Finite Group Databasebeta

← #14288374

Subgroups — #14288374

Order 1920.

432 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 78 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#11754477C211yesmaximal, characteristic
2#11750822C211yesmaximal, characteristic, complemented
3#11748843C211yesmaximal, characteristic, complemented
4#11748465C211yesmaximal, characteristic
5C5×#4470C211yesmaximal, characteristic
6C3×#64689C211yesmaximal, characteristic, complemented
7#11745965C211yesmaximal, characteristic, complemented
8#10599089—31nomaximal, Hall
9C2×C4⋊Dic15C2211yescharacteristic
10#91813C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C2×C3×#683C2211yescharacteristic
13Dic5×#67—21no—
14C2×Dic3⋊Dic5—21no—
15#91539—21no—
16#91432—21no—
17#91423—21no—
18#91342—21no—
19#91336—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21#91101—21no—
22#91100—21no—
23C5×C3⋊#95C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25#90994—21no—
26#90988—21no—
27#90967—21no—
28#68134—51nomaximal, Hall
29#65936—31no—
30#65322—31no—
31#65010—31no—
32#64950—31no—
33C5×#327—31no—
34#64689D311yescharacteristic, complemented
35#64672—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×Dic30D411yescharacteristic
39C2×C5×#67—21no—
40C22×C5×Dic3—21no—
41C2×C5×D12D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×D3×Dic5—21no—
45C2×C3×C5×C8—21no—
46#6719—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50#6712—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C3×#683—21no—
54C3×#683—21no—
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—42no—
58#6669—21no—
59#6669—21no—
60(C2×D3)⋊Dic5—21no—
61(C2×D3)⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63Dic3×Dic5—21no—
64#5515—51no—
65#4981—51no—
66#4736—51no—
67#4721—51no—
68C3×#324—51no—
69#4470D511yescharacteristic
70#4467—51no—
71C5×#121—31no—
72#4081—61no—
73#4081—61no—
74D4×Dic5—61no—
75C2×C4⋊Dic5—31no—
76C2×C4⋊Dic5—61no—
77#4070—31no—
78C2×#683C2×D311yescharacteristic
79#4035—61no—
80#4025—61no—
81#4024—61no—
82C5×C22⋊C8C2×D311yescharacteristic
83C5×#95—31no—
84#3964—61no—
85#3963—61no—
86C22⋊#168C2×D311yescharacteristic
87#3949—61no—
88#3948—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C5×D3—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—41no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101Dic30—41no—
102C5×#67—41no—
103C5×#67—41no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C5×D12—41no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—41no—
114D3×Dic5—81no—
115C3×C5×C8—41no—
116C3×#168—41no—
117C2×C3×C4⋊C4—51no—
118#930C2×D511yescharacteristic
119#929—101no—
120C4×#67—101no—
121C2×C4⋊Dic3—51no—
122#924—51no—
123C2×Dic3⋊C4—101no—
124#898—101no—
125#896—101no—
126#894—101no—
127#889—101no—
128C3×C22⋊C8—51no—
129C3×C22⋊C8C2×D511yescharacteristic
130C3⋊#95—101no—
131C3⋊#95C2×D511yescharacteristic
132#821—101no—
133#818—101no—
134#817—101no—
135#816—101no—
136C2×C5×D4—31no—
137C2×C5×D4—61no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—61no—
141C22×Dic5—61no—
142C22×Dic5D1211yescharacteristic
143C22×Dic5D1211yescharacteristic
144C2×Dic10—31no—
145C2×C5×C8—21no—
146C5×C4⋊C4—31no—
147C5×C22⋊C4—61no—
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150C22⋊Dic5—61no—
151C22⋊Dic5—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—122no—
157#683—21no—
158#683—21no—
159#683—61no—
160#683—61no—
161#683—61no—
162C4×Dic5—61no—
163C2×#168—21no—
164#539—151no—
165#483—151no—
166#480—151no—
167#398—151no—
168#328—151no—
169#327—31no—
170#324—51no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
176C2×C5×D3—41no—
177C2×C5×D3—41no—
178C2×C5×D3—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181Dic15—41no—
182Dic15—41no—
183Dic15—81no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C5×Dic3—42no—
187C5×Dic3—41no—
188C22×C3×C4—51no—
189C22×C3×C4—51no—
190C22×C3×C4C22×D511yescharacteristic
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3—101no—
194C2×D12D2011yescharacteristic
195C2×C4×D3—101no—
196C2×Dic6—51no—
197C2×C3×C8—21no—
198C2×C3×C8—101no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201#217—101no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3—101no—
208C4⋊Dic3—101no—
209C4⋊Dic3D2011yescharacteristic
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214Dic3⋊C4—202no—
215C4×Dic3—101no—
216C23×C5—61no—
217C23×C5C2×D1211yescharacteristic
218C5×D4—121no—
219C5×D4—121no—
220C5×D4—121no—
221C2×C4×C5—41no—
222C2×C4×C5—62no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5—121no—
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×Dic5—21no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—41no—
233C2×Dic5—61no—
234C2×Dic5—61no—
235C2×Dic5—121no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238C2×Dic5—241no—
239Dic10—121no—
240C5×C8—41no—
241#168—41no—
242#126—301no—
243#125—301no—
244#123—301no—
245#123—301no—
246C22⋊Q8—151no—
247C22⋊Q8—301no—
248#121—31no—
249C4×D4—301no—
250C2×C4⋊C4—51no—
251C2×C4⋊C4—151no—
252C2×C4⋊C4—301no—
253#107—301no—
254#106—301no—
255#103—301no—
256#102—301no—
257C22⋊C8—51no—
258C22⋊C8D3×D511yescharacteristic
259#95—31no—
260#95—301no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45611yescharacteristic
265C2×C3×C5#45811yescharacteristic
266C5×D3—81no—
267C23×C3D4×D511yescharacteristic
268C22×D3—21no—
269C2×C3×C4—41no—
270C2×C3×C4—101no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—101no—
274C2×C3×C4—201no—
275C2×C3×C4C2×D2011yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277#67—41no—
278#67—41no—
279C2×Dic3—22no—
280C2×Dic3—21no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—101no—
284C2×Dic3—101no—
285C2×Dic3—201no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288D12—41no—
289C4×D3—401no—
290Dic6—201no—
291C3×C8—41no—
292C3×C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—121no—
296C22×C5—121no—
297C22×C5—121no—
298C22×C5#88211yescharacteristic
299C22×C5#90411yescharacteristic
300C22×C5#90811yescharacteristic
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—122no—
304C4×C5—121no—
305Dic5—41no—
306Dic5—41no—
307Dic5—121no—
308Dic5—121no—
309Dic5—241no—
310C2×Q8—151no—
311C2×D4—31no—
312C2×D4—61no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—61no—
316C22×C4—301no—
317C22×C4—301no—
318C22×C4C2×D3×D511yescharacteristic
319C2×C8—21no—
320C2×C8—101no—
321C4⋊C4—31no—
322C4⋊C4—101no—
323C4⋊C4—101no—
324C4⋊C4—151no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—602no—
332C22⋊C4—61no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—301no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3#402811yescharacteristic
342C22×C3#405711yescharacteristic
343C22×C3#406211yescharacteristic
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—41no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—201no—
350C3×C4—201no—
351Dic3—42no—
352Dic3—41no—
353Dic3—201no—
354Dic3—201no—
355Dic3—401no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—241no—
359C2×C5#473411yescharacteristic
360C2×C5#474211yescharacteristic
361C2×C5#475211yescharacteristic
362C23—61no—
363C23D5×D1211yescharacteristic
364Q8—601no—
365D4—121no—
366D4—121no—
367D4—121no—
368C2×C4—41no—
369C2×C4—62no—
370C2×C4—61no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—121no—
376C2×C4—121no—
377C2×C4—201no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—1201no—
384C2×C4D3×D2011yescharacteristic
385C2×C4#679011yescharacteristic
386C8—41no—
387C8—201no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3#6503111yescharacteristic
391C2×C3#6507011yescharacteristic
392C2×C3#6511511yescharacteristic
393D3—81no—
394C5#6813411yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22#9125011yescharacteristic
401C22#9126911yescharacteristic
402C22#9147611yescharacteristic
403C4—21no—
404C4—21no—
405C4—122no—
406C4—121no—
407C4—201no—
408C4—201no—
409C4—601no—
410C4—601no—
411C4—1201no—
412C3#1059908911yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—241no—
416C2#1174713611yescharacteristic
417C2#1174816311yescharacteristic
418C2#1174826211yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#930C22
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1609
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. #11750822C2semidirect
3. #11748843C2semidirect
6. C3×#64689C2semidirect
7. #11745965C2semidirect
34. #64689D3semidirect
338. C3×C5#1609semidirect
394. C5#68134semidirect
412. C3#10599089semidirect

Maximal subgroups

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

subgroupindex
#117544772
#117508222
#117488432
#117484652
C5×#44702
C3×#646892
#117459652
#105990893
#681345