Finite Group Databasebeta

← #14313550

Subgroups — #14313550

Order 1920.

476 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
1C5×#5825C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic
3C3×#65529C211yesmaximal, characteristic
4#11746010C214yesmaximal, complemented
5#10602664—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C5×Dic6C411yescharacteristic, complemented
8#91815—21no—
9C5×#944C412yescomplemented
10C5×#936C2212yes—
11C5×#935—21no—
12C5×#935—21no—
13C5×#926C411yescharacteristic, complemented
14C5×#924—21no—
15C5×#924—21no—
16C3×#4072—21no—
17#91118—21no—
18#91118C2212yes—
19C3×#3966—21no—
20C3×#3966C2212yes—
21#70059—51nomaximal, Hall
22C5×#536—31no—
23#65529—31no—
24#65529D311yescharacteristic
25#64761—34no—
26C3×C5×#41—41no—
27C3×C5×#41—41no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C2×C3×C5×D4D411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4C2311yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C5×Dic3—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6—41no—
38C2×C5×Dic6—41no—
39C2×C5×Dic6C2×C412yes—
40#6719—22no—
41C4⋊Dic15—41no—
42C4×Dic15—41no—
43C5×#217—21no—
44C5×#217—22no—
45C5×#217—22no—
46C5×C4⋊Dic3—21no—
47C5×Dic3⋊C4—22no—
48C5×Dic3⋊C4—22no—
49C4×C5×Dic3C2×C412yes—
50C3×C22⋊Dic5—22no—
51C3×C4⋊Dic5—41no—
52C3×C4×Dic5—41no—
53#5825D511yescharacteristic
54C3×#410—51no—
55#5240—51no—
56#4473—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×C5×Q8—31no—
59C5×C4⋊Q8—32no—
60C5×#124—32no—
61C5×#123—61no—
62C5×#123—61no—
63C5×C22⋊Q8—61no—
64C5×C22⋊Q8—61no—
65C5×#117—31no—
66#4072—21no—
67#4072—61no—
68#3966—21no—
69#3966—32no—
70#3966—61no—
71#3966C2×D312yes—
72#2129—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C3×C5×Q8—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×Dic15—42no—
91C2×C5×Dic3—22no—
92C2×C5×Dic3—22no—
93C2×C5×Dic3—42no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C5×Dic6—42no—
97C2×C3×Dic5—42no—
98C2×C3×#41C2×D511yescharacteristic
99C22×Dic6Dic511yescharacteristic, complemented
100C3×#117—101no—
101#944Dic512yescomplemented
102#936C2×D512yes—
103#935—21no—
104#935—21no—
105#926—101no—
106#926Dic511yescharacteristic, complemented
107#924—21no—
108#924—21no—
109C3×#99—52no—
110C3×#99—101no—
111#834—52no—
112#834—101no—
113C5×#41—41no—
114C5×#41—41no—
115C2×C5×Q8—32no—
116C2×C5×Q8—61no—
117C2×C5×Q8—121no—
118C2×C5×Q8—121no—
119C2×C5×Q8C4×D311yescharacteristic
120C2×C5×D4D1211yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C2×C5×D4C22×D311yescharacteristic
123C22×C4×C5—61no—
124C22×C4×C5C4×D311yescharacteristic
125C22×C4×C5D1211yescharacteristic
126C22×C4×C5#6711yescharacteristic
127C5×C4⋊C4—61no—
128C5×C4⋊C4—62no—
129C5×C4⋊C4—62no—
130C5×C22⋊C4—61no—
131C5×C22⋊C4—62no—
132C5×C22⋊C4—62no—
133C42×C5—32no—
134C22⋊Dic5—22no—
135C22⋊Dic5—62no—
136C4⋊Dic5—41no—
137C4⋊Dic5—121no—
138C4×Dic5—41no—
139C4×Dic5—121no—
140#536—31no—
141#410—51no—
142#410—151no—
143#354—154no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—41no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5#9911yescharacteristic
155C3×C4×C5#9911yescharacteristic
156Dic15—82no—
157C3×Dic5—82no—
158C5×Dic3—42no—
159C5×Dic3—42no—
160C3×#41—41no—
161C3×#41—41no—
162C2×C3×Q8C2×Dic511yescharacteristic
163C2×C3×D4C22⋊D511yescharacteristic
164C2×C3×D4C22⋊D511yescharacteristic
165C2×C3×D4C22×D511yescharacteristic
166C22×C3×C4C2×Dic511yescharacteristic
167C22×C3×C4C22⋊D511yescharacteristic
168C22×C3×C4C22⋊D511yescharacteristic
169C22×Dic3—21no—
170C2×Dic6—21no—
171C2×Dic6—41no—
172C2×Dic6—41no—
173C2×Dic6C2×Dic512yes—
174C3×C4⋊C4—201no—
175C3×C22⋊C4—102no—
176C3×C42—201no—
177#217—21no—
178#217—22no—
179#217—22no—
180#217—102no—
181C4⋊Dic3—21no—
182C4⋊Dic3—201no—
183Dic3⋊C4—22no—
184Dic3⋊C4—22no—
185C4×Dic3—201no—
186C4×Dic3C2×Dic512yes—
187C23×C5(C2×D3)⋊C411yescharacteristic
188C23×C5C2×D1211yescharacteristic
189C23×C5C2×#6711yescharacteristic
190C5×Q8—41no—
191C5×Q8—122no—
192C5×Q8—121no—
193C5×Q8—121no—
194C5×D4—41no—
195C5×D4—41no—
196C5×D4—41no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—62no—
204C2×C4×C5—62no—
205C2×C4×C5—122no—
206C2×C4×C5(C2×D3)⋊C411yescharacteristic
207C2×C4×C5(C2×D3)⋊C411yescharacteristic
208C2×C4×C5(C2×D3)⋊C411yescharacteristic
209C2×C4×C5C2×C4×D311yescharacteristic
210C2×Dic5—42no—
211C2×Dic5—122no—
212C2×#41D3×D511yescharacteristic
213C22×Q8—31no—
214C4⋊Q8—32no—
215#124—32no—
216#123—61no—
217#123—61no—
218C22⋊Q8—61no—
219C22⋊Q8—61no—
220#117—31no—
221#117—101no—
222#117—301no—
223#99—52no—
224#99—101no—
225#99—152no—
226#99—301no—
227C2×C3×C5—21no—
228C2×C3×C5—41no—
229C2×C3×C5—41no—
230C2×C3×C5—41no—
231C2×C3×C5C2×#9911yescharacteristic
232C23×C3C22⋊Dic511yescharacteristic
233C23×C3C2×C22⋊D511yescharacteristic
234C23×C3C2×C22⋊D511yescharacteristic
235C3×Q8—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—202no—
246C2×C3×C4C22⋊Dic511yescharacteristic
247C2×C3×C4C22⋊Dic511yescharacteristic
248C2×C3×C4C22⋊Dic511yescharacteristic
249C2×C3×C4C22×Dic511yescharacteristic
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—42no—
253C2×Dic3—202no—
254Dic6—41no—
255Dic6—41no—
256Dic6—42no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5C2×(C2×D3)⋊C411yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—122no—
268C4×C5—122no—
269C4×C5#80611yescharacteristic
270C4×C5#80611yescharacteristic
271Dic5—82no—
272Dic5—242no—
273#41—41no—
274#41—41no—
275C2×Q8—32no—
276C2×Q8—61no—
277C2×Q8—121no—
278C2×Q8—121no—
279C2×Q8D3×Dic511yescharacteristic
280C2×D4#120111yescharacteristic
281C2×D4#120311yescharacteristic
282C2×D4C2×D3×D511yescharacteristic
283C22×C4—61no—
284C22×C4D3×Dic511yescharacteristic
285C22×C4#120111yescharacteristic
286C22×C4#120311yescharacteristic
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—61no—
290C4⋊C4—201no—
291C4⋊C4—601no—
292C22⋊C4—61no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—102no—
296C22⋊C4—302no—
297C42—32no—
298C42—201no—
299C42—601no—
300C3×C5#212911yescharacteristic, complemented, Hall
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C2×C22⋊Dic511yescharacteristic
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—402no—
312C3×C4#396611yescharacteristic
313C3×C4#396611yescharacteristic
314Dic3—42no—
315Dic3—42no—
316Dic3—402no—
317C2×C5—21no—
318C2×C5—41no—
319C2×C5—41no—
320C2×C5—41no—
321C2×C5C2×#80611yescharacteristic
322C23(C2×D3)⋊Dic511yescharacteristic
323C23C2×#120111yescharacteristic
324C23C2×#120311yescharacteristic
325Q8—41no—
326Q8—122no—
327Q8—121no—
328Q8—121no—
329D4—41no—
330D4—41no—
331D4—41no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—122no—
341C2×C4—202no—
342C2×C4—602no—
343C2×C4(C2×D3)⋊Dic511yescharacteristic
344C2×C4(C2×D3)⋊Dic511yescharacteristic
345C2×C4(C2×D3)⋊Dic511yescharacteristic
346C2×C4C2×D3×Dic511yescharacteristic
347C2×C3—21no—
348C2×C3—41no—
349C2×C3—41no—
350C2×C3—41no—
351C2×C3C2×#396611yescharacteristic
352C5#7005911yescharacteristic, complemented, Sylow
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22C2×(C2×D3)⋊Dic511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—122no—
364C4—122no—
365C4—402no—
366C4—1202no—
367C4#9099611yescharacteristic
368C4#9099611yescharacteristic
369C3#1060266411yescharacteristic, complemented, Sylow
370C2—21no—
371C2—41no—
372C2—41no—
373C2—41no—
374C2C2×#9099611yescharacteristic
subgroupG/H
centerC2C2×#90996
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2129
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
4. #11746010C2semidirect
7. C22×C5×Dic6C4semidirect
9. C5×#944C4semidirect
13. C5×#926C4semidirect
99. C22×Dic6Dic5semidirect
101. #944Dic5semidirect
106. #926Dic5semidirect
300. C3×C5#2129semidirect
352. C5#70059semidirect
369. C3#10602664semidirect

Maximal subgroups

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

subgroupindex
C5×#58252
#117513412
C3×#655292
#117460102
#106026643
#700595