Finite Group Databasebeta

← #14288595

Subgroups — #14288595

Order 1920.

472 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 82 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#11754468C211yesmaximal, characteristic
2#11750823C211yesmaximal, characteristic, complemented
3#11748774C211yesmaximal, characteristic
4#11748467C211yesmaximal, characteristic, complemented
5C5×#4467C211yesmaximal, characteristic, complemented
6C3×#64688C211yesmaximal, characteristic
7#11745965C211yesmaximal, characteristic, complemented
8#10599115—31nomaximal, Hall
9C2×C4⋊Dic15C2211yescharacteristic
10#91813C2211yescharacteristic
11C5×#924C2211yescharacteristic
12C2×C3×#685C2211yescharacteristic
13#91574—21no—
14D5×#217—21no—
15C2×Dic3⋊Dic5—21no—
16C2×#6665—21no—
17#91431—21no—
18#91430—21no—
19#91422—21no—
20#91421—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22#91102—21no—
23#91100—21no—
24C5×C3⋊#95C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90988—21no—
27#90973—21no—
28#68117—51nomaximal, Hall
29#65968—31no—
30#65333—31no—
31#65011—31no—
32#64966—31no—
33C5×#328—31no—
34#64688D311yescharacteristic
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30D411yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×Dic6D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×#1204—21no—
44C2×D5×Dic3—21no—
45C2×D5×Dic3—21no—
46C2×C3×C5×C8—21no—
47#6719—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C5×#217—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C5×Dic3⋊C4—21no—
55C3×#685—21no—
56C3×#685—21no—
57C2×C3×#168—21no—
58Dic3⋊Dic5—21no—
59Dic3⋊Dic5—42no—
60#6669—21no—
61#6668—21no—
62#6665—21no—
63#6665—21no—
64#6665—42no—
65#5483—51no—
66#4949—51no—
67#4722—51no—
68#4722—51no—
69C3×#323—51no—
70#4467—51no—
71#4467D511yescharacteristic, complemented
72C5×C22⋊Q8—31no—
73#4092—61no—
74C2×#685—61no—
75C2×#685C2×D311yescharacteristic
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—61no—
78#4070—31no—
79#4043—61no—
80#4042—61no—
81#4042—61no—
82D5×C22⋊C4—61no—
83#4024—61no—
84C5×C22⋊C8C2×D311yescharacteristic
85C5×#95—31no—
86#3967—61no—
87C22⋊#168C2×D311yescharacteristic
88#3950—61no—
89#3948—61no—
90#3939—61no—
91#1614—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×C3×D5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C22×C3×D5Q1612yes—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—41no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106Dic30—41no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C5×Dic6—41no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—41no—
115#1204—81no—
116D5×Dic3—81no—
117D5×Dic3—81no—
118C3×C5×C8—41no—
119C3×#168—41no—
120C2×C3×C22⋊C4—51no—
121C2×#217—101no—
122C2×#217—101no—
123C2×C4⋊Dic3—51no—
124#924—51no—
125#924—101no—
126#924C2×D511yescharacteristic
127C2×Dic3⋊C4—101no—
128#878—101no—
129#878—101no—
130#878—101no—
131#878—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3⋊#95C2×D511yescharacteristic
135#818—101no—
136#818—101no—
137#816—101no—
138#816—101no—
139C23×D5D1211yescharacteristic
140C2×C5×Q8—31no—
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—61no—
144C22×Dic5D1211yescharacteristic
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C2×Dic10—61no—
149C2×C5×C8—21no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4—61no—
152C5×C22⋊C4—61no—
153C22⋊Dic5—61no—
154#685—21no—
155#685—21no—
156#685—61no—
157#685—61no—
158#685—122no—
159C4⋊Dic5—31no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163C4⋊Dic5—122no—
164#683—61no—
165#683—61no—
166#683—61no—
167C2×#168—21no—
168#543—151no—
169#484—151no—
170#484—151no—
171#399—151no—
172#328—31no—
173#328—151no—
174#323—51no—
175C22×C3×C5—21no—
176C22×C3×C5—21no—
177C22×C3×C5#12011yescharacteristic
178C22×C3×C5C2×Q1611yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C3×D5—22no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C2×C3×D5—42no—
184C2×C3×D5—81no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187Dic15—41no—
188Dic15—41no—
189Dic15—81no—
190C3×Dic5—41no—
191C5×Dic3—42no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C24×C3—51no—
195C22×C3×C4—51no—
196C22×C3×C4C22×D511yescharacteristic
197C22×Dic3—21no—
198C22×Dic3—101no—
199C22×Dic3—101no—
200C22×Dic3—101no—
201C2×Dic6—51no—
202C2×Dic6—101no—
203C2×Dic6D2011yescharacteristic
204C2×C3×C8—21no—
205C2×C3×C8—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208#217—21no—
209#217—101no—
210#217—101no—
211#217—101no—
212#217—202no—
213C4⋊Dic3—51no—
214C4⋊Dic3—101no—
215C4⋊Dic3—101no—
216C4⋊Dic3—101no—
217C4⋊Dic3D2011yescharacteristic
218Dic3⋊C4—21no—
219Dic3⋊C4—101no—
220Dic3⋊C4—101no—
221Dic3⋊C4—101no—
222Dic3⋊C4—202no—
223C23×C5C2×D1211yescharacteristic
224C22×D5—21no—
225C22×D5—21no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5Dic1212yes—
229C5×Q8—121no—
230C2×C4×C5—41no—
231C2×C4×C5—62no—
232C2×C4×C5—61no—
233C2×C4×C5—61no—
234C2×C4×C5—121no—
235C2×C4×C5—121no—
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×Dic5—21no—
239C2×Dic5—41no—
240C2×Dic5—61no—
241C2×Dic5—61no—
242C2×Dic5—121no—
243C2×Dic5—121no—
244C2×Dic5—121no—
245C4×D5—241no—
246C4×D5—241no—
247Dic10—121no—
248Dic10—241no—
249C5×C8—41no—
250#168—41no—
251C22⋊Q8—31no—
252C22⋊Q8—151no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C22⋊Q8—301no—
256C22⋊Q8—301no—
257C22⋊Q8—301no—
258C2×C4⋊C4—151no—
259C2×C4⋊C4—301no—
260C2×C22⋊C4—51no—
261C2×C22⋊C4—301no—
262C2×C22⋊C4—301no—
263#107—301no—
264#107—301no—
265#103—301no—
266#103—301no—
267C22⋊C8—51no—
268C22⋊C8D3×D511yescharacteristic
269#95—31no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5#45111yescharacteristic
273C2×C3×C5#45311yescharacteristic
274C2×C3×C5#45811yescharacteristic
275C3×D5—42no—
276C23×C3—52no—
277C23×C3—101no—
278C23×C3—101no—
279C23×C3—201no—
280C23×C3—201no—
281C23×C3D4×D511yescharacteristic
282C2×C3×C4—41no—
283C2×C3×C4—101no—
284C2×C3×C4—201no—
285C2×C3×C4C2×D2011yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—101no—
293C2×Dic3—101no—
294C2×Dic3—201no—
295C2×Dic3—201no—
296C2×Dic3—201no—
297C2×Dic3—401no—
298C2×Dic3—401no—
299Dic6—41no—
300Dic6—201no—
301Dic6—401no—
302C3×C8—41no—
303C3×C8—201no—
304C22×C5—21no—
305C22×C5—21no—
306C22×C5#88211yescharacteristic
307C22×C5C2×Dic1211yescharacteristic
308C22×C5#90911yescharacteristic
309C2×D5—22no—
310C2×D5—41no—
311C2×D5—41no—
312C2×D5—42no—
313C2×D5—81no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—122no—
317C4×C5—121no—
318C4×C5—121no—
319Dic5—41no—
320Dic5—121no—
321Dic5—121no—
322Dic5—241no—
323C24—51no—
324C2×Q8—31no—
325C2×Q8—151no—
326C2×Q8—301no—
327C22×C4—51no—
328C22×C4—61no—
329C22×C4—301no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4C2×D3×D511yescharacteristic
333C2×C8—21no—
334C2×C8—101no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—151no—
338C4⋊C4—301no—
339C4⋊C4—301no—
340C4⋊C4—301no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4—301no—
344C4⋊C4—602no—
345C22⋊C4—61no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—301no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—602no—
352C3×C5#161411yescharacteristic, complemented, Hall
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—102no—
356C22×C3—202no—
357C22×C3—201no—
358C22×C3—201no—
359C22×C3—401no—
360C22×C3#402811yescharacteristic
361C22×C3#406111yescharacteristic
362C22×C3D5×Q1611yescharacteristic
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—201no—
366Dic3—42no—
367Dic3—41no—
368Dic3—41no—
369Dic3—201no—
370Dic3—201no—
371Dic3—401no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#473911yescharacteristic
375C2×C5#474211yescharacteristic
376C2×C5#474711yescharacteristic
377D5—42no—
378C23—52no—
379C23—101no—
380C23—101no—
381C23—201no—
382C23—201no—
383C23D5×D1211yescharacteristic
384Q8—121no—
385Q8—601no—
386Q8—1201no—
387C2×C4—41no—
388C2×C4—62no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—101no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—201no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4—1201no—
401C2×C4—1201no—
402C2×C4D3×D2011yescharacteristic
403C2×C4#679011yescharacteristic
404C8—41no—
405C8—201no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—202no—
409C2×C3#6503111yescharacteristic
410C2×C3#6509711yescharacteristic
411C2×C3#6511111yescharacteristic
412C5#6811711yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—102no—
416C22—202no—
417C22—201no—
418C22—201no—
419C22—401no—
420C22D5×Dic1211yescharacteristic
421C22#9126011yescharacteristic
422C22#9147611yescharacteristic
423C4—21no—
424C4—21no—
425C4—122no—
426C4—121no—
427C4—121no—
428C4—201no—
429C4—601no—
430C4—601no—
431C4—1201no—
432C3#1059911511yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—202no—
436C2#1174713611yescharacteristic
437C2#1174813011yescharacteristic
438C2#1174824811yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5#120
prime radicalC23×C3×D5D4
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1614
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750823C2semidirect
4. #11748467C2semidirect
5. C5×#4467C2semidirect
7. #11745965C2semidirect
71. #4467D5semidirect
352. C3×C5#1614semidirect
412. C5#68117semidirect
432. C3#10599115semidirect

Maximal subgroups

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

subgroupindex
#117544682
#117508232
#117487742
#117484672
C5×#44672
C3×#646882
#117459652
#105991153
#681175