Finite Group Databasebeta

← #14288616

Subgroups — #14288616

Order 1920.

416 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#11756274C211yesmaximal, characteristic
2#11751087C211yesmaximal, characteristic, complemented
3#11750836C211yesmaximal, characteristic
4#11750823C211yesmaximal, characteristic, complemented
5C3×C5×#324C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic
7#11746288C211yesmaximal, characteristic, complemented
8#10598929—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10#91819C2211yescharacteristic
11#91818—21no—
12C4×#1220—21no—
13C2×C4⋊Dic15C2211yescharacteristic
14#91813C2211yescharacteristic
15#91787—21no—
16#91785—21no—
17#91783—21no—
18#91778—21no—
19C3×C5×C22⋊C8C2211yescharacteristic
20C3×C5×C22⋊C8C2211yescharacteristic
21#91115—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24#91105—21no—
25#91102—21no—
26#91101—21no—
27#91100—21no—
28#68136—51nomaximal, Hall
29#65849—31no—
30#65275—31no—
31#65024—31no—
32#65011—31no—
33C5×#324D311yescharacteristic, complemented
34#64690—31no—
35#64687—31no—
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C22×Dic15—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49#6719—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C4⋊Dic15D411yescharacteristic
57C4⋊Dic15D411yescharacteristic
58#6712—21no—
59#6712—21no—
60#6712—21no—
61#6712—21no—
62C4×Dic15—21no—
63#5515—51no—
64#4986—51no—
65#4735—51no—
66#4722—51no—
67C3×#324D511yescharacteristic, complemented
68#4470—51no—
69#4467—51no—
70C2×C5×C4⋊C4C2×D311yescharacteristic
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74C2×C4⋊Dic5—31no—
75#4070—31no—
76#4044—61no—
77#4042—61no—
78#4040—61no—
79#4035—61no—
80C5×C22⋊C8C2×D311yescharacteristic
81C5×C22⋊C8C2×D311yescharacteristic
82#3963—31no—
83#3963—61no—
84#3963—61no—
85#3953—61no—
86#3950—61no—
87#3949—61no—
88#3948—61no—
89#1615—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×D15—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—41no—
101#1220—41no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×Dic15—42no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110D60—41no—
111C4×D15—81no—
112Dic30—41no—
113C3×C5×C8—41no—
114C3×C5×C8—41no—
115C2×C3×C4⋊C4C2×D511yescharacteristic
116#930—51no—
117#929—101no—
118C4×#67—101no—
119C2×C4⋊Dic3—51no—
120#924—51no—
121#898—101no—
122#896—101no—
123#894—101no—
124#889—101no—
125C3×C22⋊C8C2×D511yescharacteristic
126C3×C22⋊C8C2×D511yescharacteristic
127C3⋊#95—51no—
128C3⋊#95—101no—
129C3⋊#95—101no—
130#821—101no—
131#818—101no—
132#817—101no—
133#816—101no—
134C22×C4×C5D1211yescharacteristic
135C22×C4×C5D1211yescharacteristic
136C22×C4×C5C22×D311yescharacteristic
137C2×C22⋊D5—61no—
138C22×Dic5—61no—
139C22×Dic5—61no—
140C2×D20—31no—
141C2×C4×D5—61no—
142C2×Dic10—31no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C22⋊Dic5—61no—
148#685—61no—
149#685—61no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156#683—61no—
157#683—61no—
158#683—61no—
159#683—61no—
160C4×Dic5—61no—
161#539—151no—
162#484—151no—
163#481—151no—
164#400—151no—
165#328—151no—
166#327—151no—
167#324D1511yescharacteristic, complemented
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5#13511yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180Dic15—41no—
181Dic15—41no—
182Dic15—41no—
183Dic15—81no—
184Dic15—81no—
185C22×C3×C4D2011yescharacteristic
186C22×C3×C4D2011yescharacteristic
187C22×C3×C4C22×D511yescharacteristic
188C2×#67—101no—
189C22×Dic3—101no—
190C22×Dic3—101no—
191C2×D12—51no—
192C2×C4×D3—101no—
193C2×Dic6—51no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198#217—101no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3—51no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—101no—
212C23×C5C2×D1211yescharacteristic
213C22×D5—61no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—21no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C22⋊D5—121no—
223C22⋊D5—121no—
224C2×Dic5—61no—
225C2×Dic5—61no—
226C2×Dic5—61no—
227C2×Dic5—121no—
228C2×Dic5—121no—
229C2×Dic5—122no—
230C2×Dic5—121no—
231C2×Dic5—121no—
232D20—121no—
233C4×D5—241no—
234Dic10—121no—
235C5×C8—41no—
236C5×C8—41no—
237#126—301no—
238#125—301no—
239#123—301no—
240#123—301no—
241C22⋊Q8—151no—
242C22⋊Q8—301no—
243#121—151no—
244C4×D4—301no—
245C2×C4⋊C4—151no—
246C2×C4⋊C4C2×D1511yescharacteristic
247#107—301no—
248#106—301no—
249#103—301no—
250#102—301no—
251C22⋊C8C2×D1511yescharacteristic
252C22⋊C8C2×D1511yescharacteristic
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
261D15—81no—
262C23×C3C2×D2011yescharacteristic
263C22×D3—101no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272#67—201no—
273#67—201no—
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—101no—
277C2×Dic3—201no—
278C2×Dic3—201no—
279C2×Dic3—202no—
280C2×Dic3—201no—
281C2×Dic3—201no—
282D12—201no—
283C4×D3—401no—
284Dic6—201no—
285C3×C8—41no—
286C3×C8—41no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5#88211yescharacteristic
290C22×C5#90411yescharacteristic
291C22×C5#90911yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299Dic5—121no—
300Dic5—121no—
301Dic5—121no—
302Dic5—241no—
303Dic5—241no—
304C2×Q8—151no—
305C2×D4—151no—
306C2×D4—301no—
307C22×C4—301no—
308C22×C4—301no—
309C22×C4—301no—
310C22×C4D6011yescharacteristic
311C22×C4D6011yescharacteristic
312C22×C4C22×D1511yescharacteristic
313C2×C8—21no—
314C2×C8—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C22⋊C4—301no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C22⋊C4—301no—
329C22⋊C4—301no—
330C42—301no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3#402811yescharacteristic
335C22×C3#405011yescharacteristic
336C22×C3#405511yescharacteristic
337C2×D3—201no—
338C2×D3—201no—
339C2×D3—201no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344Dic3—201no—
345Dic3—201no—
346Dic3—201no—
347Dic3—401no—
348Dic3—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#473311yescharacteristic
352C2×C5#474211yescharacteristic
353C2×C5#475311yescharacteristic
354D5—241no—
355C23—301no—
356C23C2×D6011yescharacteristic
357Q8—601no—
358D4—601no—
359D4—601no—
360D4—601no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—301no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4—601no—
371C2×C4—601no—
372C2×C4—602no—
373C2×C4—601no—
374C2×C4—601no—
375C2×C4—1201no—
376C2×C4D4×D1511yescharacteristic
377C2×C4D4×D1511yescharacteristic
378C8—41no—
379C8—41no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6502211yescharacteristic
383C2×C3#6503111yescharacteristic
384C2×C3#6504211yescharacteristic
385D3—401no—
386C5#6813611yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—601no—
390C22—601no—
391C22—601no—
392C22#9177111yescharacteristic
393C22#9179311yescharacteristic
394C22#9179811yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—601no—
400C4—601no—
401C4—601no—
402C4—1201no—
403C4—1201no—
404C3#1059892911yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—1201no—
408C2#1175083411yescharacteristic
409C2#1175084311yescharacteristic
410C2#1175085411yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#324C2
socleC22×C3×C5#120
prime radical#91819C22
hypercenter#324D15
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #11751087C2semidirect
4. #11750823C2semidirect
5. C3×C5×#324C2semidirect
7. #11746288C2semidirect
33. C5×#324D3semidirect
67. C3×#324D5semidirect
167. #324D15semidirect
331. C3×C5#1615semidirect
386. C5#68136semidirect
404. C3#10598929semidirect

Maximal subgroups

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

subgroupindex
#117562742
#117510872
#117508362
#117508232
C3×C5×#3242
#117462912
#117462882
#105989293
#681365