Finite Group Databasebeta

← #14299913

Subgroups — #14299913

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
2C2×C5×#805C211yesmaximal, characteristic
3C3×#65213C211yesmaximal, characteristic, complemented
4#11748480C211yesmaximal, characteristic, complemented
5#11748424C211yesmaximal, characteristic
6#11746344C211yesmaximal, characteristic, complemented
7#11745991C211yesmaximal, characteristic, complemented
8#10601168—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19C5×#805C412yescomplemented
20C5×#805C412yescomplemented
21C3×C4⋊#168—22no—
22#90993—22no—
23#90978—22no—
24#70530—51nomaximal, Hall
25#66153—31no—
26C2×C5×#104—31no—
27#65525—31no—
28#65414—31no—
29#65213D311yescharacteristic, complemented
30#64779—31no—
31#64743—31no—
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#6719—21no—
46C4⋊Dic15—21no—
47C4×Dic15—21no—
48#6710—21no—
49#6710D412yes—
50C2×C3⋊#168—21no—
51C5×#208—21no—
52C5×#208C2×C412yes—
53C2×C5×C3⋊C8—21no—
54C3×#681—21no—
55C3×#681—21no—
56C3×#681—21no—
57C3×#681—21no—
58C2×C3×#168—21no—
59C2×C3×#168D412yes—
60#6650—24no—
61D3×#168—24no—
62#5745—51no—
63C3×#423—51no—
64#5139—51no—
65#5124—51no—
66C2×#805D511yescharacteristic
67#4556—51no—
68#4523—51no—
69C2×C5×#41—31no—
70C2×C5×M16—31no—
71C2×C42×C5C2×D311yescharacteristic
72#4094—62no—
73#4094—62no—
74#4072—31no—
75C2×#681—31no—
76C2×#681—62no—
77C2×#681C2×D311yescharacteristic
78C2×#681C2×D311yescharacteristic
79C5×#104—32no—
80C5×#104—32no—
81#3969—62no—
82#3951—62no—
83C4⋊#168—22no—
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
96C2×Dic15—41no—
97C5×#67—22no—
98C5×#67—22no—
99C2×C5×Dic3—21no—
100C5×D12—21no—
101C5×D12C4⋊C412yes—
102C4×C5×D3—22no—
103C4×C5×D3—22no—
104C5×Dic6—21no—
105C5×Dic6C4⋊C412yes—
106C3⋊#168—22no—
107C3×#168—22no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C2×#235C2×D511yescharacteristic
111C2×C3×M16—51no—
112C2×C3×M16—51no—
113C2×C3×C42C2×D511yescharacteristic
114#926—51no—
115C2×#208—51no—
116C2×#208C2×D511yescharacteristic
117#907—102no—
118D3×M16—102no—
119#901—102no—
120C3×C4⋊C8—102no—
121#825—102no—
122#822—102no—
123#805Dic512yescomplemented
124#805Dic512yescomplemented
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—61no—
142C4⋊Dic5—61no—
143C4×Dic5—61no—
144#681—21no—
145#681—21no—
146#681—21no—
147#681—21no—
148#681—32no—
149#681—64no—
150#681—61no—
151C2×#168—21no—
152C2×#168—64no—
153C2×#168—61no—
154C2×#168#6712yes—
155#568—151no—
156#430—151no—
157#423—51no—
158#421—151no—
159C2×#104—31no—
160#344—151no—
161#339—151no—
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
174Dic15—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—101no—
187C3×M16—101no—
188C3×M16—101no—
189C3×M16—101no—
190C2×C3×C8—52no—
191C2×C3×C8—101no—
192C3×C42—21no—
193C3×C42C2×Dic511yescharacteristic
194C3×C42C2×Dic511yescharacteristic
195#217—101no—
196C4⋊Dic3—101no—
197C4×Dic3—101no—
198#208—21no—
199#208—52no—
200#208—101no—
201#208C2×Dic512yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—101no—
204ΓL(1,𝔽25)—104no—
205D3×C8—104no—
206C23×C5—61no—
207C23×C5#23511yescharacteristic
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×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5D3×Q811yescharacteristic
224C2×C4×C5#23911yescharacteristic
225C2×C4×C5C2×#6711yescharacteristic
226C2×Dic5—121no—
227C5×C8—62no—
228#168—22no—
229#168—41no—
230#168—62no—
231C2×#41—31no—
232#131—302no—
233#131—302no—
234C2×M16—31no—
235C2×M16—51no—
236C2×M16—51no—
237C2×M16—151no—
238C2×M16—302no—
239#117—151no—
240C2×C42D3×D511yescharacteristic
241#108—302no—
242C4⋊C8—102no—
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×C4C2×Dic1011yescharacteristic
257C2×C3×C4C2×D2011yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4#71111yescharacteristic
261C2×C3×C4C22×Dic511yescharacteristic
262#67—22no—
263#67—22no—
264C2×Dic3—21no—
265C2×Dic3—201no—
266D12—21no—
267D12C4⋊Dic512yes—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6C4⋊Dic512yes—
272C3×C8—102no—
273C3×C8—201no—
274C3⋊C8—22no—
275C3⋊C8—102no—
276C22×C5—41no—
277C22×C5—62no—
278C22×C5—241no—
279C22×C5#89411yescharacteristic
280C22×C5#89611yescharacteristic
281C22×C5C4×#6711yescharacteristic
282C4×C5—22no—
283C4×C5—41no—
284C4×C5—62no—
285C4×C5D3×C4⋊C411yescharacteristic
286C4×C5#89311yescharacteristic
287C4×C5#93711yescharacteristic
288C4×C5#94611yescharacteristic
289Dic5—241no—
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—61no—
302M16—101no—
303M16—101no—
304M16—101no—
305M16—101no—
306M16—152no—
307M16—304no—
308M16—301no—
309C2×C8—52no—
310C2×C8—61no—
311C2×C8—101no—
312C2×C8—304no—
313C2×C8—301no—
314C4⋊C4—301no—
315C22⋊C4—301no—
316C42—21no—
317C42—301no—
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#402411yescharacteristic
330C3×C4#402811yescharacteristic
331C3×C4C2×C4⋊Dic511yescharacteristic
332C3×C4D4×Dic511yescharacteristic
333Dic3—22no—
334Dic3—401no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—122no—
339C2×C5#498911yescharacteristic
340C23—61no—
341C23#678211yescharacteristic
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—601no—
355C2×C4D3×Dic1011yescharacteristic
356C2×C4#676811yescharacteristic
357C2×C4D3×D2011yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4C2×D3×Dic511yescharacteristic
360C2×C4D5×#6711yescharacteristic
361C8—62no—
362C8—102no—
363C8—201no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6523911yescharacteristic
369D3—42no—
370C5#7053011yescharacteristic, complemented, Sylow
371C22—41no—
372C22—62no—
373C22—241no—
374C22#9142711yescharacteristic
375C22#9143611yescharacteristic
376C22Dic5×#6711yescharacteristic
377C4—22no—
378C4—41no—
379C4—62no—
380C4—1201no—
381C4#9141011yescharacteristic
382C4D3×C4⋊Dic511yescharacteristic
383C4#9143511yescharacteristic
384C4#9147411yescharacteristic
385C3#1060116811yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—122no—
390C2#1174889711yescharacteristic
subgroupG/H
centerC4#91474
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
3. C3×#65213C2semidirect
4. #11748480C2semidirect
6. #11746344C2semidirect
7. #11745991C2semidirect
19. C5×#805C4semidirect
20. C5×#805C4semidirect
29. #65213D3semidirect
123. #805Dic5semidirect
124. #805Dic5semidirect
320. C3×C5#1861semidirect
370. C5#70530semidirect
385. C3#10601168semidirect

Maximal subgroups

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

subgroupindex
#117541252
C2×C5×#8052
C3×#652132
#117484802
#117484242
#117463442
#117459912
#106011683
#705305