Finite Group Databasebeta

← #14299900

Subgroups — #14299900

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
2C5×#5005C211yesmaximal, characteristic
3#11748478C211yesmaximal, characteristic, complemented
4#11748431C211yesmaximal, characteristic, complemented
5C2×#90979C211yesmaximal, characteristic
6#11746354C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10601191—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19C5×#805—22no—
20#90992—22no—
21#90982—22no—
22#90979C412yescomplemented
23#90979C412yescomplemented
24#68773—51nomaximal, Hall
25#66153—31no—
26C5×#421—31no—
27C2×#3969—31no—
28#65413—31no—
29#65407—31no—
30#64753—31no—
31#64752D311yescharacteristic, complemented
32C22×C3×C4×C5C2311yescharacteristic
33C2×C5×#67—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235C2×C412yes—
37C5×#235D412yes—
38C2×C5×D12Q811yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6Q811yescharacteristic
41C22×C3×Dic5—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C22⋊C4—21no—
44C3×C42×C5—21no—
45#6710—21no—
46#6710—21no—
47#6710—21no—
48#6710C2×C412yes—
49C2×C3⋊#168—21no—
50C2×C3⋊#168D412yes—
51C5×#208—21no—
52C5×#208—21no—
53C2×C5×C3⋊C8—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5C2×C411yescharacteristic
56C3×C4×Dic5C2×C411yescharacteristic
57C3×#681—21no—
58C3×#681D412yes—
59C2×C3×#168—21no—
60#6650—24no—
61D3×#168—24no—
62#5745—51no—
63#5124—51no—
64#5005D511yescharacteristic
65C2×#805—51no—
66#4924—51no—
67C3×#339—51no—
68#4533—51no—
69C2×C5×#41—31no—
70C2×C5×M16—31no—
71C5×#117C2×D311yescharacteristic
72#4094—62no—
73#4094—62no—
74C2×C4×Dic5C2×D311yescharacteristic
75C2×#681—31no—
76C2×#681—31no—
77C2×#681—62no—
78C2×#681C2×D311yescharacteristic
79C5×#104—62no—
80#3969—32no—
81#3969—32no—
82#3954—62no—
83#3946—62no—
84#1861—151noSylow
85C23×C3×C5#4111yescharacteristic
86C22×C5×D3—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×Q811yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C5×#67—22no—
95C5×#67—22no—
96C2×C5×Dic3—21no—
97C5×D12—21no—
98C5×D12C4⋊C412yes—
99C4×C5×D3—22no—
100C4×C5×D3—22no—
101C5×Dic6—21no—
102C5×Dic6C4⋊C412yes—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—42no—
106C3⋊#168—22no—
107C3⋊#168—22no—
108C3×#168—22no—
109C5×C3⋊C8—41no—
110C2×#235C2×D511yescharacteristic
111C2×C3×M16—51no—
112C3×#117C2×D511yescharacteristic
113C2×C3×C42—51no—
114C2×#208—51no—
115C2×#208—51no—
116C2×#208C2×D511yescharacteristic
117#907—102no—
118D3×M16—102no—
119#901—102no—
120#822—102no—
121#805—22no—
122#805—52no—
123#805—52no—
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—61no—
133C22×C4×C5C22×D311yescharacteristic
134C22×Dic5—21no—
135C5×M16—61no—
136C5×M16—61no—
137C2×C5×C8—61no—
138C5×C4⋊C4—21no—
139C5×C22⋊C4—21no—
140C42×C5—21no—
141C4×Dic5—21no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5C4×D311yescharacteristic
144#681—21no—
145#681—32no—
146#681—64no—
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—31no—
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×C5×D3—22no—
167C2×C5×D3—81no—
168C3×C4×C5—81no—
169C3×C4×C5C2×C4⋊C411yescharacteristic
170C3×C4×C5C4×D411yescharacteristic
171C3×C4×C5#12011yescharacteristic
172C3×C4×C5C22⋊Q811yescharacteristic
173C3×Dic5—22no—
174C3×Dic5—41no—
175C5×Dic3—22no—
176C22×C3×C4—101no—
177C22×C3×C4C22×D511yescharacteristic
178C2×#67—21no—
179#235—21no—
180#235—21no—
181#235C4×D512yes—
182#235C22⋊D512yes—
183C2×D12Dic1011yescharacteristic
184C2×C4×D3—21no—
185C2×Dic6Dic1011yescharacteristic
186C3×M16—52no—
187C3×M16—101no—
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C42—21no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—101no—
195#208—21no—
196#208—21no—
197#208—52no—
198#208—101no—
199#208—101no—
200#208—101no—
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—41no—
215C2×C4×C5—61no—
216C2×C4×C5—62no—
217C2×C4×C5—62no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×C4×C5C2×D1211yescharacteristic
220C2×C4×C5#23511yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5D3×Q811yescharacteristic
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—42no—
227C5×C8—121no—
228#168—22no—
229#168—62no—
230#168—62no—
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#117D3×D511yescharacteristic
240C2×C42—51no—
241#108—302no—
242C4⋊C8—302no—
243#104—62no—
244#104—152no—
245#104—152no—
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—41no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—202no—
257C2×C3×C4C2×Dic1011yescharacteristic
258C2×C3×C4C2×C4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4#71111yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263#67—22no—
264#67—22no—
265C2×Dic3—21no—
266D12—21no—
267D12#68312yes—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6#68312yes—
272C3×C8—102no—
273C3⋊C8—41no—
274C3⋊C8—102no—
275C3⋊C8—102no—
276C22×C5—41no—
277C22×C5—62no—
278C22×C5—241no—
279C22×C5#67⋊C411yescharacteristic
280C22×C5#88311yescharacteristic
281C22×C5#89711yescharacteristic
282C4×C5—62no—
283C4×C5—81no—
284C4×C5C4×D1211yescharacteristic
285C4×C5#88211yescharacteristic
286C4×C5D3×C4⋊C411yescharacteristic
287C4×C5#89611yescharacteristic
288Dic5—22no—
289Dic5—41no—
290#41—32no—
291#41—32no—
292#41—61no—
293#41—61no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—61no—
298C22×C4—101no—
299C22×C4C2×D3×D511yescharacteristic
300M16—52no—
301M16—61no—
302M16—61no—
303M16—101no—
304M16—152no—
305M16—304no—
306M16—301no—
307M16—301no—
308M16—301no—
309C2×C8—61no—
310C2×C8—101no—
311C2×C8—152no—
312C2×C8—304no—
313C2×C8—301no—
314C4⋊C4—21no—
315C22⋊C4—21no—
316C42—21no—
317C42—51no—
318C42—51no—
319C42—101no—
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—41no—
322C22×C3#402411yescharacteristic
323C22×C3#402711yescharacteristic
324C22×C3#408111yescharacteristic
325C2×D3—22no—
326C2×D3—81no—
327C3×C4—81no—
328C3×C4—102no—
329C3×C4—201no—
330C3×C4#402411yescharacteristic
331C3×C4#402711yescharacteristic
332C3×C4C2×#68311yescharacteristic
333C3×C4#408311yescharacteristic
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—41no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—62no—
352C2×C4—101no—
353C2×C4—101no—
354C2×C4—202no—
355C2×C4D3×Dic1011yescharacteristic
356C2×C4C4×D3×D511yescharacteristic
357C2×C4D5×D1211yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4#678211yescharacteristic
360C2×C4D3×C22⋊D511yescharacteristic
361C8—102no—
362C8—121no—
363C8—302no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6523511yescharacteristic
369D3—42no—
370C5#6877311yescharacteristic, complemented, Sylow
371C22—41no—
372C22—62no—
373C22—241no—
374C22#9141711yescharacteristic
375C22#9144211yescharacteristic
376C22#9155511yescharacteristic
377C4—62no—
378C4—81no—
379C4—102no—
380C4—201no—
381C4D3×#68311yescharacteristic
382C4#9140511yescharacteristic
383C4#9143611yescharacteristic
384C4#9147511yescharacteristic
385C3#1060119111yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—122no—
390C2#1174889311yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1861
LCSG ▷ C2×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
3. #11748478C2semidirect
4. #11748431C2semidirect
6. #11746354C2semidirect
7. C3×#64752C2semidirect
22. #90979C4semidirect
23. #90979C4semidirect
31. #64752D3semidirect
320. C3×C5#1861semidirect
370. C5#68773semidirect
385. C3#10601191semidirect

Maximal subgroups

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

subgroupindex
#117541252
C5×#50052
#117484782
#117484312
C2×#909792
#117463542
C3×#647522
#106011913
#687735