Finite Group Databasebeta

← #14289423

Subgroups — #14289423

Order 1920.

512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756312C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4#11751186C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746305C211yesmaximal, characteristic, complemented
8#10601934—31nomaximal, Hall
9C2×#6817—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C2×#6717—22no—
13#91829—21no—
14#91819—21no—
15#91782—21no—
16#91773—22no—
17#91763C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22#91094—21no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71141—51nomaximal, Hall
27#65887—31no—
28C5×#476D311yescharacteristic, complemented
29#65380—31no—
30#65374—31no—
31D4⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×#1220—22no—
38C2×#1220—22no—
39#6817—42no—
40#6817—42no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60D412yes—
44C2×C4×D15—22no—
45C2×Dic30D411yescharacteristic
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52#6717—44no—
53#6714—22no—
54C4⋊Dic15D411yescharacteristic
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5553—51no—
60C3×#476D511yescharacteristic, complemented
61#5091—51no—
62#5085—51no—
63D4⋊(C3⋊C8)—51no—
64#4485—51no—
65#4484—51no—
66C2×#709—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C4×C5×D4C2×D311yescharacteristic
69C2×#688—62no—
70#4086—61no—
71#4076—61no—
72#4039—61no—
73#4030—62no—
74#4020—31no—
75C4×Dic10—31no—
76C5×#106—21no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—21no—
79#3942—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1631—151noSylow
84C23×C3×C5—21no—
85C22×D15—22no—
86C3×C5×Q8—42no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96#1220—44no—
97#1220—82no—
98C2×Dic15—21no—
99C2×Dic15—21no—
100D60—42no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105C4×D15—44no—
106Dic30—21no—
107Dic30SD1612yescomplemented
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C3⋊#168—41no—
111C2×#235—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C4×D4C2×D511yescharacteristic
114C2×#215—102no—
115#940—101no—
116#930—101no—
117#893—101no—
118#884—102no—
119#874—51no—
120C4×Dic6—51no—
121C3×#106—21no—
122C3×C4⋊C8C2×D511yescharacteristic
123C3×#102—21no—
124#810—101no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C4×C3⋊C8—51no—
128C2×C5×Q8—21no—
129C2×C5×D4#6711yescharacteristic
130C22×C4×C5—21no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—32no—
136C2×D20—61no—
137C2×D20—61no—
138C2×C4×D5—62no—
139C2×Dic10—31no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4#6711yescharacteristic
144C5×C22⋊C4—21no—
145C42×C5C22×D311yescharacteristic
146#688—124no—
147#685—62no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—61no—
152C2×#168—61no—
153#550—151no—
154#492—151no—
155#477—151no—
156#476D1511yescharacteristic, complemented
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—42no—
165C2×D15—42no—
166C2×D15—42no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5—81no—
170C3×C4×C5C2×SD1611yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—22no—
175Dic15—41no—
176C2×C3×Q8—21no—
177C2×C3×D4C22⋊D511yescharacteristic
178C22×C3×C4—21no—
179C2×#67—102no—
180C2×#67—102no—
181#235—202no—
182#235—202no—
183C2×D12—52no—
184C2×D12—101no—
185C2×D12—101no—
186C2×C4×D3—102no—
187C2×Dic6—51no—
188C2×C3×C8—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4C22⋊D511yescharacteristic
192C3×C22⋊C4—21no—
193C3×C42C22×D511yescharacteristic
194#215—204no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—51no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C22×D5—62no—
203C5×Q8—42no—
204C5×D4—21no—
205C5×D4—21no—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—124no—
223Dic10—32no—
224Dic10—61no—
225C5×C8—41no—
226#168—62no—
227#168—121no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8C2×D1511yescharacteristic
231#127—151no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—151no—
236C4×D4—301no—
237C4×D4C2×D1511yescharacteristic
238#107—301no—
239#106—21no—
240C4⋊C8—151no—
241C4⋊C8C2×D1511yescharacteristic
242#103—301no—
243#102—21no—
244C4×C8—151no—
245C2×C3×C5—81no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249D15—82no—
250C23×C3—21no—
251C22×D3—102no—
252C3×Q8—42no—
253C3×D4—21no—
254C3×D4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—101no—
265C2×Dic3—101no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—204no—
272Dic6—52no—
273Dic6—101no—
274C3×C8—41no—
275C3⋊C8—102no—
276C3⋊C8—201no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5#93711yescharacteristic
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—81no—
287C4×C5D3×SD1611yescharacteristic
288C4×C5#91411yescharacteristic
289C4×C5#94211yescharacteristic
290C4×C5#95011yescharacteristic
291Dic5—62no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—21no—
296C2×Q8—151no—
297C2×D4—152no—
298C2×D4—302no—
299C2×D4—302no—
300C2×D4—301no—
301C2×D4—301no—
302C2×D4#122011yescharacteristic
303C22×C4—21no—
304C22×C4—302no—
305SD16—604no—
306C2×C8—21no—
307C2×C8—301no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—151no—
312C4⋊C4—301no—
313C4⋊C4#122011yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—302no—
316C42—301no—
317C42C22×D1511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3#408311yescharacteristic
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—81no—
329C3×C4D5×SD1611yescharacteristic
330C3×C4#406011yescharacteristic
331C3×C4#408811yescharacteristic
332C3×C4#409611yescharacteristic
333Dic3—102no—
334Dic3—201no—
335C2×C5—81no—
336C2×C5#504711yescharacteristic
337C2×C5#516911yescharacteristic
338C2×C5#519811yescharacteristic
339D5—242no—
340C23—21no—
341C23—302no—
342Q8—42no—
343Q8—152no—
344Q8—301no—
345D4—21no—
346D4—21no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—604no—
361C2×C4D4×D1511yescharacteristic
362C2×C4D4×D1511yescharacteristic
363C2×C4C2×#122011yescharacteristic
364C8—41no—
365C8—302no—
366C8—601no—
367C2×C3—81no—
368C2×C3#6533611yescharacteristic
369C2×C3#6545811yescharacteristic
370C2×C3#6548711yescharacteristic
371D3—402no—
372C5#7114111yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9182611yescharacteristic
380C4—21no—
381C4—41no—
382C4—81no—
383C4—302no—
384C4—601no—
385C4SD16×D1511yescharacteristic
386C4#9180311yescharacteristic
387C4#9183111yescharacteristic
388C4#9183911yescharacteristic
389C3#1060193411yescharacteristic, complemented, Sylow
390C2—81no—
391C2—1202no—
392C2#1175114811yescharacteristic
393C2#1175127011yescharacteristic
394C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radical#11756312C2
hypercenter#476D15
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. #11751192C2semidirect
4. #11751186C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746306C2semidirect
7. #11746305C2semidirect
28. C5×#476D3semidirect
60. C3×#476D5semidirect
107. Dic30SD16semidirect
156. #476D15semidirect
318. C3×C5#1631semidirect
372. C5#71141semidirect
389. C3#10601934semidirect

Maximal subgroups

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

subgroupindex
#117563122
C3×C5×#4762
#117511922
#117511862
D4⋊(C3⋊#168)2
#117463062
#117463052
#106019343
#711415