Finite Group Databasebeta

← #14313735

Subgroups — #14313735

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66164C211yesmaximal, characteristic
2#11751338C211yesmaximal, characteristic, complemented
3C5×#5237C211yesmaximal, characteristic, complemented
4#11746012C214yesmaximal, complemented
5#10600942—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C3×D20C411yescharacteristic
8C2×#6710—21no—
9C2×C5×#208—21no—
10C3×#4093C2212yes—
11C3×#4086C412yes—
12C3×#4083—21no—
13C3×#4083—21no—
14C3×#4076—21no—
15C3×#4076—21no—
16C3×#4072C411yescharacteristic
17#91120C2212yescomplemented
18#91117—21no—
19C5×#836C2212yescomplemented
20C5×#833—21no—
21#71862—51nomaximal, Hall
22#66164D311yescharacteristic
23C5×#413—31no—
24#65526—31no—
25#64697—34no—
26C23×C3×D5—21no—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8C2311yescharacteristic
30C2×C3×C5×D4C2×C411yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4D411yescharacteristic
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—41no—
40C2×C3×D20—41no—
41C2×C3×D20C2×C412yes—
42#6710—22no—
43#6710—41no—
44C2×C3⋊#168—41no—
45C5×#208—22no—
46C5×#208—41no—
47C2×C5×C3⋊C8—41no—
48C3×C22⋊Dic5—21no—
49C3×#685—22no—
50C3×#685—22no—
51C3×C4⋊Dic5—21no—
52C3×C4×Dic5C2×C412yes—
53C3×#535—51no—
54#5237—51no—
55#5237D511yescharacteristic, complemented
56#4542—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×D20Dic311yescharacteristic
59C2×C5×M16—61no—
60#4093C2×D312yes—
61#4086Dic312yes—
62#4083—21no—
63#4083—21no—
64#4076—21no—
65#4076—21no—
66#4072Dic311yescharacteristic
67C2×#681—61no—
68C5×#101—32no—
69C5×#100—61no—
70#3968—32no—
71#3965—61no—
72#2134—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22⋊C411yescharacteristic
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×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C3×C22⋊D5—82no—
94C3×C22⋊D5—82no—
95C2×C3×Dic5—22no—
96C3×D20—42no—
97C3×D20—41no—
98C3×D20—41no—
99C3⋊#168—42no—
100C5×C3⋊C8—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×C3×D4—51no—
103C3×#127—52no—
104C3×#124—52no—
105C3×#121—101no—
106C3×#121—101no—
107C3×#120—101no—
108C3×#120—101no—
109C3×#117—51no—
110C2×#208—21no—
111C2×#208—101no—
112#836—52no—
113#836C2×D512yescomplemented
114#833—21no—
115#833—101no—
116C23×D5—21no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8C22×D311yescharacteristic
120C2×C5×D4C2×Dic311yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C2×C5×D4#6711yescharacteristic
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—41no—
130C2×D20—41no—
131C2×D20C2×Dic312yes—
132C5×M16—62no—
133C5×M16—121no—
134C2×C5×C8—121no—
135C22⋊Dic5—21no—
136#685—22no—
137#685—22no—
138C4⋊Dic5—21no—
139C4×Dic5C2×Dic312yes—
140#681—62no—
141#681—121no—
142C2×#168—121no—
143#535—51no—
144#413—31no—
145#413—151no—
146#355—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
163C3×Dic5—42no—
164C24×C3—101no—
165C3×#41—41no—
166C3×#41—41no—
167C2×C3×Q8C22×D511yescharacteristic
168C2×C3×D4—52no—
169C2×C3×D4—102no—
170C2×C3×D4—102no—
171C2×C3×D4—101no—
172C2×C3×D4—201no—
173C2×C3×D4—201no—
174C2×C3×D4C4×D511yescharacteristic
175C2×C3×D4D2011yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4C4×D511yescharacteristic
178C22×C3×C4D2011yescharacteristic
179C22×C3×C4C22⋊D511yescharacteristic
180C3×C4⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C42—52no—
185#208—22no—
186#208—41no—
187#208—102no—
188#208—201no—
189C2×C3⋊C8—41no—
190C2×C3⋊C8—201no—
191C23×C5#21711yescharacteristic
192C23×C5#21711yescharacteristic
193C23×C5#21711yescharacteristic
194C22×D5—22no—
195C22×D5—42no—
196C22×D5—82no—
197C5×Q8—41no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5#21711yescharacteristic
208C2×C4×C5C22×Dic311yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C22⋊D5—82no—
212C22⋊D5—82no—
213C2×Dic5—22no—
214D20—42no—
215D20—41no—
216D20—41no—
217C5×C8—122no—
218#168—122no—
219C2×#41D3×D511yescharacteristic
220C22×D4—51no—
221C2×M16—61no—
222C2×M16—301no—
223#127—52no—
224#124—52no—
225#121—101no—
226#121—101no—
227#120—101no—
228#120—101no—
229#117—51no—
230#101—32no—
231#101—152no—
232#100—61no—
233#100—301no—
234C2×C3×C5—21no—
235C2×C3×C5—41no—
236C2×C3×C5—41no—
237C2×C3×C5—41no—
238C2×C3×C5C2×#9911yescharacteristic
239C3×D5—82no—
240C23×C3—102no—
241C23×C3—202no—
242C23×C3—402no—
243C23×C3#68511yescharacteristic
244C23×C3#68511yescharacteristic
245C23×C3#68511yescharacteristic
246C3×Q8—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—202no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—402no—
254C3×D4—402no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—102no—
262C2×C3×C4#68511yescharacteristic
263C2×C3×C4C2×C4×D511yescharacteristic
264C2×C3×C4C2×D2011yescharacteristic
265C2×C3×C4C2×C22⋊D511yescharacteristic
266C3⋊C8—42no—
267C3⋊C8—202no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5C2×#21711yescharacteristic
275C2×D5—42no—
276C2×D5—42no—
277C2×D5—42no—
278C2×D5—84no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5#83411yescharacteristic
283C4×C5#83411yescharacteristic
284Dic5—42no—
285C24—101no—
286#41—41no—
287#41—41no—
288C2×Q8C2×D3×D511yescharacteristic
289C2×D4—52no—
290C2×D4—102no—
291C2×D4—102no—
292C2×D4—101no—
293C2×D4—201no—
294C2×D4—201no—
295C2×D4D5×Dic311yescharacteristic
296C2×D4#120111yescharacteristic
297C2×D4#120211yescharacteristic
298C22×C4D5×Dic311yescharacteristic
299C22×C4#120111yescharacteristic
300C22×C4#120211yescharacteristic
301M16—62no—
302M16—121no—
303M16—302no—
304M16—601no—
305C2×C8—121no—
306C2×C8—601no—
307C4⋊C4—101no—
308C22⋊C4—101no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C42—52no—
312C3×C5#213411yescharacteristic, complemented, Hall
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3—404no—
323C22×C3C2×#68511yescharacteristic
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—202no—
328C3×C4#393811yescharacteristic
329C3×C4#393811yescharacteristic
330C2×C5—21no—
331C2×C5—41no—
332C2×C5—41no—
333C2×C5—41no—
334C2×C5C2×#83411yescharacteristic
335D5—82no—
336C23—102no—
337C23—202no—
338C23—402no—
339C23#666511yescharacteristic
340C23#666511yescharacteristic
341C23#666511yescharacteristic
342Q8—41no—
343D4—41no—
344D4—41no—
345D4—41no—
346D4—202no—
347D4—201no—
348D4—201no—
349D4—402no—
350D4—402no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—102no—
358C2×C4#666511yescharacteristic
359C2×C4C2×D5×Dic311yescharacteristic
360C2×C4C2×#120111yescharacteristic
361C2×C4C2×#120211yescharacteristic
362C8—122no—
363C8—602no—
364C2×C3—21no—
365C2×C3—41no—
366C2×C3—41no—
367C2×C3—41no—
368C2×C3—402no—
369C2×C3C2×#393811yescharacteristic
370C5#7186211yescharacteristic, complemented, Sylow
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—202no—
378C22—202no—
379C22—202no—
380C22—404no—
381C22C2×#666511yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—202no—
386C4#9099511yescharacteristic
387C4#9099511yescharacteristic
388C3#1060094211yescharacteristic, complemented, Sylow
389C2—21no—
390C2—41no—
391C2—41no—
392C2—41no—
393C2—402no—
394C2C2×#9099511yescharacteristic
subgroupG/H
centerC2C2×#90995
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC3×#66164C2
cosocleC2×C3×C5×Q8C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2134
LCSG ▷ C2×C3×C4×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. #11751338C2semidirect
3. C5×#5237C2semidirect
4. #11746012C2semidirect
17. #91120C22semidirect
19. C5×#836C22semidirect
55. #5237D5semidirect
113. #836C2×D5semidirect
312. C3×C5#2134semidirect
370. C5#71862semidirect
388. C3#10600942semidirect

Maximal subgroups

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

subgroupindex
C3×#661642
#117513382
C5×#52372
#117460122
#106009423
#718625