Finite Group Databasebeta

← #14288421

Subgroups — #14288421

Order 1920.

420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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#11756382C211yesmaximal, characteristic
2C3×C5×#483C211yesmaximal, characteristic
3#11751084C211yesmaximal, characteristic
4#11751072C211yesmaximal, characteristic
5#11746359C211yesmaximal, characteristic
6#11746290C211yesmaximal, characteristic
7#11746288C211yesmaximal, characteristic
8#10601968—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91833—21no—
12#91813C2211yescharacteristic
13C2×#6712—21no—
14C2×#6712C2211yescharacteristic
15#91778—21no—
16#91778—21no—
17#91777—21no—
18#91767—21no—
19#91766—21no—
20C3×C5×#106—21no—
21C3×C5×#103—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115—21no—
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91094—21no—
27#91092—21no—
28#71175—51nomaximal, Hall
29#65957—31no—
30C5×#483D311yescharacteristic
31#65269—31no—
32#65260—31no—
33#64758—31no—
34#64689—31no—
35#64687—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D411yescharacteristic
41C22×Dic15D411yescharacteristic
42C2×Dic30—21no—
43C2×Dic30D411yescharacteristic
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50#6719—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57#6712—21no—
58#6712—21no—
59#6712—21no—
60#6712—42no—
61C4×Dic15—21no—
62C4×Dic15—21no—
63C2×C3⋊#168—21no—
64#5623—51no—
65C3×#483D511yescharacteristic
66#4983—51no—
67#4971—51no—
68#4538—51no—
69#4469—51no—
70#4467—51no—
71C5×C22⋊Q8C2×D311yescharacteristic
72C2×C5×C4⋊C4C2×D311yescharacteristic
73#4090—61no—
74#4070—31no—
75C2×#683—31no—
76C2×#683—61no—
77#4035—61no—
78#4035—61no—
79#4034—61no—
80#4024—61no—
81#4023—61no—
82C5×#106—21no—
83C5×#103—21no—
84C5×C22⋊C8C2×D311yescharacteristic
85#3963—31no—
86#3963—61no—
87C22⋊#168—31no—
88#3942—61no—
89#3940—61no—
90#1611—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—22no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110C2×Dic15SD1612yes—
111Dic30—41no—
112Dic30—81no—
113C3×C5×C8—41no—
114C3⋊#168—41no—
115C3×C22⋊Q8C2×D511yescharacteristic
116C2×C3×C4⋊C4C2×D511yescharacteristic
117#944—101no—
118#924—51no—
119C2×Dic3⋊C4—51no—
120C2×Dic3⋊C4—101no—
121#889—101no—
122#889—101no—
123#888—101no—
124#878—101no—
125#877—101no—
126C3×#106—21no—
127C3×#103—21no—
128C3×C22⋊C8C2×D511yescharacteristic
129C3⋊#95—51no—
130C3⋊#95—101no—
131#830—51no—
132#810—101no—
133#808—101no—
134C2×C5×Q8#6711yescharacteristic
135C22×C4×C5—21no—
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5—31no—
138C22×Dic5—31no—
139C22×Dic5—61no—
140C2×Dic10—31no—
141C2×Dic10—61no—
142C2×C5×C8—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4#6711yescharacteristic
147C5×C22⋊C4—21no—
148C22⋊Dic5—61no—
149C4⋊Dic5—31no—
150C4⋊Dic5—61no—
151#683—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156#683—61no—
157#683—61no—
158#683—122no—
159C4×Dic5—61no—
160C4×Dic5—61no—
161C2×#168—61no—
162#544—151no—
163#483—151no—
164#483D1511yescharacteristic
165#398—151no—
166#328—151no—
167#328—151no—
168#324—151no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5#12011yescharacteristic
172C22×C3×C5C2×SD1611yescharacteristic
173C22×C3×C5#13711yescharacteristic
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—41no—
177C3×C4×C5—41no—
178C3×C4×C5—81no—
179Dic15—22no—
180Dic15—42no—
181Dic15—41no—
182Dic15—41no—
183Dic15—41no—
184C2×C3×Q8C22⋊D511yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4C22×D511yescharacteristic
187C22×Dic3—51no—
188C22×Dic3—51no—
189C22×Dic3—101no—
190C2×Dic6—51no—
191C2×Dic6—101no—
192C2×C3×C8—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C22⋊D511yescharacteristic
197C3×C22⋊C4—21no—
198#217—101no—
199C4⋊Dic3—51no—
200C4⋊Dic3—101no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—202no—
209C4×Dic3—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—101no—
212C23×C5D3×D411yescharacteristic
213C5×Q8—41no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×Dic5—32no—
223C2×Dic5—61no—
224C2×Dic5—61no—
225C2×Dic5—62no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228C2×Dic5—61no—
229C2×Dic5—121no—
230C2×Dic5—121no—
231C2×Dic5—121no—
232Dic10—121no—
233Dic10—241no—
234C5×C8—41no—
235#168—121no—
236C4⋊Q8—301no—
237C4⋊Q8—301no—
238#125—301no—
239#125—301no—
240C22⋊Q8—151no—
241C22⋊Q8—301no—
242C22⋊Q8C2×D1511yescharacteristic
243#117—301no—
244C2×C4⋊C4—151no—
245C2×C4⋊C4—301no—
246C2×C4⋊C4C2×D1511yescharacteristic
247#106—21no—
248#106—301no—
249#103—21no—
250#103—301no—
251C22⋊C8—151no—
252C22⋊C8C2×D1511yescharacteristic
253#95—151no—
254#95—301no—
255C2×C3×C5—21no—
256C2×C3×C5—21no—
257C2×C3×C5#44811yescharacteristic
258C2×C3×C5#45611yescharacteristic
259C2×C3×C5#45811yescharacteristic
260C23×C3D4×D511yescharacteristic
261C3×Q8—41no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×Dic3—52no—
271C2×Dic3—101no—
272C2×Dic3—101no—
273C2×Dic3—102no—
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—101no—
277C2×Dic3—201no—
278C2×Dic3—201no—
279C2×Dic3—201no—
280Dic6—201no—
281Dic6—401no—
282C3×C8—41no—
283C3⋊C8—201no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5D3×SD1611yescharacteristic
287C22×C5#91511yescharacteristic
288C22×C5#93711yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—41no—
293C4×C5—81no—
294Dic5—62no—
295Dic5—122no—
296Dic5—121no—
297Dic5—121no—
298Dic5—121no—
299C2×Q8—151no—
300C2×Q8—301no—
301C2×Q8#122011yescharacteristic
302C22×C4—21no—
303C22×C4—151no—
304C22×C4—151no—
305C22×C4—301no—
306C22×C4C22×D1511yescharacteristic
307C2×C8—21no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4—301no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—602no—
322C4⋊C4#122011yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—301no—
325C42—301no—
326C42—301no—
327C3×C5#161111yescharacteristic, complemented, Hall
328C22×C3—21no—
329C22×C3—21no—
330C22×C3D5×SD1611yescharacteristic
331C22×C3#406111yescharacteristic
332C22×C3#408311yescharacteristic
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—41no—
337C3×C4—81no—
338Dic3—102no—
339Dic3—202no—
340Dic3—201no—
341Dic3—201no—
342Dic3—201no—
343C2×C5—21no—
344C2×C5—21no—
345C2×C5#505311yescharacteristic
346C2×C5#517011yescharacteristic
347C2×C5#520511yescharacteristic
348C23D4×D1511yescharacteristic
349Q8—41no—
350Q8—601no—
351Q8—1201no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—152no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—302no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—301no—
365C2×C4—601no—
366C2×C4—601no—
367C2×C4—601no—
368C2×C4D4×D1511yescharacteristic
369C2×C4C2×#122011yescharacteristic
370C8—41no—
371C8—601no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3#6534211yescharacteristic
375C2×C3#6545911yescharacteristic
376C2×C3#6549411yescharacteristic
377C5#7117511yescharacteristic, complemented, Sylow
378C22—21no—
379C22—21no—
380C22SD16×D1511yescharacteristic
381C22#9180411yescharacteristic
382C22#9182611yescharacteristic
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—302no—
389C4—602no—
390C4—601no—
391C4—601no—
392C4—601no—
393C3#1060196811yescharacteristic, complemented, Sylow
394C2—21no—
395C2—21no—
396C2#1175115411yescharacteristic
397C2#1175127111yescharacteristic
398C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#483C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#483D15
hypocenterC3×C5#1611
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
327. C3×C5#1611semidirect
377. C5#71175semidirect
393. C3#10601968semidirect

Maximal subgroups

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

subgroupindex
#117563822
C3×C5×#4832
#117510842
#117510722
#117463592
#117462902
#117462882
#106019683
#711755