Finite Group Databasebeta

← #14289279

Subgroups — #14289279

Order 1920.

432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756301C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic
3#11751176C211yesmaximal, characteristic, complemented
4#11751171C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10601812—31nomaximal, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12#91825—21no—
13C2×#6716—21no—
14#91815—21no—
15#91813—21no—
16#91776—21no—
17#91768—22no—
18#91758C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22#91116—22no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71019—51nomaximal, Hall
27#65876—31no—
28C5×#459D311yescharacteristic
29#65364—31no—
30#65359—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64702—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×Dic30—21no—
40C2×Dic30D411yescharacteristic
41C3×C5×D8—42no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6719—22no—
47#6719—22no—
48#6716—42no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D412yes—
52#6712—22no—
53#6712—21no—
54C4×Dic15—22no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58#5542—51no—
59C3×#459D511yescharacteristic
60#5075—51no—
61#5070—51no—
62D4⋊(C3⋊C8)—51no—
63#4484—51no—
64#4482—51no—
65C2×C5×D8—21no—
66C5×#127C2×D311yescharacteristic
67C4×C5×D4C2×D311yescharacteristic
68#4082—61no—
69C2×#687—61no—
70#4072—61no—
71#4070—61no—
72#4033—61no—
73#4025—62no—
74#4015—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#102—21no—
78#3964—62no—
79#3964—61no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1628—151noSylow
83C23×C3×C5—21no—
84C23×C3×C5—41no—
85C3×C5×D4—21no—
86C3×C5×D4—21no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—21no—
100C2×Dic15—22no—
101Dic30—21no—
102Dic30—21no—
103Dic30—41no—
104Dic30—41no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C2×C3×D8—21no—
109C3×#127C2×D511yescharacteristic
110C3×C4×D4C2×D511yescharacteristic
111#936—101no—
112C2×#214—101no—
113#926—101no—
114#924—101no—
115#887—101no—
116#879—102no—
117#869—51no—
118C4×Dic6—51no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×#102—21no—
121#832—102no—
122#832—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×Dic10—31no—
131C2×Dic10—61no—
132C5×D8—42no—
133C2×C5×C8—21no—
134C5×C4⋊C4#6711yescharacteristic
135C5×C22⋊C4—21no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—62no—
138C22⋊Dic5—62no—
139#687—122no—
140C4⋊Dic5—31no—
141C4⋊Dic5—32no—
142C4⋊Dic5—61no—
143#683—62no—
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—61no—
148C2×#168—61no—
149#556—151no—
150#486—151no—
151#460—151no—
152#459D1511yescharacteristic
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5—41no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5—81no—
160C22×C3×C5—81no—
161C22×C3×C5—81no—
162C22×C3×C5#12011yescharacteristic
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169Dic15—41no—
170Dic15—42no—
171Dic15—41no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4C22⋊D511yescharacteristic
176C22×C3×C4—21no—
177C2×Dic6—51no—
178C2×Dic6—101no—
179C3×D8—42no—
180C2×C3×C8—21no—
181C3×C4⋊C4C22⋊D511yescharacteristic
182C3×C22⋊C4—21no—
183C3×C42C22×D511yescharacteristic
184#217—102no—
185#217—102no—
186#214—202no—
187C4⋊Dic3—51no—
188C4⋊Dic3—52no—
189C4⋊Dic3—101no—
190Dic3⋊C4—102no—
191Dic3⋊C4—101no—
192C4×Dic3—102no—
193C4×Dic3—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C23×C5—41no—
198C5×D4—21no—
199C5×D4—21no—
200C5×D4—42no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C2×C4×C5—21no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×Dic5—61no—
212C2×Dic5—61no—
213C2×Dic5—62no—
214Dic10—61no—
215Dic10—61no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—41no—
219#168—121no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—21no—
223C4⋊Q8—151no—
224#127C2×D1511yescharacteristic
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—151no—
229C4×Q8—301no—
230C4×D4C2×D1511yescharacteristic
231#117—301no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234#102—21no—
235#102—301no—
236#102—302no—
237C4×C8—151no—
238C2×C3×C5—81no—
239C2×C3×C5—161no—
240C2×C3×C5#44911yescharacteristic
241C2×C3×C5#44911yescharacteristic
242C2×C3×C5#45411yescharacteristic
243C23×C3—21no—
244C23×C3—41no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—42no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C2×C3×C4—21no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×Dic3—101no—
259C2×Dic3—101no—
260C2×Dic3—102no—
261Dic6—101no—
262Dic6—101no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—41no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—41no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5#93711yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5#91111yescharacteristic
278C4×C5#91211yescharacteristic
279C4×C5#93211yescharacteristic
280C4×C5#95011yescharacteristic
281Dic5—121no—
282Dic5—121no—
283Dic5—122no—
284C2×Q8—151no—
285C2×Q8—301no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4#122011yescharacteristic
290C22×C4—21no—
291SD16—602no—
292D8—42no—
293C2×C8—21no—
294C2×C8—301no—
295C2×C8—301no—
296C4⋊C4—151no—
297C4⋊C4—152no—
298C4⋊C4—302no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C4⋊C4#122011yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—302no—
304C22⋊C4—302no—
305C42—302no—
306C42—301no—
307C42C22×D1511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3—81no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—41no—
318C3×C4#405711yescharacteristic
319C3×C4#405811yescharacteristic
320C3×C4#407811yescharacteristic
321C3×C4#409611yescharacteristic
322Dic3—202no—
323Dic3—201no—
324Dic3—201no—
325C2×C5—81no—
326C2×C5—161no—
327C2×C5#503711yescharacteristic
328C2×C5#515811yescharacteristic
329C2×C5#520111yescharacteristic
330C23—21no—
331C23—41no—
332Q8—301no—
333Q8—301no—
334Q8—601no—
335Q8—601no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—301no—
347C2×C4—302no—
348C2×C4—301no—
349C2×C4D4×D1511yescharacteristic
350C2×C4D4×D1511yescharacteristic
351C2×C4C2×#122011yescharacteristic
352C8—41no—
353C8—601no—
354C8—601no—
355C2×C3—81no—
356C2×C3—161no—
357C2×C3#6532611yescharacteristic
358C2×C3#6544711yescharacteristic
359C2×C3#6549011yescharacteristic
360C5#7101911yescharacteristic, complemented, Sylow
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#9182611yescharacteristic
368C4—21no—
369C4—41no—
370C4—601no—
371C4—601no—
372C4—602no—
373C4#9180011yescharacteristic
374C4#9180111yescharacteristic
375C4#9182111yescharacteristic
376C4#9183911yescharacteristic
377C3#1060181211yescharacteristic, complemented, Sylow
378C2—81no—
379C2—161no—
380C2#1175113811yescharacteristic
381C2#1175125911yescharacteristic
382C2#1175130211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#459C2
socleC22×C3×C5#120
hypercenter#459D15
hypocenterC3×C5#1628
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11756301C2semidirect
3. #11751176C2semidirect
4. #11751171C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746305C2semidirect
7. #11746303C2semidirect
308. C3×C5#1628semidirect
360. C5#71019semidirect
377. C3#10601812semidirect

Maximal subgroups

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

subgroupindex
#117563012
C3×C5×#4592
#117511762
#117511712
D4⋊(C3⋊#168)2
#117463052
#117463032
#106018123
#710195