Finite Group Databasebeta

← #14299914

Subgroups — #14299914

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#11754130C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic
3C5×#4924C211yesmaximal, characteristic, complemented
4#11748478C211yesmaximal, characteristic, complemented
5#11748429C211yesmaximal, characteristic
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745992C211yesmaximal, characteristic, complemented
8#10601323—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×#208C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91292—22no—
17#91291—22no—
18#91290—22no—
19#91089C412yescomplemented
20#91089C412yescomplemented
21C5×C4⋊(C3⋊C8)—22no—
22#90992—22no—
23#90981—22no—
24#68773—51nomaximal, Hall
25#66079—31no—
26C5×#423—31no—
27#65428—31no—
28#65413—31no—
29C2×#3937—31no—
30#64776—31no—
31#64743D311yescharacteristic, complemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220—21no—
35#6817—21no—
36#6817—21no—
37#6817C2×C412yes—
38#6817D412yes—
39C2×D60Q811yescharacteristic
40C2×C4×D15—21no—
41C2×Dic30Q811yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2×C411yescharacteristic
44C3×C42×C5C2×C411yescharacteristic
45#6710—21no—
46#6710C2×C412yes—
47C2×C3⋊#168—21no—
48C5×#208—21no—
49C5×#208—21no—
50C5×#208—21no—
51C5×#208—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8D412yes—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4×Dic5—21no—
57C3×#681—21no—
58C3×#681D412yes—
59C2×C3×#168—21no—
60#6651—24no—
61#6648—24no—
62#5745—51no—
63#5124—51no—
64#5005—51no—
65C2×#805—51no—
66#4924D511yescharacteristic, complemented
67C3×#339—51no—
68#4533—51no—
69C2×#709—31no—
70C2×C5×M16—31no—
71C2×C5×M16—31no—
72C2×C42×C5C2×D311yescharacteristic
73#4072C2×D311yescharacteristic
74C2×#681—31no—
75C2×#681C2×D311yescharacteristic
76#4053—62no—
77D5×M16—62no—
78#4047—62no—
79C5×C4⋊C8—62no—
80#3957—62no—
81#3954—62no—
82#3937—32no—
83#3937—32no—
84#1861—151noSylow
85C23×C3×C5#4111yescharacteristic
86C22×D15—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
96#1220—22no—
97#1220—22no—
98C2×Dic15—21no—
99D60—21no—
100D60C4⋊C412yes—
101C4×D15—22no—
102C4×D15—22no—
103Dic30—21no—
104Dic30C4⋊C412yes—
105C2×C3×Dic5—41no—
106C3⋊#168—22no—
107C3×#168—22no—
108C5×C3⋊C8—22no—
109C5×C3⋊C8—41no—
110C2×#235—51no—
111C2×C3×M16—51no—
112C3×#117—51no—
113C2×C3×C42C2×D511yescharacteristic
114C2×#208—51no—
115C2×#208C2×D511yescharacteristic
116C2×#208C2×D511yescharacteristic
117#907—102no—
118D3×M16—102no—
119#901—102no—
120#822—102no—
121#805—52no—
122#805—52no—
123#805—102no—
124C4⋊(C3⋊C8)—22no—
125C22×C4×C5—21no—
126C22×C4×C5C22×D311yescharacteristic
127C2×C22⋊D5—61no—
128#709—32no—
129#709—32no—
130#709—61no—
131#709—61no—
132C2×D20—31no—
133C2×C4×D5—61no—
134C2×Dic10—31no—
135C5×M16—61no—
136C5×M16—61no—
137C5×M16—61no—
138C5×M16—61no—
139C2×C5×C8—32no—
140C2×C5×C8—61no—
141C42×C5—21no—
142C42×C5C4×D311yescharacteristic
143C42×C5C4×D311yescharacteristic
144C22⋊Dic5—21no—
145C4⋊Dic5—21no—
146C4×Dic5—21no—
147#681—21no—
148#681—32no—
149#681—61no—
150#681D1212yes—
151C2×#168—21no—
152C2×#168—61no—
153#676—64no—
154C8×D5—64no—
155#568—151no—
156#430—151no—
157#423—31no—
158#421—151no—
159C2×#104—151no—
160#344—151no—
161#339—51no—
162C22×C3×C5—41no—
163C22×C3×C5C4×D411yescharacteristic
164C22×C3×C5C22⋊Q811yescharacteristic
165C22×C3×C5#12311yescharacteristic
166C2×D15—22no—
167C2×D15—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
174Dic15—22no—
175C3×Dic5—81no—
176C22×C3×C4—21no—
177C22×C3×C4C22×D511yescharacteristic
178C2×#67—101no—
179#235—52no—
180#235—52no—
181#235—101no—
182#235—101no—
183C2×D12—51no—
184C2×C4×D3—101no—
185C2×Dic6—51no—
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×C42C4×D511yescharacteristic
194C3×C42C4×D511yescharacteristic
195#208—21no—
196#208—21no—
197#208—21no—
198#208—21no—
199#208—52no—
200#208—101no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—101no—
203C2×C3⋊C8C22⋊D512yes—
204ΓL(1,𝔽25)—104no—
205D3×C8—104no—
206C23×C5#23711yescharacteristic
207C22×D5—61no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—42no—
211C2×C4×C5C2×C4×D311yescharacteristic
212C2×C4×C5C2×D1211yescharacteristic
213C2×C4×C5#23511yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5D3×Q811yescharacteristic
217C22⋊D5—62no—
218C22⋊D5—62no—
219C2×Dic5—41no—
220C2×Dic5—61no—
221D20—32no—
222D20—61no—
223C4×D5—62no—
224C4×D5—62no—
225Dic10—32no—
226Dic10—61no—
227C5×C8—62no—
228C5×C8—121no—
229#168—22no—
230#168—62no—
231C2×#41—151no—
232#131—302no—
233#131—302no—
234C2×M16—31no—
235C2×M16—31no—
236C2×M16—51no—
237C2×M16—151no—
238C2×M16—302no—
239#117—51no—
240C2×C42D3×D511yescharacteristic
241#108—302no—
242C4⋊C8—62no—
243#104—152no—
244#104—152no—
245#104—302no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5#38511yescharacteristic
250D15—42no—
251C23×C3#70911yescharacteristic
252C22×D3—101no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—201no—
257C2×C3×C4C2×C4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4Q8×D511yescharacteristic
261C2×C3×C4#71311yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263#67—102no—
264#67—102no—
265C2×Dic3—101no—
266D12—52no—
267D12—101no—
268C4×D3—102no—
269C4×D3—102no—
270Dic6—52no—
271Dic6—101no—
272C3×C8—102no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C3⋊C8—102no—
276C22×C5—41no—
277C22×C5#67⋊C411yescharacteristic
278C22×C5#88311yescharacteristic
279C22×C5#89711yescharacteristic
280C2×D5—62no—
281C2×D5—241no—
282C4×C5—22no—
283C4×C5—41no—
284C4×C5C4×D1211yescharacteristic
285C4×C5#88211yescharacteristic
286C4×C5D3×C4⋊C411yescharacteristic
287C4×C5#89611yescharacteristic
288Dic5—62no—
289Dic5—81no—
290#41—152no—
291#41—152no—
292#41—301no—
293#41—301no—
294C2×Q8—151no—
295C2×D4—151no—
296C2×D4—301no—
297C22×C4—21no—
298C22×C4—301no—
299C22×C4C2×D3×D511yescharacteristic
300M16—52no—
301M16—61no—
302M16—61no—
303M16—61no—
304M16—61no—
305M16—101no—
306M16—152no—
307M16—304no—
308M16—301no—
309C2×C8—32no—
310C2×C8—61no—
311C2×C8—101no—
312C2×C8—304no—
313C2×C8—301no—
314C4⋊C4—101no—
315C22⋊C4—101no—
316C42—21no—
317C42—101no—
318C42#120011yescharacteristic
319C42#120011yescharacteristic
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—41no—
322C22×C3#404011yescharacteristic
323C22×C3#404211yescharacteristic
324C22×C3C4×C22⋊D511yescharacteristic
325C2×D3—102no—
326C2×D3—401no—
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—401no—
330C3×C4D5×C4⋊C411yescharacteristic
331C3×C4#403911yescharacteristic
332C3×C4#408311yescharacteristic
333C3×C4#409211yescharacteristic
334Dic3—102no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5#466811yescharacteristic
339D5—122no—
340C23—301no—
341C23#677911yescharacteristic
342Q8—152no—
343Q8—301no—
344D4—152no—
345D4—302no—
346D4—302no—
347D4—301no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—201no—
352C2×C4—301no—
353C2×C4—302no—
354C2×C4—302no—
355C2×C4D15⋊Q811yescharacteristic
356C2×C4#677311yescharacteristic
357C2×C4D5×D1211yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4C2×#120011yescharacteristic
360C2×C4D3×C22⋊D511yescharacteristic
361C8—62no—
362C8—102no—
363C8—121no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6527811yescharacteristic
369D3—202no—
370C5#6877311yescharacteristic, complemented, Sylow
371C22—41no—
372C22—302no—
373C22—1201no—
374C22#9135611yescharacteristic
375C22#9141911yescharacteristic
376C22#9155611yescharacteristic
377C4—22no—
378C4—41no—
379C4—302no—
380C4—401no—
381C4#9141811yescharacteristic
382C4#9142411yescharacteristic
383C4#9143711yescharacteristic
384C4#9147511yescharacteristic
385C3#1060132311yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—602no—
390C2#1174890211yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC2×C3×C5#385
prime radicalC2×#6817C22
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
3. C5×#4924C2semidirect
4. #11748478C2semidirect
6. C3×#64743C2semidirect
7. #11745992C2semidirect
19. #91089C4semidirect
20. #91089C4semidirect
31. #64743D3semidirect
66. #4924D5semidirect
320. C3×C5#1861semidirect
370. C5#68773semidirect
385. C3#10601323semidirect

Maximal subgroups

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

subgroupindex
#117541302
C2×#910892
C5×#49242
#117484782
#117484292
C3×#647432
#117459922
#106013233
#687735