Finite Group Databasebeta

← #14299694

Subgroups — #14299694

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#11754130C211yesmaximal, characteristic
2#11751233C211yesmaximal, characteristic
3C3×#65414C211yesmaximal, characteristic, complemented
4#11748478C211yesmaximal, characteristic, complemented
5#11748350C211yesmaximal, characteristic
6C5×#4558C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10599738—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×#208C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91292—22no—
17#91291—22no—
18#91290—22no—
19#91108C412yes—
20#91107C412yes—
21C3×#3951—22no—
22#90992—22no—
23#90957—22no—
24#70734—51nomaximal, Hall
25#66079—31no—
26#65421—31no—
27#65414D311yescharacteristic, complemented
28#65413—31no—
29#65399—31no—
30C5×#341—31no—
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×M16C2×C412yes—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710C2×C412yes—
46C2×C3⋊#168—21no—
47C5×#208—21no—
48C5×#208D412yes—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×#681—21no—
54C3×#681—21no—
55C3×#681—21no—
56C3×#681D412yes—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59#6651—24no—
60#6648—24no—
61#5745—51no—
62C3×#430—51no—
63#5132—51no—
64#5129—51no—
65#5124—51no—
66#4558—51no—
67#4558D511yescharacteristic, complemented
68C2×#709—31no—
69C2×C5×M16—31no—
70C2×C5×M16C2×D311yescharacteristic
71C22×C5×C8—31no—
72C2×#681—31no—
73C2×#681C2×D311yescharacteristic
74C2×#681C2×D311yescharacteristic
75#4053—62no—
76D5×M16—62no—
77#4047—62no—
78#3956—32no—
79#3955—32no—
80#3954—62no—
81#3952—62no—
82#3951—22no—
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⋊#168—22no—
103C3×#168—22no—
104C3×#168—41no—
105C5×C3⋊C8—22no—
106C5×C3⋊C8—41no—
107C2×#235—51no—
108C2×C3×M16—51no—
109C2×C3×M16—51no—
110C2×C3×M16C2×D511yescharacteristic
111C2×#208—51no—
112C2×#208C2×D511yescharacteristic
113C22×C3⋊C8C2×D511yescharacteristic
114#907—102no—
115D3×M16—102no—
116#901—102no—
117C3×#108—102no—
118#824—52no—
119#823—52no—
120#822—102no—
121(C2×D3)⋊C8—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—32no—
133C5×M16—61no—
134C5×M16C4×D312yes—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140#681—21no—
141#681—21no—
142#681—21no—
143#681—32no—
144#681—61no—
145#681#6712yes—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—61no—
149#676—64no—
150C8×D5—64no—
151#568—151no—
152#430—51no—
153#430—151no—
154#413—151no—
155#408—151no—
156#341—31no—
157#341—151no—
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—52no—
180C3×M16—101no—
181C3×M16—101no—
182C3×M16—101no—
183C3×M16C4×D512yes—
184C2×C3×C8—21no—
185C2×C3×C8—101no—
186C2×C3×C8—101no—
187#208—21no—
188#208—52no—
189#208—101no—
190#208D2012yes—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196ΓL(1,𝔽25)—104no—
197D3×C8—104no—
198C23×C5D3×Q811yescharacteristic
199C22×D5—32no—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5#23511yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5#23911yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
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—62no—
217C5×C8—121no—
218#168—22no—
219#168—41no—
220#168—62no—
221C2×#41—151no—
222#131—302no—
223#131—302no—
224C2×M16—31no—
225C2×M16—51no—
226C2×M16—51no—
227C2×M16—151no—
228C2×M16—302no—
229C2×M16D3×D511yescharacteristic
230C22×C8—31no—
231#108—102no—
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—102no—
260C3×C8—201no—
261C3⋊C8—22no—
262C3⋊C8—41no—
263C3⋊C8—102no—
264C22×C5—41no—
265C22×C5D3×C4⋊C411yescharacteristic
266C22×C5#89611yescharacteristic
267C22×C5#94611yescharacteristic
268C2×D5—62no—
269C2×D5—122no—
270C4×C5#89311yescharacteristic
271C4×C5#89411yescharacteristic
272C4×C5C4×#6711yescharacteristic
273C4×C5#93711yescharacteristic
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×C4C2×D3×D511yescharacteristic
284M16—21no—
285M16—32no—
286M16—52no—
287M16—61no—
288M16—101no—
289M16—101no—
290M16—101no—
291M16—152no—
292M16—304no—
293M16—301no—
294M16#120012yes—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—101no—
301C2×C8—101no—
302C2×C8—304no—
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#498911yescharacteristic
320D5—122no—
321C23—152no—
322C23D15⋊Q811yescharacteristic
323Q8—301no—
324Q8—301no—
325D4—302no—
326D4—302no—
327D4—301no—
328D4—301no—
329C2×C4—152no—
330C2×C4—302no—
331C2×C4—302no—
332C2×C4#676911yescharacteristic
333C2×C4D3×D2011yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4#678211yescharacteristic
336C2×C4C2×#120011yescharacteristic
337C2×C4D5×#6711yescharacteristic
338C8—22no—
339C8—62no—
340C8—102no—
341C8—121no—
342C8—201no—
343C8—302no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#6495711yescharacteristic
348D3—202no—
349C5#7073411yescharacteristic, complemented, Sylow
350C22—41no—
351C22—302no—
352C22—602no—
353C22#9141111yescharacteristic
354C22#9142911yescharacteristic
355C22#9143711yescharacteristic
356C4—302no—
357C4#9142811yescharacteristic
358C4#9143811yescharacteristic
359C4#9147411yescharacteristic
360C4#9155211yescharacteristic
361C3#1059973811yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—602no—
366C2#1174889811yescharacteristic
subgroupG/H
centerC4#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#385
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1858
LCSG ▷ C2×C3×C4×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×#65414C2semidirect
4. #11748478C2semidirect
6. C5×#4558C2semidirect
7. #11745983C2semidirect
27. #65414D3semidirect
67. #4558D5semidirect
304. C3×C5#1858semidirect
349. C5#70734semidirect
361. C3#10599738semidirect

Maximal subgroups

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

subgroupindex
#117541302
#117512332
C3×#654142
#117484782
#117483502
C5×#45582
#117459832
#105997383
#707345