Finite Group Databasebeta

← #14416259

Subgroups — #14416259

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
1C3×#65856C211yesmaximal, characteristic, complemented
2Dic5×#235C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic
4#11751099C211yesmaximal, characteristic, complemented
5C5×#5002C211yesmaximal, characteristic, complemented
6#11748365C211yesmaximal, characteristic, complemented
7C2×Dic5×C3⋊C8C211yesmaximal, characteristic, complemented
8#11747263C212yesmaximal, complemented
9#11747261C212yesmaximal, complemented
10#11747218C212yesmaximal, complemented
11#11747216C212yesmaximal, complemented
12#10610549—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16#91815C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C3×#4039C2212yes—
21C3×#4033C2212yes—
22C3×#4027—22no—
23C3×#4018—21no—
24C3×C42×D5—21no—
25Dic5×#67—22no—
26Dic5×D12C2212yes—
27C4×D3×Dic5—21no—
28#91371—21no—
29Dic5×Dic6C2212yes—
30C2×#6661C2211yescharacteristic
31C2×#6656C2211yescharacteristic
32C2×#6655C2211yescharacteristic
33#91297C418yescomplemented
34C2×#6652C2211yescharacteristic
35#91092C2212yes—
36#91091C2212yes—
37C5×#810C2212yes—
38C5×#809C2212yes—
39#90971C2212yes—
40#90965C2212yes—
41Dic5×C3⋊C8C2212yes—
42Dic5×C3⋊C8C2212yes—
43C4×#950—51nomaximal, Hall
44#41×Dic5—31no—
45C2×#4096—31no—
46#65856D311yescharacteristic, complemented
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—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C5×#235—22no—
58C5×#235C2×C414yescomplemented
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×C22⋊D5—21no—
63C22×C3×Dic5D412yes—
64C3×#709—22no—
65C3×#709C2×C414yescomplemented
66C2×C3×D20C2311yescharacteristic
67C2×C3×C4×D5—21no—
68C2×C3×C4×D5—22no—
69C2×C3×Dic10C2311yescharacteristic
70C2×D3×Dic5—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
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yes—
82C3×#685—22no—
83C3×#683—22no—
84C3×C4×Dic5—22no—
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5C2312yes—
88Dic3⋊Dic5—22no—
89(C2×D3)⋊Dic5—22no—
90Dic3×Dic5—22no—
91#6661C2×C414yescomplemented
92#6656C2×C414yescomplemented
93#6655C2×C414yescomplemented
94#6652C2×C414yescomplemented
95C3×C4×#41—51no—
96C2×#950—51no—
97C4×#235—51no—
98#5233—51no—
99C4×#216—52no—
100C4×#215—52no—
101C4×#214—52no—
102C4×#213—52no—
103#5002D511yescharacteristic, complemented
104#4998—51no—
105C2×C4×C3⋊C8—51no—
106C2×C5×#41—31no—
107C2×#709C2×D311yescharacteristic
108C22×C5×C8—31no—
109C5×#117C2×D311yescharacteristic
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—31no—
119#4072—61no—
120C2×C4×Dic5—61no—
121C2×C4×Dic5C2×D311yescharacteristic
122C22×#168—31no—
123#4039C2×D312yes—
124#4033C2×D312yes—
125#4027—22no—
126#4018—21no—
127C42×D5—21no—
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×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—
148C5×D12—21no—
149C5×D12C22×C412yes—
150C4×C5×D3—24no—
151C5×Dic6—21no—
152C5×Dic6C22×C412yes—
153C3×C22⋊D5—24no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—24no—
156C2×C3×Dic5C2×D412yes—
157C2×C3×Dic5C2×D412yes—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—24no—
161C3×C4×D5—44no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164D3×Dic5—44no—
165C3⋊#168C22×C412yes—
166C3⋊#168C22×C412yes—
167C5×C3⋊C8—22no—
168C2×C3×#41—51no—
169C2×#235C2×D511yescharacteristic
170C3×C4×Q8—52no—
171C3×C4×D4—52no—
172C3×C4×D4—102no—
173C3×#117—101no—
174C3×#117C2×D511yescharacteristic
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#926—51no—
184C22×C3⋊C8—51no—
185C22×C3⋊C8C2×D511yescharacteristic
186C4×D12—52no—
187#872—101no—
188C42×D3—101no—
189C4×Dic6—52no—
190#835—52no—
191#832—52no—
192#810C2×D512yes—
193#809C2×D512yes—
194#808—52no—
195#807—52no—
196C4×C3⋊C8—52no—
197C4×C3⋊C8—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—62no—
207C22×Dic5#6712yes—
208#709—22no—
209#709C4×D314yescomplemented
210C2×D20C22×D311yescharacteristic
211C2×C4×D5—21no—
212C2×C4×D5—22no—
213C2×Dic10C22×D311yescharacteristic
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C5×C4⋊C4C22×D312yes—
217C5×C22⋊C4—21no—
218C42×C5—21no—
219C22⋊Dic5—61no—
220C22⋊Dic5—62no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—22no—
226C4⋊Dic5—32no—
227C4⋊Dic5—62no—
228#683—22no—
229C4×Dic5—22no—
230C4×Dic5—61no—
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×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—
262C3×Dic5—22no—
263C3×Dic5#13514yescomplemented
264C5×Dic3—22no—
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—51no—
268C2×C3×D4—51no—
269C2×C3×D4—101no—
270C22×C3×C4—52no—
271C22×C3×C4—102no—
272C22×C3×C4—101no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—21no—
275#235—22no—
276#235C4×D514yescomplemented
277C2×D12C22×D511yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—102no—
280C2×Dic6C22×D511yescharacteristic
281C3×C4⋊C4—102no—
282C3×C4⋊C4C22×D512yes—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—102no—
285C3×C42—21no—
286C3×C42—51no—
287C3×C42—51no—
288C3×C42—52no—
289C3×C42—102no—
290#217—101no—
291#216—54no—
292#215—54no—
293#214—54no—
294#213—54no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—52no—
297Dic3⋊C4—102no—
298C4×Dic3—102no—
299C4×Dic3—101no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—54no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—51no—
304C2×C3⋊C8C22×D512yes—
305C23×C5—61no—
306C23×C5C2×#6711yescharacteristic
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—61no—
315C2×C4×C5—64no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5#23512yes—
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—24no—
321C2×Dic5—21no—
322C2×Dic5—24no—
323C2×Dic5—62no—
324C2×Dic5—124no—
325C2×Dic5C2×#6712yes—
326C2×Dic5C2×#6712yes—
327D20—21no—
328D20C2×C4×D312yes—
329C4×D5—24no—
330C4×D5—44no—
331Dic10—21no—
332Dic10C2×C4×D312yes—
333C5×C8—62no—
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—31no—
344C22×C8—151no—
345C4×Q8—52no—
346C4×Q8—152no—
347C4×D4—52no—
348C4×D4—102no—
349C4×D4—152no—
350C4×D4—302no—
351#117—101no—
352#117—151no—
353#117—301no—
354#117D3×D511yescharacteristic
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×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—22no—
380C2×C3×C4—52no—
381C2×C3×C4—52no—
382C2×C3×C4—104no—
383C2×C3×C4—101no—
384C2×C3×C4—104no—
385C2×C3×C4—204no—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4D4×D511yescharacteristic
388C2×C3×C4#71112yes—
389C2×C3×C4C23×D511yescharacteristic
390#67—24no—
391C2×Dic3—21no—
392C2×Dic3—102no—
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×C5C4×#6712yes—
406C22×C5C22×#6711yescharacteristic
407C2×D5—22no—
408C2×D5—42no—
409C4×C5—42no—
410C4×C5—62no—
411C4×C5C4×#6712yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23511yescharacteristic
414Dic5—22no—
415Dic5—22no—
416Dic5—122no—
417Dic5#95014yescomplemented
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—52no—
429C22×C4—61no—
430C22×C4—102no—
431C22×C4—101no—
432C22×C4—302no—
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—102no—
444C4⋊C4—152no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D512yes—
447C22⋊C4—21no—
448C22⋊C4—102no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—21no—
452C42—51no—
453C42—51no—
454C42—52no—
455C42—102no—
456C42—302no—
457C42—301no—
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—42no—
467C3×C4—54no—
468C3×C4—102no—
469C3×C4—102no—
470C3×C4#402712yes—
471C3×C4C22×C4×D511yescharacteristic
472C3×C4C2×#71111yescharacteristic
473Dic3—22no—
474Dic3—202no—
475C2×C5—22no—
476C2×C5—122no—
477C2×C5C2×C4×#6711yescharacteristic
478C2×C5C2×#95012yes—
479D5—42no—
480C23—61no—
481C23—101no—
482C23D5×#6711yescharacteristic
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—52no—
495C2×C4—52no—
496C2×C4—61no—
497C2×C4—64no—
498C2×C4—104no—
499C2×C4—101no—
500C2×C4—104no—
501C2×C4—204no—
502C2×C4—302no—
503C2×C4—604no—
504C2×C4#677212yes—
505C2×C4C4×D3×D512yes—
506C2×C4D5×#6711yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—202no—
513C2×C3C2×#402711yescharacteristic
514C2×C3D5×#13512yes—
515D3—42no—
516C5C4×#95011yescharacteristic, complemented, Sylow
517C22—22no—
518C22—62no—
519C22—102no—
520C22—122no—
521C22—202no—
522C22#9144012yes—
523C22C2×D5×#6711yescharacteristic
524C4—42no—
525C4—54no—
526C4—62no—
527C4—102no—
528C4—102no—
529C4—602no—
530C4#9144012yes—
531C4C2×#677211yescharacteristic
532C4C2×C4×D3×D511yescharacteristic
533C3#1061054911yescharacteristic, complemented, Sylow
534C2—22no—
535C2—122no—
536C2—202no—
537C2C2×#9144011yescharacteristic
538C2D5×#95012yes—
subgroupG/H
centerC2×C4D5×#67
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. C3×#65856C2semidirect
2. Dic5×#235C2semidirect
4. #11751099C2semidirect
5. C5×#5002C2semidirect
6. #11748365C2semidirect
7. C2×Dic5×C3⋊C8C2semidirect
8. #11747263C2semidirect
9. #11747261C2semidirect
10. #11747218C2semidirect
11. #11747216C2semidirect
33. #91297C4semidirect
46. #65856D3semidirect
58. C5×#235C2×C4semidirect
65. C3×#709C2×C4semidirect
77. C2×C3⋊#168C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
93. #6655C2×C4semidirect
94. #6652C2×C4semidirect
103. #5002D5semidirect
209. #709C4×D3semidirect
263. C3×Dic5#135semidirect
276. #235C4×D5semidirect
417. Dic5#950semidirect
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
C3×#658562
Dic5×#2352
C2×#912972
#117510992
C5×#50022
#117483652
C2×Dic5×C3⋊C82
#117472632
#117472612
#117472182
#117472162
#106105493
C4×#9505