Finite Group Databasebeta

← #14288652

Subgroups — #14288652

Order 1920.

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

normal subgroups only

This group has 416 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×#5645C211yesmaximal, characteristic
2C3×#65333C211yesmaximal, characteristic, complemented
3#11748622C211yesmaximal, characteristic, complemented
4#11748385C211yesmaximal, characteristic
5#11746359C211yesmaximal, characteristic, complemented
6#11745957C211yesmaximal, characteristic
7#11745952C211yesmaximal, characteristic, complemented
8#10602680—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#930C2211yescharacteristic
12C2×C5×Dic3⋊C4C2211yescharacteristic
13C5×#898—21no—
14C5×#894—21no—
15C5×#890—21no—
16C5×#886—21no—
17C5×#67⋊C4—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19#91115C2211yescharacteristic
20#91114C2211yescharacteristic
21C3×#3967—21no—
22C3×C22⋊#168C2211yescharacteristic
23C3×#3939—21no—
24#90994—21no—
25#90994—21no—
26#90986—21no—
27#90966—21no—
28#71178—51nomaximal, Hall
29C5×#539—31no—
30#65333D311yescharacteristic, complemented
31#65323—31no—
32#65275—31no—
33#64758—31no—
34#64757—31no—
35#64748—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×C5×#67—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C5×D12D411yescharacteristic
43C2×C4×C5×D3—21no—
44C22×C3×Dic5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C4×C5×Dic3—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63#5645D511yescharacteristic
64C3×#484—51no—
65#4985—51no—
66#4968—51no—
67#4538—51no—
68#4470—51no—
69#4469—51no—
70C5×#126—61no—
71C5×#125—61no—
72C5×#123—61no—
73C5×#123—61no—
74C5×C22⋊Q8—61no—
75C5×C22⋊Q8C2×D311yescharacteristic
76C5×#121—31no—
77C4×C5×D4—61no—
78C2×C5×C4⋊C4—31no—
79C2×C4⋊Dic5C2×D311yescharacteristic
80#3967—21no—
81#3964—61no—
82#3963—31no—
83#3963—61no—
84#3963—61no—
85C22⋊#168—31no—
86C22⋊#168C2×D311yescharacteristic
87#3940—61no—
88#3939—21no—
89#1615—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×C5×D3—21no—
92C3×C5×Q8—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—41no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101C5×#67—41no—
102C5×#67—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—41no—
109C5×D12—41no—
110C4×C5×D3—81no—
111C2×C3×Dic5—42no—
112C2×C3×Dic5—41no—
113C3⋊#168—41no—
114C3×#168—41no—
115C3×C22⋊Q8C2×D511yescharacteristic
116C2×C3×C4⋊C4—51no—
117#946—21no—
118#930C2×D511yescharacteristic
119C2×Dic3⋊C4C2×D511yescharacteristic
120#898—21no—
121#894—21no—
122#890—21no—
123#886—21no—
124#67⋊C4—21no—
125C3×#107—101no—
126C3×#103—101no—
127C3×C22⋊C8—51no—
128C3⋊#95—51no—
129C3⋊#95—101no—
130C3⋊#95—101no—
131#830—51no—
132#809—101no—
133#808—101no—
134C2×C5×Q8#6711yescharacteristic
135C2×C5×D4—31no—
136C2×C5×D4—61no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—21no—
142C22×Dic5—61no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—31no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4#6711yescharacteristic
151C5×C22⋊C4—21no—
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C42×C5—61no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C2×#168—21no—
160C2×#168—61no—
161#539—31no—
162#484—51no—
163#481—151no—
164#400—151no—
165#328—151no—
166#327—151no—
167#324—151no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5#13511yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180Dic15—81no—
181C3×Dic5—81no—
182C5×Dic3—41no—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C2×C3×Q8C22⋊D511yescharacteristic
186C22×C3×C4—101no—
187C22×C3×C4C22×D511yescharacteristic
188C2×#67—21no—
189C22×Dic3—101no—
190C22×Dic3C22⋊D511yescharacteristic
191C22×Dic3C22⋊D511yescharacteristic
192C2×D12C22⋊D511yescharacteristic
193C2×C4×D3—21no—
194C2×C3×C8—101no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4C22⋊D511yescharacteristic
199C3×C22⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3C22⋊D511yescharacteristic
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—21no—
210C4×Dic3—21no—
211C2×C3⋊C8—101no—
212C23×C5—61no—
213C23×C5D3×D411yescharacteristic
214C5×Q8—41no—
215C5×D4—121no—
216C5×D4—121no—
217C5×D4—121no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—41no—
221C2×C4×C5—61no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—121no—
227C2×C4×C5—241no—
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C2×Dic5—42no—
231C2×Dic5—41no—
232C2×Dic5—121no—
233C2×Dic5—121no—
234C2×Dic5—121no—
235#168—41no—
236#168—121no—
237#126—61no—
238#125—61no—
239#123—61no—
240#123—61no—
241C22⋊Q8—61no—
242C22⋊Q8D3×D511yescharacteristic
243#121—31no—
244C4×D4—61no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—51no—
247#107—101no—
248#106—301no—
249#103—101no—
250#102—301no—
251C22⋊C8—51no—
252C22⋊C8—151no—
253#95—151no—
254#95—301no—
255#95—301no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5#45211yescharacteristic
259C2×C3×C5#45411yescharacteristic
260C2×C3×C5#45811yescharacteristic
261C5×D3—81no—
262C23×C3C2×C22⋊D511yescharacteristic
263C22×D3—21no—
264C3×Q8—41no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—41no—
268C2×C3×C4—202no—
269C2×C3×C4—201no—
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272#67—41no—
273#67—41no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280C2×Dic3—201no—
281C2×Dic3—201no—
282C2×Dic3—201no—
283D12—41no—
284C4×D3—81no—
285C3×C8—201no—
286C3⋊C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—121no—
290C22×C5—121no—
291C22×C5—121no—
292C22×C5#91811yescharacteristic
293C22×C5#91911yescharacteristic
294C22×C5#93711yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—121no—
300C4×C5—121no—
301C4×C5—121no—
302Dic5—81no—
303Dic5—241no—
304C2×Q8#120111yescharacteristic
305C2×D4—31no—
306C2×D4—61no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—61no—
310C22×C4—101no—
311C22×C4—301no—
312C22×C4C2×D3×D511yescharacteristic
313C2×C8—101no—
314C2×C8—301no—
315C4⋊C4—21no—
316C4⋊C4—31no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—101no—
323C4⋊C4—101no—
324C4⋊C4#120111yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4—61no—
329C22⋊C4—61no—
330C42—61no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3#409611yescharacteristic
335C22×C3#409711yescharacteristic
336C22×C3#409911yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—401no—
345Dic3—41no—
346Dic3—41no—
347Dic3—41no—
348Dic3—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—241no—
352C2×C5#505311yescharacteristic
353C2×C5#518711yescharacteristic
354C2×C5#520111yescharacteristic
355C23—61no—
356C23D3×C22⋊D511yescharacteristic
357Q8—41no—
358D4—121no—
359D4—121no—
360D4—121no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—61no—
369C2×C4—121no—
370C2×C4—202no—
371C2×C4—201no—
372C2×C4—241no—
373C2×C4—601no—
374C2×C4—601no—
375C2×C4—601no—
376C2×C4C2×#120111yescharacteristic
377C2×C4D3×C22⋊D511yescharacteristic
378C8—201no—
379C8—601no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6552811yescharacteristic
383C2×C3#6553211yescharacteristic
384C2×C3#6553411yescharacteristic
385D3—81no—
386C5#7117811yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—121no—
390C22—121no—
391C22—121no—
392C22#9151011yescharacteristic
393C22#9151911yescharacteristic
394C22#9156811yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—121no—
400C4—121no—
401C4—121no—
402C4—401no—
403C4—1201no—
404C3#1060268011yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—241no—
408C2#1174918311yescharacteristic
409C2#1174930511yescharacteristic
410C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5#120
prime radicalC5×#930C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65333C2semidirect
3. #11748622C2semidirect
5. #11746359C2semidirect
7. #11745952C2semidirect
30. #65333D3semidirect
331. C3×C5#1615semidirect
386. C5#71178semidirect
404. C3#10602680semidirect

Maximal subgroups

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

subgroupindex
C5×#56452
C3×#653332
#117486222
#117483852
#117463592
#117459572
#117459522
#106026803
#711785