Finite Group Databasebeta

← #14303110

Subgroups — #14303110

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5816C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic, complemented
4C2×C3×#3968C211yesmaximal, characteristic, complemented
5#11748355C211yesmaximal, characteristic
6#11745989C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10602659—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#947—21no—
14C5×#946—22no—
15C5×#944—21no—
16C5×#929C414yes—
17C5×#926C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91288—22no—
21D3×#681—22no—
22#91286—22no—
23#91120—22no—
24C3×#3968—22no—
25#90962—21no—
26#90959—21no—
27#70124—51nomaximal, Hall
28C5×#536—31no—
29#66153—31no—
30#65526—31no—
31C2×#3968—31no—
32C2×#3968D311yescharacteristic, complemented
33#64753—31no—
34#64753—31no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41C22×C3×C4×C5C2×C412yes—
42C22×C3×C4×C5C2311yescharacteristic
43C2×C5×#67C2×C412yes—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12D411yescharacteristic
49C2×C4×C5×D3D412yes—
50C2×C5×Dic6D411yescharacteristic
51#6710—21no—
52#6710—21no—
53#6710—21no—
54#6710D412yes—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C5×#217C2×C412yes—
58C5×(C2×D3)⋊C4—24no—
59C5×C4⋊Dic3—21no—
60C5×Dic3⋊C4—24no—
61C4×C5×Dic3—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C3×#681D412yes—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6650—24no—
69D3×#168—24no—
70#5816D511yescharacteristic
71#5745—51no—
72C2×C3×#101—51no—
73C2×#836—51no—
74#5132—51no—
75#4559—51no—
76#4556—51no—
77C2×C5×#41—31no—
78C22×C5×Q8C2×D311yescharacteristic
79C5×C4⋊Q8—61no—
80C5×#124—61no—
81C5×#123—34no—
82C5×C22⋊Q8—62no—
83C5×#117—31no—
84#4094—62no—
85#4094—62no—
86C2×#681—31no—
87C2×#681—31no—
88C2×#681—62no—
89C2×#681C2×D311yescharacteristic
90C2×#681C2×D311yescharacteristic
91#3968—22no—
92#3968—61no—
93#3968—62no—
94#3965—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C5×D3C22⋊C412yes—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C3×C5×Q8—41no—
101C3×C5×Q8—41no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C5×#67—22no—
112C5×#67—22no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3C22⋊C412yes—
115C5×D12—21no—
116C5×D12—21no—
117C4×C5×D3—22no—
118C4×C5×D3—22no—
119C5×Dic6—21no—
120C5×Dic6—21no—
121C3⋊#168—22no—
122C3⋊#168—41no—
123C3×#168—22no—
124C3×#168—41no—
125C22×C3×Q8C2×D511yescharacteristic
126C2×#235C2×D511yescharacteristic
127C2×C3×M16—51no—
128C2×C3×M16—51no—
129#947—21no—
130#946—22no—
131#944—21no—
132#929Dic514yes—
133#926C2×D511yescharacteristic
134C2×#208—51no—
135C2×#208—51no—
136#907—102no—
137D3×M16—102no—
138#901—102no—
139C3×#101—102no—
140#836—102no—
141#824—101no—
142#823—101no—
143C5×#41—61no—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—31no—
154C2×C5×D4—32no—
155C2×C5×D4—31no—
156C22×C4×C5—32no—
157C22×C4×C5C4×D312yes—
158C22×C4×C5C22×D311yescharacteristic
159C5×C4⋊C4—64no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—32no—
162C5×C22⋊C4—64no—
163C42×C5—61no—
164#681—21no—
165#681—21no—
166#681—21no—
167#681—32no—
168#681—64no—
169#681—61no—
170#681—61no—
171#681—61no—
172#681#6712yes—
173C2×#168—21no—
174C2×#168—21no—
175C2×#168—64no—
176C2×#168—61no—
177C2×#168—61no—
178#568—151no—
179#536—31no—
180#413—151no—
181C2×#101—51no—
182C2×#101—151no—
183#344—151no—
184#344—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×C5×D3—22no—
190C2×C5×D3—42no—
191C3×C4×C5—42no—
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12111yescharacteristic
195C3×C4×C5#12311yescharacteristic
196C5×Dic3—22no—
197C5×Dic3—42no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C22×C3×C4C2×Dic512yes—
205C22×C3×C4C22×D511yescharacteristic
206C2×#67C2×Dic512yes—
207#235—21no—
208#235—21no—
209#235—21no—
210#235—21no—
211C2×D12C22⋊D511yescharacteristic
212C2×C4×D3C22⋊D512yes—
213C2×Dic6C22⋊D511yescharacteristic
214C3×M16—52no—
215C3×M16—101no—
216C3×M16—101no—
217C3×M16—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220#217C2×Dic512yes—
221(C2×D3)⋊C4—24no—
222C4⋊Dic3—21no—
223Dic3⋊C4—24no—
224C4×Dic3—21no—
225#208—52no—
226#208—101no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—104no—
232D3×C8—104no—
233C23×C5—32no—
234C23×C5C2×C4×D311yescharacteristic
235C5×Q8—41no—
236C5×Q8—41no—
237C5×Q8—41no—
238C5×Q8—41no—
239C5×Q8—61no—
240C5×Q8—61no—
241C5×D4—62no—
242C5×D4—62no—
243C5×D4—61no—
244C5×D4—61no—
245C2×C4×C5—22no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—32no—
249C2×C4×C5—62no—
250C2×C4×C5—62no—
251C2×C4×C5—62no—
252C2×C4×C5#23511yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5#23711yescharacteristic
257C2×C4×C5C2×#6711yescharacteristic
258#168—22no—
259#168—41no—
260#168—62no—
261#168—121no—
262C2×#41—31no—
263C22×Q8D3×D511yescharacteristic
264#131—302no—
265#131—302no—
266C2×M16—51no—
267C2×M16—51no—
268C2×M16—151no—
269C2×M16—151no—
270C2×M16—302no—
271C4⋊Q8—61no—
272#124—61no—
273#123—34no—
274C22⋊Q8—62no—
275#117—31no—
276#101—102no—
277#101—301no—
278#101—302no—
279#100—301no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284C5×D3—42no—
285C23×C3C22×Dic511yescharacteristic
286C22×D3C22⋊Dic512yes—
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—41no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4C2×C22⋊D511yescharacteristic
299C2×C3×C4C2×C22⋊D511yescharacteristic
300#67—22no—
301#67—22no—
302C2×Dic3—22no—
303C2×Dic3C22⋊Dic512yes—
304D12—21no—
305D12—21no—
306C4×D3—22no—
307C4×D3—22no—
308Dic6—21no—
309Dic6—21no—
310C3×C8—102no—
311C3×C8—201no—
312C3⋊C8—102no—
313C3⋊C8—201no—
314C22×C5—41no—
315C22×C5—62no—
316C22×C5—122no—
317C22×C5D3×C22⋊C411yescharacteristic
318C22×C5#67⋊C411yescharacteristic
319C22×C5C4×#6711yescharacteristic
320C4×C5—42no—
321C4×C5—62no—
322C4×C5—122no—
323C4×C5#88311yescharacteristic
324C4×C5#88411yescharacteristic
325C4×C5#93711yescharacteristic
326C4×C5#93811yescharacteristic
327#41—61no—
328#41—61no—
329#41—61no—
330#41—61no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—31no—
338C2×D4—32no—
339C2×D4—31no—
340C22×C4—32no—
341C22×C4D3×Dic512yes—
342C22×C4C2×D3×D511yescharacteristic
343M16—52no—
344M16—101no—
345M16—101no—
346M16—101no—
347M16—152no—
348M16—304no—
349M16—301no—
350M16—301no—
351M16—301no—
352C2×C8—101no—
353C2×C8—101no—
354C2×C8—304no—
355C2×C8—301no—
356C2×C8—301no—
357C4⋊C4—64no—
358C4⋊C4—61no—
359C22⋊C4—32no—
360C22⋊C4—64no—
361C42—61no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3D4×Dic511yescharacteristic
365C22×C3D4×Dic511yescharacteristic
366C22×C3C2×C22⋊Dic511yescharacteristic
367C2×D3—22no—
368C2×D3—42no—
369C3×C4—42no—
370C3×C4#408111yescharacteristic
371C3×C4#408311yescharacteristic
372C3×C4#408511yescharacteristic
373C3×C4#408511yescharacteristic
374Dic3—22no—
375Dic3—42no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5—122no—
380C2×C5#495611yescharacteristic
381C23—32no—
382C23C2×D3×Dic511yescharacteristic
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—61no—
388Q8—61no—
389D4—62no—
390D4—62no—
391D4—61no—
392D4—61no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—32no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4#678011yescharacteristic
401C2×C4#678211yescharacteristic
402C2×C4D5×#6711yescharacteristic
403C2×C4D3×C22⋊D511yescharacteristic
404C2×C4D3×C22⋊D511yescharacteristic
405C2×C4#679011yescharacteristic
406C8—102no—
407C8—201no—
408C8—302no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6550911yescharacteristic
414D3—42no—
415C5#7012411yescharacteristic, complemented, Sylow
416C22—41no—
417C22—62no—
418C22—122no—
419C22Dic5×#6711yescharacteristic
420C22D3×C22⋊Dic511yescharacteristic
421C22#67⋊Dic511yescharacteristic
422C4—42no—
423C4—62no—
424C4—122no—
425C4#9155511yescharacteristic
426C4#9155811yescharacteristic
427C4#9156511yescharacteristic
428C4#9157711yescharacteristic
429C3#1060265911yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—122no—
434C2#1174951911yescharacteristic
subgroupG/H
centerC2#11749519
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC2×C3×C5#386
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#91120C2semidirect
4. C2×C3×#3968C2semidirect
6. #11745989C2semidirect
7. #11745988C2semidirect
32. C2×#3968D3semidirect
362. C3×C5#1915semidirect
415. C5#70124semidirect
429. C3#10602659semidirect

Maximal subgroups

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

subgroupindex
C5×#58162
#117541252
C2×#911202
C2×C3×#39682
#117483552
#117459892
#117459882
#106026593
#701245