Finite Group Databasebeta

← #14288613

Subgroups — #14288613

Order 1920.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756361C211yesmaximal, characteristic
2#11751135C211yesmaximal, characteristic
3#11750823C211yesmaximal, characteristic, complemented
4#11750760C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic
6#11746290C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599091—31nomaximal, Hall
9C3×C5×#121C2211yescharacteristic
10#91824—21no—
11#91824—21no—
12D4×Dic15—21no—
13C2×C4⋊Dic15C2211yescharacteristic
14#91813C2211yescharacteristic
15C2×#6712C2211yescharacteristic
16#91778—21no—
17#91768—21no—
18#91767—21no—
19C3×C5×C22⋊C8C2211yescharacteristic
20C3×C5×#95C2211yescharacteristic
21#91116—21no—
22#91115—21no—
23#91115—21no—
24#91114C2211yescharacteristic
25#91102—21no—
26#91100—21no—
27#91092—21no—
28#68298—51nomaximal, Hall
29#65936—31no—
30#65323—31no—
31#65011—31no—
32#64948—31no—
33C5×#327D311yescharacteristic
34#64689—31no—
35#64672—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15—21no—
42C22×Dic15D411yescharacteristic
43C22×Dic15D411yescharacteristic
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6719—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15D411yescharacteristic
56#6712—21no—
57#6712—21no—
58#6712—21no—
59#6712—21no—
60#6712—21no—
61C4×Dic15—21no—
62C2×C3⋊#168—21no—
63#5602—51no—
64#5034—51no—
65#4722—51no—
66#4659—51no—
67C3×#327D511yescharacteristic
68#4469—51no—
69#4452—51no—
70C5×#121C2×D311yescharacteristic
71#4081—61no—
72#4081—61no—
73D4×Dic5—61no—
74C2×C4⋊Dic5—31no—
75#4070—31no—
76C2×#683—31no—
77#4035—61no—
78#4025—61no—
79#4024—61no—
80C5×C22⋊C8C2×D311yescharacteristic
81C5×#95C2×D311yescharacteristic
82#3964—61no—
83#3963—61no—
84#3963—61no—
85C22⋊#168—31no—
86#3950—61no—
87#3948—61no—
88#3940—61no—
89#1615—151noSylow
90C23×C3×C5—21no—
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—41no—
109C2×Dic15—42no—
110C2×Dic15—41no—
111C2×Dic15—81no—
112Dic30—41no—
113C3×C5×C8—41no—
114C3⋊#168—41no—
115C3×#121C2×D511yescharacteristic
116#935—101no—
117#935—101no—
118D4×Dic3—101no—
119C2×C4⋊Dic3—51no—
120#924—51no—
121C2×Dic3⋊C4—51no—
122#889—101no—
123#879—101no—
124#878—101no—
125C3×C22⋊C8C2×D511yescharacteristic
126C3×#95C2×D511yescharacteristic
127#832—101no—
128C3⋊#95—101no—
129C3⋊#95—101no—
130#830—51no—
131#818—101no—
132#816—101no—
133#808—101no—
134C2×C5×D4—21no—
135C2×C5×D4D1211yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5C22×D311yescharacteristic
138C22×Dic5—31no—
139C22×Dic5—31no—
140C22×Dic5—61no—
141C22×Dic5—61no—
142C2×Dic10—31no—
143C2×C5×C8—21no—
144C5×C4⋊C4D1211yescharacteristic
145C5×C22⋊C4—21no—
146C22⋊Dic5—61no—
147C22⋊Dic5—61no—
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—61no—
152C4⋊Dic5—61no—
153C4⋊Dic5—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159C4×Dic5—61no—
160C2×#168—61no—
161#539—151no—
162#484—151no—
163#481—151no—
164#400—151no—
165#328—151no—
166#327D1511yescharacteristic
167#324—151no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—81no—
180Dic15—41no—
181Dic15—41no—
182Dic15—41no—
183Dic15—41no—
184Dic15—81no—
185C2×C3×D4—21no—
186C2×C3×D4D2011yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4C22×D511yescharacteristic
189C22×Dic3—51no—
190C22×Dic3—51no—
191C22×Dic3—101no—
192C22×Dic3—101no—
193C2×Dic6—51no—
194C2×C3×C8—21no—
195C3×C4⋊C4D2011yescharacteristic
196C3×C22⋊C4—21no—
197#217—101no—
198#217—101no—
199#217—101no—
200#217—101no—
201C4⋊Dic3—51no—
202C4⋊Dic3—101no—
203C4⋊Dic3—101no—
204C4⋊Dic3—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—101no—
212C23×C5—21no—
213C23×C5D3×D411yescharacteristic
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C2×C4×C5—21no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5C2×D1211yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C2×Dic5—61no—
225C2×Dic5—61no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228C2×Dic5—61no—
229C2×Dic5—61no—
230C2×Dic5—121no—
231C2×Dic5—122no—
232C2×Dic5—121no—
233C2×Dic5—241no—
234Dic10—121no—
235C5×C8—41no—
236#168—121no—
237#126—301no—
238#125—301no—
239#123—301no—
240#123—301no—
241C22⋊Q8—151no—
242C22⋊Q8—301no—
243#121C2×D1511yescharacteristic
244C4×D4—301no—
245C2×C4⋊C4—151no—
246C2×C4⋊C4—151no—
247#107—301no—
248#106—301no—
249#103—301no—
250#102—301no—
251C22⋊C8—151no—
252C22⋊C8C2×D1511yescharacteristic
253#95—301no—
254#95—301no—
255#95C2×D1511yescharacteristic
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—81no—
259C2×C3×C5#45211yescharacteristic
260C2×C3×C5#45411yescharacteristic
261C2×C3×C5#45811yescharacteristic
262C23×C3—21no—
263C23×C3D4×D511yescharacteristic
264C3×D4—41no—
265C3×D4—41no—
266C3×D4—41no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4C2×D2011yescharacteristic
273C2×C3×C4D4×D511yescharacteristic
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—101no—
277C2×Dic3—101no—
278C2×Dic3—101no—
279C2×Dic3—101no—
280C2×Dic3—201no—
281C2×Dic3—202no—
282C2×Dic3—201no—
283C2×Dic3—401no—
284Dic6—201no—
285C3×C8—41no—
286C3⋊C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5#88211yescharacteristic
293C22×C5#91211yescharacteristic
294C22×C5#91511yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—81no—
299Dic5—121no—
300Dic5—121no—
301Dic5—121no—
302Dic5—121no—
303Dic5—241no—
304C2×Q8—151no—
305C2×D4—21no—
306C2×D4D6011yescharacteristic
307C22×C4—21no—
308C22×C4—151no—
309C22×C4—151no—
310C22×C4—301no—
311C22×C4—301no—
312C22×C4C22×D1511yescharacteristic
313C2×C8—21no—
314C2×C8—301no—
315C4⋊C4—151no—
316C4⋊C4—301no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4D6011yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C22⋊C4—301no—
329C22⋊C4—301no—
330C42—301no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#402811yescharacteristic
338C22×C3#405811yescharacteristic
339C22×C3#406111yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—81no—
344Dic3—201no—
345Dic3—201no—
346Dic3—201no—
347Dic3—201no—
348Dic3—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5#474211yescharacteristic
353C2×C5#478311yescharacteristic
354C2×C5#482711yescharacteristic
355C23—21no—
356C23D4×D1511yescharacteristic
357Q8—601no—
358D4—41no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—301no—
367C2×C4—301no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—301no—
372C2×C4—601no—
373C2×C4—602no—
374C2×C4—601no—
375C2×C4—1201no—
376C2×C4C2×D6011yescharacteristic
377C2×C4D4×D1511yescharacteristic
378C8—41no—
379C8—601no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3#6503111yescharacteristic
384C2×C3#6507211yescharacteristic
385C2×C3#6511611yescharacteristic
386C5#6829811yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#9177111yescharacteristic
393C22#9180111yescharacteristic
394C22#9180411yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—81no—
399C4—601no—
400C4—601no—
401C4—601no—
402C4—601no—
403C4—1201no—
404C3#1059909111yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—81no—
408C2#1175084311yescharacteristic
409C2#1175088411yescharacteristic
410C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenter#327D15
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
3. #11750823C2semidirect
4. #11750760C2semidirect
6. #11746290C2semidirect
7. #11746273C2semidirect
331. C3×C5#1615semidirect
386. C5#68298semidirect
404. C3#10599091semidirect

Maximal subgroups

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

subgroupindex
#117563612
#117511352
#117508232
#117507602
C3×C5×#3272
#117462902
#117462732
#105990913
#682985