
403Dic5—122no—
404Dic5#87214yescomplemented
405C24—151no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—51no—
410C22×C4—51no—
411C22×C4—52no—
412C22×C4—154no—
413C22×C4—154no—
414C22×C4—151no—
415C22×C4—154no—
416C22×C4—154no—
417C22×C4—154no—
418C22×C4—152no—
419C22×C4—304no—
420C22×C4—304no—
421C22×C4C2×D3×D512yes—
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—64no—
424C4⋊C4—104no—
425C4⋊C4—304no—
426C4⋊C4—304no—
427C4⋊C4—304no—
428C4⋊C4—304no—
429C22⋊C4—304no—
430C22⋊C4—304no—
431C42—22no—
432C42—34no—
433C42—54no—
434C42—62no—
435C42—102no—
436C42—154no—
437C42—154no—
438C42—302no—
439C3×C5#228511yescharacteristic, complemented, Hall
440C22×C3C22×C4×D511yescharacteristic
441C22×C3C2×#70912yes—
442C22×C3C2×D4×D511yescharacteristic
443C22×C3C2×Q8×D511yescharacteristic
444C22×C3D5×#4112yes—
445C2×D3—54no—
446C2×D3—102no—
447C2×D3—102no—
448C2×D3—104no—
449C2×D3—104no—
450C3×C4—42no—
451C3×C4—54no—
452C3×C4—102no—
453C3×C4—202no—
454C3×C4D5×C4⋊C414yes—
455Dic3—22no—
456Dic3—42no—
457Dic3—54no—
458Dic3—202no—
459Dic3#401814yescomplemented
460C2×C5C2×#87211yescharacteristic
461C2×C5C2×D3×C4⋊C411yescharacteristic
462C2×C5D3×#11711yescharacteristic
463C2×C5#554812yes—
464C2×C5#557812yes—
465D5—64no—
466C23—152no—
467C23—152no—
468C23—152no—
469C23—302no—
470C23—302no—
471C23C22×D3×D511yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—32no—
476C2×C4—34no—
477C2×C4—32no—
478C2×C4—52no—
479C2×C4—54no—
480C2×C4—52no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—152no—
490C2×C4—152no—
491C2×C4—152no—
492C2×C4—1516no—
493C2×C4—308no—
494C2×C4—308no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4D15⋊Q812yes—
499C2×C4C4×D3×D512yes—
500C2×C4#679012yes—
501C2×C3C2×#401811yescharacteristic
502C2×C3C2×D5×C4⋊C411yescharacteristic
503C2×C3D5×#11711yescharacteristic
504C2×C3#6588212yes—
505C2×C3#6591212yes—
506D3—104no—
507C5#7375311yescharacteristic, complemented, Sylow
508C22—154no—
509C22—302no—
510C22—302no—
511C22—304no—
512C22—304no—
513C22C2×D15⋊Q811yescharacteristic
514C22C2×C4×D3×D511yescharacteristic
515C22D5×#23512yes—
516C22D3×#70912yes—
517C22C2×#679011yescharacteristic
518C4—34no—
519C4—42no—
520C4—54no—
521C4—62no—
522C4—102no—
523C4—122no—
524C4—154no—
525C4—202no—
526C4—602no—
527C4#9140414yes—
528C3#1060548411yescharacteristic, complemented, Sylow
529C2—304no—
530C2#1175258812yes—
531C2D5×#87211yescharacteristic
532C2D3×#401811yescharacteristic
533C2C2×#9140411yescharacteristic
534C2#1175455512yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2285
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C4×C5×Dic3⋊C4C2semidirect
5. C3×C4×#683C2semidirect
8. C4×Dic3⋊Dic5C2semidirect
9. C4×#6668C2semidirect
10. #11748644C2semidirect
11. #11748641C2semidirect
33. C4×#1200C4semidirect
48. C4×#683D3semidirect
93. C4×Dic3⋊C4D5semidirect
141. C4×D15C4⋊C4semidirect
245. C3×Dic5#117semidirect
248. C5×Dic3#117semidirect
404. Dic5#872semidirect
439. C3×C5#2285semidirect
459. Dic3#4018semidirect
507. C5#73753semidirect
528. C3#10605484semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C4×#12002
C2×#913862
C4×C5×Dic3⋊C42
C3×C4×#6832
#117488822
#117488762
C4×Dic3⋊Dic52
C4×#66682
#117486442
#117486412
#106054843
#737535