Finite Group Databasebeta

← #14301583

Subgroups — #14301583

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91368C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3C2×C5×#824C211yesmaximal, characteristic, complemented
4C3×#65420C211yesmaximal, characteristic
5#11748367C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10600897—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×#6665—22no—
17#91529—22no—
18#91368—22no—
19#91368C414yescomplemented
20#91344—22no—
21Dic5×Dic6—22no—
22C5×#824—22no—
23C3×#3953—22no—
24#90965—22no—
25#70325—51nomaximal, Hall
26C2×#4093—31no—
27#66146—31no—
28C2×C5×#101—31no—
29#65420—31no—
30#65420D311yescharacteristic
31#64775—31no—
32#64775—31no—
33C23×C3×D5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C22×C5×Dic3D412yes—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6—21no—
41C2×C5×Dic6C2×C412yes—
42C2×C5×Dic6D412yes—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20C2×C412yes—
49C3×C5×M16—21no—
50C3×C5×M16—21no—
51C2×C3×C5×C8—21no—
52#6719—21no—
53C4⋊Dic15D412yes—
54C4×Dic15—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C412yes—
57C5×#208—21no—
58C5×#208—21no—
59C2×C5×C3⋊C8—21no—
60C3×C22⋊Dic5—21no—
61C3×C4⋊Dic5D412yes—
62C3×C4×Dic5—21no—
63Dic3⋊Dic5—24no—
64#6665—28no—
65Dic3×Dic5—24no—
66C2×#936—51no—
67#5516—51no—
68C3×#418—51no—
69#5215—51no—
70C2×#824D511yescharacteristic, complemented
71#4555—51no—
72#4532—51no—
73C22×C5×Q8—31no—
74C22×D20C2×D311yescharacteristic
75C2×C5×M16—31no—
76C2×C5×M16C2×D311yescharacteristic
77#4093—34no—
78#4093—62no—
79Q8×Dic5—62no—
80Q8×Dic5—62no—
81C2×#685—62no—
82#4072—31no—
83#4072—62no—
84#4072C2×D311yescharacteristic
85C2×C4×Dic5—31no—
86C5×#101—62no—
87#3953—22no—
88#3953—62no—
89#1888—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C3×D5—22no—
92C22×C3×D5—44no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×Dic15—22no—
102C2×Dic15—22no—
103C2×Dic15—42no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3C22⋊C414yes—
107C5×Dic6—22no—
108C5×Dic6—22no—
109C5×Dic6—22no—
110C5×Dic6—22no—
111C2×C3×Dic5—22no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—41no—
115C3×D20—41no—
116C3×C5×C8—41no—
117C5×C3⋊C8—41no—
118C22×C3×D4—51no—
119C22×Dic6C2×D511yescharacteristic
120C2×C3×M16C2×D511yescharacteristic
121C3×#117—51no—
122C2×#217—102no—
123#936—54no—
124#936—102no—
125#926—51no—
126C2×C4×Dic3—51no—
127C2×#208C2×D511yescharacteristic
128#887—102no—
129#877—102no—
130C4×Dic6—102no—
131C3×#102—102no—
132#832—102no—
133#824—22no—
134C23×D5—21no—
135C2×C5×Q8—32no—
136C2×C5×Q8—32no—
137C2×C5×Q8—61no—
138C2×C5×Q8—61no—
139C2×C5×Q8—61no—
140C2×C5×Q8—61no—
141C22×C4×C5—32no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—61no—
144C2×D20—21no—
145C2×D20—21no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20—21no—
149C2×D20C4×D312yes—
150C5×M16—21no—
151C5×M16—21no—
152C5×M16—61no—
153C5×M16—61no—
154C2×C5×C8—21no—
155C2×C5×C8—61no—
156C22⋊Dic5—21no—
157C22⋊Dic5—61no—
158#685—68no—
159C4⋊Dic5—32no—
160C4⋊Dic5—64no—
161C4⋊Dic5#6712yes—
162C4×Dic5—21no—
163C4×Dic5—32no—
164C4×Dic5—64no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167C2×#124—151no—
168#519—151no—
169#418—51no—
170#418—151no—
171C2×#101—31no—
172#339—151no—
173#339—151no—
174C22×C3×C5—22no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C2×C3×D5—44no—
179C2×C3×D5—42no—
180C2×C3×D5—82no—
181C2×C3×D5—82no—
182C3×C4×C5C4×D411yescharacteristic
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5#12111yescharacteristic
185C3×C4×C5#12111yescharacteristic
186Dic15—42no—
187Dic15—42no—
188C3×Dic5—42no—
189C5×Dic3—24no—
190C24×C3—101no—
191C2×C3×D4—52no—
192C2×C3×D4—101no—
193C2×C3×D4—101no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—101no—
199C22×Dic3D2012yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6C4×D512yes—
205C2×Dic6C22⋊D512yes—
206C3×M16—21no—
207C3×M16—21no—
208C2×C3×C8—21no—
209C3×C4⋊C4—52no—
210C3×C22⋊C4—101no—
211C3×C42—101no—
212#217—101no—
213#217—108no—
214C4⋊Dic3—52no—
215Dic3⋊C4—104no—
216C4×Dic3—52no—
217C4×Dic3—104no—
218C4×Dic3—101no—
219C4×Dic3—101no—
220#208—21no—
221#208—21no—
222C2×C3⋊C8—21no—
223C23×C5D3×D411yescharacteristic
224C22×D5—22no—
225C22×D5—44no—
226C22×D5—41no—
227C22×D5—41no—
228C5×Q8—62no—
229C5×Q8—62no—
230C5×Q8—62no—
231C5×Q8—62no—
232C2×C4×C5—34no—
233C2×C4×C5—62no—
234C2×C4×C5—62no—
235C2×C4×C5C2×C4×D311yescharacteristic
236C2×C4×C5#23511yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C2×Dic5—22no—
242C2×Dic5—62no—
243C2×Dic5—62no—
244C2×Dic5—122no—
245D20—22no—
246D20—22no—
247D20—41no—
248D20—41no—
249C5×C8—41no—
250C5×C8—121no—
251C22×Q8—31no—
252C22×D4—51no—
253C2×M16—31no—
254C2×M16D3×D511yescharacteristic
255#124—154no—
256#124—302no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—51no—
260#117—151no—
261#117—302no—
262C2×C22⋊C4—302no—
263C2×C42—151no—
264#102—102no—
265#102—302no—
266#101—62no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#38611yescharacteristic
270C2×C3×C5#45412yes—
271C3×D5—82no—
272C23×C3—102no—
273C23×C3—204no—
274C23×C3—201no—
275C23×C3—201no—
276C23×C3C2×D2011yescharacteristic
277C3×D4—102no—
278C3×D4—102no—
279C3×D4—201no—
280C3×D4—201no—
281C2×C3×C4—102no—
282C2×C3×C4C2×C4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4D4×D511yescharacteristic
285C2×C3×C4#71111yescharacteristic
286C2×C3×C4#71111yescharacteristic
287C2×C3×C4C2×C22⋊D511yescharacteristic
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—102no—
291C2×Dic3—102no—
292C2×Dic3—202no—
293C2×Dic3#68514yes—
294Dic6—22no—
295Dic6—22no—
296Dic6—22no—
297Dic6—22no—
298C3×C8—41no—
299C3⋊C8—41no—
300C22×C5—22no—
301C22×C5D3×C22⋊C411yescharacteristic
302C22×C5#88311yescharacteristic
303C22×C5#93711yescharacteristic
304C2×D5—44no—
305C2×D5—42no—
306C2×D5—82no—
307C2×D5—82no—
308C4×C5—64no—
309C4×C5#67⋊C411yescharacteristic
310C4×C5#88411yescharacteristic
311C4×C5C4×#6711yescharacteristic
312C4×C5#93811yescharacteristic
313Dic5—42no—
314Dic5—122no—
315Dic5—122no—
316C24—101no—
317C2×Q8—32no—
318C2×Q8—32no—
319C2×Q8—61no—
320C2×Q8—61no—
321C2×Q8—61no—
322C2×Q8—61no—
323C2×D4—52no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C2×D4—101no—
329C22×C4—32no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332M16—21no—
333M16—21no—
334M16—61no—
335M16—61no—
336C2×C8—21no—
337C2×C8—61no—
338C4⋊C4—52no—
339C4⋊C4—152no—
340C4⋊C4—304no—
341C22⋊C4—101no—
342C22⋊C4—308no—
343C22⋊C4—301no—
344C42—101no—
345C42—152no—
346C42—304no—
347C42—301no—
348C42—301no—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—204no—
352C22×C3—202no—
353C22×C3—402no—
354C22×C3—402no—
355C22×C3#402811yescharacteristic
356C22×C3#403211yescharacteristic
357C22×C3C2×#68511yescharacteristic
358C3×C4—202no—
359C3×C4#402711yescharacteristic
360C3×C4#402711yescharacteristic
361C3×C4#408511yescharacteristic
362C3×C4#408511yescharacteristic
363Dic3—24no—
364Dic3—202no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5#495611yescharacteristic
369C2×C5#520112yes—
370D5—82no—
371C23—102no—
372C23—204no—
373C23—201no—
374C23—201no—
375C23D3×D2011yescharacteristic
376Q8—62no—
377Q8—62no—
378Q8—62no—
379Q8—62no—
380D4—102no—
381D4—102no—
382D4—201no—
383D4—201no—
384C2×C4—34no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—102no—
388C2×C4—302no—
389C2×C4—302no—
390C2×C4—602no—
391C2×C4#677211yescharacteristic
392C2×C4C4×D3×D511yescharacteristic
393C2×C4#677711yescharacteristic
394C2×C4#678011yescharacteristic
395C2×C4D5×#6711yescharacteristic
396C2×C4D3×C22⋊D511yescharacteristic
397C8—41no—
398C8—121no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—402no—
402C2×C3#6504212yes—
403C2×C3#6524711yescharacteristic
404C5#7032511yescharacteristic, complemented, Sylow
405C22—22no—
406C22—204no—
407C22—202no—
408C22—402no—
409C22—402no—
410C22#9145711yescharacteristic
411C22D3×#68511yescharacteristic
412C22#9147411yescharacteristic
413C4—64no—
414C4—202no—
415C4—602no—
416C4—602no—
417C4#9144011yescharacteristic
418C4#9144211yescharacteristic
419C4#9145311yescharacteristic
420C4#9156511yescharacteristic
421C3#1060089711yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—402no—
425C2#1174825512yes—
426C2#1174891111yescharacteristic
subgroupG/H
centerC22#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754211C2semidirect
3. C2×C5×#824C2semidirect
6. #11746376C2semidirect
7. #11745973C2semidirect
19. #91368C4semidirect
70. C2×#824D5semidirect
349. C3×C5#1888semidirect
404. C5#70325semidirect
421. C3#10600897semidirect

Maximal subgroups

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

subgroupindex
C2×#913682
#117542112
C2×C5×#8242
C3×#654202
#117483672
#117463762
#117459732
#106008973
#703255