Finite Group Databasebeta

← #14299912

Subgroups — #14299912

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754125C211yesmaximal, characteristic
2#11751025C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic
4#11748480C211yesmaximal, characteristic, complemented
5#11748425C211yesmaximal, characteristic
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745993C211yesmaximal, characteristic, complemented
8#10601168—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19C4⋊(C3⋊#168)—22no—
20C5×#805C412yescomplemented
21C5×#805C412yescomplemented
22#90993—22no—
23#90979—22no—
24#68773—51nomaximal, Hall
25#66153—31no—
26C2×C5×#104—31no—
27#65525—31no—
28#65414—31no—
29#65213—31no—
30#64779—31no—
31#64743D311yescharacteristic, complemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×C5×#67—21no—
35C5×#235—21no—
36C5×#235—21no—
37C5×#235C2×C412yes—
38C5×#235D412yes—
39C2×C5×D12Q811yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C5×Dic6Q811yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2×C411yescharacteristic
44C3×C42×C5C2×C411yescharacteristic
45#6710—21no—
46#6710—21no—
47#6710—21no—
48#6710—21no—
49C2×C3⋊#168—21no—
50C2×C3⋊#168D412yes—
51C5×#208—21no—
52C5×#208C2×C412yes—
53C2×C5×C3⋊C8—21no—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4×Dic5—21no—
57C3×#681—21no—
58C3×#681D412yes—
59C2×C3×#168—21no—
60#6650—24no—
61D3×#168—24no—
62#5745—51no—
63#5124—51no—
64#5005—51no—
65C2×#805D511yescharacteristic
66#4924—51no—
67C3×#339—51no—
68#4533—51no—
69C2×C5×#41—31no—
70C2×C5×M16—31no—
71C2×C42×C5C2×D311yescharacteristic
72#4094—62no—
73#4094—62no—
74#4072C2×D311yescharacteristic
75C2×#681—31no—
76C2×#681—31no—
77C2×#681—62no—
78C2×#681C2×D311yescharacteristic
79C5×#104—32no—
80C5×#104—32no—
81#3969—62no—
82#3951—62no—
83C4⋊#168—62no—
84#1861—151noSylow
85C23×C3×C5#4111yescharacteristic
86C22×C5×D3—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×Q811yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C5×#67—22no—
97C5×#67—22no—
98C2×C5×Dic3—21no—
99C5×D12—21no—
100C5×D12C4⋊C412yes—
101C4×C5×D3—22no—
102C4×C5×D3—22no—
103C5×Dic6—21no—
104C5×Dic6C4⋊C412yes—
105C2×C3×Dic5—41no—
106C3⋊#168—22no—
107C3⋊#168—41no—
108C3×#168—22no—
109C5×C3⋊C8—22no—
110C2×#235C2×D511yescharacteristic
111C2×C3×M16—51no—
112C3×#117—51no—
113C2×C3×C42C2×D511yescharacteristic
114C2×#208—51no—
115C2×#208—51no—
116C2×#208C2×D511yescharacteristic
117#907—102no—
118D3×M16—102no—
119#901—102no—
120#822—102no—
121#805—102no—
122#805Dic512yescomplemented
123#805Dic512yescomplemented
124C4⋊(C3⋊C8)—102no—
125C5×#41—32no—
126C5×#41—32no—
127C5×#41—61no—
128C5×#41—61no—
129C2×C5×Q8—31no—
130C2×C5×D4—31no—
131C2×C5×D4—61no—
132C22×C4×C5—21no—
133C22×C4×C5—61no—
134C22×C4×C5C22×D311yescharacteristic
135C5×M16—32no—
136C5×M16—61no—
137C2×C5×C8—61no—
138C42×C5—21no—
139C42×C5C4×D311yescharacteristic
140C42×C5C4×D311yescharacteristic
141C22⋊Dic5—21no—
142C4⋊Dic5—21no—
143C4×Dic5—21no—
144#681—21no—
145#681—64no—
146#681—61no—
147#681—61no—
148#681—61no—
149#681—61no—
150#681D1212yes—
151C2×#168—21no—
152C2×#168—32no—
153C2×#168—64no—
154C2×#168—61no—
155#568—151no—
156#430—151no—
157#423—151no—
158#421—151no—
159C2×#104—31no—
160#344—151no—
161#339—51no—
162C22×C3×C5—41no—
163C22×C3×C5C4×D411yescharacteristic
164C22×C3×C5C22⋊Q811yescharacteristic
165C22×C3×C5#12311yescharacteristic
166C2×C5×D3—22no—
167C2×C5×D3—81no—
168C3×C4×C5—22no—
169C3×C4×C5—41no—
170C3×C4×C5C2×C4⋊C411yescharacteristic
171C3×C4×C5C4×D411yescharacteristic
172C3×C4×C5#12011yescharacteristic
173C3×C4×C5C22⋊Q811yescharacteristic
174C3×Dic5—81no—
175C5×Dic3—22no—
176C22×C3×C4—21no—
177C22×C3×C4C22×D511yescharacteristic
178C2×#67—21no—
179#235—21no—
180#235—21no—
181#235D2012yes—
182#235C2×Dic512yes—
183C2×D12Dic1011yescharacteristic
184C2×C4×D3—21no—
185C2×Dic6Dic1011yescharacteristic
186C3×M16—52no—
187C3×M16—101no—
188C2×C3×C8—101no—
189C3×C4⋊C4—101no—
190C3×C22⋊C4—101no—
191C3×C42—21no—
192C3×C42—101no—
193C3×C42C2×Dic511yescharacteristic
194C3×C42C2×Dic511yescharacteristic
195#208—21no—
196#208—101no—
197#208—101no—
198#208—101no—
199#208—101no—
200#208C2×Dic512yes—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—52no—
203C2×C3⋊C8—101no—
204ΓL(1,𝔽25)—104no—
205D3×C8—104no—
206C23×C5—61no—
207C23×C5#23711yescharacteristic
208C5×Q8—32no—
209C5×Q8—61no—
210C5×D4—32no—
211C5×D4—62no—
212C5×D4—62no—
213C5×D4—61no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—42no—
217C2×C4×C5—61no—
218C2×C4×C5—62no—
219C2×C4×C5—62no—
220C2×C4×C5C2×C4×D311yescharacteristic
221C2×C4×C5C2×D1211yescharacteristic
222C2×C4×C5#23511yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5D3×Q811yescharacteristic
226C2×Dic5—41no—
227C5×C8—62no—
228#168—22no—
229#168—62no—
230#168—121no—
231C2×#41—31no—
232#131—302no—
233#131—302no—
234C2×M16—31no—
235C2×M16—51no—
236C2×M16—151no—
237C2×M16—151no—
238C2×M16—302no—
239#117—51no—
240C2×C42D3×D511yescharacteristic
241#108—302no—
242C4⋊C8—302no—
243#104—32no—
244#104—32no—
245#104—302no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5#38511yescharacteristic
250C5×D3—42no—
251C23×C3#71111yescharacteristic
252C22×D3—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—201no—
257C2×C3×C4C2×Dic1011yescharacteristic
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4#71111yescharacteristic
262C2×C3×C4C22×Dic511yescharacteristic
263#67—22no—
264#67—22no—
265C2×Dic3—21no—
266D12—21no—
267D12C4⋊Dic512yes—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6C4⋊Dic512yes—
272C3×C8—102no—
273C3⋊C8—22no—
274C3⋊C8—102no—
275C3⋊C8—201no—
276C22×C5—41no—
277C22×C5—62no—
278C22×C5—241no—
279C22×C5#67⋊C411yescharacteristic
280C22×C5#88311yescharacteristic
281C22×C5#89711yescharacteristic
282C4×C5—22no—
283C4×C5—41no—
284C4×C5—62no—
285C4×C5C4×D1211yescharacteristic
286C4×C5#88211yescharacteristic
287C4×C5D3×C4⋊C411yescharacteristic
288C4×C5#89611yescharacteristic
289Dic5—81no—
290#41—32no—
291#41—32no—
292#41—61no—
293#41—61no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—21no—
298C22×C4—61no—
299C22×C4C2×D3×D511yescharacteristic
300M16—32no—
301M16—52no—
302M16—61no—
303M16—101no—
304M16—304no—
305M16—301no—
306M16—301no—
307M16—301no—
308M16—301no—
309C2×C8—61no—
310C2×C8—101no—
311C2×C8—152no—
312C2×C8—304no—
313C2×C8—301no—
314C4⋊C4—101no—
315C22⋊C4—101no—
316C42—21no—
317C42—101no—
318C42D3×Dic511yescharacteristic
319C42D3×Dic511yescharacteristic
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—41no—
322C22×C3#402411yescharacteristic
323C22×C3#403211yescharacteristic
324C22×C3D4×Dic511yescharacteristic
325C2×D3—22no—
326C2×D3—81no—
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—401no—
330C3×C4#402411yescharacteristic
331C3×C4#402811yescharacteristic
332C3×C4C2×C4⋊Dic511yescharacteristic
333C3×C4D4×Dic511yescharacteristic
334Dic3—22no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—122no—
339C2×C5#466811yescharacteristic
340C23—61no—
341C23#678011yescharacteristic
342Q8—32no—
343Q8—61no—
344D4—32no—
345D4—62no—
346D4—62no—
347D4—61no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—61no—
352C2×C4—62no—
353C2×C4—62no—
354C2×C4—201no—
355C2×C4D3×Dic1011yescharacteristic
356C2×C4#677211yescharacteristic
357C2×C4D5×D1211yescharacteristic
358C2×C4D3×D2011yescharacteristic
359C2×C4C2×D3×Dic511yescharacteristic
360C2×C4#679011yescharacteristic
361C8—62no—
362C8—102no—
363C8—302no—
364C8—601no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6523911yescharacteristic
369D3—42no—
370C5#6877311yescharacteristic, complemented, Sylow
371C22—41no—
372C22—62no—
373C22—241no—
374C22#9141711yescharacteristic
375C22#9145711yescharacteristic
376C22#67⋊Dic511yescharacteristic
377C4—22no—
378C4—41no—
379C4—62no—
380C4—401no—
381C4Dic5×D1211yescharacteristic
382C4D3×C4⋊Dic511yescharacteristic
383C4#9143211yescharacteristic
384C4#9147611yescharacteristic
385C3#1060116811yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—122no—
390C2#1174890311yescharacteristic
subgroupG/H
centerC4#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1861
LCSG ▷ C2×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
2. #11751025C2semidirect
4. #11748480C2semidirect
6. C3×#64743C2semidirect
7. #11745993C2semidirect
20. C5×#805C4semidirect
21. C5×#805C4semidirect
31. #64743D3semidirect
122. #805Dic5semidirect
123. #805Dic5semidirect
320. C3×C5#1861semidirect
370. C5#68773semidirect
385. C3#10601168semidirect

Maximal subgroups

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

subgroupindex
#117541252
#117510252
C2×C5×#8052
#117484802
#117484252
C3×#647432
#117459932
#106011683
#687735