Finite Group Databasebeta

← #14309037

Subgroups — #14309037

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5517C211yesmaximal, characteristic, complemented
2#11751106C211yesmaximal, characteristic
3#11748626C211yesmaximal, characteristic
4C2×#90980C211yesmaximal, characteristic
5C3×#64751C211yesmaximal, characteristic, complemented
6#11745989C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10602635—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C5×#926C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C5×#890—21no—
15C5×#888—21no—
16C5×#878—22no—
17C4×C5×Dic6—22no—
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91089—22no—
21#90997—22no—
22#90980—21no—
23#90980—21no—
24#68714—51nomaximal, Hall
25C5×#533—31no—
26#65295—31no—
27#65294—31no—
28C2×#3937—31no—
29#64753—31no—
30#64751D311yescharacteristic, complemented
31#64743—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—21no—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37#6817—21no—
38C2×D60Q811yescharacteristic, complemented
39C2×C4×D15—21no—
40C2×Dic30Q811yescharacteristic, complemented
41C22×C5×Dic3—21no—
42C2×C5×Dic6—22no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5D412yes—
46#6710—21no—
47#6710—21no—
48C2×C3⋊#168—21no—
49C5×#217D412yes—
50C5×C4⋊Dic3—22no—
51C5×C4⋊Dic3—21no—
52C5×Dic3⋊C4—22no—
53C5×Dic3⋊C4—22no—
54C4×C5×Dic3—21no—
55C4×C5×Dic3—21no—
56C4×C5×Dic3D411yescharacteristic
57C4×C5×Dic3D411yescharacteristic
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5—21no—
60C3×C4×Dic5—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64#5517D511yescharacteristic, complemented
65C2×#825—51no—
66#5006—51no—
67#5005—51no—
68C3×H(3,ℤ/4)—51no—
69#4559—51no—
70#4532—51no—
71C2×#709—31no—
72C5×C4⋊Q8—61no—
73C5×#125—61no—
74C5×C22⋊Q8—62no—
75C4×C5×Q8—62no—
76C5×#117—31no—
77C5×#117C2×D311yescharacteristic
78C2×C42×C5—31no—
79#4072C2×D311yescharacteristic
80C2×#681—31no—
81C2×#681C2×D311yescharacteristic
82#3938—62no—
83#3937—61no—
84#3937—61no—
85#3937—62no—
86#2031—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×D15—21no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×Q811yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96#1220—41no—
97#1220—41no—
98C2×Dic15—21no—
99D60—21no—
100D60—21no—
101C4×D15—41no—
102C4×D15—41no—
103Dic30—21no—
104Dic30—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—42no—
109C5×Dic6—44no—
110C2×C3×Dic5—41no—
111C3⋊#168—41no—
112C3×#168—41no—
113C2×#235—51no—
114C2×C3×M16—51no—
115C3×#117—51no—
116C3×#117C2×D511yescharacteristic
117#926C2×D511yescharacteristic
118C2×C4×Dic3C2×D511yescharacteristic
119C2×#208—51no—
120#890—21no—
121#888—21no—
122#878—22no—
123C4×Dic6—22no—
124#825—101no—
125#825—101no—
126#806—102no—
127#805—102no—
128C2×C5×Q8—62no—
129C22×C4×C5—61no—
130C22×C4×C5C22×D311yescharacteristic
131C2×C22⋊D5—61no—
132#709—61no—
133#709—61no—
134#709—61no—
135#709—61no—
136C2×D20—31no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—62no—
141C5×C4⋊C4—62no—
142C5×C4⋊C4—62no—
143C5×C4⋊C4—61no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—32no—
146C42×C5—31no—
147C42×C5—31no—
148C42×C5—61no—
149C42×C5—61no—
150C42×C5D1212yes—
151C22⋊Dic5—21no—
152C4⋊Dic5—21no—
153C4×Dic5—21no—
154#681—21no—
155#681—21no—
156#681—61no—
157#681—61no—
158C2×#168—21no—
159C2×#168—61no—
160#533—31no—
161#421—151no—
162C2×#104—151no—
163#410—151no—
164#344—151no—
165#339—151no—
166H(3,ℤ/4)—51no—
167C22×C3×C5—41no—
168C22×C3×C5#12011yescharacteristic
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12411yescharacteristic
171C2×D15—41no—
172C2×D15—81no—
173C3×C4×C5—42no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178Dic15—41no—
179C3×Dic5—81no—
180C5×Dic3—22no—
181C5×Dic3—42no—
182C5×Dic3—41no—
183C22×C3×C4C22×D511yescharacteristic
184C2×#67—101no—
185C22×Dic3—21no—
186#235—101no—
187#235—101no—
188#235—101no—
189#235—101no—
190C2×D12—51no—
191C2×C4×D3—101no—
192C2×Dic6—22no—
193C2×Dic6—51no—
194C3×M16—101no—
195C3×M16—101no—
196C2×C3×C8—101no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—101no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—101no—
201C3×C42—101no—
202C3×C42C22⋊D512yes—
203#217C22⋊D512yes—
204C4⋊Dic3—22no—
205C4⋊Dic3—21no—
206Dic3⋊C4—22no—
207Dic3⋊C4—22no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3C22⋊D511yescharacteristic
211C4×Dic3C22⋊D511yescharacteristic
212#208—101no—
213#208—101no—
214C2×C3⋊C8—101no—
215C23×C5D3×D411yescharacteristic
216C22×D5—61no—
217C5×Q8—124no—
218C2×C4×C5—22no—
219C2×C4×C5—61no—
220C2×C4×C5—61no—
221C2×C4×C5—62no—
222C2×C4×C5—122no—
223C2×C4×C5C2×D1211yescharacteristic
224C2×C4×C5#23511yescharacteristic
225C2×C4×C5#23511yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5#23711yescharacteristic
228C2×C4×C5D3×Q811yescharacteristic
229C22⋊D5—121no—
230C22⋊D5—121no—
231C2×Dic5—41no—
232C2×Dic5—61no—
233D20—61no—
234D20—61no—
235C4×D5—121no—
236C4×D5—121no—
237Dic10—61no—
238Dic10—61no—
239#168—41no—
240#168—121no—
241C2×#41—151no—
242C2×M16—51no—
243C2×M16—151no—
244C4⋊Q8—61no—
245#125—61no—
246C22⋊Q8—62no—
247C4×Q8—62no—
248#117—31no—
249#117—51no—
250#117D3×D511yescharacteristic
251C2×C42—31no—
252#104—301no—
253#104—301no—
254#104—302no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#39311yescharacteristic
260D15—81no—
261C23×C3C2×C22⋊D511yescharacteristic
262C22×D3—101no—
263C2×C3×C4—22no—
264C2×C3×C4—201no—
265C2×C3×C4Q8×D511yescharacteristic
266C2×C3×C4#71311yescharacteristic
267C2×C3×C4#71311yescharacteristic
268C2×C3×C4#71311yescharacteristic
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271#67—201no—
272#67—201no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—22no—
276C2×Dic3—42no—
277C2×Dic3—101no—
278D12—101no—
279D12—101no—
280C4×D3—201no—
281C4×D3—201no—
282Dic6—44no—
283Dic6—101no—
284Dic6—101no—
285C3×C8—201no—
286C3⋊C8—201no—
287C22×C5—41no—
288C22×C5#88211yescharacteristic
289C22×C5#88511yescharacteristic
290C22×C5#89611yescharacteristic
291C2×D5—121no—
292C2×D5—241no—
293C4×C5—42no—
294C4×C5—62no—
295C4×C5—121no—
296C4×C5—122no—
297C4×C5#87511yescharacteristic
298C4×C5#88511yescharacteristic
299C4×C5#89611yescharacteristic
300C4×C5#89711yescharacteristic
301Dic5—81no—
302Dic5—121no—
303#41—301no—
304#41—301no—
305#41—301no—
306#41—301no—
307C2×Q8—62no—
308C2×Q8—151no—
309C2×D4—151no—
310C2×D4—301no—
311C22×C4—61no—
312C22×C4—301no—
313C22×C4C2×D3×D511yescharacteristic
314M16—101no—
315M16—101no—
316M16—301no—
317M16—301no—
318C2×C8—101no—
319C2×C8—301no—
320C4⋊C4—21no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C4⋊C4—62no—
324C4⋊C4—61no—
325C4⋊C4—101no—
326C22⋊C4—21no—
327C22⋊C4—32no—
328C22⋊C4—101no—
329C42—31no—
330C42—31no—
331C42—61no—
332C42—61no—
333C42—101no—
334C42#120312yes—
335C3×C5#203111yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3#409211yescharacteristic
338C22×C3#409311yescharacteristic
339C22×C3#409911yescharacteristic
340C2×D3—201no—
341C2×D3—401no—
342C3×C4—42no—
343C3×C4—401no—
344C3×C4#409211yescharacteristic
345C3×C4#409211yescharacteristic
346C3×C4#409311yescharacteristic
347C3×C4#409311yescharacteristic
348Dic3—22no—
349Dic3—42no—
350Dic3—41no—
351Dic3—201no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5#467311yescharacteristic
356D5—241no—
357C23—301no—
358C23D3×C22⋊D511yescharacteristic
359Q8—124no—
360Q8—301no—
361Q8—301no—
362D4—301no—
363D4—301no—
364D4—601no—
365D4—601no—
366C2×C4—22no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—62no—
370C2×C4—122no—
371C2×C4—201no—
372C2×C4—301no—
373C2×C4—601no—
374C2×C4—601no—
375C2×C4#676611yescharacteristic
376C2×C4D15⋊Q811yescharacteristic
377C2×C4#677311yescharacteristic
378C2×C4#677311yescharacteristic
379C2×C4C2×#120311yescharacteristic
380C2×C4D3×C22⋊D511yescharacteristic
381C8—201no—
382C8—601no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3#6552011yescharacteristic
387D3—401no—
388C5#6871411yescharacteristic, complemented, Sylow
389C22—41no—
390C22—601no—
391C22—1201no—
392C22#9142411yescharacteristic
393C22#9145511yescharacteristic
394C22#9157011yescharacteristic
395C4—42no—
396C4—62no—
397C4—121no—
398C4—122no—
399C4—401no—
400C4—601no—
401C4#9137511yescharacteristic
402C4#9138311yescharacteristic
403C4#9142411yescharacteristic
404C4#9145511yescharacteristic
405C3#1060263511yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—1201no—
410C2#1174878411yescharacteristic
subgroupG/H
centerC4#91375
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#393
prime radicalC2×#6817C22
hypercenter#117D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5517C2semidirect
5. C3×#64751C2semidirect
6. #11745989C2semidirect
7. #11745974C2semidirect
30. #64751D3semidirect
38. C2×D60Q8semidirect
40. C2×Dic30Q8semidirect
64. #5517D5semidirect
335. C3×C5#2031semidirect
388. C5#68714semidirect
405. C3#10602635semidirect

Maximal subgroups

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

subgroupindex
C5×#55172
#117511062
#117486262
C2×#909802
C3×#647512
#117459892
#117459742
#106026353
#687145