Finite Group Databasebeta

← #14299667

Subgroups — #14299667

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756504C211yesmaximal, characteristic
2#11751233C211yesmaximal, characteristic
3#11751226C211yesmaximal, characteristic, complemented
4#11751225C211yesmaximal, characteristic, complemented
5#11751211C211yesmaximal, characteristic
6C3×C5×#341C211yesmaximal, characteristic, complemented
7#11746373C211yesmaximal, characteristic, complemented
8#10599738—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16#91796—22no—
17M16×D15—22no—
18#91790—22no—
19#91108C412yes—
20#91107C412yes—
21#91106—22no—
22#91104—22no—
23#91103—22no—
24#68945—51nomaximal, Hall
25#66079—31no—
26#65421—31no—
27#65414—31no—
28#65413—31no—
29#65399—31no—
30C5×#341D311yescharacteristic, complemented
31#64772—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220Q812yes—
34#6817—21no—
35#6817—21no—
36#6817—21no—
37#6817—21no—
38C2×D60C2×C411yescharacteristic
39C2×C4×D15D412yes—
40C2×Dic30C2×C411yescharacteristic
41C3×C5×M16—21no—
42C3×C5×M16—21no—
43C3×C5×M16C2×C412yes—
44C3×C5×M16D412yes—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50#6710—21no—
51#6710—21no—
52#6710—21no—
53#6710—21no—
54#6710C2×C412yes—
55#6710D412yes—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#6705—24no—
60C8×D15—24no—
61#5745—51no—
62#5132—51no—
63#5125—51no—
64#5124—51no—
65#5110—51no—
66C3×#341D511yescharacteristic, complemented
67#4552—51no—
68C2×#709—31no—
69C2×C5×M16C2×D311yescharacteristic
70C2×C5×M16C2×D311yescharacteristic
71C22×C5×C8C2×D311yescharacteristic
72C2×#681—31no—
73C2×#681—31no—
74C2×#681—31no—
75#4053—62no—
76D5×M16—62no—
77#4047—62no—
78#3956—32no—
79#3955—32no—
80#3954—62no—
81#3952—62no—
82#3951—62no—
83#1858—151noSylow
84C23×C3×C5C2×Q811yescharacteristic
85C22×D15C4⋊C412yes—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92#1220—22no—
93#1220—22no—
94C2×Dic15C4⋊C412yes—
95D60—21no—
96D60—21no—
97C4×D15—22no—
98C4×D15—22no—
99Dic30—21no—
100Dic30—21no—
101C3×C5×C8—22no—
102C3×C5×C8—22no—
103C3×C5×C8—41no—
104C3⋊#168—22no—
105C3⋊#168—22no—
106C3⋊#168—41no—
107C2×#235—51no—
108C2×C3×M16C2×D511yescharacteristic
109C2×C3×M16C2×D511yescharacteristic
110C22×C3×C8C2×D511yescharacteristic
111C2×#208—51no—
112C2×#208—51no—
113C2×#208—51no—
114#907—102no—
115D3×M16—102no—
116#901—102no—
117#824—52no—
118#823—52no—
119#822—102no—
120(C2×D3)⋊C8—102no—
121#819—102no—
122C22×C4×C5C22×D311yescharacteristic
123C2×C22⋊D5—32no—
124#709—61no—
125#709—61no—
126#709—61no—
127#709—61no—
128C2×D20—31no—
129C2×C4×D5—32no—
130C2×Dic10—31no—
131C5×M16—21no—
132C5×M16—21no—
133C5×M16C4×D312yes—
134C5×M16D1212yes—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C2×C5×C8—21no—
140#681—32no—
141#681—32no—
142#681—61no—
143#681—61no—
144#681—61no—
145#681—61no—
146C2×#168—61no—
147C2×#168—61no—
148C2×#168—61no—
149#676—64no—
150C8×D5—64no—
151#568—151no—
152#430—151no—
153#430—151no—
154#413—151no—
155#408—151no—
156#341—151no—
157#341D1511yescharacteristic, complemented
158C22×C3×C5—41no—
159C22×C3×C5C2×C4⋊C411yescharacteristic
160C22×C3×C5C22⋊Q811yescharacteristic
161C22×C3×C5C22⋊Q811yescharacteristic
162C2×D15—22no—
163C2×D15—42no—
164C3×C4×C5C4×D411yescharacteristic
165C3×C4×C5C4×D411yescharacteristic
166C3×C4×C5#12011yescharacteristic
167C3×C4×C5#12311yescharacteristic
168Dic15—22no—
169C22×C3×C4C22×D511yescharacteristic
170C2×#67—52no—
171#235—101no—
172#235—101no—
173#235—101no—
174#235—101no—
175C2×D12—51no—
176C2×C4×D3—52no—
177C2×Dic6—51no—
178C3×M16—21no—
179C3×M16—21no—
180C3×M16C4×D512yes—
181C3×M16D2012yes—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187#208—52no—
188#208—52no—
189#208—101no—
190#208—101no—
191#208—101no—
192#208—101no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196ΓL(1,𝔽25)—104no—
197D3×C8—104no—
198C23×C5D3×Q811yescharacteristic
199C22×D5—32no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5#23511yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5#23711yescharacteristic
206C22⋊D5—62no—
207C22⋊D5—62no—
208C2×Dic5—32no—
209D20—61no—
210D20—61no—
211C4×D5—62no—
212C4×D5—62no—
213Dic10—61no—
214Dic10—61no—
215C5×C8—22no—
216C5×C8—22no—
217C5×C8—41no—
218#168—62no—
219#168—62no—
220#168—121no—
221C2×#41—151no—
222#131—302no—
223#131—302no—
224C2×M16—151no—
225C2×M16—151no—
226C2×M16—151no—
227C2×M16—302no—
228C2×M16C2×D1511yescharacteristic
229C2×M16C2×D1511yescharacteristic
230C22×C8C2×D1511yescharacteristic
231#108—302no—
232#108—302no—
233#101—152no—
234#100—152no—
235C22⋊C8—302no—
236C2×C3×C5—21no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5#38511yescharacteristic
240D15—42no—
241C23×C3Q8×D511yescharacteristic
242C22×D3—52no—
243C2×C3×C4C2×C4×D511yescharacteristic
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4#70911yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4#71111yescharacteristic
249#67—102no—
250#67—102no—
251C2×Dic3—52no—
252D12—101no—
253D12—101no—
254C4×D3—102no—
255C4×D3—102no—
256Dic6—101no—
257Dic6—101no—
258C3×C8—22no—
259C3×C8—22no—
260C3×C8—41no—
261C3⋊C8—102no—
262C3⋊C8—102no—
263C3⋊C8—201no—
264C22×C5—41no—
265C22×C5D3×C4⋊C411yescharacteristic
266C22×C5#89611yescharacteristic
267C22×C5#89711yescharacteristic
268C2×D5—62no—
269C2×D5—122no—
270C4×C5C4×D1211yescharacteristic
271C4×C5#67⋊C411yescharacteristic
272C4×C5#88211yescharacteristic
273C4×C5#88311yescharacteristic
274Dic5—62no—
275#41—301no—
276#41—301no—
277#41—301no—
278#41—301no—
279C2×Q8—151no—
280C2×D4—152no—
281C2×D4—151no—
282C22×C4—152no—
283C22×C4C22×D1511yescharacteristic
284M16—21no—
285M16—21no—
286M16—152no—
287M16—152no—
288M16—304no—
289M16—301no—
290M16—301no—
291M16—301no—
292M16—301no—
293M16C4×D1512yes—
294M16D6012yes—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—304no—
301C2×C8—301no—
302C2×C8—301no—
303C2×C8—301no—
304C3×C5#185811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3D5×C4⋊C411yescharacteristic
307C22×C3#404211yescharacteristic
308C22×C3#404311yescharacteristic
309C2×D3—102no—
310C2×D3—202no—
311C3×C4C4×D2011yescharacteristic
312C3×C4#402711yescharacteristic
313C3×C4#402811yescharacteristic
314C3×C4#402911yescharacteristic
315Dic3—102no—
316C2×C5—21no—
317C2×C5—21no—
318C2×C5—21no—
319C2×C5#466811yescharacteristic
320D5—122no—
321C23—152no—
322C23Q8×D1511yescharacteristic
323Q8—301no—
324Q8—301no—
325D4—302no—
326D4—302no—
327D4—301no—
328D4—301no—
329C2×C4—152no—
330C2×C4—302no—
331C2×C4—302no—
332C2×C4C2×C4×D1511yescharacteristic
333C2×C4C2×D6011yescharacteristic
334C2×C4#681711yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C2×C4D4×D1511yescharacteristic
337C2×C4#681911yescharacteristic
338C8—22no—
339C8—22no—
340C8—41no—
341C8—302no—
342C8—302no—
343C8—601no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#6495711yescharacteristic
348D3—202no—
349C5#6894511yescharacteristic, complemented, Sylow
350C22—41no—
351C22—302no—
352C22—602no—
353C22C4⋊C4×D1511yescharacteristic
354C22#9178511yescharacteristic
355C22#9178611yescharacteristic
356C4—302no—
357C4C4×D6011yescharacteristic
358C4#9177011yescharacteristic
359C4#9177111yescharacteristic
360C4#9177211yescharacteristic
361C3#1059973811yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—602no—
366C2#1175076911yescharacteristic
subgroupG/H
centerC4#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#341C2
socleC2×C3×C5#385
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#341D15
hypocenterC3×C5#1858
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
3. #11751226C2semidirect
4. #11751225C2semidirect
6. C3×C5×#341C2semidirect
7. #11746373C2semidirect
30. C5×#341D3semidirect
66. C3×#341D5semidirect
157. #341D15semidirect
304. C3×C5#1858semidirect
349. C5#68945semidirect
361. C3#10599738semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117512332
#117512262
#117512252
#117512112
C3×C5×#3412
#117463732
#105997383
#689455