Finite Group Databasebeta

← #14298583

Subgroups — #14298583

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6817C211yesmaximal, characteristic
2#11751233C211yesmaximal, characteristic
3#11751107C211yesmaximal, characteristic
4C3×C5×#339C211yesmaximal, characteristic, complemented
5#11746378C211yesmaximal, characteristic, complemented
6#11746352C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10599530—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C4×#1220—22no—
14#91815C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C4×D60—21no—
18#91761C412yescomplemented
19C42×D15C412yescomplemented
20C4×Dic30—21no—
21#91108—21no—
22#91107—21no—
23#91090—22no—
24#68737—51nomaximal, Hall
25C4×#709—31no—
26#65421—31no—
27#65295—31no—
28C5×#339D311yescharacteristic, complemented
29#64777—31no—
30#64751—31no—
31#64743—31no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220D412yes—
35#6817—21no—
36#6817—21no—
37#6817—21no—
38#6817—21no—
39C2×D60D411yescharacteristic
40C2×C4×D15—22no—
41C2×C4×D15C2×C412yes—
42C2×Dic30D411yescharacteristic
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C3×C42×C5C2×C411yescharacteristic
51C3×C42×C5C2×C411yescharacteristic
52#6719—21no—
53#6719—21no—
54#6714—22no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57#6712—22no—
58C4×Dic15—22no—
59C4×Dic15—21no—
60C4×Dic15C2×C412yes—
61#6710—21no—
62#6710—21no—
63C2×C3⋊#168—21no—
64C4×#235—51no—
65#5132—51no—
66#5006—51no—
67C3×#339D511yescharacteristic, complemented
68#4557—51no—
69#4531—51no—
70#4523—51no—
71C2×#709—31no—
72C2×C5×M16C2×D311yescharacteristic
73C5×#117C2×D311yescharacteristic
74C2×C42×C5C2×D311yescharacteristic
75C4×C22⋊D5—62no—
76#4072—31no—
77#4072—31no—
78C2×#681—31no—
79C4×D20—61no—
80#4018—32no—
81C42×D5—32no—
82C4×Dic10—61no—
83#3956—61no—
84#3955—61no—
85#3938—62no—
86#1827—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×D15C22⋊C412yes—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99#1220—22no—
100#1220—22no—
101C2×Dic15—22no—
102C2×Dic15—41no—
103C2×Dic15C22⋊C412yes—
104D60—21no—
105D60—21no—
106C4×D15—22no—
107C4×D15—22no—
108C4×D15—44no—
109Dic30—21no—
110Dic30—21no—
111C3×C5×C8—41no—
112C3⋊#168—41no—
113C2×#235—51no—
114C2×C3×M16C2×D511yescharacteristic
115C3×#117C2×D511yescharacteristic
116C2×C3×C42C2×D511yescharacteristic
117C4×#67—102no—
118#926—51no—
119#926—51no—
120C2×#208—51no—
121C4×D12—101no—
122#872—52no—
123C42×D3—52no—
124C4×Dic6—101no—
125#824—101no—
126#823—101no—
127#806—102no—
128C22×C4×C5—21no—
129C22×C4×C5C22×D311yescharacteristic
130C2×C22⋊D5—32no—
131#709—61no—
132#709—61no—
133#709—61no—
134#709—61no—
135C2×D20—31no—
136C2×C4×D5—32no—
137C2×C4×D5—62no—
138C2×Dic10—31no—
139C5×M16—21no—
140C5×M16—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5—21no—
145C42×C5—21no—
146C42×C5C4×D311yescharacteristic
147C42×C5C4×D311yescharacteristic
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150#685—62no—
151C4⋊Dic5—61no—
152C4⋊Dic5—61no—
153#683—62no—
154C4×Dic5—32no—
155C4×Dic5—62no—
156C4×Dic5—61no—
157#681—61no—
158#681—61no—
159C2×#168—61no—
160C4×#41—151no—
161#413—151no—
162#410—151no—
163#339—151no—
164#339D1511yescharacteristic, complemented
165H(3,ℤ/4)—151no—
166H(3,ℤ/4)—151no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#12311yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C2×D15—22no—
172C2×D15—42no—
173C3×C4×C5—22no—
174C3×C4×C5—41no—
175C3×C4×C5—81no—
176C3×C4×C5#11711yescharacteristic
177C3×C4×C5#11711yescharacteristic
178C3×C4×C5#12311yescharacteristic
179C3×C4×C5#12311yescharacteristic
180Dic15—22no—
181Dic15—42no—
182Dic15—81no—
183C22×C3×C4—21no—
184C22×C3×C4C22×D511yescharacteristic
185C2×#67—52no—
186#235—101no—
187#235—101no—
188#235—101no—
189#235—101no—
190C2×D12—51no—
191C2×C4×D3—52no—
192C2×C4×D3—102no—
193C2×Dic6—51no—
194C3×M16—21no—
195C3×M16—21no—
196C2×C3×C8—21no—
197C3×C4⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42C4×D511yescharacteristic
202C3×C42C4×D511yescharacteristic
203#217—101no—
204#217—101no—
205(C2×D3)⋊C4—102no—
206C4⋊Dic3—101no—
207C4⋊Dic3—101no—
208Dic3⋊C4—102no—
209C4×Dic3—52no—
210C4×Dic3—102no—
211C4×Dic3—101no—
212#208—101no—
213#208—101no—
214C2×C3⋊C8—101no—
215C23×C5D3×D411yescharacteristic
216C22×D5—32no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5—42no—
220C2×C4×C5—41no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C2×C4×C5#23511yescharacteristic
223C2×C4×C5#23511yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5#23711yescharacteristic
226C2×C4×C5#23911yescharacteristic
227C22⋊D5—62no—
228C22⋊D5—62no—
229C2×Dic5—32no—
230C2×Dic5—62no—
231C2×Dic5—121no—
232D20—61no—
233D20—61no—
234C4×D5—62no—
235C4×D5—62no—
236C4×D5—124no—
237Dic10—61no—
238Dic10—61no—
239C5×C8—41no—
240#168—121no—
241C2×#41—151no—
242C2×M16—151no—
243C2×M16C2×D1511yescharacteristic
244C4×Q8—301no—
245C4×D4—301no—
246C4×D4—302no—
247#117—151no—
248#117—152no—
249#117—151no—
250#117C2×D1511yescharacteristic
251C2×C42—152no—
252C2×C42C2×D1511yescharacteristic
253#101—301no—
254#100—301no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#38111yescharacteristic
260D15—42no—
261C23×C3D4×D511yescharacteristic
262C22×D3—52no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—42no—
266C2×C3×C4—41no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4#70911yescharacteristic
269C2×C3×C4#70911yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4#71111yescharacteristic
272C2×C3×C4#71311yescharacteristic
273#67—102no—
274#67—102no—
275C2×Dic3—52no—
276C2×Dic3—102no—
277C2×Dic3—201no—
278D12—101no—
279D12—101no—
280C4×D3—102no—
281C4×D3—102no—
282C4×D3—204no—
283Dic6—101no—
284Dic6—101no—
285C3×C8—41no—
286C3⋊C8—201no—
287C22×C5—41no—
288C22×C5D3×C22⋊C411yescharacteristic
289C22×C5#88311yescharacteristic
290C22×C5#89411yescharacteristic
291C2×D5—62no—
292C2×D5—122no—
293C4×C5—22no—
294C4×C5—41no—
295C4×C5—81no—
296C4×C5#87211yescharacteristic
297C4×C5#88311yescharacteristic
298C4×C5#89211yescharacteristic
299C4×C5#89411yescharacteristic
300Dic5—62no—
301Dic5—122no—
302Dic5—241no—
303#41—301no—
304#41—301no—
305#41—301no—
306#41—301no—
307C2×Q8—151no—
308C2×D4—152no—
309C2×D4—151no—
310C22×C4—21no—
311C22×C4—152no—
312C22×C4—302no—
313C22×C4C22×D1511yescharacteristic
314M16—21no—
315M16—21no—
316M16—301no—
317M16—301no—
318C2×C8—21no—
319C2×C8—301no—
320C4⋊C4—21no—
321C4⋊C4—302no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C22⋊C4—21no—
325C22⋊C4—302no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—21no—
329C42—21no—
330C42—152no—
331C42—302no—
332C42—301no—
333C42C4×D1511yescharacteristic
334C42C4×D1511yescharacteristic
335C3×C5#182711yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3D5×C22⋊C411yescharacteristic
338C22×C3#402911yescharacteristic
339C22×C3#404011yescharacteristic
340C2×D3—102no—
341C2×D3—202no—
342C3×C4—22no—
343C3×C4—41no—
344C3×C4—81no—
345C3×C4#401811yescharacteristic
346C3×C4#402911yescharacteristic
347C3×C4#403811yescharacteristic
348C3×C4#404011yescharacteristic
349Dic3—102no—
350Dic3—202no—
351Dic3—401no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5#466411yescharacteristic
356D5—122no—
357C23—152no—
358C23D4×D1511yescharacteristic
359Q8—301no—
360Q8—301no—
361D4—302no—
362D4—302no—
363D4—301no—
364D4—301no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—152no—
370C2×C4—302no—
371C2×C4—302no—
372C2×C4—302no—
373C2×C4—604no—
374C2×C4—601no—
375C2×C4C2×C4×D1511yescharacteristic
376C2×C4#681711yescharacteristic
377C2×C4#681711yescharacteristic
378C2×C4D4×D1511yescharacteristic
379C2×C4#681911yescharacteristic
380C2×C4#682111yescharacteristic
381C8—41no—
382C8—601no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3#6495311yescharacteristic
387D3—202no—
388C5#6873711yescharacteristic, complemented, Sylow
389C22—41no—
390C22—302no—
391C22—602no—
392C22C22⋊C4×D1511yescharacteristic
393C22#9177211yescharacteristic
394C22#9178311yescharacteristic
395C4—22no—
396C4—41no—
397C4—81no—
398C4—302no—
399C4—602no—
400C4—1201no—
401C4#9176111yescharacteristic
402C4#9177211yescharacteristic
403C4#9178111yescharacteristic
404C4#9178311yescharacteristic
405C3#1059953011yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—602no—
410C2#1175076511yescharacteristic
subgroupG/H
centerC4#91781
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC2×C3×C5#381
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#339D15
hypocenterC3×C5#1827
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. C3×C5×#339C2semidirect
5. #11746378C2semidirect
6. #11746352C2semidirect
7. #11746344C2semidirect
18. #91761C4semidirect
19. C42×D15C4semidirect
28. C5×#339D3semidirect
67. C3×#339D5semidirect
164. #339D15semidirect
335. C3×C5#1827semidirect
388. C5#68737semidirect
405. C3#10599530semidirect

Maximal subgroups

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

subgroupindex
C4×#68172
#117512332
#117511072
C3×C5×#3392
#117463782
#117463522
#117463442
#105995303
#687375