Finite Group Databasebeta

← #14417778

Subgroups — #14417778

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65838C211yesmaximal, characteristic, complemented
2#11754513C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic
4C2×#91092C211yesmaximal, characteristic, complemented
5C5×#4966C211yesmaximal, characteristic, complemented
6#11748369C211yesmaximal, characteristic, complemented
7#11748320C211yesmaximal, characteristic, complemented
8#11747468C212yesmaximal, complemented
9#11747262C212yesmaximal, complemented
10#11747261C212yesmaximal, complemented
11#11747218C212yesmaximal, complemented
12#10610600—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×C4×C22⋊D5—22no—
20C3×#4072C2211yescharacteristic
21C3×#4039C2212yes—
22C3×#4038—21no—
23C3×D5×C4⋊C4—21no—
24C3×#4033C2212yes—
25#67⋊Dic5—22no—
26D3×C4⋊Dic5—21no—
27Dic5×D12C2212yes—
28#91338—21no—
29Dic5×Dic6C2212yes—
30C2×#6661C2211yescharacteristic
31C2×#6656C2211yescharacteristic
32C2×#6655C2211yescharacteristic
33#91297C418yescomplemented
34C2×#6652C2211yescharacteristic
35#91092C2212yes—
36#91092C2212yes—
37C5×#810C2212yes—
38C5×#809C2212yes—
39#90971C2212yes—
40#90965C2212yes—
41#90952C2212yes—
42Dic5×C3⋊C8C2212yes—
43#82558—51nomaximal, Hall
44#66161—31no—
45C2×#4096—31no—
46#65838D311yescharacteristic, complemented
47C5×#417—31no—
48#65422—31no—
49#65411—31no—
50C2×#3940—31no—
51#65078—32no—
52#65077—32no—
53#65074—32no—
54#65047—32no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C2×C5×#67—21no—
59C5×#235—22no—
60C5×#235C2×C414yescomplemented
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2311yescharacteristic
64C2×C3×C22⋊D5—21no—
65C3×#709—22no—
66C3×#709C2×C414yescomplemented
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×C4×D5—22no—
70C2×C3×Dic10C2311yescharacteristic
71C2×D3×Dic5—22no—
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4C2312yes—
74C4⋊Dic15—21no—
75C4⋊Dic15C2312yes—
76C2×C3⋊#168C2×C414yescomplemented
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C5×#208—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×C22⋊Dic5D412yes—
82C3×#685—22no—
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4⋊Dic5D411yescharacteristic
85C3×#683—22no—
86C3×C4×Dic5—22no—
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×#520—51no—
96C2×#950—51no—
97#5523—51no—
98#5232—51no—
99#5030—52no—
100C4×#215—52no—
101C4×#214—52no—
102#5014—52no—
103#4997—51no—
104#4966D511yescharacteristic, complemented
105C2×#808—51no—
106C2×C5×#41—31no—
107C2×#709C2×D311yescharacteristic
108C2×C5×M16—31no—
109C2×C5×C4⋊C4C2×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—
118C4×C22⋊D5—22no—
119#4072—61no—
120#4072C2×D311yescharacteristic
121C2×C4⋊Dic5—31no—
122C2×C4⋊Dic5—61no—
123C22×#168—31no—
124#4039C2×D312yes—
125#4038—21no—
126D5×C4⋊C4—21no—
127#4033C2×D312yes—
128C5×#103—32no—
129C5×#102—32no—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133C8×Dic5—32no—
134#3940—32no—
135#3940—32no—
136#2952—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C22×C3×D5—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—81no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15—81no—
148C5×#67—24no—
149C2×C5×Dic3—21no—
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×Dic5C2×D412yes—
158C2×C3×Dic5C2×D412yes—
159C3×D20—21no—
160C3×D20C22×C412yes—
161C3×C4×D5—24no—
162C3×C4×D5—82no—
163C3×Dic10—21no—
164C3×Dic10C22×C412yes—
165D3×Dic5—82no—
166C3⋊#168C22×C412yes—
167C3⋊#168C22×C412yes—
168C5×C3⋊C8—22no—
169C2×C3×#41—51no—
170C2×#235C2×D511yescharacteristic
171C3×C4×Q8—52no—
172C3×C4×D4—52no—
173C3×C4×D4—102no—
174C3×#117—51no—
175C3×#117—101no—
176C2×C3×C4⋊C4—101no—
177C2×C3×C4⋊C4C2×D511yescharacteristic
178#950—58no—
179C2×#216—51no—
180C2×#215—51no—
181C2×#214—51no—
182C2×#213—51no—
183C2×C4⋊Dic3—51no—
184C2×#208C2×D511yescharacteristic
185C22×C3⋊C8—51no—
186#892—101no—
187D3×C4⋊C4—101no—
188#67⋊C4—102no—
189C4×D12—52no—
190C4×Dic6—52no—
191#835—52no—
192#832—52no—
193#810C2×D512yes—
194#809C2×D512yes—
195#808—52no—
196#808—52no—
197#803—52no—
198C4×C3⋊C8—52no—
199C5×#41—34no—
200C5×#41—62no—
201C2×C5×Q8—31no—
202C2×C5×D4—31no—
203C2×C5×D4—61no—
204C22×C4×C5—21no—
205C22×C4×C5—61no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—21no—
208C22×Dic5—61no—
209C22×Dic5—62no—
210#709—22no—
211#709C4×D314yescomplemented
212C2×D20C22×D311yescharacteristic
213C2×C4×D5—21no—
214C2×C4×D5—22no—
215C2×Dic10C22×D311yescharacteristic
216C5×M16—62no—
217C2×C5×C8—32no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4C22×D312yes—
220C22⋊Dic5—62no—
221C22⋊Dic5#6712yes—
222#689—34no—
223#688—34no—
224#687—34no—
225#686—34no—
226#685—22no—
227C4⋊Dic5—32no—
228C4⋊Dic5—61no—
229C4⋊Dic5—62no—
230C4⋊Dic5#6711yescharacteristic
231C4⋊Dic5#6711yescharacteristic
232#683—22no—
233C4×Dic5—22no—
234C4×Dic5—62no—
235C4×Dic5C22×D312yes—
236C2×#168—34no—
237C2×#168—31no—
238C2×#168—31no—
239C2×#135—151no—
240#520—51no—
241#520—151no—
242#442—152no—
243#441—152no—
244C4×SD16—152no—
245C4×SD16—152no—
246C2×#106—151no—
247#417—31no—
248#417—151no—
249#405—151no—
250C22×C3×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×C5×D3—22no—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C2×C3×D5—22no—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C3×C4×C5—42no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—42no—
265C3×Dic5—22no—
266C3×Dic5—22no—
267C3×Dic5—22no—
268C5×Dic3—22no—
269C3×#41—54no—
270C3×#41—102no—
271C2×C3×Q8—51no—
272C2×C3×D4—51no—
273C2×C3×D4—101no—
274C22×C3×C4—21no—
275C22×C3×C4—102no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—21no—
279C22×Dic3—101no—
280#235—22no—
281#235C4×D514yescomplemented
282C2×D12C22×D511yescharacteristic
283C2×C4×D3—21no—
284C2×C4×D3—102no—
285C2×Dic6C22×D511yescharacteristic
286C3×C4⋊C4—21no—
287C3×C4⋊C4—51no—
288C3×C4⋊C4—51no—
289C3×C4⋊C4—102no—
290C3×C4⋊C4C22×D512yes—
291C3×C22⋊C4—52no—
292C3×C22⋊C4—102no—
293C3×C42—52no—
294C3×C42—102no—
295#216—54no—
296#215—54no—
297#214—54no—
298#213—54no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—52no—
301C4⋊Dic3—101no—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304#208—22no—
305C2×C3⋊C8—54no—
306C2×C3⋊C8—51no—
307C2×C3⋊C8—51no—
308C2×C3⋊C8C22×D512yes—
309C23×C5—61no—
310C23×C5C2×#6711yescharacteristic
311C22×D5—21no—
312C5×Q8—32no—
313C5×Q8—61no—
314C5×D4—32no—
315C5×D4—64no—
316C5×D4—61no—
317C2×C4×C5—22no—
318C2×C4×C5—61no—
319C2×C4×C5—64no—
320C2×C4×C5—81no—
321C2×C4×C5C2×C4×D312yes—
322C2×C4×C5#23512yes—
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—24no—
326C2×Dic5—21no—
327C2×Dic5—62no—
328C2×Dic5—242no—
329C2×Dic5—241no—
330C2×Dic5C2×#6712yes—
331C2×Dic5C2×#6712yes—
332D20—21no—
333D20C2×C4×D312yes—
334C4×D5—24no—
335C4×D5—82no—
336Dic10—21no—
337Dic10C2×C4×D312yes—
338C5×C8—62no—
339#168—32no—
340#168—32no—
341C2×#41—31no—
342C2×#41—51no—
343#135—158no—
344C2×Q16—151no—
345C2×SD16—151no—
346C2×SD16—151no—
347C2×D8—151no—
348C2×M16—31no—
349C22×C8—151no—
350C4×Q8—52no—
351C4×Q8—152no—
352C4×D4—52no—
353C4×D4—102no—
354C4×D4—152no—
355C4×D4—302no—
356#117—51no—
357#117—101no—
358#117—301no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4—151no—
361C2×C4⋊C4—301no—
362C2×C4⋊C4D3×D511yescharacteristic
363#106—152no—
364#106—152no—
365#103—32no—
366#103—152no—
367#102—32no—
368#102—152no—
369#97—152no—
370C4×C8—152no—
371C2×C3×C5—22no—
372C2×C3×C5C2×C4×D411yescharacteristic
373C2×C3×C5#57711yescharacteristic
374C2×C3×C5#57711yescharacteristic
375C3×D5—42no—
376C5×D3—42no—
377C23×C3—101no—
378C23×C3D4×D511yescharacteristic
379C22×D3—21no—
380C3×Q8—52no—
381C3×Q8—101no—
382C3×D4—52no—
383C3×D4—104no—
384C3×D4—101no—
385C2×C3×C4—22no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—81no—
389C2×C3×C4—101no—
390C2×C3×C4—104no—
391C2×C3×C4—402no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4D4×D511yescharacteristic
394C2×C3×C4#71112yes—
395C2×C3×C4C23×D511yescharacteristic
396#67—24no—
397C2×Dic3—21no—
398C2×Dic3—102no—
399C2×Dic3—401no—
400D12—21no—
401D12C2×C4×D512yes—
402C4×D3—24no—
403C4×D3—402no—
404Dic6—21no—
405Dic6C2×C4×D512yes—
406C3⋊C8—22no—
407C3⋊C8—52no—
408C3⋊C8—52no—
409C22×C5—21no—
410C22×C5—21no—
411C22×C5—62no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5C4×#6712yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—22no—
417C2×D5—41no—
418C2×D5—41no—
419C4×C5—42no—
420C4×C5—62no—
421C4×C5C4×#6712yes—
422C4×C5C22×C4×D311yescharacteristic
423C4×C5C2×#23511yescharacteristic
424Dic5—22no—
425Dic5—22no—
426Dic5—22no—
427Dic5—122no—
428#41—34no—
429#41—54no—
430#41—62no—
431#41—102no—
432C2×Q8—31no—
433C2×Q8—51no—
434C2×D4—31no—
435C2×D4—51no—
436C2×D4—61no—
437C2×D4—101no—
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—102no—
441C22×C4—101no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445Q16—154no—
446SD16—154no—
447SD16—154no—
448D8—154no—
449M16—62no—
450C2×C8—32no—
451C2×C8—154no—
452C2×C8—151no—
453C2×C8—151no—
454C4⋊C4—21no—
455C4⋊C4—51no—
456C4⋊C4—51no—
457C4⋊C4—102no—
458C4⋊C4—152no—
459C4⋊C4—302no—
460C4⋊C4—301no—
461C4⋊C4C2×D3×D512yes—
462C22⋊C4—52no—
463C22⋊C4—102no—
464C22⋊C4—302no—
465C42—52no—
466C42—102no—
467C42—302no—
468C3×C5#295211yescharacteristic, complemented, Hall
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—102no—
472C22×C3—201no—
473C22×C3—201no—
474C22×C3#402712yes—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—22no—
477C2×D3—41no—
478C2×D3—41no—
479C3×C4—42no—
480C3×C4—102no—
481C3×C4—102no—
482C3×C4—102no—
483C3×C4#402712yes—
484C3×C4C22×C4×D511yescharacteristic
485C3×C4C2×#71111yescharacteristic
486Dic3—22no—
487Dic3—202no—
488C2×C5—22no—
489C2×C5—122no—
490C2×C5C2×C4×#6711yescharacteristic
491C2×C5#583611yescharacteristic
492C2×C5#583711yescharacteristic
493D5—42no—
494C23—61no—
495C23—101no—
496C23D5×#6711yescharacteristic
497Q8—32no—
498Q8—52no—
499Q8—61no—
500Q8—101no—
501D4—32no—
502D4—52no—
503D4—64no—
504D4—61no—
505D4—104no—
506D4—101no—
507C2×C4—22no—
508C2×C4—52no—
509C2×C4—52no—
510C2×C4—61no—
511C2×C4—64no—
512C2×C4—81no—
513C2×C4—101no—
514C2×C4—104no—
515C2×C4—302no—
516C2×C4—402no—
517C2×C4—1202no—
518C2×C4—1201no—
519C2×C4#677212yes—
520C2×C4C4×D3×D512yes—
521C2×C4D5×#6711yescharacteristic
522C2×C4C22×D3×D511yescharacteristic
523C8—62no—
524C8—152no—
525C8—152no—
526C2×C3—22no—
527C2×C3—202no—
528C2×C3C2×#402711yescharacteristic
529C2×C3#6610911yescharacteristic
530C2×C3#6611211yescharacteristic
531D3—42no—
532C5#8255811yescharacteristic, complemented, Sylow
533C22—21no—
534C22—21no—
535C22—62no—
536C22—102no—
537C22—121no—
538C22—121no—
539C22—201no—
540C22—201no—
541C22#9144012yes—
542C22C2×D5×#6711yescharacteristic
543C4—42no—
544C4—62no—
545C4—102no—
546C4—102no—
547C4—102no—
548C4—602no—
549C4#9144012yes—
550C4C2×#677211yescharacteristic
551C4C2×C4×D3×D511yescharacteristic
552C3#1061060011yescharacteristic, complemented, Sylow
553C2—22no—
554C2—122no—
555C2—202no—
556C2C2×#9144011yescharacteristic
557C2#1175470811yescharacteristic
558C2#1175508611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91297C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65838C2semidirect
2. #11754513C2semidirect
4. C2×#91092C2semidirect
5. C5×#4966C2semidirect
6. #11748369C2semidirect
7. #11748320C2semidirect
8. #11747468C2semidirect
9. #11747262C2semidirect
10. #11747261C2semidirect
11. #11747218C2semidirect
33. #91297C4semidirect
46. #65838D3semidirect
60. C5×#235C2×C4semidirect
66. C3×#709C2×C4semidirect
76. C2×C3⋊#168C2×C4semidirect
91. #6661C2×C4semidirect
92. #6656C2×C4semidirect
93. #6655C2×C4semidirect
94. #6652C2×C4semidirect
104. #4966D5semidirect
211. #709C4×D3semidirect
281. #235C4×D5semidirect
468. C3×C5#2952semidirect
532. C5#82558semidirect
552. C3#10610600semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
#117545132
C2×#912972
C2×#910922
C5×#49662
#117483692
#117483202
#117474682
#117472622
#117472612
#117472182
#106106003
#825585