Finite Group Databasebeta

← #14416265

Subgroups — #14416265

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
1C2×#91839C211yesmaximal, characteristic
2C3×#41×Dic5C211yesmaximal, characteristic, complemented
3#11754414C211yesmaximal, characteristic, complemented
4C5×#5233C211yesmaximal, characteristic, complemented
5#11749244C212yesmaximal, complemented
6#11749221C212yesmaximal, complemented
7#11748998C212yesmaximal, complemented
8#11748975C212yesmaximal, complemented
9#11748469C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic, complemented
11C2×Dic5×C3⋊C8C211yesmaximal, characteristic, complemented
12#10610549—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15#91839C418yescomplemented
16C2×#6718C2211yescharacteristic
17C2×#6717C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C5×#926C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×Q8×Dic5C2212yes—
24C3×D4×Dic5—22no—
25C3×D4×Dic5C2212yes—
26C3×#4072—21no—
27C3×#4072C2211yescharacteristic
28C2×C3×C4×Dic5—21no—
29C2×C3×C4×Dic5C2211yescharacteristic
30#91552—22no—
31#91418C2212yes—
32C4×#1200—21no—
33#91386—21no—
34#91333C2212yes—
35C5×#835C2212yes—
36C5×#832C2212yes—
37#90989C2212yes—
38#90986C2212yes—
39#90974C2212yes—
40#90968C2212yes—
41Dic5×C3⋊C8C2212yes—
42Dic5×C3⋊C8C2212yes—
43C4×#950—51nomaximal, Hall
44#41×Dic5D311yescharacteristic, complemented
45C2×#4096—31no—
46#65856—31no—
47C5×#416—31no—
48#65402—31no—
49C2×C8×Dic5—31no—
50#65287—31no—
51#65079—32no—
52#65077—32no—
53#65047—32no—
54#65045—32no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817C2×C414yescomplemented
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C22×C3×Dic5—22no—
69C22×C3×Dic5D412yes—
70C2×#1200—22no—
71#6718C2×C414yescomplemented
72#6717C2×C414yescomplemented
73#6716C2×C414yescomplemented
74#6715C2×C414yescomplemented
75C2×C3⋊#168C2×C414yescomplemented
76C2×C3⋊#168C2311yescharacteristic
77C2×C3⋊#168C2311yescharacteristic
78C5×#217—21no—
79C5×C4⋊Dic3C2312yes—
80C4×C5×Dic3—21no—
81C2×C5×C3⋊C8—22no—
82C2×C5×C3⋊C8C2312yes—
83C3×C22⋊Dic5—21no—
84C3×C22⋊Dic5—22no—
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5C2312yes—
87C3×C4×Dic5—21no—
88C3×C4×Dic5—22no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2312yes—
92#6669—22no—
93#6667—22no—
94Dic3×Dic5—22no—
95C3×C4×#41—51no—
96C2×#950—51no—
97C4×#235—51no—
98#5233D511yescharacteristic, complemented
99C4×#216—52no—
100C4×#215—52no—
101C4×#214—52no—
102C4×#213—52no—
103#5002—51no—
104#4998—51no—
105C2×C4×C3⋊C8—51no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C22×C5×C8—31no—
109C5×#117—31no—
110#4096—38no—
111Q8×Dic5C2×D312yes—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—22no—
115D4×Dic5C2×D312yes—
116C2×#687—31no—
117C2×#686—31no—
118#4072—21no—
119#4072C2×D311yescharacteristic
120C2×C4×Dic5—21no—
121C2×C4×Dic5C2×D311yescharacteristic
122C22×#168—31no—
123#4039—32no—
124#4033—32no—
125#4027—62no—
126#4018—61no—
127C42×D5—61no—
128C5×#103—32no—
129C5×#102—32no—
130#3953—32no—
131#3948—32no—
132C8×Dic5—32no—
133C8×Dic5—32no—
134#3940—32no—
135#3939—32no—
136C4×#135—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—24no—
152C2×Dic15—21no—
153D60—21no—
154D60C22×C412yes—
155C4×D15—24no—
156Dic30—21no—
157Dic30C22×C412yes—
158C2×C5×Dic3—22no—
159C2×C3×Dic5—24no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—44no—
162C2×C3×Dic5C2×D412yes—
163C2×C3×Dic5C2×D412yes—
164#1200—44no—
165C3⋊#168C22×C412yes—
166C3⋊#168C22×C412yes—
167C5×C3⋊C8—22no—
168C2×C3×#41C2×D511yescharacteristic
169C2×#235—51no—
170C3×C4×Q8—52no—
171C3×C4×D4—52no—
172C3×C4×D4—102no—
173C3×#117—51no—
174C3×#117—101no—
175C2×C3×C42—51no—
176C2×C3×C42—101no—
177#950—58no—
178C2×#216—51no—
179C2×#215—51no—
180C2×#214—51no—
181C2×#213—51no—
182C4×#67—102no—
183#926C2×D511yescharacteristic
184C22×C3⋊C8—51no—
185C22×C3⋊C8C2×D511yescharacteristic
186C4×D12—52no—
187#872—101no—
188C42×D3—101no—
189C4×Dic6—52no—
190#835C2×D512yes—
191#832C2×D512yes—
192#810—52no—
193#809—52no—
194#808—52no—
195#807—52no—
196C4×C3⋊C8—52no—
197C4×C3⋊C8—52no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—22no—
207C22×Dic5#6712yes—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C5×C4⋊C4—32no—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219C22⋊Dic5—21no—
220C22⋊Dic5—22no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—62no—
226C4⋊Dic5—22no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229C4×Dic5—21no—
230C4×Dic5—22no—
231C4×Dic5—62no—
232C4×Dic5#6711yescharacteristic
233C4×Dic5#6711yescharacteristic
234C4×Dic5C22×D312yes—
235C2×#168—34no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#135—151no—
239C4×#41—51no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—151no—
246#416—31no—
247#416—151no—
248C2×C4×C8—151no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—42no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—42no—
256C3×C4×C5—22no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261C3×Dic5—22no—
262C3×Dic5—42no—
263C3×Dic5#13514yescomplemented
264C5×Dic3—42no—
265C3×#41—22no—
266C3×#41C4×D514yescomplemented
267C2×C3×Q8C22×D511yescharacteristic
268C2×C3×D4—21no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4—52no—
272C22×C3×C4—102no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—101no—
275#235—54no—
276#235—102no—
277C2×D12—51no—
278C2×C4×D3—101no—
279C2×C4×D3—102no—
280C2×Dic6—51no—
281C3×C4⋊C4—52no—
282C3×C4⋊C4—102no—
283C3×C22⋊C4—102no—
284C3×C22⋊C4—101no—
285C3×C42—51no—
286C3×C42—51no—
287C3×C42—52no—
288C3×C42—102no—
289C3×C42—101no—
290#217—21no—
291#216—54no—
292#215—54no—
293#214—54no—
294#213—54no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3C22×D512yes—
297Dic3⋊C4—102no—
298C4×Dic3—21no—
299C4×Dic3—102no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—54no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—51no—
304C2×C3⋊C8C22×D512yes—
305C23×C5—21no—
306C23×C5C2×#6711yescharacteristic
307C22×D5—61no—
308C5×Q8—21no—
309C5×Q8C2×C4×D312yes—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4C2×C4×D312yes—
313C2×C4×C5—21no—
314C2×C4×C5—24no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5#23512yes—
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—64no—
321C2×Dic5—24no—
322C2×Dic5—22no—
323C2×Dic5—44no—
324C2×Dic5—61no—
325C2×Dic5C2×#6712yes—
326C2×Dic5C2×#6712yes—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—62no—
334#168—32no—
335#168—32no—
336C2×#41—151no—
337C2×#41D3×D511yescharacteristic
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—31no—
344C22×C8—151no—
345C4×Q8—52no—
346C4×Q8—152no—
347C4×D4—52no—
348C4×D4—102no—
349C4×D4—152no—
350C4×D4—302no—
351#117—31no—
352#117—51no—
353#117—101no—
354#117—301no—
355C2×C42—51no—
356C2×C42—101no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—32no—
361#103—152no—
362#102—32no—
363#102—152no—
364C4×C8—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5C2×#13512yes—
370D15—42no—
371C23×C3—21no—
372C23×C3D4×D511yescharacteristic
373C22×D3—101no—
374C3×Q8—21no—
375C3×Q8C2×C4×D512yes—
376C3×D4—24no—
377C3×D4—21no—
378C3×D4C2×C4×D512yes—
379C2×C3×C4—21no—
380C2×C3×C4—24no—
381C2×C3×C4—52no—
382C2×C3×C4—52no—
383C2×C3×C4—104no—
384C2×C3×C4—102no—
385C2×C3×C4—204no—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4#71112yes—
389C2×C3×C4C23×D511yescharacteristic
390#67—104no—
391C2×Dic3—22no—
392C2×Dic3—101no—
393D12—52no—
394D12—101no—
395C4×D3—104no—
396C4×D3—204no—
397Dic6—52no—
398Dic6—101no—
399C3⋊C8—22no—
400C3⋊C8—52no—
401C3⋊C8—52no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—42no—
405C22×C5C4×#6712yes—
406C22×C5C22×#6711yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—22no—
410C4×C5—122no—
411C4×C5C4×#6712yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23511yescharacteristic
414Dic5—22no—
415Dic5—42no—
416Dic5—62no—
417Dic5#95014yescomplemented
418#41—22no—
419#41—154no—
420#41—302no—
421#41#120014yescomplemented
422C2×Q8—151no—
423C2×Q8C2×D3×D511yescharacteristic
424C2×D4—21no—
425C2×D4—151no—
426C2×D4—301no—
427C2×D4C2×D3×D511yescharacteristic
428C22×C4—21no—
429C22×C4—52no—
430C22×C4—102no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—32no—
439C2×C8—62no—
440C2×C8—154no—
441C2×C8—151no—
442C2×C8—151no—
443C4⋊C4—32no—
444C4⋊C4—52no—
445C4⋊C4—102no—
446C4⋊C4—302no—
447C22⋊C4—61no—
448C22⋊C4—102no—
449C22⋊C4—101no—
450C22⋊C4—302no—
451C42—51no—
452C42—51no—
453C42—52no—
454C42—61no—
455C42—102no—
456C42—101no—
457C42—302no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—42no—
462C22×C3#402712yes—
463C22×C3C2×D4×D511yescharacteristic
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—22no—
467C3×C4—54no—
468C3×C4—102no—
469C3×C4—202no—
470C3×C4#402712yes—
471C3×C4C22×C4×D511yescharacteristic
472C3×C4C2×#71111yescharacteristic
473Dic3—42no—
474Dic3—102no—
475C2×C5—22no—
476C2×C5—42no—
477C2×C5C2×C4×#6711yescharacteristic
478C2×C5C2×#95012yes—
479D5—122no—
480C23—21no—
481C23—301no—
482C23D5×#6711yescharacteristic
483Q8—21no—
484Q8—152no—
485Q8—301no—
486Q8C2×#120012yes—
487D4—24no—
488D4—21no—
489D4—152no—
490D4—304no—
491D4—301no—
492D4C2×#120012yes—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—52no—
496C2×C4—52no—
497C2×C4—62no—
498C2×C4—104no—
499C2×C4—102no—
500C2×C4—204no—
501C2×C4—301no—
502C2×C4—304no—
503C2×C4—604no—
504C2×C4#678212yes—
505C2×C4C2×#120012yes—
506C2×C4D5×#6711yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—42no—
513C2×C3C2×#402711yescharacteristic
514C2×C3D5×#13512yes—
515D3—202no—
516C5C4×#95011yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—42no—
520C22—302no—
521C22—602no—
522C22#9155212yes—
523C22C2×D5×#6711yescharacteristic
524C4—22no—
525C4—54no—
526C4—102no—
527C4—122no—
528C4—202no—
529C4—302no—
530C4#9155212yes—
531C4C2×#678211yescharacteristic
532C4C22×#120011yescharacteristic
533C3#1061054911yescharacteristic, complemented, Sylow
534C2—22no—
535C2—42no—
536C2—602no—
537C2D5×#95012yes—
538C2C2×#9155211yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#41×Dic5C2semidirect
3. #11754414C2semidirect
4. C5×#5233C2semidirect
5. #11749244C2semidirect
6. #11749221C2semidirect
7. #11748998C2semidirect
8. #11748975C2semidirect
9. #11748469C2semidirect
10. #11748411C2semidirect
11. C2×Dic5×C3⋊C8C2semidirect
15. #91839C4semidirect
44. #41×Dic5D3semidirect
56. C3×C5×#41C2×C4semidirect
64. #6817C2×C4semidirect
71. #6718C2×C4semidirect
72. #6717C2×C4semidirect
73. #6716C2×C4semidirect
74. #6715C2×C4semidirect
75. C2×C3⋊#168C2×C4semidirect
98. #5233D5semidirect
199. C5×#41C4×D3semidirect
263. C3×Dic5#135semidirect
266. C3×#41C4×D5semidirect
417. Dic5#950semidirect
421. #41#1200semidirect
458. C3×C5C4×#135semidirect
516. C5C4×#950semidirect
533. C3#10610549semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C3×#41×Dic52
#117544142
C5×#52332
#117492442
#117492212
#117489982
#117489752
#117484692
#117484112
C2×Dic5×C3⋊C82
#106105493
C4×#9505