Finite Group Databasebeta

← #14288604

Subgroups — #14288604

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
2C3×C5×#400C211yesmaximal, characteristic, complemented
3#11751071C211yesmaximal, characteristic, complemented
4#11751069C211yesmaximal, characteristic
5#11746349C211yesmaximal, characteristic, complemented
6#11746273C211yesmaximal, characteristic, complemented
7#11746272C211yesmaximal, characteristic
8#10600510—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91819C2211yescharacteristic
12#91818—21no—
13C4×#1220—21no—
14#91813C2211yescharacteristic
15#91787—21no—
16#91785—21no—
17#91783—21no—
18#91778—21no—
19C3×C5×#95—21no—
20C3×C5×#95—21no—
21C3×C5×#95C2211yescharacteristic
22#91114C2211yescharacteristic
23#91114C2211yescharacteristic
24#91094—21no—
25#91093—21no—
26#91092—21no—
27#91091—21no—
28#69717—51nomaximal, Hall
29#65849—31no—
30C5×#400D311yescharacteristic, complemented
31#65259—31no—
32#65257—31no—
33#64748—31no—
34#64672—31no—
35#64671—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C22×C3×C4×C5C2311yescharacteristic
41C2×#1220—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—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⋊Dic15D411yescharacteristic
55C4⋊Dic15D411yescharacteristic
56#6712—21no—
57#6712—21no—
58#6712—21no—
59#6712—21no—
60C4×Dic15—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#5515—51no—
64C3×#400D511yescharacteristic, complemented
65#4970—51no—
66#4968—51no—
67#4528—51no—
68#4452—51no—
69#4451—51no—
70C2×C5×C4⋊C4C2×D311yescharacteristic
71C2×C5×C4⋊C4C2×D311yescharacteristic
72#4076—31no—
73#4075—61no—
74C4×C22⋊D5—61no—
75#4070—31no—
76#4044—61no—
77#4042—61no—
78#4040—61no—
79#4035—61no—
80C5×#95—21no—
81C5×#95—21no—
82C5×#95C2×D311yescharacteristic
83C22⋊#168—31no—
84C22⋊#168—31no—
85#3942—61no—
86#3941—61no—
87#3940—61no—
88#3939—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×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105#1220—41no—
106#1220—41no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110D60—41no—
111C4×D15—81no—
112Dic30—41no—
113C3⋊#168—41no—
114C3⋊#168—41no—
115C2×C3×C4⋊C4C2×D511yescharacteristic
116C2×C3×C4⋊C4C2×D511yescharacteristic
117#930—51no—
118#929—101no—
119C4×#67—101no—
120#924—51no—
121#898—101no—
122#896—101no—
123#894—101no—
124#889—101no—
125C3×#95—21no—
126C3×#95—21no—
127C3×#95C2×D511yescharacteristic
128#830—51no—
129#830—51no—
130#810—101no—
131#809—101no—
132#808—101no—
133#807—101no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5#6711yescharacteristic
138C22×C4×C5C22×D311yescharacteristic
139C2×C22⋊D5—61no—
140C2×D20—31no—
141C2×C4×D5—61no—
142C2×Dic10—31no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—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—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158C4×Dic5—61no—
159C2×#168—61no—
160C2×#168—61no—
161#539—151no—
162#484—151no—
163#481—151no—
164#400D1511yescharacteristic, complemented
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×D15—41no—
174C2×D15—41no—
175C2×D15—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—81no—
181C3×C4×C5—81no—
182Dic15—41no—
183Dic15—41no—
184Dic15—41no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4C22⋊D511yescharacteristic
188C22×C3×C4C22⋊D511yescharacteristic
189C22×C3×C4C22×D511yescharacteristic
190C2×#67—101no—
191C2×D12—51no—
192C2×C4×D3—101no—
193C2×Dic6—51no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—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—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209C4×Dic3—101no—
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212C23×C5C2×#6711yescharacteristic
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×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—42no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C22⋊D5—121no—
228C22⋊D5—121no—
229C2×Dic5—61no—
230C2×Dic5—61no—
231C2×Dic5—61no—
232D20—121no—
233C4×D5—241no—
234Dic10—121no—
235#168—121no—
236#168—121no—
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⋊C4C2×D1511yescharacteristic
246C2×C4⋊C4C2×D1511yescharacteristic
247#107—301no—
248#106—301no—
249#103—301no—
250#102—301no—
251C22⋊C8—151no—
252C22⋊C8—151no—
253#95—21no—
254#95—21no—
255#95C2×D1511yescharacteristic
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5#45211yescharacteristic
259C2×C3×C5#45411yescharacteristic
260C2×C3×C5#45811yescharacteristic
261D15—81no—
262C23×C3C2×C22⋊D511yescharacteristic
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×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277#67—201no—
278#67—201no—
279C2×Dic3—101no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282D12—201no—
283C4×D3—401no—
284Dic6—201no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5#93711yescharacteristic
290C22×C5#94211yescharacteristic
291C22×C5#95011yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—81no—
300C4×C5—81no—
301Dic5—121no—
302Dic5—121no—
303Dic5—121no—
304C2×Q8—151no—
305C2×D4—151no—
306C2×D4—301no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—301no—
310C22×C4#122011yescharacteristic
311C22×C4#122011yescharacteristic
312C22×C4C22×D1511yescharacteristic
313C2×C8—301no—
314C2×C8—301no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—151no—
320C4⋊C4—151no—
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#408311yescharacteristic
335C22×C3#408811yescharacteristic
336C22×C3#409611yescharacteristic
337C2×D3—201no—
338C2×D3—201no—
339C2×D3—201no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—81no—
345C3×C4—81no—
346Dic3—201no—
347Dic3—201no—
348Dic3—201no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#504711yescharacteristic
352C2×C5#505311yescharacteristic
353C2×C5#506211yescharacteristic
354D5—241no—
355C23—301no—
356C23C2×#122011yescharacteristic
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—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—301no—
373C2×C4—301no—
374C2×C4—301no—
375C2×C4—1201no—
376C2×C4D4×D1511yescharacteristic
377C2×C4D4×D1511yescharacteristic
378C8—601no—
379C8—601no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6533611yescharacteristic
383C2×C3#6534211yescharacteristic
384C2×C3#6535111yescharacteristic
385D3—401no—
386C5#6971711yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—601no—
390C22—601no—
391C22—601no—
392C22#9182611yescharacteristic
393C22#9183111yescharacteristic
394C22#9183911yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—601no—
402C4—601no—
403C4—601no—
404C3#1060051011yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—1201no—
408C2#1175114811yescharacteristic
409C2#1175115411yescharacteristic
410C2#1175116311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#400C2
socleC22×C3×C5#120
prime radical#91819C22
hypercenter#400D15
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C3×C5×#400C2semidirect
3. #11751071C2semidirect
5. #11746349C2semidirect
6. #11746273C2semidirect
30. C5×#400D3semidirect
64. C3×#400D5semidirect
164. #400D15semidirect
331. C3×C5#1615semidirect
386. C5#69717semidirect
404. C3#10600510semidirect

Maximal subgroups

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

subgroupindex
#117562742
C3×C5×#4002
#117510712
#117510692
#117463492
#117462732
#117462722
#106005103
#697175