Finite Group Databasebeta

← #14295541

Subgroups — #14295541

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91286C211yesmaximal, characteristic
2C5×#5132C211yesmaximal, characteristic
3C3×#65411C211yesmaximal, characteristic, complemented
4#11748625C211yesmaximal, characteristic
5#11748324C211yesmaximal, characteristic, complemented
6#11746380C211yesmaximal, characteristic, complemented
7#11745993C211yesmaximal, characteristic, complemented
8#10600926—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6650C412yescomplemented
17#91286—21no—
18#91286—21no—
19#91286—21no—
20#91286—21no—
21C2×D3×#168C412yescomplemented
22C5×#824C412yescomplemented
23C5×#823C412yescomplemented
24C3×#3947—21no—
25C3×C8×Dic5—21no—
26#90996C414yes—
27#90954—21no—
28#90951—21no—
29#69898—51nomaximal, Hall
30C2×#4094—31no—
31C5×#413—31no—
32#65529—31no—
33#65411—31no—
34#65411D311yescharacteristic, complemented
35#64779—31no—
36#64779—31no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C5×#67C2×C412yes—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3C2×C412yes—
45C2×C5×Dic6C2×C411yescharacteristic
46C3×C5×M16—21no—
47C3×C5×M16C2×C412yes—
48C2×C3×C5×C8—21no—
49#6719C2×C412yes—
50C4⋊Dic15—21no—
51C4×Dic15—21no—
52#6710—21no—
53#6710—21no—
54C2×C3⋊#168C2×C412yes—
55C5×#208—21no—
56C5×#208C2×C412yes—
57C2×C5×C3⋊C8—21no—
58C3×C22⋊Dic5C2×C412yes—
59C3×C4⋊Dic5—21no—
60C3×C4×Dic5—21no—
61C2×C3×#168C2×C411yescharacteristic
62C2×C3×#168C2×C411yescharacteristic
63C2×C3×#168D411yescharacteristic
64C2×C3×#168D411yescharacteristic
65C2×C3×#168D411yescharacteristic
66C2×C3×#168D411yescharacteristic
67#6650—22no—
68#6650—22no—
69D3×#168—22no—
70D3×#168—22no—
71C2×#901—51no—
72C3×#405—51no—
73#5132D511yescharacteristic
74#5101—51no—
75#5006—51no—
76#4559—51no—
77#4533—51no—
78C2×C5×#41—31no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81#4094—61no—
82#4094—61no—
83#4094—61no—
84#4094—61no—
85#4072—31no—
86#4072C2×D311yescharacteristic
87C2×#681—31no—
88C2×#681—32no—
89C22×#168—32no—
90C22×#168C2×D311yescharacteristic
91C5×#101—32no—
92C5×#100—32no—
93#3966—34no—
94#3947—21no—
95#3947—61no—
96C8×Dic5—21no—
97C8×Dic5—61no—
98#1757—151noSylow
99C23×C3×C5C22×C411yescharacteristic
100C22×C5×D3C4212yes—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—22no—
108C5×#67—22no—
109C5×#67—22no—
110C2×C5×Dic3C4212yes—
111C5×D12—21no—
112C5×D12—21no—
113C4×C5×D3—22no—
114C4×C5×D3—22no—
115C5×Dic6—21no—
116C5×Dic6—21no—
117C2×C3×Dic5—22no—
118C3×C5×C8—22no—
119C3⋊#168—22no—
120C3×#168C22⋊C411yescharacteristic
121C3×#168C22⋊C411yescharacteristic
122C3×#168C22⋊C411yescharacteristic
123C3×#168C22⋊C411yescharacteristic
124C5×C3⋊C8—22no—
125C2×#235C2×D511yescharacteristic
126C2×C3×M16C2×D511yescharacteristic
127C22×C3×C8—51no—
128C3×#117—51no—
129#926—51no—
130C2×#208—51no—
131C2×#208C2×D511yescharacteristic
132#901—101no—
133#901—101no—
134#901—101no—
135#901—101no—
136C2×ΓL(1,𝔽25)—52no—
137C2×D3×C8—52no—
138C3×#97—101no—
139C3×C4×C8—101no—
140#824Dic512yescomplemented
141#823Dic512yescomplemented
142#815—101no—
143C8×Dic3—101no—
144#806—54no—
145C5×#41—61no—
146C5×#41—61no—
147C5×#41—61no—
148C5×#41—61no—
149C2×C5×Q8—31no—
150C2×C5×D4—32no—
151C2×C5×D4—31no—
152C22×C4×C5—32no—
153C22×C4×C5C22×D311yescharacteristic
154C5×M16—21no—
155C5×M16—32no—
156C5×M16—61no—
157C5×M16C4×D312yes—
158C2×C5×C8—21no—
159C2×C5×C8—61no—
160C22⋊Dic5—32no—
161C22⋊Dic5C4×D312yes—
162C4⋊Dic5—21no—
163C4⋊Dic5—61no—
164C4×Dic5—21no—
165C4×Dic5—61no—
166#681—61no—
167#681—61no—
168#681—62no—
169#681—62no—
170C2×#168—32no—
171C2×#168—62no—
172C2×#168—62no—
173C2×#168C4×D311yescharacteristic
174C2×#168C4×D311yescharacteristic
175C2×#168D1211yescharacteristic
176C2×#168D1211yescharacteristic
177C2×#168#6711yescharacteristic
178C2×#168#6711yescharacteristic
179C2×#131—151no—
180#413—31no—
181#410—151no—
182#405—51no—
183#405—151no—
184#344—151no—
185#344—151no—
186C22×C3×C5—41no—
187C22×C3×C5C2×C4211yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C2×C5×D3—22no—
191C2×C5×D3—42no—
192C3×C4×C5C2×C22⋊C411yescharacteristic
193C3×C4×C5#11711yescharacteristic
194C3×C4×C5C4×D411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196Dic15—42no—
197C3×Dic5—42no—
198C5×Dic3—22no—
199C22×C3×C4C22×D511yescharacteristic
200C2×#67C4×D512yes—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205C2×D12C2×Dic511yescharacteristic
206C2×C4×D3C4×D512yes—
207C2×Dic6C2×Dic511yescharacteristic
208C3×M16—21no—
209C3×M16C2×Dic512yes—
210C2×C3×C8—21no—
211C2×C3×C8—51no—
212C2×C3×C8—51no—
213C2×C3×C8—51no—
214C2×C3×C8—51no—
215C2×C3×C8—51no—
216C2×C3×C8—51no—
217C3×C4⋊C4—101no—
218C3×C22⋊C4—52no—
219C3×C42—101no—
220#217—52no—
221C4⋊Dic3—101no—
222C4×Dic3—101no—
223#208—21no—
224#208—101no—
225#208—101no—
226#208C2×Dic512yes—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—52no—
229ΓL(1,𝔽25)—102no—
230ΓL(1,𝔽25)—102no—
231D3×C8—102no—
232D3×C8—102no—
233C23×C5—32no—
234C23×C5C2×C4×D311yescharacteristic
235C5×Q8—61no—
236C5×Q8—61no—
237C5×D4—62no—
238C5×D4—62no—
239C5×D4—61no—
240C5×D4—61no—
241C2×C4×C5—32no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5C2×C4×D311yescharacteristic
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5C2×D1211yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5#23511yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×Dic5—22no—
251C2×Dic5—62no—
252C5×C8—22no—
253C5×C8—62no—
254#168—62no—
255#168(C2×D3)⋊C411yescharacteristic
256#168(C2×D3)⋊C411yescharacteristic
257#168(C2×D3)⋊C411yescharacteristic
258#168(C2×D3)⋊C411yescharacteristic
259C2×#41—31no—
260#131—301no—
261#131—301no—
262#131—301no—
263#131—301no—
264C2×M16—31no—
265C2×M16—152no—
266C2×M16—151no—
267C2×M16D3×D511yescharacteristic
268C22×C8—51no—
269C22×C8—152no—
270#117—51no—
271#117—151no—
272#101—32no—
273#100—32no—
274#99—154no—
275#97—101no—
276#97—301no—
277C4×C8—101no—
278C4×C8—301no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5C4×C22⋊C411yescharacteristic
283C5×D3—42no—
284C23×C3C2×C4×D511yescharacteristic
285C22×D3C4×Dic512yes—
286C2×C3×C4—102no—
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4#71111yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4C22×Dic511yescharacteristic
293#67—22no—
294#67—22no—
295C2×Dic3—102no—
296C2×Dic3C4×Dic512yes—
297D12—21no—
298D12—21no—
299C4×D3—22no—
300C4×D3—22no—
301Dic6—21no—
302Dic6—21no—
303C3×C8—22no—
304C3×C8—51no—
305C3×C8—51no—
306C3×C8—51no—
307C3×C8—51no—
308C3⋊C8—22no—
309C3⋊C8—102no—
310C22×C5—41no—
311C22×C5—62no—
312C22×C5—122no—
313C22×C5C42×D311yescharacteristic
314C22×C5C4×D1211yescharacteristic
315C22×C5C4×#6711yescharacteristic
316C4×C5—62no—
317C4×C5#87211yescharacteristic
318C4×C5C4×D1211yescharacteristic
319C4×C5C2×(C2×D3)⋊C411yescharacteristic
320C4×C5C4×#6711yescharacteristic
321Dic5—42no—
322Dic5—122no—
323#41—61no—
324#41—61no—
325#41—61no—
326#41—61no—
327C2×Q8—31no—
328C2×D4—32no—
329C2×D4—31no—
330C22×C4—32no—
331C22×C4C2×D3×D511yescharacteristic
332M16—21no—
333M16—32no—
334M16—61no—
335M16—302no—
336M16—302no—
337M16—301no—
338M16—301no—
339M16D3×Dic512yes—
340C2×C8—21no—
341C2×C8—51no—
342C2×C8—51no—
343C2×C8—51no—
344C2×C8—51no—
345C2×C8—51no—
346C2×C8—51no—
347C2×C8—61no—
348C2×C8—152no—
349C2×C8—302no—
350C2×C8—302no—
351C4⋊C4—101no—
352C4⋊C4—301no—
353C22⋊C4—52no—
354C22⋊C4—152no—
355C42—101no—
356C42—301no—
357C3×C5#175711yescharacteristic, complemented, Hall
358C22×C3—41no—
359C22×C3#402711yescharacteristic
360C22×C3#402711yescharacteristic
361C22×C3C2×C4×Dic511yescharacteristic
362C2×D3—22no—
363C2×D3—42no—
364C3×C4—202no—
365C3×C4#402311yescharacteristic
366C3×C4D5×C22⋊C411yescharacteristic
367C3×C4D4×Dic511yescharacteristic
368C3×C4D4×Dic511yescharacteristic
369Dic3—22no—
370Dic3—202no—
371C2×C5—21no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—122no—
375C2×C5C4×(C2×D3)⋊C411yescharacteristic
376C23—32no—
377C23C4×D3×D511yescharacteristic
378Q8—61no—
379Q8—61no—
380D4—62no—
381D4—62no—
382D4—61no—
383D4—61no—
384C2×C4—32no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—102no—
388C2×C4—302no—
389C2×C4#677211yescharacteristic
390C2×C4C4×D3×D511yescharacteristic
391C2×C4D5×D1211yescharacteristic
392C2×C4C2×D3×Dic511yescharacteristic
393C2×C4#678211yescharacteristic
394C2×C4D5×#6711yescharacteristic
395C8—22no—
396C8—51no—
397C8—51no—
398C8—51no—
399C8—51no—
400C8—62no—
401C8—302no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3C22⋊C4×Dic511yescharacteristic
406D3—42no—
407C5#6989811yescharacteristic, complemented, Sylow
408C22—41no—
409C22—62no—
410C22—122no—
411C22C4×D3×Dic511yescharacteristic
412C22#9140511yescharacteristic
413C22#9144011yescharacteristic
414C4—62no—
415C4—202no—
416C4—602no—
417C4#9139811yescharacteristic
418C4Dic5×D1211yescharacteristic
419C4D5×(C2×D3)⋊C411yescharacteristic
420C4Dic5×#6711yescharacteristic
421C3#1060092611yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—21no—
425C2—122no—
426C2Dic5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4D5×(C2×D3)⋊C4
commutatorC22×C3×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1757
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C3×#65411C2semidirect
5. #11748324C2semidirect
6. #11746380C2semidirect
7. #11745993C2semidirect
16. C2×#6650C4semidirect
21. C2×D3×#168C4semidirect
22. C5×#824C4semidirect
23. C5×#823C4semidirect
34. #65411D3semidirect
140. #824Dic5semidirect
141. #823Dic5semidirect
357. C3×C5#1757semidirect
407. C5#69898semidirect
421. C3#10600926semidirect

Maximal subgroups

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

subgroupindex
C2×#912862
C5×#51322
C3×#654112
#117486252
#117483242
#117463802
#117459932
#106009263
#698985