Finite Group Databasebeta

← #14303609

Subgroups — #14303609

Order 1920.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#427C211yesmaximal, characteristic
2#11751100C211yesmaximal, characteristic
3#11751098C211yesmaximal, characteristic
4#11746373C211yesmaximal, characteristic
5#11746371C211yesmaximal, characteristic
6#11746353C211yesmaximal, characteristic
7#11746353C211yesmaximal, characteristic
8#10601454—31nomaximal, Hall
9C22×C3×C5×C8C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C3×C5×#107C411yescharacteristic, complemented
17C3×C5×#107C411yescharacteristic, complemented
18C3×C5×#106C411yescharacteristic, complemented
19C3×C5×#106C411yescharacteristic, complemented
20C4⋊(C3⋊#168)—21no—
21C4⋊(C3⋊#168)—21no—
22#91087—21no—
23C4×C3⋊#168—21no—
24#70661—51nomaximal, Hall
25C5×#427D311yescharacteristic
26#65288—31no—
27#65286—31no—
28#64772—31no—
29#64770—31no—
30#64752—31no—
31#64752—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C2×C3×C5×C8—21no—
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8C2×C411yescharacteristic
37C2×C3×C5×C8C2×C411yescharacteristic
38C3×C5×C4⋊C4C2×C411yescharacteristic
39C3×C5×C4⋊C4C2×C411yescharacteristic
40C3×C5×C4⋊C4C2×C411yescharacteristic
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C5×C22⋊C4—21no—
44C3×C42×C5—21no—
45C3×C42×C5—21no—
46C4×Dic15—21no—
47C4×Dic15—21no—
48#6710—21no—
49#6710—21no—
50#6710—21no—
51#6710Q812yes—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168D411yescharacteristic
57C2×C3⋊#168D411yescharacteristic
58C3×#427D511yescharacteristic
59#4999—51no—
60#4997—51no—
61#4552—51no—
62#4550—51no—
63#4532—51no—
64#4532—51no—
65C22×C5×C8C2×D311yescharacteristic
66C5×#117C2×D311yescharacteristic
67C5×#117C2×D311yescharacteristic
68C2×C4×Dic5—31no—
69C2×#681—31no—
70C2×#681—31no—
71C22×#168—31no—
72C5×#107Dic311yescharacteristic, complemented
73C5×#107Dic311yescharacteristic, complemented
74C5×#106Dic311yescharacteristic, complemented
75C5×#106Dic311yescharacteristic, complemented
76C4⋊#168—61no—
77C4⋊#168—61no—
78#3935—61no—
79C4×#168—61no—
80#1922—151noSylow
81C23×C3×C5#4111yescharacteristic
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×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×Q811yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×Dic15—22no—
93C2×Dic15—41no—
94C2×Dic15—41no—
95C3×C5×C8—21no—
96C3×C5×C8—21no—
97C3⋊#168—22no—
98C3⋊#168—21no—
99C3⋊#168—21no—
100C3⋊#168—41no—
101C22×C3×C8C2×D511yescharacteristic
102C3×#117C2×D511yescharacteristic
103C3×#117C2×D511yescharacteristic
104C2×C4×Dic3—51no—
105C2×#208—51no—
106C2×#208—51no—
107C22×C3⋊C8—51no—
108C3×#107Dic511yescharacteristic, complemented
109C3×#107Dic511yescharacteristic, complemented
110C3×#106Dic511yescharacteristic, complemented
111C3×#106Dic511yescharacteristic, complemented
112C4⋊(C3⋊C8)—101no—
113C4⋊(C3⋊C8)—101no—
114#803—101no—
115C4×C3⋊C8—101no—
116C22×C4×C5C22×D311yescharacteristic
117C22×Dic5—61no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C2×C5×C8C2×Dic311yescharacteristic
121C2×C5×C8C2×Dic311yescharacteristic
122C5×C4⋊C4C2×Dic311yescharacteristic
123C5×C4⋊C4C2×Dic311yescharacteristic
124C5×C4⋊C4C2×Dic311yescharacteristic
125C5×C4⋊C4C2×Dic311yescharacteristic
126C5×C22⋊C4—21no—
127C5×C22⋊C4—21no—
128C42×C5—21no—
129C42×C5—21no—
130C4×Dic5—61no—
131C4×Dic5—61no—
132#681—32no—
133#681—61no—
134#681—61no—
135#681—61no—
136C2×#168—31no—
137C2×#168—31no—
138C2×#168—61no—
139C2×#168—61no—
140C2×#168—61no—
141C2×#168—61no—
142#427D1511yescharacteristic
143#424—151no—
144#405—151no—
145#341—151no—
146#339—151no—
147#339—151no—
148#336—151no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5C4×D411yescharacteristic
152C22×C3×C5#12511yescharacteristic
153C22×C3×C5#12611yescharacteristic
154C3×C4×C5—41no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5#11711yescharacteristic
159C3×C4×C5C4×Q811yescharacteristic
160C3×C4×C5C22⋊Q811yescharacteristic
161C3×C4×C5#12311yescharacteristic
162Dic15—42no—
163C22×C3×C4C22×D511yescharacteristic
164C22×Dic3—101no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8C2×Dic511yescharacteristic
168C2×C3×C8C2×Dic511yescharacteristic
169C3×C4⋊C4C2×Dic511yescharacteristic
170C3×C4⋊C4C2×Dic511yescharacteristic
171C3×C4⋊C4C2×Dic511yescharacteristic
172C3×C4⋊C4C2×Dic511yescharacteristic
173C3×C22⋊C4—21no—
174C3×C22⋊C4—21no—
175C3×C42—21no—
176C3×C42—21no—
177C4×Dic3—101no—
178C4×Dic3—101no—
179#208—52no—
180#208—101no—
181#208—101no—
182#208—101no—
183C2×C3⋊C8—51no—
184C2×C3⋊C8—51no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C2×C3⋊C8—101no—
189C23×C5#23711yescharacteristic
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5#23511yescharacteristic
195C2×C4×C5#23511yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×Q811yescharacteristic
198C2×C4×C5#23911yescharacteristic
199C2×C4×C5C22×Dic311yescharacteristic
200C2×Dic5—62no—
201C2×Dic5—121no—
202C2×Dic5—121no—
203C5×C8—21no—
204C5×C8—21no—
205#168—61no—
206#168—61no—
207#168—62no—
208#168—121no—
209C2×M16—151no—
210C2×M16—151no—
211C22×C8—151no—
212C22×C8C2×D1511yescharacteristic
213#117C2×D1511yescharacteristic
214#117C2×D1511yescharacteristic
215C2×C42—151no—
216#107Dic1511yescharacteristic, complemented
217#107Dic1511yescharacteristic, complemented
218#106Dic1511yescharacteristic, complemented
219#106Dic1511yescharacteristic, complemented
220C4⋊C8—301no—
221C4⋊C8—301no—
222#97—301no—
223C4×C8—301no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5#38711yescharacteristic
227C2×C3×C5#44311yescharacteristic
228C2×C3×C5#44411yescharacteristic
229C23×C3#71111yescharacteristic
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4#70911yescharacteristic
235C2×C3×C4#70911yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4Q8×D511yescharacteristic
238C2×C3×C4#71311yescharacteristic
239C2×C3×C4C22×Dic511yescharacteristic
240C2×Dic3—102no—
241C2×Dic3—201no—
242C2×Dic3—201no—
243C3×C8—21no—
244C3×C8—21no—
245C3⋊C8—101no—
246C3⋊C8—101no—
247C3⋊C8—102no—
248C3⋊C8—201no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5#88911yescharacteristic
252C22×C5#89811yescharacteristic
253C22×C5D4×Dic311yescharacteristic
254C4×C5—41no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5#89411yescharacteristic
259C4×C5#89611yescharacteristic
260C4×C5#92611yescharacteristic
261C4×C5Q8×Dic311yescharacteristic
262Dic5—122no—
263C22×C4—301no—
264C22×C4C22×D1511yescharacteristic
265M16—152no—
266M16—301no—
267M16—301no—
268M16—301no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—151no—
272C2×C8—151no—
273C2×C8—301no—
274C2×C8—301no—
275C2×C8—301no—
276C2×C8—301no—
277C2×C8C2×Dic1511yescharacteristic
278C2×C8C2×Dic1511yescharacteristic
279C4⋊C4C2×Dic1511yescharacteristic
280C4⋊C4C2×Dic1511yescharacteristic
281C4⋊C4C2×Dic1511yescharacteristic
282C4⋊C4C2×Dic1511yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C42—21no—
286C42—21no—
287C42—301no—
288C42—301no—
289C3×C5#192211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3#403511yescharacteristic
293C22×C3#404411yescharacteristic
294C22×C3D4×Dic511yescharacteristic
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4#404011yescharacteristic
300C3×C4#404211yescharacteristic
301C3×C4#407211yescharacteristic
302C3×C4Q8×Dic511yescharacteristic
303Dic3—202no—
304C2×C5—21no—
305C2×C5—21no—
306C2×C5#498011yescharacteristic
307C2×C5#519611yescharacteristic
308C2×C5#519711yescharacteristic
309C23#681911yescharacteristic
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4#681711yescharacteristic
318C2×C4#681711yescharacteristic
319C2×C4D4×D1511yescharacteristic
320C2×C4Q8×D1511yescharacteristic
321C2×C4#682111yescharacteristic
322C2×C4C22×Dic1511yescharacteristic
323C8—21no—
324C8—21no—
325C8—301no—
326C8—301no—
327C8—302no—
328C8—601no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3#6527011yescharacteristic
332C2×C3#6548511yescharacteristic
333C2×C3#6548611yescharacteristic
334C5#7066111yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22#9177811yescharacteristic
338C22#9178711yescharacteristic
339C22D4×Dic1511yescharacteristic
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—602no—
345C4#9178311yescharacteristic
346C4#9178511yescharacteristic
347C4#9181511yescharacteristic
348C4Q8×Dic1511yescharacteristic
349C3#1060145411yescharacteristic, complemented, Sylow
350C2—21no—
351C2—21no—
352C2#1175108111yescharacteristic
353C2#1175129711yescharacteristic
354C2#1175129811yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#427C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C3×C4×C5C23
hypercenter#427D15
hypocenterC3×C5#1922
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
16. C3×C5×#107C4semidirect
17. C3×C5×#107C4semidirect
18. C3×C5×#106C4semidirect
19. C3×C5×#106C4semidirect
72. C5×#107Dic3semidirect
73. C5×#107Dic3semidirect
74. C5×#106Dic3semidirect
75. C5×#106Dic3semidirect
108. C3×#107Dic5semidirect
109. C3×#107Dic5semidirect
110. C3×#106Dic5semidirect
111. C3×#106Dic5semidirect
216. #107Dic15semidirect
217. #107Dic15semidirect
218. #106Dic15semidirect
219. #106Dic15semidirect
289. C3×C5#1922semidirect
334. C5#70661semidirect
349. C3#10601454semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4272
#117511002
#117510982
#117463732
#117463712
#117463532
#106014543
#706615