Finite Group Databasebeta

← #14301604

Subgroups — #14301604

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#875C211yesmaximal, characteristic
2#11754211C211yesmaximal, characteristic, complemented
3#11748389C211yesmaximal, characteristic
4#11748386C211yesmaximal, characteristic
5C2×#90962C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10602517—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—22no—
15C5×#875—22no—
16C5×#875C414yescomplemented
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91529—22no—
20#91344—22no—
21Dic5×Dic6—22no—
22#90967—22no—
23#90966—22no—
24#90962—22no—
25#68766—51nomaximal, Hall
26C2×C5×#124—31no—
27#66146—31no—
28C2×#3968—31no—
29#65504—31no—
30#65504—31no—
31#64743—31no—
32#64743D311yescharacteristic, complemented
33C23×C5×D3—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C5×Dic3D412yes—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12C2×C412yes—
43C2×C5×Dic6—21no—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6C2×C412yes—
48C2×C5×Dic6D412yes—
49C3×C42×C5—21no—
50C3×C42×C5C2×C412yes—
51#6719—21no—
52C4⋊Dic15D412yes—
53C4×Dic15—21no—
54#6710—21no—
55#6710—21no—
56C2×C3⋊#168—21no—
57C5×(C2×D3)⋊C4—28no—
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5D412yes—
60C3×C4×Dic5—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64Dic3⋊Dic5—24no—
65Dic3×Dic5—24no—
66#5516—51no—
67C2×#875D511yescharacteristic
68C2×#824—51no—
69#5131—51no—
70#5001—51no—
71C3×#339—51no—
72#4523—51no—
73C22×C5×Q8—31no—
74C22×C5×D4—31no—
75C5×#124—34no—
76C5×#124—62no—
77C2×C5×C22⋊C4—62no—
78C2×C42×C5C2×D311yescharacteristic
79Q8×Dic5—62no—
80Q8×Dic5—62no—
81#4072—31no—
82#4072—62no—
83#4072C2×D311yescharacteristic
84C2×#681—31no—
85C2×#681C2×D311yescharacteristic
86#3968—62no—
87#3964—62no—
88#3964—62no—
89#1888—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C5×D3—22no—
92C22×C5×D3—44no—
93C22×C5×D3—41no—
94C22×C5×D3—41no—
95C2×C3×C4×C5—22no—
96C2×C3×C4×C5—42no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3C22⋊C414yes—
107C5×D12—22no—
108C5×D12—22no—
109C5×D12—41no—
110C5×D12—41no—
111C5×Dic6—22no—
112C5×Dic6—22no—
113C5×Dic6—22no—
114C5×Dic6—22no—
115C2×C3×Dic5—22no—
116C3⋊#168—41no—
117C3×#168—41no—
118C22×D12C2×D511yescharacteristic
119C22×Dic6C2×D511yescharacteristic
120C2×C3×M16—51no—
121C3×#117—51no—
122C2×C3×C42C2×D511yescharacteristic
123C2×(C2×D3)⋊C4—22no—
124#926—51no—
125C2×#208—51no—
126#887—102no—
127#877—102no—
128#875—22no—
129#875Dic514yescomplemented
130C4×Dic6—102no—
131#824—102no—
132#821—102no—
133#809—102no—
134C24×C5—61no—
135C2×C5×Q8—32no—
136C2×C5×Q8—32no—
137C2×C5×Q8—61no—
138C2×C5×Q8—61no—
139C2×C5×Q8—61no—
140C2×C5×Q8—61no—
141C2×C5×D4—32no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C2×C5×D4—61no—
145C2×C5×D4—61no—
146C2×C5×D4—61no—
147C22×C4×C5—21no—
148C22×C4×C5—32no—
149C22×C4×C5C22×D311yescharacteristic
150C5×C22⋊C4—68no—
151C42×C5—21no—
152C42×C5C4×D312yes—
153C22⋊Dic5—21no—
154C22⋊Dic5—61no—
155C4⋊Dic5—32no—
156C4⋊Dic5—64no—
157C4⋊Dic5D1212yes—
158C4×Dic5—21no—
159C4×Dic5—64no—
160C4×Dic5—61no—
161#681—21no—
162#681—21no—
163#681—61no—
164#681—61no—
165C2×#168—21no—
166C2×#168—61no—
167C2×#124—31no—
168#519—151no—
169#418—151no—
170#418—151no—
171C2×#101—151no—
172#339—51no—
173#339—151no—
174C22×C3×C5—22no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C2×C5×D3—44no—
179C2×C5×D3—42no—
180C2×C5×D3—82no—
181C2×C5×D3—82no—
182C3×C4×C5—42no—
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5#12111yescharacteristic
186C3×C4×C5#12111yescharacteristic
187Dic15—42no—
188C3×Dic5—42no—
189C5×Dic3—24no—
190C23×D3—21no—
191C22×C3×C4—21no—
192C22×C3×C4C22×D511yescharacteristic
193C22×Dic3C22⋊D512yes—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C2×Dic512yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6C2×Dic512yes—
205C2×Dic6C22⋊D512yes—
206C3×M16—101no—
207C3×M16—101no—
208C2×C3×C8—101no—
209C3×C4⋊C4—52no—
210C3×C22⋊C4—101no—
211C3×C42—21no—
212C3×C42—101no—
213C3×C42C2×Dic512yes—
214#217—101no—
215(C2×D3)⋊C4—28no—
216C4⋊Dic3—52no—
217Dic3⋊C4—104no—
218C4×Dic3—104no—
219C4×Dic3—101no—
220#208—101no—
221#208—101no—
222C2×C3⋊C8—101no—
223C23×C5—62no—
224C23×C5—124no—
225C23×C5—121no—
226C23×C5—121no—
227C23×C5D3×D411yescharacteristic
228C5×Q8—62no—
229C5×Q8—62no—
230C5×Q8—62no—
231C5×Q8—62no—
232C5×D4—62no—
233C5×D4—62no—
234C5×D4—121no—
235C5×D4—121no—
236C2×C4×C5—22no—
237C2×C4×C5—34no—
238C2×C4×C5—42no—
239C2×C4×C5—62no—
240C2×C4×C5—62no—
241C2×C4×C5C2×C4×D311yescharacteristic
242C2×C4×C5C2×D1211yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23911yescharacteristic
247C2×Dic5—22no—
248C2×Dic5—62no—
249#168—41no—
250#168—121no—
251C22×Q8—31no—
252C22×D4—31no—
253C2×M16—51no—
254C2×M16—151no—
255#124—34no—
256#124—62no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—51no—
260#117—151no—
261#117—302no—
262C2×C22⋊C4—62no—
263C2×C42D3×D511yescharacteristic
264#102—302no—
265#102—302no—
266#101—302no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#38611yescharacteristic
270C2×C3×C5#45412yes—
271C5×D3—82no—
272C23×C3C2×C22⋊D511yescharacteristic
273C22×D3—22no—
274C22×D3—44no—
275C22×D3—41no—
276C22×D3—41no—
277C2×C3×C4—22no—
278C2×C3×C4—42no—
279C2×C3×C4—102no—
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×C3×C4#71111yescharacteristic
283C2×C3×C4#71111yescharacteristic
284C2×C3×C4C22×Dic511yescharacteristic
285C2×C3×C4C2×C22⋊D511yescharacteristic
286C2×Dic3—22no—
287C2×Dic3—22no—
288C2×Dic3—102no—
289C2×Dic3C22⋊Dic514yes—
290D12—22no—
291D12—22no—
292D12—41no—
293D12—41no—
294Dic6—22no—
295Dic6—22no—
296Dic6—22no—
297Dic6—22no—
298C3×C8—201no—
299C3⋊C8—201no—
300C22×C5—22no—
301C22×C5—124no—
302C22×C5—122no—
303C22×C5—242no—
304C22×C5—242no—
305C22×C5D3×C22⋊C411yescharacteristic
306C22×C5#88211yescharacteristic
307C22×C5#89411yescharacteristic
308C4×C5—42no—
309C4×C5—64no—
310C4×C5C4×D1211yescharacteristic
311C4×C5#88411yescharacteristic
312C4×C5#89311yescharacteristic
313C4×C5#89511yescharacteristic
314Dic5—42no—
315Dic5—122no—
316C24—61no—
317C2×Q8—32no—
318C2×Q8—32no—
319C2×Q8—61no—
320C2×Q8—61no—
321C2×Q8—61no—
322C2×Q8—61no—
323C2×D4—32no—
324C2×D4—61no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—61no—
328C2×D4—61no—
329C22×C4—21no—
330C22×C4—32no—
331C22×C4C2×D3×D511yescharacteristic
332M16—101no—
333M16—101no—
334M16—301no—
335M16—301no—
336C2×C8—101no—
337C2×C8—301no—
338C4⋊C4—52no—
339C4⋊C4—152no—
340C4⋊C4—304no—
341C22⋊C4—68no—
342C22⋊C4—101no—
343C22⋊C4—301no—
344C42—21no—
345C42—101no—
346C42—304no—
347C42—301no—
348C42D3×Dic512yes—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3#408111yescharacteristic
352C22×C3#408311yescharacteristic
353C22×C3C2×C22⋊Dic511yescharacteristic
354C2×D3—44no—
355C2×D3—42no—
356C2×D3—82no—
357C2×D3—82no—
358C3×C4—42no—
359C3×C4—202no—
360C3×C4D4×Dic511yescharacteristic
361C3×C4D4×Dic511yescharacteristic
362C3×C4#408511yescharacteristic
363C3×C4#408511yescharacteristic
364Dic3—24no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5—242no—
369C2×C5#466511yescharacteristic
370C2×C5#482712yes—
371C23—62no—
372C23—124no—
373C23—121no—
374C23—121no—
375C23D3×C22⋊D511yescharacteristic
376Q8—62no—
377Q8—62no—
378Q8—62no—
379Q8—62no—
380D4—62no—
381D4—62no—
382D4—121no—
383D4—121no—
384C2×C4—22no—
385C2×C4—34no—
386C2×C4—42no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—102no—
390C2×C4—302no—
391C2×C4#676811yescharacteristic
392C2×C4#677211yescharacteristic
393C2×C4D5×D1211yescharacteristic
394C2×C4#677711yescharacteristic
395C2×C4C2×D3×Dic511yescharacteristic
396C2×C4D3×C22⋊D511yescharacteristic
397C8—201no—
398C8—601no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3#6535112yes—
402C2×C3#6550911yescharacteristic
403D3—82no—
404C5#6876611yescharacteristic, complemented, Sylow
405C22—22no—
406C22—124no—
407C22—122no—
408C22—242no—
409C22—242no—
410C22#9142311yescharacteristic
411C22#9147511yescharacteristic
412C22D3×C22⋊Dic511yescharacteristic
413C4—42no—
414C4—64no—
415C4—202no—
416C4—602no—
417C4Dic5×D1211yescharacteristic
418C4#9141611yescharacteristic
419C4#9143511yescharacteristic
420C4#9145311yescharacteristic
421C3#1060251711yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—242no—
425C2#1174712312yes—
426C2#1174890111yescharacteristic
subgroupG/H
centerC22#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11754211C2semidirect
5. C2×#90962C2semidirect
6. #11746344C2semidirect
7. C3×#64743C2semidirect
16. C5×#875C4semidirect
32. #64743D3semidirect
129. #875Dic5semidirect
349. C3×C5#1888semidirect
404. C5#68766semidirect
421. C3#10602517semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8752
#117542112
#117483892
#117483862
C2×#909622
#117463442
C3×#647432
#106025173
#687665