Finite Group Databasebeta

← #14303097

Subgroups — #14303097

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
1#11756504C211yesmaximal, characteristic
2#11754270C211yesmaximal, characteristic
3C2×C5×#824C211yesmaximal, characteristic, complemented
4C2×#90962C211yesmaximal, characteristic, complemented
5#11748357C211yesmaximal, characteristic
6C3×#64779C211yesmaximal, characteristic, complemented
7#11745992C211yesmaximal, characteristic, complemented
8#10600917—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C2×C5×#208C2211yescharacteristic
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91542C414yes—
20#91383—22no—
21#91376—21no—
22#91375—21no—
23C5×#824—22no—
24#90963—21no—
25#90962—22no—
26#90960—21no—
27#69041—51nomaximal, Hall
28#66150—31no—
29#66079—31no—
30C2×C5×#101—31no—
31C2×#3968—31no—
32#65421—31no—
33#64779D311yescharacteristic, complemented
34#64776—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220C2×C412yes—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60D411yescharacteristic
42C2×C4×D15D412yes—
43C2×Dic30D411yescharacteristic
44C22×C5×Dic3C2×C412yes—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—21no—
51C3×C5×M16—21no—
52C3×C5×M16D412yes—
53C2×C3×C5×C8—21no—
54#6710—21no—
55#6710D412yes—
56C2×C3⋊#168—21no—
57#6705—24no—
58C8×D15—24no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C22⋊Dic5C2×C412yes—
63C3×C4⋊Dic5—21no—
64C3×C4×Dic5—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68#6668—24no—
69#6667—24no—
70#5745—51no—
71#5526—51no—
72C2×#824—51no—
73C2×#824D511yescharacteristic, complemented
74#5132—51no—
75C3×#344—51no—
76#4533—51no—
77C22×C5×Q8—31no—
78C2×#709—31no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81#4093—61no—
82#4092—62no—
83#4090—61no—
84#4075—34no—
85#4072C2×D311yescharacteristic
86C2×#681—31no—
87C2×#681C2×D311yescharacteristic
88#4053—62no—
89D5×M16—62no—
90#4047—62no—
91C5×#101—62no—
92#3968—62no—
93#3956—61no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊C412yes—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104#1220—22no—
105#1220—22no—
106C2×Dic15C22⋊C412yes—
107D60—21no—
108D60—21no—
109C4×D15—22no—
110C4×D15—22no—
111Dic30—21no—
112Dic30—21no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—22no—
116C5×Dic6—41no—
117C5×Dic6—41no—
118C5×Dic6—41no—
119C5×Dic6—41no—
120C2×C3×Dic5—22no—
121C3×C5×C8—22no—
122C3⋊#168—22no—
123C3×#168—41no—
124C5×C3⋊C8—41no—
125C2×#235—51no—
126C22×Dic6C2×D511yescharacteristic
127C2×C3×M16—51no—
128C2×C3×M16C2×D511yescharacteristic
129C3×#117—51no—
130C2×#208—51no—
131C2×#208C2×D511yescharacteristic
132#907—102no—
133D3×M16—102no—
134#901—102no—
135#897—102no—
136#886—54no—
137#875—101no—
138#869—101no—
139#824—22no—
140#824—101no—
141#824—102no—
142#823—101no—
143C2×C5×Q8—61no—
144C2×C5×Q8—61no—
145C2×C5×Q8—61no—
146C2×C5×Q8—61no—
147C2×C5×Q8—61no—
148C2×C5×Q8—61no—
149C22×C4×C5—32no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—32no—
152#709—61no—
153#709—61no—
154#709—61no—
155#709—61no—
156C2×D20—31no—
157C2×C4×D5—32no—
158C2×Dic10—31no—
159C5×M16—21no—
160C5×M16—61no—
161C5×M16—61no—
162C5×M16D1212yes—
163C2×C5×C8—21no—
164C2×C5×C8—61no—
165C22⋊Dic5C4×D312yes—
166#685—64no—
167C4⋊Dic5—21no—
168#683—64no—
169C4×Dic5—21no—
170#681—21no—
171#681—21no—
172#681—32no—
173#681—61no—
174C2×#168—21no—
175C2×#168—61no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—151no—
180#413—151no—
181C2×#101—31no—
182C2×#101—151no—
183#344—51no—
184#344—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×D15—22no—
190C2×D15—42no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—22no—
196C3×Dic5—42no—
197C5×Dic3—42no—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—52no—
200C22×Dic3C4×D512yes—
201#235—101no—
202#235—101no—
203#235—101no—
204#235—101no—
205C2×D12—51no—
206C2×C4×D3—52no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—51no—
214C3×M16—21no—
215C3×M16—101no—
216C3×M16—101no—
217C3×M16C22⋊D512yes—
218C2×C3×C8—21no—
219C2×C3×C8—101no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—52no—
222C3×C42—101no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—104no—
225#208—21no—
226#208—21no—
227#208—52no—
228#208—101no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—104no—
232D3×C8—104no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5—32no—
235C5×Q8—121no—
236C5×Q8—121no—
237C5×Q8—121no—
238C5×Q8—121no—
239C2×C4×C5—62no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5C2×D1211yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23911yescharacteristic
248C22⋊D5—62no—
249C22⋊D5—62no—
250C2×Dic5—22no—
251C2×Dic5—32no—
252D20—61no—
253D20—61no—
254C4×D5—62no—
255C4×D5—62no—
256Dic10—61no—
257Dic10—61no—
258C5×C8—22no—
259C5×C8—121no—
260#168—41no—
261#168—62no—
262C2×#41—151no—
263C22×Q8—31no—
264#131—302no—
265#131—302no—
266C2×M16—31no—
267C2×M16—51no—
268C2×M16—151no—
269C2×M16—302no—
270C2×M16D3×D511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—51no—
276#101—62no—
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
284D15—42no—
285C23×C3C2×C4×D511yescharacteristic
286C22×D3—52no—
287C2×C3×C4—102no—
288C2×C3×C4#70911yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C2×C3×C4#71111yescharacteristic
293C2×C3×C4C2×C22⋊D511yescharacteristic
294#67—102no—
295#67—102no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—52no—
300D12—101no—
301D12—101no—
302C4×D3—102no—
303C4×D3—102no—
304Dic6—41no—
305Dic6—41no—
306Dic6—41no—
307Dic6—41no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—22no—
311C3×C8—201no—
312C3⋊C8—41no—
313C3⋊C8—102no—
314C22×C5—41no—
315C22×C5C4×D1211yescharacteristic
316C22×C5D3×C22⋊C411yescharacteristic
317C22×C5#89311yescharacteristic
318C2×D5—62no—
319C2×D5—122no—
320C4×C5—122no—
321C4×C5#88211yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5#89411yescharacteristic
324C4×C5#89511yescharacteristic
325Dic5—42no—
326Dic5—62no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—61no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—151no—
338C2×D4—152no—
339C2×D4—151no—
340C22×C4—32no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—61no—
345M16—61no—
346M16—101no—
347M16—101no—
348M16—152no—
349M16—304no—
350M16—301no—
351M16#120312yes—
352C2×C8—21no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—304no—
356C2×C8—301no—
357C4⋊C4—101no—
358C4⋊C4—304no—
359C22⋊C4—52no—
360C22⋊C4—304no—
361C42—101no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3D5×C22⋊C411yescharacteristic
365C22×C3#402711yescharacteristic
366C22×C3C4×C22⋊D511yescharacteristic
367C2×D3—102no—
368C2×D3—202no—
369C3×C4—202no—
370C3×C4#402911yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#408311yescharacteristic
373C3×C4#408411yescharacteristic
374Dic3—42no—
375Dic3—102no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#466511yescharacteristic
380D5—122no—
381C23—152no—
382C23C4×D3×D511yescharacteristic
383Q8—121no—
384Q8—121no—
385Q8—121no—
386Q8—121no—
387Q8—301no—
388Q8—301no—
389D4—302no—
390D4—302no—
391D4—301no—
392D4—301no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—102no—
397C2×C4—152no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#676811yescharacteristic
401C2×C4#677111yescharacteristic
402C2×C4#677711yescharacteristic
403C2×C4C2×#120311yescharacteristic
404C2×C4#679011yescharacteristic
405C2×C4#679011yescharacteristic
406C8—22no—
407C8—121no—
408C8—201no—
409C8—302no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6524511yescharacteristic
414D3—202no—
415C5#6904111yescharacteristic, complemented, Sylow
416C22—41no—
417C22—302no—
418C22—602no—
419C22#9140611yescharacteristic
420C22C4×#120311yescharacteristic
421C22#9147311yescharacteristic
422C4—122no—
423C4—202no—
424C4—302no—
425C4#9135511yescharacteristic
426C4#9146111yescharacteristic
427C4#9146611yescharacteristic
428C4#9157311yescharacteristic
429C3#1060091711yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—602no—
434C2#1174891811yescharacteristic
subgroupG/H
centerC2#11748918
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C5×#824C2semidirect
4. C2×#90962C2semidirect
6. C3×#64779C2semidirect
7. #11745992C2semidirect
33. #64779D3semidirect
73. C2×#824D5semidirect
362. C3×C5#1915semidirect
415. C5#69041semidirect
429. C3#10600917semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117542702
C2×C5×#8242
C2×#909622
#117483572
C3×#647792
#117459922
#106009173
#690415