Finite Group Databasebeta

← #14309042

Subgroups — #14309042

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5470C211yesmaximal, characteristic, complemented
2C2×C3×#3937C211yesmaximal, characteristic
3#11748624C211yesmaximal, characteristic
4#11748421C211yesmaximal, characteristic
5#11746344C211yesmaximal, characteristic, complemented
6#11745989C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10602635—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C5×#924—22no—
16C5×#870—21no—
17C5×#869—21no—
18C4×C5×Dic6—22no—
19C2×C3×#681C2211yescharacteristic
20C3×#3937—21no—
21C3×#3937—21no—
22#90995—22no—
23#90977—22no—
24#70368—51nomaximal, Hall
25C5×#533—31no—
26#65295—31no—
27#65294—31no—
28C2×#3937D311yescharacteristic
29#64753—31no—
30#64751—31no—
31#64743—31no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×C5×Dic6—22no—
35C2×C3×C22⋊D5—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C2×C3×D20Q811yescharacteristic, complemented
41C2×C3×C4×D5—21no—
42C2×C3×Dic10Q811yescharacteristic, complemented
43C3×C42×C5—21no—
44C3×C42×C5D411yescharacteristic
45C3×C42×C5D411yescharacteristic
46#6719—21no—
47C4⋊Dic15—21no—
48C4×Dic15—21no—
49#6710—21no—
50#6710—21no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×#217D412yes—
54C5×C4⋊Dic3—22no—
55C5×C4⋊Dic3—21no—
56C5×C4⋊Dic3—21no—
57C5×Dic3⋊C4—24no—
58C4×C5×Dic3—21no—
59C4×C5×Dic3D412yes—
60C3×#681—21no—
61C3×#681—21no—
62C2×C3×#168—21no—
63#5470D511yescharacteristic, complemented
64C2×C3×#104—51no—
65#5240—51no—
66#5236—51no—
67#4559—51no—
68#4557—51no—
69#4523—51no—
70C2×#709C2×D311yescharacteristic
71C5×C4⋊Q8—61no—
72C5×#125—61no—
73C5×C22⋊Q8—62no—
74C4×C5×Q8—62no—
75C5×#117—31no—
76C5×#117—31no—
77C2×C42×C5C2×D311yescharacteristic
78#4072—31no—
79C2×#681—31no—
80C2×#681C2×D311yescharacteristic
81#3938—62no—
82#3937—21no—
83#3937—21no—
84#3937—62no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C3×D5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×Q811yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—41no—
98C2×C5×Dic3—22no—
99C2×C5×Dic3—22no—
100C5×Dic6—44no—
101C3×C22⋊D5—41no—
102C3×C22⋊D5—41no—
103C2×C3×Dic5—21no—
104C3×D20—21no—
105C3×D20—21no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×Dic10—21no—
109C3×Dic10—21no—
110C3⋊#168—41no—
111C3×#168—41no—
112C2×C3×#41—51no—
113C2×C3×M16—51no—
114C2×C3×C42C2×D511yescharacteristic
115#926—51no—
116#926C2×D511yescharacteristic
117#926C2×D511yescharacteristic
118#924—22no—
119C2×#208—51no—
120#870—21no—
121#869—21no—
122C4×Dic6—22no—
123C3×#104—101no—
124C3×#104—101no—
125#837—102no—
126#834—102no—
127C2×C5×Q8—62no—
128C22×C4×C5—21no—
129C22×C4×C5C22×D311yescharacteristic
130C2×C22⋊D5—21no—
131#709—21no—
132#709—21no—
133#709—21no—
134#709—21no—
135C2×D20Dic611yescharacteristic, complemented
136C2×C4×D5—21no—
137C2×Dic10Dic611yescharacteristic, complemented
138C5×C4⋊C4—64no—
139C5×C4⋊C4—62no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C22⋊C4—32no—
143C5×C22⋊C4—61no—
144C42×C5—21no—
145C42×C5—32no—
146C42×C5—61no—
147C42×C5#6711yescharacteristic
148C42×C5#6711yescharacteristic
149C22⋊Dic5—61no—
150C4⋊Dic5—61no—
151C4×Dic5—61no—
152#681—21no—
153#681—21no—
154#681—61no—
155#681—61no—
156C2×#168—21no—
157C2×#168—61no—
158#533—31no—
159#421—151no—
160C2×#104—51no—
161#410—151no—
162#344—151no—
163#339—151no—
164H(3,ℤ/4)—151no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×C3×D5—41no—
170C2×C3×D5—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5C22⋊Q811yescharacteristic
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5#12411yescharacteristic
176C3×C4×C5#12411yescharacteristic
177Dic15—81no—
178C3×Dic5—41no—
179C5×Dic3—42no—
180C5×Dic3—42no—
181C3×#41—101no—
182C3×#41—101no—
183C3×#41—101no—
184C3×#41—101no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—21no—
189C22×C3×C4—101no—
190C22×C3×C4C22×D511yescharacteristic
191C2×Dic6—22no—
192C3×M16—101no—
193C3×M16—101no—
194C2×C3×C8—101no—
195C3×C42—21no—
196C3×C42C22⋊D511yescharacteristic
197C3×C42C22⋊D511yescharacteristic
198#217—21no—
199#217—101no—
200#217C22⋊D512yes—
201C4⋊Dic3—22no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—101no—
205Dic3⋊C4—24no—
206C4×Dic3—21no—
207C4×Dic3—101no—
208C4×Dic3C22⋊D512yes—
209#208—101no—
210#208—101no—
211C2×C3⋊C8—101no—
212C23×C5D3×D411yescharacteristic
213C22×D5—21no—
214C5×Q8—124no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—42no—
218C2×C4×C5—62no—
219C2×C4×C5—62no—
220C2×C4×C5C2×Dic611yescharacteristic
221C2×C4×C5#23511yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5#23711yescharacteristic
224C2×C4×C5#23711yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C22⋊D5—41no—
227C22⋊D5—41no—
228C2×Dic5—21no—
229C2×Dic5—121no—
230D20—21no—
231D20—21no—
232C4×D5—41no—
233C4×D5—41no—
234Dic10—21no—
235Dic10—21no—
236#168—41no—
237#168—121no—
238C2×#41—51no—
239C2×M16—51no—
240C2×M16—151no—
241C4⋊Q8—61no—
242#125—61no—
243C22⋊Q8—62no—
244C4×Q8—62no—
245#117—31no—
246#117—31no—
247#117—151no—
248C2×C42D3×D511yescharacteristic
249#104—101no—
250#104—101no—
251#104—302no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257C3×D5—81no—
258C23×C3—101no—
259C23×C3C2×C22⋊D511yescharacteristic
260C3×Q8—101no—
261C3×Q8—101no—
262C3×D4—101no—
263C3×D4—101no—
264C3×D4—201no—
265C3×D4—201no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—42no—
269C2×C3×C4—101no—
270C2×C3×C4—201no—
271C2×C3×C4—201no—
272C2×C3×C4Q8×D511yescharacteristic
273C2×C3×C4#71311yescharacteristic
274C2×C3×C4#71311yescharacteristic
275C2×C3×C4#71311yescharacteristic
276C2×C3×C4C2×C22⋊D511yescharacteristic
277C2×C3×C4C2×C22⋊D511yescharacteristic
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—201no—
281Dic6—44no—
282C3×C8—201no—
283C3⋊C8—201no—
284C22×C5—41no—
285C22×C5#87811yescharacteristic
286C22×C5#88511yescharacteristic
287C22×C5#93711yescharacteristic
288C2×D5—41no—
289C2×D5—81no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—122no—
293C4×C5—122no—
294C4×C5#87811yescharacteristic
295C4×C5#88511yescharacteristic
296C4×C5#92411yescharacteristic
297C4×C5#93611yescharacteristic
298Dic5—41no—
299Dic5—241no—
300#41—101no—
301#41—101no—
302#41—101no—
303#41—101no—
304C2×Q8—51no—
305C2×Q8—62no—
306C2×D4—51no—
307C2×D4—101no—
308C22×C4—21no—
309C22×C4—101no—
310C22×C4C2×D3×D511yescharacteristic
311M16—101no—
312M16—101no—
313M16—301no—
314M16—301no—
315C2×C8—101no—
316C2×C8—301no—
317C4⋊C4—64no—
318C4⋊C4—62no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—301no—
322C22⋊C4—32no—
323C22⋊C4—61no—
324C22⋊C4—301no—
325C42—21no—
326C42—32no—
327C42—61no—
328C42—301no—
329C42#120111yescharacteristic
330C42#120111yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3—201no—
334C22×C3—401no—
335C22×C3#409211yescharacteristic
336C22×C3#409311yescharacteristic
337C22×C3#409911yescharacteristic
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—201no—
341C3×C4#409211yescharacteristic
342C3×C4#409211yescharacteristic
343C3×C4#409311yescharacteristic
344C3×C4#409311yescharacteristic
345Dic3—42no—
346Dic3—42no—
347Dic3—401no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#494711yescharacteristic
352D5—81no—
353C23—101no—
354C23D3×C22⋊D511yescharacteristic
355Q8—101no—
356Q8—101no—
357Q8—124no—
358D4—101no—
359D4—101no—
360D4—201no—
361D4—201no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—62no—
366C2×C4—62no—
367C2×C4—101no—
368C2×C4—201no—
369C2×C4—201no—
370C2×C4—601no—
371C2×C4D5×Dic611yescharacteristic
372C2×C4#676611yescharacteristic
373C2×C4#676611yescharacteristic
374C2×C4#677311yescharacteristic
375C2×C4C2×#120111yescharacteristic
376C2×C4D3×C22⋊D511yescharacteristic
377C8—201no—
378C8—601no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6552011yescharacteristic
384C5#7036811yescharacteristic, complemented, Sylow
385C22—41no—
386C22—201no—
387C22—401no—
388C22#9142111yescharacteristic
389C22#9145511yescharacteristic
390C22#9156811yescharacteristic
391C4—22no—
392C4—41no—
393C4—122no—
394C4—122no—
395C4—201no—
396C4—1201no—
397C4#9135911yescharacteristic
398C4#9136811yescharacteristic
399C4#9142111yescharacteristic
400C4#9145511yescharacteristic
401C3#1060263511yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—401no—
406C2#1174877311yescharacteristic
subgroupG/H
centerC4#91455
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C5×#5470C2semidirect
5. #11746344C2semidirect
6. #11745989C2semidirect
7. #11745971C2semidirect
40. C2×C3×D20Q8semidirect
42. C2×C3×Dic10Q8semidirect
63. #5470D5semidirect
135. C2×D20Dic6semidirect
137. C2×Dic10Dic6semidirect
331. C3×C5#2031semidirect
384. C5#70368semidirect
401. C3#10602635semidirect

Maximal subgroups

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

subgroupindex
C5×#54702
C2×C3×#39372
#117486242
#117484212
#117463442
#117459892
#117459712
#106026353
#703685