Finite Group Databasebeta

← #14282398

Subgroups — #14282398

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754330C211yesmaximal, characteristic
2#11752417C211yesmaximal, characteristic, complemented
3C2×C3×C4×#170C211yesmaximal, characteristic, complemented
4#11746491C212yesmaximal, complemented
5#11746489C212yesmaximal, complemented
6#10604481—31nomaximal, Hall
7C2×#6782—21no—
8C2×#6762—21no—
9C22×C3×#170—21no—
10#91819C411yescharacteristic
11C5×#930C411yescharacteristic
12C2×C3×C4×Dic5C2211yescharacteristic
13#91566—21no—
14#91468C411yescharacteristic
15#91451C411yescharacteristic
16#91418C2211yescharacteristic
17Dic5×D12C2211yescharacteristic
18#91405—21no—
19#91350—21no—
20#91233—21no—
21C4⋊(C3⋊#170)C2212yes—
22C3×C4×#170—21no—
23C3×C4×#170C2212yes—
24#69735—51nomaximal, Hall
25#65930—31no—
26#65758—31no—
27C2×C4×#170D311yescharacteristic, complemented
28D4⋊#170—32no—
29#64871—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C2×#1220—21no—
32C2×D60C2×C411yescharacteristic
33C2×C5×#67—21no—
34C2×C5×D12C2×C411yescharacteristic
35C22×C3×Dic5D411yescharacteristic
36C22×C3×Dic5D411yescharacteristic
37C2×#1204—21no—
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1200—21no—
41#6782—42no—
42#6782—42no—
43C2×D3×Dic5—21no—
44#6762—42no—
45C2×C3⋊#170—22no—
46C2×C3×#170—24no—
47C2×C3×#170—22no—
48#6714—21no—
49C4⋊Dic15C2×C411yescharacteristic
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C3×C4×Dic5C2×C411yescharacteristic
53C3×C4×Dic5D411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5C2311yescharacteristic
56#6668—21no—
57#6667—21no—
58(C2×D3)⋊Dic5—21no—
59#5477—51no—
60C2×C3×C4×C8—51no—
61#4924—51no—
62#4459—52no—
63#4459—52no—
64C2×#711—61no—
65C2×#704—61no—
66C22×#170—21no—
67C5×#121—31no—
68#4086—31no—
69#4085—61no—
70D4×Dic5—31no—
71#4076—31no—
72C2×C4×Dic5C2×D311yescharacteristic
73#4039—31no—
74#4034—31no—
75#4031—61no—
76#4027—61no—
77#4004—61no—
78C4⋊#170—32no—
79C4×#170—21no—
80C4×#170C2×D312yes—
81#1492—151noSylow
82C23×C3×C5C22⋊C411yescharacteristic
83C22×D15—21no—
84C22×C5×D3—21no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88#1220—42no—
89C2×Dic15—21no—
90D60—22no—
91C5×#67—42no—
92C2×C5×Dic3—21no—
93C5×D12—22no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5C22⋊C411yescharacteristic
96C2×C3×Dic5C22⋊C411yescharacteristic
97C2×C3×Dic5D812yes—
98C2×C3×Dic5SD1612yes—
99C2×C3×Dic5C2×D411yescharacteristic
100C2×C3×Dic5C2×D411yescharacteristic
101#1204—42no—
102#1203—42no—
103#1203—42no—
104#1200—41no—
105#1200—41no—
106D3×Dic5—41no—
107D3×Dic5—41no—
108C3⋊#170—42no—
109C3×#170—24no—
110C2×#235—101no—
111C22×C3×C8—101no—
112C2×C3×C42—51no—
113#930—51no—
114#930—101no—
115#930AGL(1,𝔽5)11yescharacteristic
116C2×#208—101no—
117#875—101no—
118#874—51no—
119C4×D12—51no—
120C4×D12—51no—
121C4×D12—101no—
122#869—51no—
123C3×C4×C8—52no—
124C3×C4×C8—101no—
125C4⋊(C3⋊C8)—52no—
126C4⋊(C3⋊C8)—101no—
127C2×C5×D4—31no—
128C2×C5×D4—61no—
129C22×C4×C5C4×D311yescharacteristic
130C2×C22⋊D5—61no—
131C2×C22⋊D5—61no—
132C2×C22⋊D5—61no—
133C22×Dic5—61no—
134C22×Dic5D1211yescharacteristic
135C22×Dic5#6711yescharacteristic
136#711—122no—
137#711—122no—
138C2×D20—31no—
139C2×C4×D5—61no—
140C2×Dic10—61no—
141#704—122no—
142C2×#170—24no—
143C2×#170—22no—
144C2×#170—62no—
145C5×C4⋊C4—31no—
146C5×C22⋊C4—61no—
147C22⋊Dic5—61no—
148#685—61no—
149#685—61no—
150C4⋊Dic5—31no—
151#683—61no—
152C4×Dic5C4×D311yescharacteristic
153C4×Dic5D1211yescharacteristic
154C4×Dic5#6711yescharacteristic
155C4×Dic5C22×D311yescharacteristic
156#532—151no—
157#423—151no—
158C2×C4×C8—51no—
159D4⋊C8—152no—
160D4⋊C8—152no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5#10212yes—
164C22×C3×C5C2×C22⋊C411yescharacteristic
165C2×D15—41no—
166C2×D15—41no—
167C2×D15—41no—
168C2×C5×D3—41no—
169C2×C5×D3—41no—
170C2×C5×D3—41no—
171C3×C4×C5—21no—
172C3×C4×C5#13112yes—
173Dic15—41no—
174C3×Dic5—21no—
175C3×Dic5#10212yes—
176C3×Dic5#10412yes—
177C3×Dic5C2×D811yescharacteristic
178C3×Dic5C2×SD1611yescharacteristic
179C5×Dic3—41no—
180C22×C3×C4—51no—
181C22×C3×C4—51no—
182C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
183C2×#67—21no—
184C2×#67—101no—
185#235—202no—
186#235—202no—
187C2×D12—51no—
188C2×D12—101no—
189C2×D12—101no—
190C2×D12C2×AGL(1,𝔽5)11yescharacteristic
191C2×C4×D3—101no—
192C2×C4×D3—101no—
193C2×Dic6—101no—
194C2×C3×C8—102no—
195C2×C3×C8—104no—
196C3×C42—51no—
197C3×C42—51no—
198C3×C42—51no—
199C3×C42—51no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3—51no—
205C4⋊Dic3—101no—
206C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
207#208—202no—
208C2×C3⋊C8—102no—
209C23×C5—61no—
210C23×C5(C2×D3)⋊C411yescharacteristic
211C22×D5—61no—
212C5×D4—62no—
213C5×D4—122no—
214C2×C4×C5—22no—
215C2×C4×C5—61no—
216C2×C4×C5(C2×D3)⋊C411yescharacteristic
217C2×C4×C5C2×C4×D311yescharacteristic
218C22⋊D5—122no—
219C22⋊D5—122no—
220C22⋊D5—122no—
221C2×Dic5—22no—
222C2×Dic5—61no—
223C2×Dic5—121no—
224C2×Dic5—121no—
225C2×Dic5#20412yes—
226C2×Dic5D2412yes—
227C2×Dic5(C2×D3)⋊C411yescharacteristic
228C2×Dic5(C2×D3)⋊C411yescharacteristic
229C2×Dic5C2×D1211yescharacteristic
230C2×Dic5C2×#6711yescharacteristic
231D20—62no—
232C4×D5—121no—
233C4×D5—121no—
234Dic10—122no—
235#170—24no—
236#170—122no—
237C2×#41—301no—
238C2×M16—301no—
239C22×C8—101no—
240C4⋊Q8—151no—
241#127—151no—
242#124—301no—
243#121—31no—
244#121—151no—
245#121—301no—
246C4×D4—151no—
247C4×D4—151no—
248C4×D4—301no—
249C2×C42—51no—
250C4⋊C8—152no—
251C4⋊C8—301no—
252C4×C8—52no—
253C4×C8—101no—
254C2×C3×C5—22no—
255C2×C3×C5#40811yescharacteristic
256C2×C3×C5C2×#10211yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258D15—81no—
259C5×D3—81no—
260C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
261C22×D3—21no—
262C22×D3—101no—
263C2×C3×C4—22no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—52no—
268C2×C3×C4—52no—
269C2×C3×C4—51no—
270C2×C3×C4—102no—
271C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
272C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
273#67—42no—
274#67—202no—
275C2×Dic3—21no—
276C2×Dic3—101no—
277D12—22no—
278D12—102no—
279D12—202no—
280D12—202no—
281C4×D3—201no—
282C4×D3—201no—
283C4×D3—201no—
284C4×D3—201no—
285Dic6—202no—
286C3×C8—104no—
287C3⋊C8—202no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5—121no—
291C22×C5—121no—
292C22×C5—121no—
293C22×C5#82112yes—
294C22×C5C2×(C2×D3)⋊C411yescharacteristic
295C2×D5—121no—
296C2×D5—121no—
297C2×D5—121no—
298C4×C5—21no—
299C4×C5—121no—
300C4×C5#90112yes—
301Dic5—21no—
302Dic5—121no—
303Dic5#80512yes—
304Dic5#82112yes—
305Dic5C2×#20411yescharacteristic
306Dic5C2×D2411yescharacteristic
307#41—602no—
308#41—602no—
309C2×Q8—301no—
310C2×D4—31no—
311C2×D4—61no—
312C2×D4—151no—
313C2×D4—301no—
314C2×D4—301no—
315C2×D4—301no—
316C22×C4—51no—
317C22×C4—51no—
318C22×C4—301no—
319C22×C4—301no—
320C22×C4D3×AGL(1,𝔽5)11yescharacteristic
321M16—602no—
322C2×C8—102no—
323C2×C8—104no—
324C2×C8—302no—
325C4⋊C4—31no—
326C4⋊C4—151no—
327C4⋊C4—301no—
328C22⋊C4—61no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C42—51no—
333C42—51no—
334C42—51no—
335C42—51no—
336C3×C5#149211yescharacteristic, complemented, Hall
337C22×C3—21no—
338C22×C3—21no—
339C22×C3#400712yes—
340C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—201no—
345C2×D3—201no—
346C2×D3—201no—
347C3×C4—21no—
348C3×C4—52no—
349C3×C4—52no—
350C3×C4—51no—
351C3×C4—51no—
352C3×C4—101no—
353C3×C4#413112yes—
354Dic3—41no—
355Dic3—201no—
356C2×C5—22no—
357C2×C5—241no—
358C2×C5C2×#80511yescharacteristic
359C2×C5#511011yescharacteristic
360C2×C5C2×#82111yescharacteristic
361D5—241no—
362C23—61no—
363C23—301no—
364C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
365Q8—602no—
366D4—62no—
367D4—122no—
368D4—302no—
369D4—602no—
370D4—602no—
371D4—602no—
372C2×C4—22no—
373C2×C4—52no—
374C2×C4—52no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—51no—
378C2×C4—51no—
379C2×C4—61no—
380C2×C4—102no—
381C2×C4—301no—
382C2×C4—601no—
383C2×C4—601no—
384C2×C4—601no—
385C2×C4—601no—
386C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
387C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
388C8—104no—
389C8—602no—
390C2×C3—22no—
391C2×C3C2×#400711yescharacteristic
392C2×C3#6577511yescharacteristic
393C2×C3D5⋊#10411yescharacteristic
394D3—81no—
395D3—401no—
396C5#6973511yescharacteristic, complemented, Sylow
397C22—21no—
398C22—21no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22—601no—
403C22—601no—
404C22—601no—
405C22#9115212yes—
406C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
407C4—21no—
408C4—51no—
409C4—51no—
410C4—52no—
411C4—52no—
412C4—101no—
413C4—121no—
414C4—601no—
415C4#9192712yes—
416C3#1060448111yescharacteristic, complemented, Sylow
417C2—22no—
418C2—241no—
419C2—1201no—
420C2C2×#9115211yescharacteristic
421C2D5⋊#80511yescharacteristic
422C2#1175199911yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#11754330C2
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1492
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752417C2semidirect
3. C2×C3×C4×#170C2semidirect
4. #11746491C2semidirect
5. #11746489C2semidirect
27. C2×C4×#170D3semidirect
336. C3×C5#1492semidirect
396. C5#69735semidirect
416. C3#10604481semidirect

Maximal subgroups

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

subgroupindex
#117543302
#117524172
C2×C3×C4×#1702
#117464912
#117464892
#106044813
#697355