Finite Group Databasebeta

← #14309044

Subgroups — #14309044

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
1C3×#65804C211yesmaximal, characteristic, complemented
2C2×C5×#805C211yesmaximal, characteristic
3#11748625C211yesmaximal, characteristic
4#11748425C211yesmaximal, characteristic
5#11746344C211yesmaximal, characteristic, complemented
6#11745993C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10601161—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4070—22no—
17C3×#4016—21no—
18C3×#4015—21no—
19C3×C4×Dic10—22no—
20C5×#805—21no—
21C5×#805—21no—
22#90996—22no—
23#90979—22no—
24#71842—51nomaximal, Hall
25#65804D311yescharacteristic, complemented
26C2×C5×#104—31no—
27#65529—31no—
28#65525—31no—
29#64779—31no—
30#64777—31no—
31#64743—31no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×C5×#67—21no—
35C5×#235—21no—
36C5×#235—21no—
37C5×#235—21no—
38C5×#235—21no—
39C2×C5×D12Q811yescharacteristic, complemented
40C2×C4×C5×D3—21no—
41C2×C5×Dic6Q811yescharacteristic, complemented
42C2×C3×Dic10—22no—
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×#208—21no—
53C5×#208—21no—
54C2×C5×C3⋊C8—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5D412yes—
57C3×C4⋊Dic5—22no—
58C3×C4⋊Dic5—21no—
59C3×C4⋊Dic5—21no—
60C3×#683—24no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5D412yes—
63C3×#533—51no—
64#5006—51no—
65#5005—51no—
66C2×#805D511yescharacteristic
67#4533—51no—
68#4531—51no—
69#4523—51no—
70C2×C5×#41—31no—
71C2×C5×M16—31no—
72C2×C42×C5C2×D311yescharacteristic
73#4072—31no—
74#4072C2×D311yescharacteristic
75#4072C2×D311yescharacteristic
76#4070—22no—
77C2×#681—31no—
78#4016—21no—
79#4015—21no—
80C4×Dic10—22no—
81C5×#104—61no—
82C5×#104—61no—
83#3969—62no—
84#3966—62no—
85#2031—151noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C5×D3—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—
98C5×#67—41no—
99C5×#67—41no—
100C2×C5×Dic3—21no—
101C5×D12—21no—
102C5×D12—21no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C5×Dic6—21no—
106C5×Dic6—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C3×Dic10—44no—
110C3⋊#168—41no—
111C5×C3⋊C8—41no—
112C2×#235C2×D511yescharacteristic
113C3×C4⋊Q8—101no—
114C3×#125—101no—
115C3×C22⋊Q8—102no—
116C3×C4×Q8—102no—
117C3×#117—51no—
118C3×#117—51no—
119C2×C3×C42C2×D511yescharacteristic
120#926—51no—
121C2×#208—51no—
122C2×#208C2×D511yescharacteristic
123#806—102no—
124#805—21no—
125#805—21no—
126#805—102no—
127C5×#41—61no—
128C5×#41—61no—
129C5×#41—61no—
130C5×#41—61no—
131C2×C5×Q8—31no—
132C2×C5×D4—31no—
133C2×C5×D4—61no—
134C22×C4×C5—21no—
135C22×C4×C5—61no—
136C22×C4×C5C22×D311yescharacteristic
137C2×Dic10—22no—
138C5×M16—61no—
139C5×M16—61no—
140C2×C5×C8—61no—
141C42×C5—21no—
142C42×C5#6711yescharacteristic
143C42×C5#6711yescharacteristic
144C22⋊Dic5—21no—
145C22⋊Dic5—61no—
146C22⋊Dic5#6712yes—
147C4⋊Dic5—22no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5—61no—
151#683—24no—
152C4×Dic5—21no—
153C4×Dic5—61no—
154C4×Dic5#6712yes—
155#681—61no—
156#681—61no—
157C2×#168—61no—
158#533—51no—
159#421—151no—
160C2×#104—31no—
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×C5×D3—41no—
170C2×C5×D3—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—42no—
179C3×Dic5—42no—
180C5×Dic3—41no—
181C2×C3×Q8—102no—
182C22×C3×C4—21no—
183C22×C3×C4C22×D511yescharacteristic
184C2×#67—21no—
185#235—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189C2×D12Dic1011yescharacteristic, complemented
190C2×C4×D3—21no—
191C2×Dic6Dic1011yescharacteristic, complemented
192C3×C4⋊C4—104no—
193C3×C4⋊C4—102no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C22⋊C4—52no—
197C3×C22⋊C4—101no—
198C3×C42—21no—
199C3×C42—52no—
200C3×C42—101no—
201C3×C42C22⋊D511yescharacteristic
202C3×C42C22⋊D511yescharacteristic
203#217—101no—
204C4⋊Dic3—101no—
205C4×Dic3—101no—
206#208—21no—
207#208—21no—
208#208—101no—
209#208—101no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—101no—
212C23×C5—61no—
213C23×C5C2×#6711yescharacteristic
214C5×Q8—61no—
215C5×Q8—61no—
216C5×D4—61no—
217C5×D4—61no—
218C5×D4—121no—
219C5×D4—121no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—42no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5—121no—
226C2×C4×C5D3×Q811yescharacteristic
227C2×C4×C5#23911yescharacteristic
228C2×C4×C5#23911yescharacteristic
229C2×C4×C5#23911yescharacteristic
230C2×C4×C5C2×#6711yescharacteristic
231C2×C4×C5C2×#6711yescharacteristic
232C2×Dic5—22no—
233C2×Dic5—22no—
234C2×Dic5—121no—
235Dic10—44no—
236C5×C8—121no—
237#168—121no—
238C2×#41—31no—
239C2×M16—31no—
240C2×M16—151no—
241C4⋊Q8—101no—
242#125—101no—
243C22⋊Q8—102no—
244C4×Q8—102no—
245#117—51no—
246#117—51no—
247#117—151no—
248C2×C42D3×D511yescharacteristic
249#104—61no—
250#104—61no—
251#104—302no—
252#99—302no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257C5×D3—81no—
258C23×C3D4×D511yescharacteristic
259C22×D3—21no—
260C3×Q8—204no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—42no—
264C2×C3×C4—102no—
265C2×C3×C4—102no—
266C2×C3×C4C2×Dic1011yescharacteristic
267C2×C3×C4#70911yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4#71111yescharacteristic
270C2×C3×C4#71111yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272#67—41no—
273#67—41no—
274C2×Dic3—21no—
275C2×Dic3—201no—
276D12—21no—
277D12—21no—
278C4×D3—41no—
279C4×D3—41no—
280Dic6—21no—
281Dic6—21no—
282C3⋊C8—41no—
283C3⋊C8—201no—
284C22×C5—41no—
285C22×C5—121no—
286C22×C5—241no—
287C22×C5#94611yescharacteristic
288C22×C5#94711yescharacteristic
289C22×C5#95311yescharacteristic
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—121no—
293C4×C5#94611yescharacteristic
294C4×C5#94611yescharacteristic
295C4×C5#94711yescharacteristic
296C4×C5#94711yescharacteristic
297Dic5—42no—
298Dic5—42no—
299Dic5—241no—
300#41—61no—
301#41—61no—
302#41—61no—
303#41—61no—
304C2×Q8—31no—
305C2×Q8—102no—
306C2×D4—31no—
307C2×D4—61no—
308C22×C4—21no—
309C22×C4—61no—
310C22×C4C2×D3×D511yescharacteristic
311M16—61no—
312M16—61no—
313M16—301no—
314M16—301no—
315C2×C8—61no—
316C2×C8—301no—
317C4⋊C4—104no—
318C4⋊C4—102no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C4⋊C4—301no—
322C22⋊C4—52no—
323C22⋊C4—101no—
324C22⋊C4—301no—
325C42—21no—
326C42—52no—
327C42—101no—
328C42—301no—
329C42#120111yescharacteristic
330C42#120111yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3#402411yescharacteristic
334C22×C3#403111yescharacteristic
335C22×C3#408311yescharacteristic
336C2×D3—41no—
337C2×D3—81no—
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—202no—
341C3×C4—202no—
342C3×C4#402411yescharacteristic
343C3×C4#403111yescharacteristic
344C3×C4#407011yescharacteristic
345C3×C4#408211yescharacteristic
346Dic3—41no—
347Dic3—401no—
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—241no—
352C2×C5#523111yescharacteristic
353C23—61no—
354C23D5×#6711yescharacteristic
355Q8—61no—
356Q8—61no—
357Q8—204no—
358D4—61no—
359D4—61no—
360D4—121no—
361D4—121no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—61no—
366C2×C4—102no—
367C2×C4—102no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—601no—
371C2×C4D3×Dic1011yescharacteristic
372C2×C4#676811yescharacteristic
373C2×C4#676811yescharacteristic
374C2×C4#676911yescharacteristic
375C2×C4C2×#120111yescharacteristic
376C2×C4D5×#6711yescharacteristic
377C8—121no—
378C8—601no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6523611yescharacteristic
383D3—81no—
384C5#7184211yescharacteristic, complemented, Sylow
385C22—41no—
386C22—121no—
387C22—241no—
388C22#9132611yescharacteristic
389C22#9141011yescharacteristic
390C22#9156311yescharacteristic
391C4—22no—
392C4—41no—
393C4—121no—
394C4—202no—
395C4—202no—
396C4—1201no—
397C4#9132611yescharacteristic
398C4#9136911yescharacteristic
399C4#9137011yescharacteristic
400C4#9141011yescharacteristic
401C3#1060116111yescharacteristic, complemented, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—241no—
406C2#1174874611yescharacteristic
subgroupG/H
centerC4#91326
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#393
prime radicalC2×C5×#235C22
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. C3×#65804C2semidirect
5. #11746344C2semidirect
6. #11745993C2semidirect
7. #11745970C2semidirect
25. #65804D3semidirect
39. C2×C5×D12Q8semidirect
41. C2×C5×Dic6Q8semidirect
189. C2×D12Dic10semidirect
191. C2×Dic6Dic10semidirect
331. C3×C5#2031semidirect
384. C5#71842semidirect
401. C3#10601161semidirect

Maximal subgroups

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

subgroupindex
C3×#658042
C2×C5×#8052
#117486252
#117484252
#117463442
#117459932
#117459702
#106011613
#718425