Finite Group Databasebeta

← #14299679

Subgroups — #14299679

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
2C5×#5124C211yesmaximal, characteristic, complemented
3#11748476C211yesmaximal, characteristic, complemented
4#11748357C211yesmaximal, characteristic
5#11748349C211yesmaximal, characteristic
6C3×#64778C211yesmaximal, characteristic, complemented
7#11745984C211yesmaximal, characteristic, complemented
8#10601527—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12#91796—22no—
13M16×D15—22no—
14#91790—22no—
15C2×C5×#208C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C2×C3×#681C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C5×#822—22no—
20#90991—22no—
21#90963C412yes—
22#90960C412yes—
23#90957—22no—
24#68945—51nomaximal, Hall
25#66079—31no—
26C5×#430—31no—
27#65421—31no—
28#65418—31no—
29#65413—31no—
30#64778—31no—
31#64778D311yescharacteristic, complemented
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×M16D412yes—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710D412yes—
46C2×C3⋊#168—21no—
47#6705—24no—
48C8×D15—24no—
49C5×#208—21no—
50C5×#208—21no—
51C5×#208—21no—
52C5×#208C2×C412yes—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#681—21no—
56C3×#681C2×C412yes—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61#5745—51no—
62#5132—51no—
63#5125—51no—
64#5124D511yescharacteristic, complemented
65#5110—51no—
66C3×#341—51no—
67#4552—51no—
68C2×#709—31no—
69C2×C5×M16—31no—
70C2×C5×M16—31no—
71C2×C5×M16C2×D311yescharacteristic
72C2×#681—31no—
73C2×#681C2×D311yescharacteristic
74C22×#168C2×D311yescharacteristic
75#4053—62no—
76D5×M16—62no—
77#4047—62no—
78C5×#108—62no—
79#3956—32no—
80#3955—32no—
81#3954—62no—
82#3952—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⋊#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×M16C2×D511yescharacteristic
110C22×C3×C8—51no—
111C2×#208—51no—
112C2×#208C2×D511yescharacteristic
113C2×#208C2×D511yescharacteristic
114#907—102no—
115D3×M16—102no—
116#901—102no—
117#824—52no—
118#823—52no—
119#822—22no—
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—32no—
133C5×M16—61no—
134C5×M16—61no—
135C5×M16—61no—
136C5×M16D1212yes—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140#681—21no—
141#681—32no—
142#681—61no—
143#681C4×D312yes—
144C2×#168—21no—
145C2×#168—21no—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—61no—
149#676—64no—
150C8×D5—64no—
151#568—151no—
152#430—31no—
153#430—151no—
154#413—151no—
155#408—151no—
156#341—51no—
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×M16C22⋊D512yes—
182C2×C3×C8—21no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C2×C3×C8—101no—
186C2×C3×C8—101no—
187#208—21no—
188#208—21no—
189#208—21no—
190#208—52no—
191#208—101no—
192#208C4×D512yes—
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×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—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—31no—
226C2×M16—51no—
227C2×M16—151no—
228C2×M16—302no—
229C2×M16D3×D511yescharacteristic
230C22×C8—51no—
231#108—62no—
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×C4#70911yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4#71311yescharacteristic
248C2×C3×C4C2×C22⋊D511yescharacteristic
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#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×C4C2×D3×D511yescharacteristic
284M16—21no—
285M16—32no—
286M16—52no—
287M16—61no—
288M16—61no—
289M16—61no—
290M16—101no—
291M16—152no—
292M16—304no—
293M16—301no—
294M16#120312yes—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—101no—
299C2×C8—101no—
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#409211yescharacteristic
309C2×D3—102no—
310C2×D3—202no—
311C3×C4#403911yescharacteristic
312C3×C4#404011yescharacteristic
313C3×C4C4×C22⋊D511yescharacteristic
314C3×C4#408311yescharacteristic
315Dic3—102no—
316C2×C5—21no—
317C2×C5—21no—
318C2×C5—21no—
319C2×C5#466811yescharacteristic
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#676611yescharacteristic
333C2×C4#677111yescharacteristic
334C2×C4C4×D3×D511yescharacteristic
335C2×C4C2×#120311yescharacteristic
336C2×C4#679011yescharacteristic
337C2×C4#679011yescharacteristic
338C8—22no—
339C8—62no—
340C8—102no—
341C8—121no—
342C8—201no—
343C8—302no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3#6527811yescharacteristic
348D3—202no—
349C5#6894511yescharacteristic, complemented, Sylow
350C22—41no—
351C22—302no—
352C22—602no—
353C22#9137711yescharacteristic
354C22#9138311yescharacteristic
355C22#9140411yescharacteristic
356C4—302no—
357C4#9135411yescharacteristic
358C4#9139611yescharacteristic
359C4C4×#120311yescharacteristic
360C4#9157311yescharacteristic
361C3#1060152711yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—602no—
366C2#1174873111yescharacteristic
subgroupG/H
centerC4#91573
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
2. C5×#5124C2semidirect
3. #11748476C2semidirect
6. C3×#64778C2semidirect
7. #11745984C2semidirect
31. #64778D3semidirect
64. #5124D5semidirect
304. C3×C5#1858semidirect
349. C5#68945semidirect
361. C3#10601527semidirect

Maximal subgroups

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

subgroupindex
#117565042
C5×#51242
#117484762
#117483572
#117483492
C3×#647782
#117459842
#106015273
#689455