Finite Group Databasebeta

← #14282525

Subgroups — #14282525

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756238C211yesmaximal, characteristic
2C3×C5×#431C211yesmaximal, characteristic, complemented
3#11751025C211yesmaximal, characteristic, complemented
4#11746280C212yesmaximal, complemented
5#11746277C212yesmaximal, complemented
6#10601557—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8#91819C411yescharacteristic
9#91818—21no—
10C4×#1220—21no—
11#91813C411yescharacteristic
12C2×#6710—21no—
13#91765—21no—
14#91764C411yescharacteristic
15C4×D60C2211yescharacteristic
16#91761—21no—
17#91759C411yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8—21no—
20C3×C5×C22⋊C8—21no—
21C3×C4×C5×C8C2212yes—
22C4⋊(C3⋊#168)—21no—
23C4⋊(C3⋊#168)C2212yes—
24#70764—51nomaximal, Hall
25#65813—31no—
26C5×#431D311yescharacteristic, complemented
27#65213—31no—
28#64679—32no—
29#64676—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C2×#1220—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30C2×C411yescharacteristic
37C2×C3×C5×C8—22no—
38C3×C42×C5C2×C411yescharacteristic
39C3×C42×C5D411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5C2311yescharacteristic
42#6719—21no—
43#6714—21no—
44#6714—21no—
45#6714—21no—
46#6714—21no—
47C4⋊Dic15C2×C411yescharacteristic
48C4⋊Dic15C2×C411yescharacteristic
49#6712—21no—
50#6712—21no—
51#6712—21no—
52#6712—21no—
53C4×Dic15—21no—
54#6710—42no—
55C2×C3⋊#168—22no—
56#5479—51no—
57C3×#431D511yescharacteristic, complemented
58#4924—51no—
59#4459—52no—
60#4456—52no—
61C2×C42×C5C2×D311yescharacteristic
62#4076—31no—
63#4075—61no—
64C4×C22⋊D5—61no—
65#4070—31no—
66C2×#681—61no—
67#4022—61no—
68#4021—31no—
69C4×D20—31no—
70#4018—61no—
71#4016—31no—
72C4×Dic10—31no—
73C5×C4⋊C8—21no—
74C5×C22⋊C8—21no—
75C4×C5×C8C2×D312yes—
76C4⋊#168—32no—
77C4⋊#168—61no—
78#1495—151noSylow
79C23×C3×C5C22⋊C411yescharacteristic
80C22×D15—21no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91#1220—42no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95D60—22no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—22no—
99C3×C5×C8—42no—
100C3⋊#168—42no—
101C2×C3×C42C2×D511yescharacteristic
102#930—51no—
103#929—101no—
104C4×#67—101no—
105#924—51no—
106C2×#208—101no—
107#876—101no—
108#875—51no—
109C4×D12—51no—
110#872—101no—
111#870—51no—
112C4×Dic6—51no—
113C3×C4⋊C8—21no—
114C3×C22⋊C8—21no—
115C3×C4×C8C2×D512yes—
116C4⋊(C3⋊C8)—52no—
117C4⋊(C3⋊C8)—101no—
118C22×C4×C5C4×D311yescharacteristic
119C22×C4×C5D1211yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C2×C22⋊D5—61no—
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×Dic10—31no—
125C2×C5×C8—22no—
126C42×C5C4×D311yescharacteristic
127C42×C5D1211yescharacteristic
128C42×C5#6711yescharacteristic
129C42×C5C22×D311yescharacteristic
130C22⋊Dic5—61no—
131#685—61no—
132#685—61no—
133#685—61no—
134#685—61no—
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137#683—61no—
138#683—61no—
139#683—61no—
140#683—61no—
141C4×Dic5—61no—
142#681—122no—
143C2×#168—62no—
144#529—151no—
145#431D1511yescharacteristic, complemented
146#423—151no—
147Q8⋊C8—152no—
148D4⋊C8—152no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5#13112yes—
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—41no—
164Dic15—41no—
165Dic15—41no—
166C22×C3×C4C4×D511yescharacteristic
167C22×C3×C4D2011yescharacteristic
168C22×C3×C4C22⋊D511yescharacteristic
169C2×#67—101no—
170C2×D12—51no—
171C2×C4×D3—101no—
172C2×Dic6—51no—
173C2×C3×C8—22no—
174C3×C42C4×D511yescharacteristic
175C3×C42D2011yescharacteristic
176C3×C42C22⋊D511yescharacteristic
177C3×C42C22×D511yescharacteristic
178#217—101no—
179(C2×D3)⋊C4—101no—
180(C2×D3)⋊C4—101no—
181(C2×D3)⋊C4—101no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—51no—
184C4⋊Dic3—51no—
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190#208—202no—
191C2×C3⋊C8—102no—
192C23×C5(C2×D3)⋊C411yescharacteristic
193C22×D5—61no—
194C2×C4×C5—22no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5(C2×D3)⋊C411yescharacteristic
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C22⋊D5—122no—
205C2×Dic5—61no—
206C2×Dic5—61no—
207C2×Dic5—61no—
208D20—62no—
209C4×D5—121no—
210C4×D5—121no—
211Dic10—62no—
212C5×C8—42no—
213#168—122no—
214C2×M16—301no—
215#126—301no—
216#125—151no—
217#124—151no—
218#123—301no—
219C22⋊Q8—151no—
220#121—151no—
221C4×Q8—151no—
222C4×D4—151no—
223C4×D4—301no—
224#117—301no—
225C2×C42C2×D1511yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—152no—
228C4⋊C8—301no—
229C22⋊C8—21no—
230C4×C8C2×D1512yes—
231C2×C3×C5—41no—
232C2×C3×C5#40811yescharacteristic
233C2×C3×C5#41711yescharacteristic
234C2×C3×C5#42111yescharacteristic
235D15—81no—
236C23×C3#68511yescharacteristic
237C22×D3—101no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4#68511yescharacteristic
243C2×C3×C4#68511yescharacteristic
244C2×C3×C4#68511yescharacteristic
245C2×C3×C4C2×C4×D511yescharacteristic
246C2×C3×C4C2×D2011yescharacteristic
247C2×C3×C4C2×C22⋊D511yescharacteristic
248#67—202no—
249C2×Dic3—101no—
250C2×Dic3—101no—
251C2×Dic3—101no—
252D12—102no—
253C4×D3—201no—
254C4×D3—201no—
255Dic6—102no—
256C3×C8—42no—
257C3⋊C8—202no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5C2×(C2×D3)⋊C411yescharacteristic
262C2×D5—121no—
263C2×D5—121no—
264C2×D5—121no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5#90112yes—
270C4×C5#90811yescharacteristic
271C4×C5#90911yescharacteristic
272Dic5—121no—
273Dic5—121no—
274Dic5—121no—
275C2×Q8—151no—
276C2×D4—151no—
277C2×D4—301no—
278C22×C4—301no—
279C22×C4C4×D1511yescharacteristic
280C22×C4D6011yescharacteristic
281C22×C4#122011yescharacteristic
282M16—602no—
283C2×C8—22no—
284C2×C8—302no—
285C4⋊C4—151no—
286C4⋊C4—151no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C22⋊C4—301no—
292C22⋊C4—301no—
293C22⋊C4—301no—
294C22⋊C4—301no—
295C22⋊C4—301no—
296C42—301no—
297C42C4×D1511yescharacteristic
298C42D6011yescharacteristic
299C42#122011yescharacteristic
300C42C22×D1511yescharacteristic
301C3×C5#149511yescharacteristic, complemented, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3C2×#68511yescharacteristic
306C2×D3—201no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4#404712yes—
314C3×C4#405411yescharacteristic
315C3×C4#405511yescharacteristic
316Dic3—201no—
317Dic3—201no—
318Dic3—201no—
319C2×C5—41no—
320C2×C5#500511yescharacteristic
321C2×C5#511011yescharacteristic
322C2×C5#513311yescharacteristic
323D5—241no—
324C23—301no—
325C23#671411yescharacteristic
326Q8—302no—
327D4—302no—
328D4—602no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—301no—
334C2×C4—301no—
335C2×C4—301no—
336C2×C4—601no—
337C2×C4—601no—
338C2×C4#671411yescharacteristic
339C2×C4#671411yescharacteristic
340C2×C4#671411yescharacteristic
341C2×C4C2×C4×D1511yescharacteristic
342C2×C4C2×D6011yescharacteristic
343C2×C4C2×#122011yescharacteristic
344C8—42no—
345C8—602no—
346C2×C3—41no—
347C2×C3#6529411yescharacteristic
348C2×C3#6539911yescharacteristic
349C2×C3#6542211yescharacteristic
350D3—401no—
351C5#7076411yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—21no—
355C22—601no—
356C22—601no—
357C22—601no—
358C22C2×#671411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—601no—
364C4—601no—
365C4—601no—
366C4#9179012yes—
367C4#9179711yescharacteristic
368C4#9179811yescharacteristic
369C3#1060155711yescharacteristic, complemented, Sylow
370C2—41no—
371C2—1201no—
372C2#1175110611yescharacteristic
373C2#1175121111yescharacteristic
374C2#1175123411yescharacteristic
subgroupG/H
centerC2×C4C2×D60
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#431C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91819C4
cosocleC3×C42×C5C23
hypercenter#431D15
hypocenterC3×C5#1495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C3×C5×#431C2semidirect
3. #11751025C2semidirect
4. #11746280C2semidirect
5. #11746277C2semidirect
26. C5×#431D3semidirect
57. C3×#431D5semidirect
145. #431D15semidirect
301. C3×C5#1495semidirect
351. C5#70764semidirect
369. C3#10601557semidirect

Maximal subgroups

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

subgroupindex
#117562382
C3×C5×#4312
#117510252
#117462802
#117462772
#106015573
#707645