Finite Group Databasebeta

← #14288596

Subgroups — #14288596

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
2C3×#64966C211yesmaximal, characteristic
3#11748471C211yesmaximal, characteristic, complemented
4#11748414C211yesmaximal, characteristic, complemented
5#11746273C211yesmaximal, characteristic, complemented
6C5×#4452C211yesmaximal, characteristic, complemented
7#11745948C211yesmaximal, characteristic
8#10599115—31nomaximal, Hall
9#91813C2211yescharacteristic
10C5×#924C2211yescharacteristic
11C2×C3×#685—21no—
12C2×C3×#685C2211yescharacteristic
13C2×C3×C4⋊Dic5—21no—
14C2×C3×C4⋊Dic5C2211yescharacteristic
15#91574—21no—
16D5×#217—21no—
17#91431—21no—
18#91430—21no—
19#91422—21no—
20#91421—21no—
21C3×C5×#95C2211yescharacteristic
22#91114C2211yescharacteristic
23C5×#830C2211yescharacteristic
24#90990—21no—
25#90989—21no—
26#90974—21no—
27#90972—21no—
28#69716—51nomaximal, Hall
29#65968—31no—
30#65333—31no—
31#65011—31no—
32#64966D311yescharacteristic
33C5×#328—31no—
34#64688—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×Dic30D411yescharacteristic
40C2×C5×Dic6D411yescharacteristic
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C2×#1204—21no—
44C2×D5×Dic3—21no—
45C2×D5×Dic3—21no—
46#6719—21no—
47C4⋊Dic15D411yescharacteristic
48#6712—21no—
49C2×C3⋊#168—21no—
50C5×#217—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×#685—42no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5—42no—
60Dic3⋊Dic5—21no—
61#6669—21no—
62#6668—21no—
63#6665—21no—
64#6665—21no—
65#5483—51no—
66C3×#399—51no—
67#4970—51no—
68#4970—51no—
69#4525—51no—
70#4452—51no—
71#4452D511yescharacteristic, complemented
72C5×C22⋊Q8—31no—
73#4092—61no—
74C2×#685—21no—
75C2×#685C2×D311yescharacteristic
76C2×C4⋊Dic5—21no—
77C2×C4⋊Dic5C2×D311yescharacteristic
78#4070—31no—
79#4043—61no—
80#4042—61no—
81#4042—61no—
82D5×C22⋊C4—61no—
83#4024—61no—
84C5×C22⋊C8—31no—
85C5×#95C2×D311yescharacteristic
86#3967—61no—
87C22⋊#168—31no—
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—22no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×Dic15—21no—
105C2×Dic15—21no—
106Dic30—41no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C5×Dic6—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—41no—
112C2×C3×Dic5—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115#1204—81no—
116D5×Dic3—81no—
117D5×Dic3—81no—
118C3⋊#168—41no—
119C5×C3⋊C8—41no—
120C2×C3×C4⋊C4—51no—
121C2×C3×C4⋊C4—101no—
122C2×C3×C22⋊C4—51no—
123C2×C3×C22⋊C4—101no—
124C2×#217—101no—
125#924—51no—
126#924—101no—
127#924C2×D511yescharacteristic
128#878—101no—
129#878—101no—
130#878—101no—
131#878—101no—
132C3×#95C2×D511yescharacteristic
133#830—51no—
134#830C2×D511yescharacteristic
135#810—101no—
136#810—101no—
137#807—101no—
138#807—101no—
139C23×D5#6711yescharacteristic
140C2×C5×Q8—31no—
141C22×C4×C5—21no—
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—21no—
144C22×Dic5#6711yescharacteristic
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×Dic10—31no—
148C2×Dic10—61no—
149C2×C5×C8—61no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4—61no—
152C5×C22⋊C4—61no—
153C22⋊Dic5—61no—
154#685—21no—
155#685—21no—
156#685—42no—
157#685—61no—
158#685—61no—
159C4⋊Dic5—21no—
160C4⋊Dic5—21no—
161C4⋊Dic5—31no—
162C4⋊Dic5—42no—
163C4⋊Dic5—61no—
164#683—61no—
165#683—61no—
166#683—61no—
167C2×#168—61no—
168#543—151no—
169#484—151no—
170#484—151no—
171#399—51no—
172#328—31no—
173#328—151no—
174#323—151no—
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—
187C3×C4×C5—42no—
188Dic15—41no—
189Dic15—41no—
190C3×Dic5—41no—
191C3×Dic5—81no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C24×C3—51no—
195C22×C3×C4—21no—
196C22×C3×C4—51no—
197C22×C3×C4—101no—
198C22×C3×C4C22×D511yescharacteristic
199C22×Dic3—101no—
200C22×Dic3—101no—
201C2×Dic6—51no—
202C2×Dic6—101no—
203C2×Dic6D2011yescharacteristic
204C3×C4⋊C4—101no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—202no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—202no—
210#217—21no—
211#217—101no—
212#217—101no—
213#217—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3—101no—
216C4⋊Dic3D2011yescharacteristic
217Dic3⋊C4—21no—
218Dic3⋊C4—101no—
219Dic3⋊C4—101no—
220Dic3⋊C4—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5C2×#6711yescharacteristic
224C22×D5—21no—
225C22×D5—21no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5#21612yes—
229C5×Q8—121no—
230C2×C4×C5—22no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5D3×D411yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×Dic5—21no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5—41no—
242C2×Dic5—41no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C4×D5—241no—
246C4×D5—241no—
247Dic10—121no—
248Dic10—241no—
249C5×C8—121no—
250#168—121no—
251C22⋊Q8—31no—
252C22⋊Q8—151no—
253C22⋊Q8—301no—
254C22⋊Q8—301no—
255C22⋊Q8—301no—
256C22⋊Q8—301no—
257C22⋊Q8—301no—
258C2×C4⋊C4—51no—
259C2×C4⋊C4—101no—
260C2×C22⋊C4—51no—
261C2×C22⋊C4—101no—
262C2×C22⋊C4—301no—
263#107—301no—
264#107—301no—
265#103—301no—
266#103—301no—
267C22⋊C8—31no—
268C22⋊C8—151no—
269#95D3×D511yescharacteristic
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—22no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—101no—
287C2×C3×C4—201no—
288C2×C3×C4—201no—
289C2×C3×C4—201no—
290C2×C3×C4—201no—
291C2×C3×C4C2×D2011yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—101no—
296C2×Dic3—101no—
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#93711yescharacteristic
307C22×C5C2×#21611yescharacteristic
308C22×C5#95111yescharacteristic
309C2×D5—22no—
310C2×D5—41no—
311C2×D5—41no—
312C2×D5—42no—
313C2×D5—81no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—42no—
317C4×C5—121no—
318C4×C5—121no—
319Dic5—41no—
320Dic5—81no—
321Dic5—121no—
322Dic5—121no—
323C24—51no—
324C2×Q8—31no—
325C2×Q8—151no—
326C2×Q8—301no—
327C22×C4—21no—
328C22×C4—51no—
329C22×C4—101no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4C2×D3×D511yescharacteristic
333C2×C8—61no—
334C2×C8—301no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—101no—
338C4⋊C4—101no—
339C4⋊C4—151no—
340C4⋊C4—202no—
341C4⋊C4—301no—
342C4⋊C4—301no—
343C4⋊C4—301no—
344C4⋊C4—301no—
345C22⋊C4—61no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—202no—
349C22⋊C4—301no—
350C22⋊C4—301no—
351C22⋊C4—301no—
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—42no—
366C3×C4—201no—
367C3×C4—401no—
368Dic3—41no—
369Dic3—41no—
370Dic3—201no—
371Dic3—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5#505011yescharacteristic
375C2×C5#505311yescharacteristic
376C2×C5#507711yescharacteristic
377D5—42no—
378C23—52no—
379C23—101no—
380C23—101no—
381C23—201no—
382C23—201no—
383C23D5×#6711yescharacteristic
384Q8—121no—
385Q8—601no—
386Q8—1201no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—101no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4—201no—
397C2×C4—201no—
398C2×C4—301no—
399C2×C4—301no—
400C2×C4—1201no—
401C2×C4—1201no—
402C2×C4D3×D2011yescharacteristic
403C2×C4#677711yescharacteristic
404C8—121no—
405C8—601no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—202no—
409C2×C3#6503111yescharacteristic
410C2×C3#6509711yescharacteristic
411C2×C3#6511111yescharacteristic
412C5#6971611yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—102no—
416C22—202no—
417C22—201no—
418C22—201no—
419C22—401no—
420C22#9147411yescharacteristic
421C22#9148411yescharacteristic
422C22D5×#21611yescharacteristic
423C4—21no—
424C4—21no—
425C4—42no—
426C4—121no—
427C4—121no—
428C4—201no—
429C4—401no—
430C4—601no—
431C4—601no—
432C3#1059911511yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—202no—
436C2#1174711411yescharacteristic
437C2#1174713311yescharacteristic
438C2#1174749211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5#120
prime radicalC23×C3×D5D4
hypercenter#95D3×D5
hypocenterC3×C5#1614
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #11748471C2semidirect
4. #11748414C2semidirect
5. #11746273C2semidirect
6. C5×#4452C2semidirect
71. #4452D5semidirect
352. C3×C5#1614semidirect
412. C5#69716semidirect
432. C3#10599115semidirect

Maximal subgroups

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

subgroupindex
#117544682
C3×#649662
#117484712
#117484142
#117462732
C5×#44522
#117459482
#105991153
#697165