Finite Group Databasebeta

← #14288071

Subgroups — #14288071

Order 1920.

488 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5515C211yesmaximal, characteristic
2#11751080C211yesmaximal, characteristic, complemented
3#11748565C211yesmaximal, characteristic, complemented
4#11748553C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic
8#10602682—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6712—21no—
12C5×#930C2211yescharacteristic
13C5×#929—21no—
14C4×C5×#67—21no—
15C5×#924C2211yescharacteristic
16C5×#898—21no—
17C5×#896—21no—
18C5×#894—21no—
19C5×#889—21no—
20C2×#6663—21no—
21C2×#6659—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90975—21no—
27#90975—21no—
28#68132—51nomaximal, Hall
29C5×#539—31no—
30#65339—31no—
31#65329—31no—
32#65268—31no—
33#64758—31no—
34#64757—31no—
35#64748D311yescharacteristic, complemented
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15—21no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×Dic30—42no—
44C2×C5×#67—21no—
45C2×C5×D12D411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C5×Dic6D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50#6712—42no—
51C5×#217—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×C4⋊Dic3D411yescharacteristic
57C5×C4⋊Dic3D411yescharacteristic
58C5×Dic3⋊C4—21no—
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C4×C5×Dic3—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65#6663—42no—
66#6659—42no—
67#5515D511yescharacteristic
68#4979—51no—
69#4739—51no—
70#4738—51no—
71C3×#324—51no—
72#4470—51no—
73#4467—51no—
74C22×Dic10—31no—
75C5×#126—61no—
76C5×#125—61no—
77C5×#123—61no—
78C5×#123—61no—
79C5×C22⋊Q8—31no—
80C5×C22⋊Q8—61no—
81C5×#121—31no—
82C4×C5×D4—61no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×#689—61no—
85C2×#687—61no—
86C2×#683—61no—
87#3963—31no—
88#3963—61no—
89C22⋊#168C2×D311yescharacteristic
90C22⋊#168C2×D311yescharacteristic
91#3942—61no—
92#3942—61no—
93#1603—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×Dic15—22no—
105C2×Dic15—22no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110Dic30—22no—
111Dic30—22no—
112Dic30—41no—
113Dic30—41no—
114C5×#67—41no—
115C5×#67—41no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—21no—
119C5×D12—41no—
120C4×C5×D3—81no—
121C5×Dic6—41no—
122C3×#168—41no—
123C3×#168—41no—
124C22×Dic6—51no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126#930C2×D511yescharacteristic
127#929—21no—
128C4×#67—21no—
129#924C2×D511yescharacteristic
130C2×Dic3⋊C4—101no—
131C2×Dic12—101no—
132C2×#204—101no—
133#898—21no—
134#896—21no—
135#894—21no—
136#889—21no—
137C3×C22⋊C8—51no—
138C3×C22⋊C8—51no—
139C3⋊#95—51no—
140C3⋊#95—101no—
141#816—101no—
142#816—101no—
143C2×C5×Q8—31no—
144C2×C5×D4—31no—
145C2×C5×D4—61no—
146C22×C4×C5—61no—
147C22×C4×C5D1211yescharacteristic
148C22×C4×C5D1211yescharacteristic
149C22×C4×C5C22×D311yescharacteristic
150C22×Dic5—61no—
151C22×Dic5—61no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—122no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—31no—
158C5×C4⋊C4—31no—
159C5×C4⋊C4—61no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4—61no—
162C5×C4⋊C4—61no—
163C5×C22⋊C4—61no—
164C5×C22⋊C4—61no—
165C5×C22⋊C4—61no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C42×C5—61no—
169#689—122no—
170#687—122no—
171#683—122no—
172C2×#168—21no—
173C2×#168—21no—
174#539—31no—
175#451—151no—
176#448—151no—
177#395—151no—
178#328—151no—
179#327—151no—
180#324—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5#12011yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5#13711yescharacteristic
186C2×C5×D3—41no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×C4×C5—41no—
193Dic15—42no—
194Dic15—42no—
195C5×Dic3—41no—
196C5×Dic3—41no—
197C5×Dic3—41no—
198C22×C3×C4C22⋊D511yescharacteristic
199C22×C3×C4C22⋊D511yescharacteristic
200C22×C3×C4C22×D511yescharacteristic
201C2×#67—21no—
202C22×Dic3—101no—
203C22×Dic3—101no—
204C2×D12C22⋊D511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6—101no—
207C2×Dic6—101no—
208C2×Dic6—202no—
209C2×Dic6C22⋊D511yescharacteristic
210C2×C3×C8—101no—
211C2×C3×C8—101no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214#217—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219C4⋊Dic3C22⋊D511yescharacteristic
220C4⋊Dic3C22⋊D511yescharacteristic
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—202no—
226C4×Dic3—21no—
227Dic12—202no—
228#204—202no—
229C23×C5—61no—
230C23×C5C2×D1211yescharacteristic
231C5×Q8—121no—
232C5×D4—121no—
233C5×D4—121no—
234C5×D4—121no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—241no—
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×Dic5—62no—
248C2×Dic5—62no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C2×Dic5—121no—
252C2×Dic5—121no—
253Dic10—62no—
254Dic10—62no—
255Dic10—121no—
256Dic10—121no—
257#168—41no—
258#168—41no—
259C22×Q8—151no—
260C2×Q16—301no—
261C2×SD16—301no—
262#126—61no—
263#125—61no—
264#123—61no—
265#123—61no—
266C22⋊Q8—31no—
267C22⋊Q8—61no—
268#121—31no—
269C4×D4—61no—
270C2×C4⋊C4—301no—
271C2×C4⋊C4D3×D511yescharacteristic
272#103—301no—
273#103—301no—
274C22⋊C8—51no—
275C22⋊C8—51no—
276#95—151no—
277#95—301no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5#45211yescharacteristic
281C2×C3×C5#45611yescharacteristic
282C2×C3×C5B(4,𝔽2)11yescharacteristic
283C5×D3—81no—
284C23×C3C2×C22⋊D511yescharacteristic
285C22×D3—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4C2×C22⋊D511yescharacteristic
293C2×C3×C4C2×C22⋊D511yescharacteristic
294#67—41no—
295#67—41no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—102no—
300C2×Dic3—102no—
301C2×Dic3—201no—
302C2×Dic3—201no—
303C2×Dic3—201no—
304C2×Dic3—201no—
305D12—41no—
306C4×D3—81no—
307Dic6—41no—
308Dic6—102no—
309Dic6—102no—
310Dic6—201no—
311Dic6—201no—
312C3×C8—201no—
313C3×C8—201no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—121no—
317C22×C5—121no—
318C22×C5—121no—
319C22×C5#88211yescharacteristic
320C22×C5#90411yescharacteristic
321C22×C5#90911yescharacteristic
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—41no—
325C4×C5—41no—
326C4×C5—121no—
327C4×C5—121no—
328C4×C5—121no—
329Dic5—122no—
330Dic5—122no—
331C2×Q8—31no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—602no—
335C2×D4—31no—
336C2×D4—61no—
337C22×C4—61no—
338C22×C4—301no—
339C22×C4—301no—
340C22×C4#120311yescharacteristic
341C22×C4#120311yescharacteristic
342C22×C4C2×D3×D511yescharacteristic
343Q16—602no—
344SD16—602no—
345C2×C8—101no—
346C2×C8—101no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—31no—
350C4⋊C4—31no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—602no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C42—61no—
362C3×C5#160311yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#409611yescharacteristic
366C22×C3#409711yescharacteristic
367C22×C3#409911yescharacteristic
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375Dic3—41no—
376Dic3—41no—
377Dic3—41no—
378Dic3—202no—
379Dic3—202no—
380C2×C5—21no—
381C2×C5—21no—
382C2×C5—241no—
383C2×C5#473311yescharacteristic
384C2×C5#474111yescharacteristic
385C2×C5#475211yescharacteristic
386C23—61no—
387C23C2×#120311yescharacteristic
388Q8—121no—
389Q8—302no—
390Q8—302no—
391Q8—601no—
392Q8—601no—
393D4—121no—
394D4—121no—
395D4—121no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—241no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—601no—
409C2×C4—601no—
410C2×C4—601no—
411C2×C4—601no—
412C2×C4D3×C22⋊D511yescharacteristic
413C2×C4D3×C22⋊D511yescharacteristic
414C8—201no—
415C8—201no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3#6552811yescharacteristic
419C2×C3#6553311yescharacteristic
420C2×C3#6553511yescharacteristic
421D3—81no—
422C5#6813211yescharacteristic, complemented, Sylow
423C22—21no—
424C22—21no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22#9130311yescharacteristic
429C22#9132211yescharacteristic
430C22#9157011yescharacteristic
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—121no—
436C4—121no—
437C4—121no—
438C4—602no—
439C4—602no—
440C3#1060268211yescharacteristic, complemented, Sylow
441C2—21no—
442C2—21no—
443C2—241no—
444C2#1174836111yescharacteristic
445C2#1174917811yescharacteristic
446C2#1174939411yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC5×#930C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1603
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751080C2semidirect
3. #11748565C2semidirect
5. C3×#64748C2semidirect
6. #11745963C2semidirect
35. #64748D3semidirect
362. C3×C5#1603semidirect
422. C5#68132semidirect
440. C3#10602682semidirect

Maximal subgroups

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

subgroupindex
C5×#55152
#117510802
#117485652
#117485532
C3×#647482
#117459632
#117459572
#106026823
#681325