Finite Group Databasebeta

← #14416261

Subgroups — #14416261

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5522C211yesmaximal, characteristic, complemented
2Dic3×#709C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic
4#11751099C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic, complemented
6#11748388C211yesmaximal, characteristic, complemented
7C2×Dic3×#168C211yesmaximal, characteristic, complemented
8#11747266C212yesmaximal, complemented
9#11747264C212yesmaximal, complemented
10#11747221C212yesmaximal, complemented
11#11747219C212yesmaximal, complemented
12C4×#4096—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C2×C4×C5×Dic3C2211yescharacteristic
19C5×#893C2212yes—
20C5×#887C2212yes—
21C5×#67⋊C4—22no—
22C5×#872—21no—
23C42×C5×D3—21no—
24C22×C3×#168C2211yescharacteristic
25Dic3×C22⋊D5—22no—
26Dic3×D20C2212yes—
27C4×D5×Dic3—21no—
28#91357—21no—
29Dic3×Dic10C2212yes—
30C2×#6661C2211yescharacteristic
31C2×#6656C2211yescharacteristic
32C2×#6655C2211yescharacteristic
33#91297C418yescomplemented
34C2×#6652C2211yescharacteristic
35#91092C2212yes—
36#91091C2212yes—
37C3×#3942C2212yes—
38C3×#3941C2212yes—
39#90973C2212yes—
40#90967C2212yes—
41Dic3×#168C2212yes—
42Dic3×#168C2212yes—
43#78818—51nomaximal, Hall
44C4×C5×#41—31no—
45C2×#4096—31no—
46C4×#709—31no—
47#65522—31no—
48C4×#689—32no—
49C4×#688—32no—
50C4×#687—32no—
51C4×#686—32no—
52#65291D311yescharacteristic, complemented
53#65287—31no—
54C2×C4×#168—31no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C22×C5×Dic3D412yes—
58C5×#235—22no—
59C5×#235C2×C414yescomplemented
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C4×C5×D3—22no—
63C2×C5×Dic6C2311yescharacteristic
64C2×C3×C22⋊D5—21no—
65C3×#709—22no—
66C3×#709C2×C414yescomplemented
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×Dic10C2311yescharacteristic
70C2×D5×Dic3—22no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C22⋊C4—21no—
73C3×C42×C5—21no—
74#6719—21no—
75C4⋊Dic15C2312yes—
76C4×Dic15—21no—
77C2×C3⋊#168C2×C414yescomplemented
78C2×C3⋊#168C2311yescharacteristic
79C2×C3⋊#168C2311yescharacteristic
80C5×(C2×D3)⋊C4—22no—
81C5×Dic3⋊C4—22no—
82C4×C5×Dic3—22no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2312yes—
86C2×C3×#168—22no—
87C2×C3×#168C2312yes—
88#6668—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6661C2×C414yescomplemented
92#6656C2×C414yescomplemented
93#6655C2×C414yescomplemented
94#6652C2×C414yescomplemented
95Dic3×#41—51no—
96C2×#950—51no—
97#5522D511yescharacteristic, complemented
98C3×#416—51no—
99#5113—51no—
100C2×C8×Dic3—51no—
101#4998—51no—
102#4790—52no—
103#4788—52no—
104#4758—52no—
105#4756—52no—
106C2×C5×#41—31no—
107C2×#709C2×D311yescharacteristic
108C4×C5×Q8—32no—
109C4×C5×D4—32no—
110C4×C5×D4—62no—
111C5×#117—61no—
112C5×#117C2×D311yescharacteristic
113C2×C42×C5—31no—
114C2×C42×C5—61no—
115#4096—38no—
116C2×#689—31no—
117C2×#688—31no—
118C2×#687—31no—
119C2×#686—31no—
120C4×C22⋊D5—62no—
121#4072—31no—
122C22×#168—31no—
123C22×#168C2×D311yescharacteristic
124C4×D20—32no—
125#4018—61no—
126C42×D5—61no—
127C4×Dic10—32no—
128#3967—32no—
129#3964—32no—
130#3942C2×D312yes—
131#3941C2×D312yes—
132#3940—32no—
133#3939—32no—
134C4×#168—32no—
135C4×#168—32no—
136C4×#135—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C22×C3×D5—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C5×#67—24no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—24no—
149C2×C5×Dic3C2×D412yes—
150C2×C5×Dic3C2×D412yes—
151C5×D12—21no—
152C5×D12C22×C412yes—
153C4×C5×D3—24no—
154C4×C5×D3—44no—
155C5×Dic6—21no—
156C5×Dic6C22×C412yes—
157C3×C22⋊D5—24no—
158C2×C3×Dic5—21no—
159C3×D20—21no—
160C3×D20C22×C412yes—
161C3×C4×D5—24no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164D5×Dic3—44no—
165C3⋊#168C22×C412yes—
166C3⋊#168C22×C412yes—
167C3×#168—22no—
168C2×C3×#41—51no—
169C2×#235C2×D511yescharacteristic
170C22×C3×C8—51no—
171C3×#117C2×D511yescharacteristic
172#950—58no—
173Q8×Dic3—52no—
174C2×#216—51no—
175C2×#215—51no—
176D4×Dic3—52no—
177D4×Dic3—102no—
178C2×#214—51no—
179C2×#213—51no—
180#926—51no—
181#926—101no—
182C2×C4×Dic3—101no—
183C2×C4×Dic3C2×D511yescharacteristic
184C22×C3⋊C8—51no—
185#893C2×D512yes—
186#887C2×D512yes—
187#67⋊C4—22no—
188#872—21no—
189C42×D3—21no—
190C3×#103—52no—
191C3×#102—52no—
192#821—52no—
193#816—52no—
194C8×Dic3—52no—
195C8×Dic3—52no—
196#808—52no—
197#807—52no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—31no—
202C2×C5×D4—61no—
203C22×C4×C5—32no—
204C22×C4×C5—62no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—21no—
208#709—22no—
209#709C4×D314yescomplemented
210C2×D20C22×D311yescharacteristic
211C2×C4×D5—21no—
212C2×C4×D5—62no—
213C2×Dic10C22×D311yescharacteristic
214C5×C4⋊C4—62no—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—21no—
217C5×C22⋊C4—62no—
218C42×C5—21no—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—32no—
222C42×C5—62no—
223C22⋊Dic5—61no—
224#689—34no—
225#688—34no—
226#687—34no—
227#686—34no—
228#685—62no—
229C4⋊Dic5—32no—
230#683—62no—
231C4×Dic5—62no—
232C4×Dic5—61no—
233C2×#168—22no—
234C2×#168—34no—
235C2×#168—31no—
236C2×#168—31no—
237C2×#168C22×D312yes—
238C2×#135—151no—
239C4×#41—31no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—151no—
246#416—51no—
247#416—151no—
248C2×C4×C8—151no—
249C22×C3×C5—22no—
250C22×C3×C5C4×D412yes—
251C22×C3×C5C22×D411yescharacteristic
252C2×C5×D3—22no—
253C2×C5×D3—42no—
254C2×C3×D5—22no—
255C2×C3×D5—42no—
256C3×C4×C5—42no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—42no—
261C3×Dic5—22no—
262C5×Dic3—22no—
263C5×Dic3—22no—
264C5×Dic3#13514yescomplemented
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—51no—
268C2×C3×D4—51no—
269C2×C3×D4—101no—
270C22×C3×C4—101no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—21no—
273C22×Dic3—102no—
274C22×Dic3C22⋊D512yes—
275#235—22no—
276#235C4×D514yescomplemented
277C2×D12C22×D511yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—22no—
280C2×Dic6C22×D511yescharacteristic
281C2×C3×C8—52no—
282C2×C3×C8—102no—
283C3×C4⋊C4C22×D512yes—
284C3×C22⋊C4—21no—
285C3×C42—21no—
286#217—101no—
287#217—102no—
288#216—54no—
289#215—54no—
290#214—54no—
291#213—54no—
292(C2×D3)⋊C4—22no—
293C4⋊Dic3—52no—
294C4⋊Dic3—102no—
295Dic3⋊C4—22no—
296C4×Dic3—22no—
297C4×Dic3—101no—
298C4×Dic3—102no—
299C4×Dic3C22⋊D511yescharacteristic
300C4×Dic3C22⋊D511yescharacteristic
301C4×Dic3C22×D512yes—
302C2×C3⋊C8—54no—
303C2×C3⋊C8—51no—
304C2×C3⋊C8—51no—
305C23×C5—61no—
306C23×C5D3×D411yescharacteristic
307C22×D5—21no—
308C5×Q8—32no—
309C5×Q8—61no—
310C5×D4—32no—
311C5×D4—64no—
312C5×D4—61no—
313C2×C4×C5—22no—
314C2×C4×C5—32no—
315C2×C4×C5—32no—
316C2×C4×C5—64no—
317C2×C4×C5—61no—
318C2×C4×C5—64no—
319C2×C4×C5—124no—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5#23712yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—24no—
325C2×Dic5—21no—
326C2×Dic5—62no—
327D20—21no—
328D20C2×C4×D312yes—
329C4×D5—24no—
330C4×D5—124no—
331Dic10—21no—
332Dic10C2×C4×D312yes—
333#168—22no—
334#168—32no—
335#168—32no—
336C2×#41—31no—
337C2×#41—51no—
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—51no—
344C22×C8—151no—
345C4×Q8—32no—
346C4×Q8—152no—
347C4×D4—32no—
348C4×D4—62no—
349C4×D4—152no—
350C4×D4—302no—
351#117—61no—
352#117—151no—
353#117—301no—
354#117D3×D511yescharacteristic
355C2×C42—31no—
356C2×C42—61no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—52no—
361#103—152no—
362#102—52no—
363#102—152no—
364C4×C8—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5C2×#13512yes—
369C3×D5—42no—
370C5×D3—42no—
371C23×C3—101no—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—21no—
374C3×Q8—52no—
375C3×Q8—101no—
376C3×D4—52no—
377C3×D4—104no—
378C3×D4—101no—
379C2×C3×C4—22no—
380C2×C3×C4—101no—
381C2×C3×C4—104no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4#70912yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—24no—
387C2×Dic3—21no—
388C2×Dic3—24no—
389C2×Dic3—102no—
390C2×Dic3—204no—
391C2×Dic3C2×C22⋊D512yes—
392C2×Dic3C2×C22⋊D512yes—
393D12—21no—
394D12C2×C4×D512yes—
395C4×D3—24no—
396C4×D3—44no—
397Dic6—21no—
398Dic6C2×C4×D512yes—
399C3×C8—102no—
400C3⋊C8—52no—
401C3⋊C8—52no—
402C22×C5—22no—
403C22×C5—62no—
404C22×C5—122no—
405C22×C5#67⋊C412yes—
406C22×C5C2×D3×D411yescharacteristic
407C2×D5—22no—
408C2×D5—42no—
409C4×C5—34no—
410C4×C5—42no—
411C4×C5—62no—
412C4×C5—62no—
413C4×C5#67⋊C412yes—
414C4×C5C22×C4×D311yescharacteristic
415C4×C5C2×#23711yescharacteristic
416Dic5—22no—
417Dic5—122no—
418#41—34no—
419#41—54no—
420#41—62no—
421#41—102no—
422C2×Q8—31no—
423C2×Q8—51no—
424C2×D4—31no—
425C2×D4—51no—
426C2×D4—61no—
427C2×D4—101no—
428C22×C4—32no—
429C22×C4—62no—
430C22×C4—61no—
431C22×C4—101no—
432C22×C4—302no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—52no—
439C2×C8—102no—
440C2×C8—154no—
441C2×C8—151no—
442C2×C8—151no—
443C4⋊C4—62no—
444C4⋊C4—152no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—21no—
448C22⋊C4—62no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—21no—
452C42—31no—
453C42—31no—
454C42—32no—
455C42—62no—
456C42—302no—
457C42—301no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—102no—
461C22×C3—202no—
462C22×C3C4×C22⋊D512yes—
463C22×C3C22×C22⋊D511yescharacteristic
464C2×D3—22no—
465C2×D3—42no—
466C3×C4—42no—
467C3×C4—102no—
468C3×C4C4×C22⋊D512yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#70911yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—202no—
474Dic3#409614yescomplemented
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×#67⋊C411yescharacteristic
478C2×C5D3×#13512yes—
479D5—42no—
480C23—61no—
481C23—101no—
482C23D3×C22⋊D511yescharacteristic
483Q8—32no—
484Q8—52no—
485Q8—61no—
486Q8—101no—
487D4—32no—
488D4—52no—
489D4—64no—
490D4—61no—
491D4—104no—
492D4—101no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—64no—
497C2×C4—61no—
498C2×C4—64no—
499C2×C4—101no—
500C2×C4—104no—
501C2×C4—124no—
502C2×C4—302no—
503C2×C4—604no—
504C2×C4#676512yes—
505C2×C4C4×D3×D512yes—
506C2×C4D3×C22⋊D511yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—102no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—202no—
513C2×C3C2×C4×C22⋊D511yescharacteristic
514C2×C3C2×#409612yes—
515D3—42no—
516C5#7881811yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—102no—
520C22—122no—
521C22—202no—
522C22#9144112yes—
523C22C2×D3×C22⋊D511yescharacteristic
524C4—34no—
525C4—42no—
526C4—62no—
527C4—62no—
528C4—102no—
529C4—602no—
530C4#9144112yes—
531C4C2×#676511yescharacteristic
532C4C2×C4×D3×D511yescharacteristic
533C3C4×#409611yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—202no—
537C2C2×#9144111yescharacteristic
538C2D3×#409612yes—
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91297C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5522C2semidirect
2. Dic3×#709C2semidirect
4. #11751099C2semidirect
5. C3×#65291C2semidirect
6. #11748388C2semidirect
7. C2×Dic3×#168C2semidirect
8. #11747266C2semidirect
9. #11747264C2semidirect
10. #11747221C2semidirect
11. #11747219C2semidirect
33. #91297C4semidirect
52. #65291D3semidirect
59. C5×#235C2×C4semidirect
66. C3×#709C2×C4semidirect
77. C2×C3⋊#168C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
93. #6655C2×C4semidirect
94. #6652C2×C4semidirect
97. #5522D5semidirect
209. #709C4×D3semidirect
264. C5×Dic3#135semidirect
276. #235C4×D5semidirect
458. C3×C5C4×#135semidirect
474. Dic3#4096semidirect
516. C5#78818semidirect
533. C3C4×#4096semidirect

Maximal subgroups

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

subgroupindex
C5×#55222
Dic3×#7092
C2×#912972
#117510992
C3×#652912
#117483882
C2×Dic3×#1682
#117472662
#117472642
#117472212
#117472192
C4×#40963
#788185