Finite Group Databasebeta

← #14301581

Subgroups — #14301581

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×#91370C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3C5×#5131C211yesmaximal, characteristic
4C2×C3×#3956C211yesmaximal, characteristic, complemented
5#11748389C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10601118—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C2×(C2×D3)⋊Dic5—22no—
17#91528—22no—
18#91370—22no—
19#91370C414yescomplemented
20#91331—22no—
21Dic3×Dic10—22no—
22C5×#821—22no—
23C3×#3956—22no—
24#90967—22no—
25#70104—51nomaximal, Hall
26C2×#4082—31no—
27#65850—31no—
28C5×#418—31no—
29#65504—31no—
30C2×#3956D311yescharacteristic, complemented
31#64775—31no—
32#64752—31no—
33C23×C5×D3—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12C2×C412yes—
42C22×C3×Dic5D412yes—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C412yes—
48C2×C3×Dic10D412yes—
49C3×C5×M16—21no—
50C3×C5×M16—21no—
51C2×C3×C5×C8—21no—
52#6719—21no—
53C4⋊Dic15D412yes—
54C4×Dic15—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C412yes—
57C5×#217—21no—
58C5×C4⋊Dic3D412yes—
59C4×C5×Dic3—21no—
60C3×#681—21no—
61C3×#681—21no—
62C2×C3×#168—21no—
63#6668—24no—
64(C2×D3)⋊Dic5—28no—
65Dic3×Dic5—24no—
66C2×#947—51no—
67#5812—51no—
68C2×C3×#101—51no—
69#5131—51no—
70#5131D511yescharacteristic
71#4555—51no—
72#4555—51no—
73C22×C5×D4—31no—
74C22×Dic10C2×D311yescharacteristic
75C2×C5×M16C2×D311yescharacteristic
76C5×#117—31no—
77C2×C22⋊Dic5—62no—
78#4082—34no—
79#4082—62no—
80#4072—31no—
81C2×C4×Dic5—31no—
82C2×#681C2×D311yescharacteristic
83#4033—62no—
84#4023—62no—
85C4×Dic10—62no—
86C5×#102—62no—
87#3964—62no—
88#3956—22no—
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×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×Dic15—22no—
102C2×Dic15—22no—
103C2×Dic15—42no—
104C2×C5×Dic3—22no—
105C5×D12—22no—
106C5×D12—22no—
107C5×D12—41no—
108C5×D12—41no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5C22⋊C414yes—
112C3×Dic10—22no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3×C5×C8—41no—
117C3×#168—41no—
118C22×C3×Q8—51no—
119C22×D12C2×D511yescharacteristic
120C2×C3×M16—51no—
121C2×C3×M16C2×D511yescharacteristic
122#947—54no—
123#947—102no—
124Q8×Dic3—102no—
125Q8×Dic3—102no—
126C2×(C2×D3)⋊C4—102no—
127#926—51no—
128#926—102no—
129#926C2×D511yescharacteristic
130C2×C4×Dic3—51no—
131C3×#101—102no—
132#821—22no—
133#821—102no—
134C24×C5—61no—
135C2×C5×D4—32no—
136C2×C5×D4—61no—
137C2×C5×D4—61no—
138C2×C5×D4—61no—
139C2×C5×D4—61no—
140C2×C5×D4—61no—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—61no—
143C22×Dic5D1212yes—
144C2×Dic10—21no—
145C2×Dic10—21no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10C4×D312yes—
149C2×Dic10#6712yes—
150C5×M16—21no—
151C5×M16—21no—
152C2×C5×C8—21no—
153C5×C4⋊C4—32no—
154C5×C22⋊C4—61no—
155C42×C5—61no—
156C22⋊Dic5—61no—
157C22⋊Dic5—68no—
158C4⋊Dic5—32no—
159#683—64no—
160C4×Dic5—32no—
161C4×Dic5—64no—
162C4×Dic5—61no—
163C4×Dic5—61no—
164#681—21no—
165#681—21no—
166C2×#168—21no—
167C2×#124—151no—
168#519—151no—
169#418—31no—
170#418—151no—
171C2×#101—51no—
172#339—151no—
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×C5C4×D411yescharacteristic
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5#12111yescharacteristic
185C3×C4×C5#12111yescharacteristic
186Dic15—42no—
187Dic15—42no—
188C3×Dic5—24no—
189C5×Dic3—42no—
190C23×D3—21no—
191C2×C3×Q8—52no—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C22×C3×C4—52no—
198C22×C3×C4C22×D511yescharacteristic
199C22×Dic3—101no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12C4×D512yes—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—21no—
211C2×C3×C8—101no—
212#217—21no—
213#217—101no—
214(C2×D3)⋊C4—108no—
215C4⋊Dic3—52no—
216C4⋊Dic3—104no—
217C4⋊Dic3C22⋊D512yes—
218C4×Dic3—21no—
219C4×Dic3—52no—
220C4×Dic3—104no—
221C4×Dic3—101no—
222C4×Dic3—101no—
223C23×C5—62no—
224C23×C5—124no—
225C23×C5—121no—
226C23×C5—121no—
227C23×C5C2×D1211yescharacteristic
228C5×D4—62no—
229C5×D4—62no—
230C5×D4—121no—
231C5×D4—121no—
232C2×C4×C5—62no—
233C2×C4×C5C2×C4×D311yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×C4×C5D3×D411yescharacteristic
236C2×C4×C5#23711yescharacteristic
237C2×C4×C5#23711yescharacteristic
238C2×C4×C5C2×#6711yescharacteristic
239C2×Dic5—22no—
240C2×Dic5—22no—
241C2×Dic5—62no—
242C2×Dic5—62no—
243C2×Dic5—122no—
244C2×Dic5(C2×D3)⋊C414yes—
245Dic10—22no—
246Dic10—22no—
247Dic10—22no—
248Dic10—22no—
249C5×C8—41no—
250#168—41no—
251C22×Q8—51no—
252C22×D4—31no—
253C2×M16—51no—
254C2×M16D3×D511yescharacteristic
255#124—154no—
256#124—302no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—31no—
260#117—151no—
261#117—302no—
262C2×C22⋊C4—302no—
263C2×C42—151no—
264#102—62no—
265#102—302no—
266#101—102no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#38611yescharacteristic
270C2×C3×C5#45412yes—
271C5×D3—82no—
272C23×C3D4×D511yescharacteristic
273C22×D3—22no—
274C22×D3—44no—
275C22×D3—41no—
276C22×D3—41no—
277C3×Q8—102no—
278C3×Q8—102no—
279C3×Q8—102no—
280C3×Q8—102no—
281C2×C3×C4—54no—
282C2×C3×C4—102no—
283C2×C3×C4—102no—
284C2×C3×C4C2×C4×D511yescharacteristic
285C2×C3×C4#70911yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4#71111yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290C2×Dic3—22no—
291C2×Dic3—102no—
292C2×Dic3—102no—
293C2×Dic3—202no—
294D12—22no—
295D12—22no—
296D12—41no—
297D12—41no—
298C3×C8—41no—
299C3×C8—201no—
300C22×C5—22no—
301C22×C5—124no—
302C22×C5—122no—
303C22×C5—242no—
304C22×C5—242no—
305C22×C5#88211yescharacteristic
306C22×C5#88611yescharacteristic
307C22×C5C2×(C2×D3)⋊C411yescharacteristic
308C4×C5—122no—
309C4×C5#67⋊C411yescharacteristic
310C4×C5#67⋊C411yescharacteristic
311C4×C5#93911yescharacteristic
312C4×C5#93911yescharacteristic
313Dic5—24no—
314Dic5—122no—
315Dic5—122no—
316C24—61no—
317C2×Q8—52no—
318C2×Q8—52no—
319C2×Q8—101no—
320C2×Q8—101no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×D4—32no—
324C2×D4—61no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—61no—
328C2×D4—61no—
329C22×C4—52no—
330C22×C4—301no—
331C22×C4C2×D3×D511yescharacteristic
332M16—21no—
333M16—21no—
334M16—101no—
335M16—101no—
336C2×C8—21no—
337C2×C8—101no—
338C4⋊C4—32no—
339C4⋊C4—152no—
340C4⋊C4—304no—
341C22⋊C4—61no—
342C22⋊C4—308no—
343C22⋊C4—301no—
344C42—61no—
345C42—152no—
346C42—304no—
347C42—301no—
348C42—301no—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3D5×C22⋊C411yescharacteristic
352C22×C3#402911yescharacteristic
353C22×C3#408311yescharacteristic
354C2×D3—44no—
355C2×D3—42no—
356C2×D3—82no—
357C2×D3—82no—
358C3×C4—104no—
359C3×C4#402711yescharacteristic
360C3×C4#403011yescharacteristic
361C3×C4C4×C22⋊D511yescharacteristic
362C3×C4#408411yescharacteristic
363Dic3—42no—
364Dic3—202no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5—242no—
369C2×C5#475312yes—
370C2×C5#495811yescharacteristic
371C23—62no—
372C23—124no—
373C23—121no—
374C23—121no—
375C23D5×D1211yescharacteristic
376Q8—102no—
377Q8—102no—
378Q8—102no—
379Q8—102no—
380D4—62no—
381D4—62no—
382D4—121no—
383D4—121no—
384C2×C4—54no—
385C2×C4—62no—
386C2×C4—102no—
387C2×C4—102no—
388C2×C4—302no—
389C2×C4—302no—
390C2×C4—602no—
391C2×C4#676511yescharacteristic
392C2×C4C4×D3×D511yescharacteristic
393C2×C4#677711yescharacteristic
394C2×C4#678011yescharacteristic
395C2×C4D5×#6711yescharacteristic
396C2×C4D3×C22⋊D511yescharacteristic
397C8—41no—
398C8—201no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3#6524511yescharacteristic
402C2×C3#6549012yes—
403D3—82no—
404C5#7010411yescharacteristic, complemented, Sylow
405C22—22no—
406C22—124no—
407C22—122no—
408C22—242no—
409C22—242no—
410C22#9141411yescharacteristic
411C22D5×(C2×D3)⋊C411yescharacteristic
412C22#9147511yescharacteristic
413C4—104no—
414C4—122no—
415C4—602no—
416C4—602no—
417C4#9140811yescharacteristic
418C4#9144111yescharacteristic
419C4#9144211yescharacteristic
420C4#9154911yescharacteristic
421C3#1060111811yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—242no—
425C2#1174825912yes—
426C2#1174890611yescharacteristic
subgroupG/H
centerC22#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
4. C2×C3×#3956C2semidirect
6. #11746376C2semidirect
7. #11745975C2semidirect
19. #91370C4semidirect
30. C2×#3956D3semidirect
349. C3×C5#1888semidirect
404. C5#70104semidirect
421. C3#10601118semidirect

Maximal subgroups

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

subgroupindex
C2×#913702
#117541882
C5×#51312
C2×C3×#39562
#117483892
#117463762
#117459752
#106011183
#701045