Finite Group Databasebeta

← #14416275

Subgroups — #14416275

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
1#11754455C211yesmaximal, characteristic, complemented
2#11754444C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic
4C2×C8×Dic15C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748469C211yesmaximal, characteristic, complemented
8#11747828C212yesmaximal, complemented
9#11747737C212yesmaximal, complemented
10#11747735C212yesmaximal, complemented
11#11747733C212yesmaximal, complemented
12#10610549—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C2×C4×Dic15C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#67⋊Dic5—22no—
21#91559—22no—
22#91435C2212yes—
23#91434C2212yes—
24C4×D3×Dic5—21no—
25C4×D5×Dic3—21no—
26#91371—21no—
27#91357—21no—
28#91344C2212yes—
29#91331C2212yes—
30C2×#6661C2211yescharacteristic
31C2×#6656C2211yescharacteristic
32C2×#6655C2211yescharacteristic
33#91297C418yescomplemented
34C2×#6652C2211yescharacteristic
35C8×Dic15C2212yes—
36C8×Dic15C2212yes—
37C5×#821C2212yes—
38C5×#816C2212yes—
39C3×#3953C2212yes—
40C3×#3948C2212yes—
41#90989C2212yes—
42#90986C2212yes—
43#78818—51nomaximal, Hall
44#41×Dic5—31no—
45C2×#4096—31no—
46#65856—31no—
47C5×#416—31no—
48#65402D311yescharacteristic, complemented
49C2×C8×Dic5—31no—
50#65287—31no—
51#65079—32no—
52#65077—32no—
53#65047—32no—
54#65045—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15D412yes—
57C2×C5×#67—21no—
58C5×#235—22no—
59C5×#235C2×C414yescomplemented
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C5×Dic6C2311yescharacteristic
63C2×C3×C22⋊D5—21no—
64C3×#709—22no—
65C3×#709C2×C414yescomplemented
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×D3×Dic5—22no—
70C2×D5×Dic3—22no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2312yes—
73C4×Dic15D411yescharacteristic
74C4×Dic15D411yescharacteristic
75C4×Dic15C2312yes—
76C2×C3⋊#168C2×C414yescomplemented
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C5×#217—21no—
80C5×C4⋊Dic3C2312yes—
81C4×C5×Dic3—21no—
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×C4×Dic5—21no—
85Dic3⋊Dic5—22no—
86#6668—22no—
87(C2×D3)⋊Dic5—22no—
88#6665—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C414yescomplemented
92#6656C2×C414yescomplemented
93#6655C2×C414yescomplemented
94#6652C2×C414yescomplemented
95Dic3×#41—51no—
96C2×#950—51no—
97#5522—51no—
98C3×#416—51no—
99#5113D511yescharacteristic, complemented
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
108C22×C5×C8C2×D311yescharacteristic
109C5×#117—31no—
110#4096—38no—
111Q8×Dic5—32no—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—32no—
115D4×Dic5—62no—
116C2×#687—31no—
117C2×#686—31no—
118#4072—61no—
119#4072C2×D311yescharacteristic
120C2×C4×Dic5—31no—
121C2×C4×Dic5—61no—
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#3953C2×D312yes—
131#3948C2×D312yes—
132C8×Dic5—32no—
133C8×Dic5—32no—
134#3940—32no—
135#3939—32no—
136C4×#135—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C22×C3×D5—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5#4112yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—24no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147C5×#67—24no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—22no—
150C5×D12—21no—
151C5×D12C22×C412yes—
152C4×C5×D3—24no—
153C5×Dic6—21no—
154C5×Dic6C22×C412yes—
155C3×C22⋊D5—24no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—24no—
161C3×Dic10—21no—
162C3×Dic10C22×C412yes—
163D3×Dic5—44no—
164D5×Dic3—44no—
165C3×C5×C8—22no—
166C3⋊#168C22×C412yes—
167C3⋊#168C22×C412yes—
168C2×C3×#41—51no—
169C2×#235C2×D511yescharacteristic
170C22×C3×C8C2×D511yescharacteristic
171C3×#117—51no—
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—101no—
181#926C2×D511yescharacteristic
182C2×C4×Dic3—51no—
183C2×C4×Dic3—101no—
184C22×C3⋊C8—51no—
185#893—52no—
186#887—52no—
187#67⋊C4—102no—
188#872—101no—
189C42×D3—101no—
190C3×#103—52no—
191C3×#102—52no—
192#821C2×D512yes—
193#816C2×D512yes—
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—61no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—21no—
206C22×Dic5—32no—
207C22×Dic5—62no—
208#709—22no—
209#709C4×D314yescomplemented
210C2×D20C22×D311yescharacteristic
211C2×C4×D5—21no—
212C2×C4×D5—62no—
213C2×Dic10C22×D311yescharacteristic
214C2×C5×C8—22no—
215C2×C5×C8C22×D312yes—
216C5×C4⋊C4—32no—
217C5×C22⋊C4—61no—
218C42×C5—61no—
219C22⋊Dic5—21no—
220C22⋊Dic5—62no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—62no—
226C4⋊Dic5—62no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229C4×Dic5—21no—
230C4×Dic5—31no—
231C4×Dic5—31no—
232C4×Dic5—32no—
233C4×Dic5—62no—
234C4×Dic5—62no—
235C2×#168—34no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#135—151no—
239C4×#41—151no—
240C4×#41—151no—
241C4×Q16—152no—
242C4×SD16—152no—
243C4×SD16—152no—
244C4×D8—152no—
245#427—151no—
246#416—31no—
247#416—51no—
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×C5C4×D412yes—
257C3×C4×C5C23×C411yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—22no—
260Dic15#13514yescomplemented
261C3×Dic5—22no—
262C3×Dic5—42no—
263C5×Dic3—22no—
264C5×Dic3—42no—
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—52no—
274C22×Dic3—102no—
275#235—22no—
276#235C4×D514yescomplemented
277C2×D12C22×D511yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—102no—
280C2×Dic6C22×D511yescharacteristic
281C2×C3×C8—22no—
282C2×C3×C8C22×D512yes—
283C3×C4⋊C4—52no—
284C3×C22⋊C4—101no—
285C3×C42—101no—
286#217—21no—
287#217—102no—
288#216—54no—
289#215—54no—
290#214—54no—
291#213—54no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—102no—
294C4⋊Dic3C22×D512yes—
295Dic3⋊C4—102no—
296C4×Dic3—21no—
297C4×Dic3—51no—
298C4×Dic3—51no—
299C4×Dic3—52no—
300C4×Dic3—102no—
301C4×Dic3—102no—
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—61no—
314C2×C4×C5—64no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5#23712yes—
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—24no—
321C2×Dic5—21no—
322C2×Dic5—22no—
323C2×Dic5—32no—
324C2×Dic5—32no—
325C2×Dic5—64no—
326C2×Dic5—124no—
327D20—21no—
328D20C2×C4×D312yes—
329C4×D5—24no—
330C4×D5—124no—
331Dic10—21no—
332Dic10C2×C4×D312yes—
333C5×C8—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—151no—
344C22×C8D3×D511yescharacteristic
345C4×Q8—152no—
346C4×Q8—152no—
347C4×D4—152no—
348C4×D4—152no—
349C4×D4—302no—
350C4×D4—302no—
351#117—31no—
352#117—51no—
353#117—301no—
354#117—301no—
355C2×C42—151no—
356C2×C42—301no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—32no—
361#103—52no—
362#102—32no—
363#102—52no—
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×C3D4×D511yescharacteristic
373C22×D3—21no—
374C3×Q8—52no—
375C3×Q8—101no—
376C3×D4—52no—
377C3×D4—104no—
378C3×D4—101no—
379C2×C3×C4—101no—
380C2×C3×C4—104no—
381C2×C3×C4—102no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71112yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—24no—
387C2×Dic3—21no—
388C2×Dic3—22no—
389C2×Dic3—52no—
390C2×Dic3—52no—
391C2×Dic3—104no—
392C2×Dic3—204no—
393D12—21no—
394D12C2×C4×D512yes—
395C4×D3—24no—
396C4×D3—204no—
397Dic6—21no—
398Dic6C2×C4×D512yes—
399C3×C8—22no—
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—62no—
410C4×C5—122no—
411C4×C5#67⋊C412yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23711yescharacteristic
414Dic5—22no—
415Dic5—34no—
416Dic5—42no—
417Dic5—62no—
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—61no—
429C22×C4—101no—
430C22×C4—152no—
431C22×C4—302no—
432C22×C4—302no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—22no—
439C2×C8—154no—
440C2×C8—151no—
441C2×C8—151no—
442C2×C8C2×D3×D512yes—
443C4⋊C4—32no—
444C4⋊C4—52no—
445C4⋊C4—302no—
446C4⋊C4—302no—
447C22⋊C4—61no—
448C22⋊C4—101no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—61no—
452C42—101no—
453C42—151no—
454C42—151no—
455C42—152no—
456C42—302no—
457C42—302no—
458C3×C5C4×#13511yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—102no—
461C22×C3—202no—
462C22×C3#402712yes—
463C22×C3C2×D4×D511yescharacteristic
464C2×D3—22no—
465C2×D3—42no—
466C3×C4—102no—
467C3×C4—202no—
468C3×C4#402712yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#71111yescharacteristic
471Dic3—22no—
472Dic3—42no—
473Dic3—54no—
474Dic3—102no—
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×#67⋊C411yescharacteristic
478C2×C5D3×#13512yes—
479D5—42no—
480C23—61no—
481C23—101no—
482C23#677711yescharacteristic
483Q8—32no—
484Q8—52no—
485Q8—61no—
486Q8—101no—
487D4—32no—
488D4—52no—
489D4—64no—
490D4—61no—
491D4—104no—
492D4—101no—
493C2×C4—61no—
494C2×C4—64no—
495C2×C4—62no—
496C2×C4—101no—
497C2×C4—104no—
498C2×C4—102no—
499C2×C4—152no—
500C2×C4—152no—
501C2×C4—304no—
502C2×C4—604no—
503C2×C4—604no—
504C2×C4C4×D3×D512yes—
505C2×C4#677711yescharacteristic
506C2×C4#678012yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—22no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—202no—
513C2×C3C2×#402711yescharacteristic
514C2×C3D5×#13512yes—
515D3—42no—
516C5#7881811yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—102no—
520C22—122no—
521C22—202no—
522C22#9144212yes—
523C22C2×#677711yescharacteristic
524C4—62no—
525C4—102no—
526C4—122no—
527C4—154no—
528C4—202no—
529C4—302no—
530C4#9144212yes—
531C4C2×C4×D3×D511yescharacteristic
532C4C2×#678011yescharacteristic
533C3#1061054911yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—202no—
537C2#1175397812yes—
538C2C2×#9144211yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91297C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C4×#135
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754455C2semidirect
2. #11754444C2semidirect
4. C2×C8×Dic15C2semidirect
5. C5×#5113C2semidirect
6. C3×#65402C2semidirect
7. #11748469C2semidirect
8. #11747828C2semidirect
9. #11747737C2semidirect
10. #11747735C2semidirect
11. #11747733C2semidirect
33. #91297C4semidirect
48. #65402D3semidirect
59. C5×#235C2×C4semidirect
65. C3×#709C2×C4semidirect
76. C2×C3⋊#168C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
93. #6655C2×C4semidirect
94. #6652C2×C4semidirect
99. #5113D5semidirect
209. #709C4×D3semidirect
260. Dic15#135semidirect
276. #235C4×D5semidirect
458. C3×C5C4×#135semidirect
516. C5#78818semidirect
533. C3#10610549semidirect

Maximal subgroups

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

subgroupindex
#117544552
#117544442
C2×#912972
C2×C8×Dic152
C5×#51132
C3×#654022
#117484692
#117478282
#117477372
#117477352
#117477332
#106105493
#788185