Finite Group Databasebeta

← #14313283

Subgroups — #14313283

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66164C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3C5×#5237C211yesmaximal, characteristic, complemented
4#11745995C214yesmaximal, complemented
5#10600939—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×D20C411yescharacteristic, complemented
8#91815—21no—
9C2×C5×#208—21no—
10C3×#4093—21no—
11C3×#4086—21no—
12C3×#4083C412yescomplemented
13C3×#4083C2212yes—
14C3×#4076—21no—
15C3×#4076—21no—
16C3×#4072C411yescharacteristic, complemented
17#91118—21no—
18#91118C2212yes—
19C5×#836—21no—
20C5×#833C2212yes—
21#71859—51nomaximal, Hall
22#66164D311yescharacteristic
23C5×#413—31no—
24#65529—31no—
25#64695—34no—
26C23×C3×D5C2×C412yes—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8D411yescharacteristic
30C2×C3×C5×D4C2×C411yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4C2311yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—41no—
41C2×C3×D20—41no—
42#6719—22no—
43C4⋊Dic15—41no—
44C4×Dic15—41no—
45C5×#208—22no—
46C5×#208—41no—
47C2×C5×C3⋊C8—41no—
48C3×C22⋊Dic5C2×C412yes—
49C3×#685—22no—
50C3×#685—22no—
51C3×C4⋊Dic5—21no—
52C3×C4×Dic5—21no—
53C3×#535—51no—
54#5240—51no—
55#5237D511yescharacteristic, complemented
56#4536—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×D20Dic311yescharacteristic, complemented
59C2×C5×M16—61no—
60#4093—21no—
61#4086—21no—
62#4083Dic312yescomplemented
63#4083C2×D312yes—
64#4076—21no—
65#4076—21no—
66#4072—61no—
67#4072Dic311yescharacteristic, complemented
68C5×#101—61no—
69C5×#100—32no—
70#3966—32no—
71#3966—61no—
72#2122—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22×C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C3×D5—22no—
77C22×C3×D5—42no—
78C22×C3×D5—82no—
79C3×C5×Q8—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—42no—
94C3×C22⋊D5—82no—
95C3×C22⋊D5—82no—
96C2×C3×Dic5—22no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C5×C3⋊C8—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×C3×D4—51no—
103C3×#127—101no—
104C3×#124—101no—
105C3×#121—101no—
106C3×#121—101no—
107C3×#120—52no—
108C3×#120—52no—
109C3×#117—51no—
110#926—101no—
111C2×#208—21no—
112#836—21no—
113#834—52no—
114#834—101no—
115#833C2×D512yes—
116C23×D5C2×Dic312yes—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8#6711yescharacteristic
120C2×C5×D4C2×Dic311yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C2×C5×D4C22×D311yescharacteristic
123C22×C4×C5C2×Dic311yescharacteristic
124C22×C4×C5#6711yescharacteristic
125C22×C4×C5#6711yescharacteristic
126C2×C22⋊D5—22no—
127C2×C22⋊D5—22no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20—41no—
131C2×D20—41no—
132C5×M16—62no—
133C5×M16—121no—
134C2×C5×C8—121no—
135C22⋊Dic5—62no—
136C22⋊Dic5C2×Dic312yes—
137#685—22no—
138#685—22no—
139C4⋊Dic5—21no—
140C4⋊Dic5—121no—
141C4×Dic5—21no—
142C4×Dic5—121no—
143#535—51no—
144#413—31no—
145#410—151no—
146AΣL(1,𝔽16)—154no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×C3×D5—42no—
155C2×C3×D5—42no—
156C2×C3×D5—42no—
157C2×C3×D5—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5#9911yescharacteristic
162C3×C4×C5#9911yescharacteristic
163Dic15—82no—
164C3×Dic5—42no—
165C24×C3—52no—
166C3×#41—41no—
167C3×#41—41no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×D4—102no—
170C2×C3×D4—102no—
171C2×C3×D4—101no—
172C2×C3×D4—101no—
173C2×C3×D4—201no—
174C2×C3×D4—201no—
175C2×C3×D4C4×D511yescharacteristic
176C2×C3×D4D2011yescharacteristic
177C2×C3×D4C22×D511yescharacteristic
178C22×C3×C4C4×D511yescharacteristic
179C22×C3×C4D2011yescharacteristic
180C22×C3×C4C22⋊D511yescharacteristic
181C3×C4⋊C4—101no—
182C3×C22⋊C4—52no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—101no—
186#217—102no—
187C4⋊Dic3—201no—
188C4×Dic3—201no—
189#208—22no—
190#208—41no—
191C2×C3⋊C8—41no—
192C23×C5#21711yescharacteristic
193C23×C5C22×Dic311yescharacteristic
194C23×C5C2×#6711yescharacteristic
195C22×D5—22no—
196C22×D5—42no—
197C22×D5—82no—
198C5×Q8—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5#21711yescharacteristic
209C2×C4×C5#21711yescharacteristic
210C2×C4×C5#21711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C22⋊D5—82no—
213C22⋊D5—82no—
214C2×Dic5—22no—
215C2×Dic5—122no—
216D20—42no—
217D20—41no—
218D20—41no—
219C5×C8—122no—
220C2×#41D3×D511yescharacteristic
221C22×D4—51no—
222C2×M16—61no—
223#127—101no—
224#124—101no—
225#121—101no—
226#121—101no—
227#120—52no—
228#120—52no—
229#117—51no—
230#117—301no—
231#101—61no—
232#100—32no—
233#99—152no—
234#99—301no—
235C2×C3×C5—21no—
236C2×C3×C5—41no—
237C2×C3×C5—41no—
238C2×C3×C5—41no—
239C2×C3×C5C2×#9911yescharacteristic
240C3×D5—82no—
241C23×C3—102no—
242C23×C3—202no—
243C23×C3—402no—
244C23×C3#68511yescharacteristic
245C23×C3C2×C4×D511yescharacteristic
246C23×C3C2×D2011yescharacteristic
247C3×Q8—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—202no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—402no—
255C3×D4—402no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—102no—
263C2×C3×C4#68511yescharacteristic
264C2×C3×C4#68511yescharacteristic
265C2×C3×C4#68511yescharacteristic
266C2×C3×C4C2×C22⋊D511yescharacteristic
267C2×Dic3—202no—
268C3⋊C8—42no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5C2×#21711yescharacteristic
276C2×D5—42no—
277C2×D5—42no—
278C2×D5—42no—
279C2×D5—84no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5#83411yescharacteristic
284C4×C5#83411yescharacteristic
285Dic5—42no—
286Dic5—242no—
287C24—52no—
288#41—41no—
289#41—41no—
290C2×Q8#120111yescharacteristic
291C2×D4—102no—
292C2×D4—102no—
293C2×D4—101no—
294C2×D4—101no—
295C2×D4—201no—
296C2×D4—201no—
297C2×D4D5×Dic311yescharacteristic
298C2×D4#120211yescharacteristic
299C2×D4C2×D3×D511yescharacteristic
300C22×C4D5×Dic311yescharacteristic
301C22×C4#120111yescharacteristic
302C22×C4#120211yescharacteristic
303M16—62no—
304M16—121no—
305C2×C8—121no—
306C4⋊C4—101no—
307C4⋊C4—601no—
308C22⋊C4—52no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—302no—
312C42—101no—
313C42—601no—
314C3×C5#212211yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—202no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—404no—
325C22×C3C2×#68511yescharacteristic
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—202no—
330C3×C4#393811yescharacteristic
331C3×C4#393811yescharacteristic
332Dic3—402no—
333C2×C5—21no—
334C2×C5—41no—
335C2×C5—41no—
336C2×C5—41no—
337C2×C5C2×#83411yescharacteristic
338D5—82no—
339C23—102no—
340C23—202no—
341C23—402no—
342C23#666511yescharacteristic
343C23C2×D5×Dic311yescharacteristic
344C23C2×#120211yescharacteristic
345Q8—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—202no—
350D4—201no—
351D4—201no—
352D4—402no—
353D4—402no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—102no—
361C2×C4—602no—
362C2×C4#666511yescharacteristic
363C2×C4#666511yescharacteristic
364C2×C4#666511yescharacteristic
365C2×C4C2×#120111yescharacteristic
366C8—122no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—402no—
372C2×C3C2×#393811yescharacteristic
373C5#7185911yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22—404no—
384C22C2×#666511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—202no—
389C4—1202no—
390C4#9099511yescharacteristic
391C4#9099511yescharacteristic
392C3#1060093911yescharacteristic, complemented, Sylow
393C2—21no—
394C2—41no—
395C2—41no—
396C2—41no—
397C2—402no—
398C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC3×#66164C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2122
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751341C2semidirect
3. C5×#5237C2semidirect
4. #11745995C2semidirect
7. C22×C3×D20C4semidirect
12. C3×#4083C4semidirect
16. C3×#4072C4semidirect
55. #5237D5semidirect
58. C22×D20Dic3semidirect
62. #4083Dic3semidirect
67. #4072Dic3semidirect
314. C3×C5#2122semidirect
373. C5#71859semidirect
392. C3#10600939semidirect

Maximal subgroups

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

subgroupindex
C3×#661642
#117513412
C5×#52372
#117459952
#106009393
#718595