Finite Group Databasebeta

← #14301279

Subgroups — #14301279

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
1C5×#5504C211yesmaximal, characteristic
2C2×#91322C211yesmaximal, characteristic
3#11751074C211yesmaximal, characteristic, complemented
4C2×#90978C211yesmaximal, characteristic
5#11748417C211yesmaximal, characteristic, complemented
6C3×#64750C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10602459—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C4×C5×#67—22no—
14C5×#926C2211yescharacteristic
15C5×#893—21no—
16C5×#892—21no—
17C5×D3×C4⋊C4—21no—
18C5×#887—21no—
19C2×C3×#681C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91322—22no—
22#91322C414yescomplemented
23C2×#6663—21no—
24C2×#6659—21no—
25#91115—22no—
26#90978—22no—
27#90975—21no—
28#90975—21no—
29#69004—51nomaximal, Hall
30C5×#520—31no—
31C2×#4097—31no—
32C2×#3969—31no—
33#65293—31no—
34#65263—31no—
35#64752—31no—
36#64750D311yescharacteristic, complemented
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—21no—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30C2×C412yescomplemented
47C2×C5×#67—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235C2×C412yes—
51C5×#235D412yes—
52C2×C5×D12D411yescharacteristic
53C2×C4×C5×D3—21no—
54C2×C4×C5×D3—22no—
55C2×C5×Dic6D411yescharacteristic
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58C4×Dic15—21no—
59C4×Dic15—21no—
60C5×#217—21no—
61C5×(C2×D3)⋊C4—22no—
62C5×C4⋊Dic3D411yescharacteristic
63C5×C4⋊Dic3D411yescharacteristic
64C5×Dic3⋊C4—22no—
65C4×C5×Dic3—22no—
66C4×C5×Dic3—21no—
67C3×#681—21no—
68C3×#681—21no—
69C3×#681—21no—
70C3×#681C2×C412yescomplemented
71C2×C3×#168—21no—
72C2×C3×#168—21no—
73#6663—24no—
74#6659—24no—
75C2×#909—51no—
76#5504D511yescharacteristic
77C2×#825—51no—
78#5120—51no—
79#4973—51no—
80C3×#343—51no—
81#4555—51no—
82C2×C5×#41—31no—
83C22×Dic10—31no—
84C4×C5×Q8—61no—
85C4×C5×D4—61no—
86C4×C5×D4—62no—
87C5×#117—31no—
88C5×#117—61no—
89C2×C5×C4⋊C4—61no—
90C2×C5×C4⋊C4C2×D311yescharacteristic
91#4097—34no—
92#4097—62no—
93C2×#689—61no—
94C2×#687—61no—
95C2×C4×Dic5—31no—
96C2×#681C2×D311yescharacteristic
97C2×#681C2×D311yescharacteristic
98#3969—62no—
99#3963—62no—
100#3942—61no—
101#3942—61no—
102#1882—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—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×Dic15—22no—
114C2×Dic15—22no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×Dic15—41no—
118C2×Dic15—41no—
119Dic30—22no—
120Dic30—22no—
121Dic30—41no—
122Dic30—41no—
123C5×#67—22no—
124C5×#67—22no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C5×D12—21no—
129C5×D12C22⋊C412yes—
130C4×C5×D3—22no—
131C4×C5×D3—22no—
132C4×C5×D3—82no—
133C5×Dic6—21no—
134C5×Dic6C22⋊C412yes—
135C3×#168—22no—
136C3×#168—41no—
137C2×#235C2×D511yescharacteristic
138C22×Dic6—51no—
139C2×C3×M16—51no—
140C2×C3×M16—51no—
141C2×C3×C4⋊C4C2×D511yescharacteristic
142C4×#67—22no—
143#926C2×D511yescharacteristic
144C2×C4×Dic3—51no—
145#909—54no—
146#909—102no—
147C2×Dic12—101no—
148C2×#204—101no—
149#893—21no—
150#892—21no—
151D3×C4⋊C4—21no—
152#887—21no—
153C3⋊#95—102no—
154#825—102no—
155#816—101no—
156#816—101no—
157C5×#41—32no—
158C5×#41—32no—
159C5×#41—61no—
160C5×#41—61no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—61no—
164C22×C4×C5—62no—
165C22×C4×C5—61no—
166C22×C4×C5D1212yes—
167C22×C4×C5C22×D311yescharacteristic
168C22×Dic5—61no—
169C22×Dic5—61no—
170C2×Dic10—32no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C2×Dic10—61no—
174C2×Dic10—61no—
175C2×Dic10—61no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—31no—
179C5×C4⋊C4—31no—
180C5×C4⋊C4—62no—
181C5×C22⋊C4—62no—
182C5×C22⋊C4—61no—
183C42×C5—62no—
184C42×C5—61no—
185#689—64no—
186#687—64no—
187C4×Dic5—61no—
188C4×Dic5—61no—
189#681—21no—
190#681—21no—
191#681—21no—
192#681C4×D312yescomplemented
193C2×#168—21no—
194C2×#168—21no—
195C2×#137—151no—
196#520—31no—
197C2×#104—151no—
198#419—151no—
199#391—151no—
200#343—51no—
201#339—151no—
202C22×C3×C5—21no—
203C22×C3×C5—21no—
204C22×C3×C5C4×D411yescharacteristic
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C2×C5×D3—22no—
208C2×C5×D3—41no—
209C2×C5×D3—41no—
210C3×C4×C5—42no—
211C3×C4×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—42no—
216Dic15—42no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3—41no—
220C22×C3×C4C22⋊D512yes—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C22×Dic3—101no—
224C22×Dic3—101no—
225#235—21no—
226#235—21no—
227#235C4×D512yes—
228#235D2012yes—
229C2×D12C22⋊D511yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—22no—
232C2×Dic6—52no—
233C2×Dic6—101no—
234C2×Dic6—101no—
235C2×Dic6—101no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6C22⋊D511yescharacteristic
239C3×M16—52no—
240C3×M16—101no—
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C2×C3×C8—101no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247#217—21no—
248(C2×D3)⋊C4—22no—
249C4⋊Dic3C22⋊D511yescharacteristic
250C4⋊Dic3C22⋊D511yescharacteristic
251Dic3⋊C4—22no—
252C4×Dic3—22no—
253C4×Dic3—21no—
254C4×Dic3—101no—
255C4×Dic3—101no—
256Dic12—104no—
257#204—104no—
258C23×C5—61no—
259C23×C5C2×D1211yescharacteristic
260C5×Q8—32no—
261C5×Q8—61no—
262C5×D4—32no—
263C5×D4—62no—
264C5×D4—62no—
265C5×D4—61no—
266C2×C4×C5—22no—
267C2×C4×C5—42no—
268C2×C4×C5—61no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—242no—
274C2×C4×C5C2×C4×D311yescharacteristic
275C2×C4×C5#23511yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5#23911yescharacteristic
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—121no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285C2×Dic5—121no—
286Dic10—62no—
287Dic10—62no—
288Dic10—121no—
289Dic10—121no—
290#168—22no—
291#168—41no—
292C2×#41—31no—
293C22×Q8—151no—
294#137—154no—
295#137—302no—
296C2×Q16—301no—
297C2×SD16—301no—
298C2×M16—51no—
299C2×M16—51no—
300C4×Q8—61no—
301C4×D4—61no—
302C4×D4—62no—
303#117—31no—
304#117—61no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C42—151no—
308#104—302no—
309#103—301no—
310#103—301no—
311#95—302no—
312C2×C3×C5—21no—
313C2×C3×C5—21no—
314C2×C3×C5#38611yescharacteristic
315C2×C3×C5#45511yescharacteristic
316C2×C3×C5#45611yescharacteristic
317C5×D3—42no—
318C23×C3C2×C22⋊D511yescharacteristic
319C22×D3—21no—
320C2×C3×C4—22no—
321C2×C3×C4—42no—
322C2×C3×C4C2×C4×D511yescharacteristic
323C2×C3×C4C2×D2011yescharacteristic
324C2×C3×C4#70911yescharacteristic
325C2×C3×C4#70911yescharacteristic
326C2×C3×C4C2×C22⋊D511yescharacteristic
327C2×C3×C4C2×C22⋊D511yescharacteristic
328#67—22no—
329#67—22no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—102no—
334C2×Dic3—102no—
335C2×Dic3—201no—
336C2×Dic3—201no—
337C2×Dic3—201no—
338C2×Dic3—201no—
339D12—21no—
340D12#68512yes—
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—82no—
344Dic6—21no—
345Dic6—102no—
346Dic6—102no—
347Dic6—201no—
348Dic6—201no—
349Dic6#68512yes—
350C3×C8—102no—
351C3×C8—201no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—62no—
355C22×C5—121no—
356C22×C5—121no—
357C22×C5C4×D1211yescharacteristic
358C22×C5#88211yescharacteristic
359C22×C5#89511yescharacteristic
360C4×C5—42no—
361C4×C5—62no—
362C4×C5—121no—
363C4×C5—121no—
364C4×C5D3×C22⋊C411yescharacteristic
365C4×C5#88411yescharacteristic
366C4×C5#89311yescharacteristic
367C4×C5#89411yescharacteristic
368Dic5—122no—
369Dic5—122no—
370#41—32no—
371#41—32no—
372#41—61no—
373#41—61no—
374C2×Q8—31no—
375C2×Q8—152no—
376C2×Q8—301no—
377C2×Q8—301no—
378C2×Q8—301no—
379C2×Q8—301no—
380C2×Q8—301no—
381C2×D4—31no—
382C2×D4—61no—
383C22×C4—62no—
384C22×C4—61no—
385C22×C4—301no—
386C22×C4—301no—
387C22×C4#120312yes—
388C22×C4C2×D3×D511yescharacteristic
389Q16—304no—
390SD16—304no—
391M16—52no—
392M16—101no—
393M16—101no—
394M16—101no—
395C2×C8—101no—
396C2×C8—101no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C22⋊C4—62no—
403C22⋊C4—61no—
404C42—62no—
405C42—61no—
406C42—301no—
407C42—301no—
408C3×C5#188211yescharacteristic, complemented, Hall
409C22×C3—21no—
410C22×C3—21no—
411C22×C3C4×C22⋊D511yescharacteristic
412C22×C3#407611yescharacteristic
413C22×C3#409911yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—42no—
418C3×C4C2×#68511yescharacteristic
419C3×C4C4×C22⋊D511yescharacteristic
420C3×C4#407511yescharacteristic
421C3×C4#407611yescharacteristic
422Dic3—22no—
423Dic3—41no—
424Dic3—41no—
425Dic3—202no—
426Dic3—202no—
427C2×C5—21no—
428C2×C5—21no—
429C2×C5—122no—
430C2×C5#466511yescharacteristic
431C2×C5#474611yescharacteristic
432C2×C5#475211yescharacteristic
433C23—61no—
434C23C2×#120311yescharacteristic
435Q8—32no—
436Q8—61no—
437Q8—302no—
438Q8—302no—
439Q8—601no—
440Q8—601no—
441D4—32no—
442D4—62no—
443D4—62no—
444D4—61no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—242no—
453C2×C4—302no—
454C2×C4—302no—
455C2×C4—601no—
456C2×C4—601no—
457C2×C4—601no—
458C2×C4—601no—
459C2×C4#676911yescharacteristic
460C2×C4#677111yescharacteristic
461C2×C4C4×D3×D511yescharacteristic
462C2×C4D3×D2011yescharacteristic
463C2×C4D3×C22⋊D511yescharacteristic
464C2×C4D3×C22⋊D511yescharacteristic
465C8—102no—
466C8—201no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3#6550211yescharacteristic
470C2×C3#6553111yescharacteristic
471C2×C3#6553511yescharacteristic
472D3—42no—
473C5#6900411yescharacteristic, complemented, Sylow
474C22—21no—
475C22—21no—
476C22—62no—
477C22—121no—
478C22—121no—
479C22C4×#120311yescharacteristic
480C22#9146011yescharacteristic
481C22#9157011yescharacteristic
482C4—42no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—602no—
487C4—602no—
488C4#9135111yescharacteristic
489C4#9144611yescharacteristic
490C4#9145411yescharacteristic
491C4D3×#68511yescharacteristic
492C3#1060245911yescharacteristic, complemented, Sylow
493C2—21no—
494C2—21no—
495C2—122no—
496C2#1174891411yescharacteristic
497C2#1174914811yescharacteristic
498C2#1174939411yescharacteristic
subgroupG/H
centerC22#91570
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×C5×#235C22
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. #11751074C2semidirect
5. #11748417C2semidirect
6. C3×#64750C2semidirect
7. #11745975C2semidirect
22. #91322C4semidirect
36. #64750D3semidirect
46. C2×Dic30C2×C4semidirect
70. C3×#681C2×C4semidirect
192. #681C4×D3semidirect
408. C3×C5#1882semidirect
473. C5#69004semidirect
492. C3#10602459semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
C2×#913222
#117510742
C2×#909782
#117484172
C3×#647502
#117459752
#106024593
#690045