Finite Group Databasebeta

← #14301282

Subgroups — #14301282

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65838C211yesmaximal, characteristic
2C2×#91307C211yesmaximal, characteristic
3C5×#4973C211yesmaximal, characteristic, complemented
4C2×#90977C211yesmaximal, characteristic
5#11748407C211yesmaximal, characteristic, complemented
6#11746351C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600486—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C3×C4×C22⋊D5—22no—
16C3×#4072C2211yescharacteristic
17C3×#4039—21no—
18C3×#4038—21no—
19C3×D5×C4⋊C4—21no—
20C3×#4033—21no—
21C2×#6661—21no—
22#91307—22no—
23#91307C414yescomplemented
24C2×#6655—21no—
25C5×C3⋊#95—22no—
26#90977—22no—
27#90972—21no—
28#90972—21no—
29#71666—51nomaximal, Hall
30C2×#4088—31no—
31#65838D311yescharacteristic
32C5×#391—31no—
33#65514—31no—
34C2×#3937—31no—
35#64750—31no—
36#64743—31no—
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C5×Dic3—21no—
40C22×C5×Dic3—21no—
41C2×C5×Dic6—21no—
42C2×C5×Dic6—21no—
43C2×C5×Dic6—21no—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6C2×C412yescomplemented
47C2×C3×C22⋊D5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709C2×C412yes—
51C3×#709D412yes—
52C2×C3×D20D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—22no—
55C2×C3×Dic10D411yescharacteristic
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61#6710C2×C412yescomplemented
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C4×C5×Dic3—21no—
65C4×C5×Dic3—21no—
66C3×C22⋊Dic5—21no—
67C3×#685—22no—
68C3×C4⋊Dic5D411yescharacteristic
69C3×C4⋊Dic5D411yescharacteristic
70C3×#683—22no—
71C3×C4×Dic5—22no—
72C3×C4×Dic5—21no—
73#6661—24no—
74#6655—24no—
75C3×#520—51no—
76C2×#951—51no—
77C2×#837—51no—
78#5004—51no—
79#4973D511yescharacteristic, complemented
80#4532—51no—
81#4530—51no—
82C22×C5×Q8—31no—
83C2×#709C2×D311yescharacteristic
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×C42×C5—31no—
86C2×#689—61no—
87#4088—34no—
88#4088—62no—
89C2×#688—61no—
90C4×C22⋊D5—22no—
91#4072C2×D311yescharacteristic
92C2×#681—31no—
93C2×#681—31no—
94#4039—21no—
95#4038—21no—
96D5×C4⋊C4—21no—
97#4033—21no—
98C5×#95—62no—
99#3967—61no—
100#3967—61no—
101#3937—62no—
102#1882—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—21no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C5×Dic3—22no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C5×Dic6—22no—
120C5×Dic6—22no—
121C5×Dic6—41no—
122C5×Dic6—41no—
123C3×C22⋊D5—22no—
124C3×C22⋊D5—22no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C3×D20—21no—
129C3×D20C22⋊C412yes—
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×C4×D5—82no—
133C3×Dic10—21no—
134C3×Dic10C22⋊C412yes—
135C3⋊#168—22no—
136C3⋊#168—41no—
137C2×C3×#41—51no—
138C22×Dic6C2×D511yescharacteristic
139C3×C4×Q8—101no—
140C3×C4×D4—101no—
141C3×C4×D4—102no—
142C3×#117—51no—
143C3×#117—101no—
144C2×C3×C4⋊C4—101no—
145C2×C3×C4⋊C4C2×D511yescharacteristic
146#951—54no—
147#951—102no—
148C2×#216—101no—
149C2×#214—101no—
150C2×C4×Dic3C2×D511yescharacteristic
151C2×#208—51no—
152C2×#208—51no—
153#837—102no—
154C3⋊#95—22no—
155#810—101no—
156#810—101no—
157C2×C5×Q8—32no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C2×C5×Q8—61no—
161C2×C5×Q8—61no—
162C2×C5×Q8—61no—
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5#6712yes—
166C22×C4×C5C22×D311yescharacteristic
167C2×C22⋊D5—21no—
168#709—21no—
169#709—21no—
170#709C4×D312yes—
171#709D1212yes—
172C2×D20#6711yescharacteristic
173C2×C4×D5—21no—
174C2×C4×D5—22no—
175C2×Dic10#6711yescharacteristic
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C42×C5—61no—
179C42×C5—61no—
180C22⋊Dic5—21no—
181#689—64no—
182#688—64no—
183#685—22no—
184C4⋊Dic5#6711yescharacteristic
185C4⋊Dic5#6711yescharacteristic
186#683—22no—
187C4×Dic5—22no—
188C4×Dic5—21no—
189#681—32no—
190#681—61no—
191#681—61no—
192#681—61no—
193C2×#168—61no—
194C2×#168—61no—
195C2×#137—151no—
196#520—51no—
197C2×#104—151no—
198#419—151no—
199#391—31no—
200#343—151no—
201#339—151no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C3×D5—22no—
208C2×C3×D5—41no—
209C2×C3×D5—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215C3×Dic5—22no—
216C3×Dic5—41no—
217C3×Dic5—41no—
218C5×Dic3—42no—
219C5×Dic3—42no—
220C3×#41—52no—
221C3×#41—52no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—51no—
225C2×C3×D4—51no—
226C2×C3×D4—101no—
227C22×C3×C4—102no—
228C22×C3×C4—101no—
229C22×C3×C4C22⋊D512yes—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—21no—
232C22×Dic3—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6C4×D512yescomplemented
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—51no—
242C3×C4⋊C4—51no—
243C3×C4⋊C4—102no—
244C3×C22⋊C4—102no—
245C3×C22⋊C4—101no—
246C3×C42—102no—
247C3×C42—101no—
248#216—104no—
249#214—104no—
250C4×Dic3—21no—
251C4×Dic3—21no—
252#208—52no—
253#208—101no—
254#208—101no—
255#208—101no—
256C2×C3⋊C8—101no—
257C2×C3⋊C8—101no—
258C23×C5C2×#6711yescharacteristic
259C22×D5—21no—
260C5×Q8—62no—
261C5×Q8—62no—
262C5×Q8—121no—
263C5×Q8—121no—
264C2×C4×C5—22no—
265C2×C4×C5—42no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5C2×D1211yescharacteristic
274C2×C4×C5#23511yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—22no—
279C22⋊D5—22no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283D20—21no—
284D20(C2×D3)⋊C412yes—
285C4×D5—22no—
286C4×D5—22no—
287C4×D5—82no—
288Dic10—21no—
289Dic10(C2×D3)⋊C412yes—
290#168—62no—
291#168—121no—
292C2×#41—51no—
293C22×Q8—31no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—151no—
299C2×M16—151no—
300C4×Q8—101no—
301C4×D4—101no—
302C4×D4—102no—
303#117—51no—
304#117—101no—
305C2×C4⋊C4—101no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C42—31no—
308#104—302no—
309#103—301no—
310#103—301no—
311#95—62no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317C3×D5—42no—
318C23×C3—101no—
319C23×C3C2×C22⋊D511yescharacteristic
320C3×Q8—52no—
321C3×Q8—101no—
322C3×D4—52no—
323C3×D4—102no—
324C3×D4—102no—
325C3×D4—101no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—101no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—402no—
334C2×C3×C4C2×C4×D511yescharacteristic
335C2×C3×C4#70911yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4#71111yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346Dic6—22no—
347Dic6—22no—
348Dic6—41no—
349Dic6—41no—
350C3⋊C8—102no—
351C3⋊C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5C4×#6711yescharacteristic
355C22×C5#93011yescharacteristic
356C22×C5#95311yescharacteristic
357C2×D5—22no—
358C2×D5—41no—
359C2×D5—41no—
360C4×C5—42no—
361C4×C5—122no—
362C4×C5—122no—
363C4×C5C2×(C2×D3)⋊C411yescharacteristic
364C4×C5C4×#6711yescharacteristic
365C4×C5#92911yescharacteristic
366C4×C5#93011yescharacteristic
367Dic5—22no—
368Dic5—41no—
369Dic5—41no—
370#41—52no—
371#41—52no—
372#41—101no—
373#41—101no—
374C2×Q8—32no—
375C2×Q8—51no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—61no—
379C2×Q8—61no—
380C2×Q8—61no—
381C2×D4—51no—
382C2×D4—101no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—102no—
386C22×C4—101no—
387C22×C4#120112yes—
388C22×C4C2×D3×D511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—152no—
392M16—301no—
393M16—301no—
394M16—301no—
395C2×C8—301no—
396C2×C8—301no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—51no—
400C4⋊C4—51no—
401C4⋊C4—102no—
402C22⋊C4—102no—
403C22⋊C4—101no—
404C42—61no—
405C42—61no—
406C42—102no—
407C42—101no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—102no—
412C22×C3—201no—
413C22×C3—201no—
414C22×C3C4×C22⋊D511yescharacteristic
415C22×C3#408311yescharacteristic
416C22×C3#408411yescharacteristic
417C3×C4—42no—
418C3×C4—102no—
419C3×C4—201no—
420C3×C4—201no—
421C3×C4D5×C22⋊C411yescharacteristic
422C3×C4#402711yescharacteristic
423C3×C4#402911yescharacteristic
424C3×C4#403011yescharacteristic
425Dic3—42no—
426Dic3—42no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5#521311yescharacteristic
430C2×C5#524211yescharacteristic
431C2×C5#524611yescharacteristic
432D5—42no—
433C23—101no—
434C23C2×#120111yescharacteristic
435Q8—52no—
436Q8—62no—
437Q8—62no—
438Q8—101no—
439Q8—121no—
440Q8—121no—
441D4—52no—
442D4—102no—
443D4—102no—
444D4—101no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—101no—
450C2×C4—102no—
451C2×C4—102no—
452C2×C4—101no—
453C2×C4—101no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—402no—
459C2×C4#677111yescharacteristic
460C2×C4#677211yescharacteristic
461C2×C4C4×D3×D511yescharacteristic
462C2×C4D5×D1211yescharacteristic
463C2×C4D5×#6711yescharacteristic
464C2×C4D5×#6711yescharacteristic
465C8—302no—
466C8—601no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—202no—
470C2×C3#6524511yescharacteristic
471C2×C3#6535011yescharacteristic
472C2×C3#6538411yescharacteristic
473C5#7166611yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—102no—
477C22—201no—
478C22—201no—
479C22C4×#120111yescharacteristic
480C22#9144911yescharacteristic
481C22#9156311yescharacteristic
482C4—42no—
483C4—102no—
484C4—122no—
485C4—122no—
486C4—201no—
487C4—201no—
488C4#9144011yescharacteristic
489C4#9144711yescharacteristic
490C4#9144811yescharacteristic
491C4D5×(C2×D3)⋊C411yescharacteristic
492C3#1060048611yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—202no—
496C2#1174890511yescharacteristic
497C2#1174914411yescharacteristic
498C2#1174939011yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1882
LCSG ▷ C2×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
3. C5×#4973C2semidirect
5. #11748407C2semidirect
6. #11746351C2semidirect
7. #11745974C2semidirect
23. #91307C4semidirect
46. C2×C5×Dic6C2×C4semidirect
61. #6710C2×C4semidirect
79. #4973D5semidirect
238. C2×Dic6C4×D5semidirect
408. C3×C5#1882semidirect
473. C5#71666semidirect
492. C3#10600486semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
C2×#913072
C5×#49732
C2×#909772
#117484072
#117463512
#117459742
#106004863
#716665