Finite Group Databasebeta

← #14289654

Subgroups — #14289654

Order 1920.

468 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C5×#5555C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3#11746924C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745858C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602704—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C5×#930—21no—
12C2×C5×C4⋊Dic3—21no—
13C5×#897—21no—
14C5×#886—22no—
15C4×C5×D12C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×#3964—21no—
21C3×#3940—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90986—21no—
24#90970—22no—
25#90966—21no—
26#71146—51nomaximal, Hall
27C5×#547—31no—
28#65382—31no—
29#65297—31no—
30#65297D311yescharacteristic, complemented
31#64767—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C22×C5×Dic3—22no—
38C5×#237—42no—
39C5×#237—42no—
40C2×C5×D12D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C5×Dic6—21no—
43C2×C3×Dic10—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3—22no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3D412yes—
54C5×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#5555D511yescharacteristic
59C3×#476—51no—
60#5084—51no—
61#5079—51no—
62D4⋊(C3⋊C8)—51no—
63#4483—51no—
64#4482—51no—
65C2×C5×#41—61no—
66C5×C4⋊Q8—31no—
67C5×#123—62no—
68C5×C22⋊Q8—61no—
69C5×#121—61no—
70C4×C5×D4—31no—
71C4×C5×D4C2×D311yescharacteristic
72C2×C5×C4⋊C4—61no—
73#4015C2×D311yescharacteristic
74#3964—21no—
75#3964—61no—
76#3942—62no—
77#3940—21no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1635—151noSylow
83C23×C3×C5—21no—
84C22×C5×D3—21no—
85C3×C5×D4—21no—
86C3×C5×D4SD1612yes—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C5×#67—44no—
94C2×C5×Dic3—22no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—44no—
97C5×D12—21no—
98C5×D12—21no—
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C5×Dic6—41no—
102C5×Dic6—41no—
103C2×C3×Dic5—41no—
104C3×Dic10—42no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C2×#237—21no—
109C3×C4⋊Q8—51no—
110C3×C4×D4C2×D511yescharacteristic
111#930—21no—
112C2×C4⋊Dic3—21no—
113#897—21no—
114#886—22no—
115C4×D12C2×D511yescharacteristic
116#869C2×D511yescharacteristic
117C3×#106—101no—
118C3×C4⋊C8—51no—
119C3×#102—101no—
120#835—102no—
121#809—101no—
122#808—101no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C5×#41—122no—
126C5×#41—122no—
127C2×C5×Q8—61no—
128C2×C5×D4—31no—
129C2×C5×D4—62no—
130C2×C5×D4#6711yescharacteristic
131C22×C4×C5—21no—
132C22×C4×C5—62no—
133C22×C4×C5—61no—
134C2×Dic10—21no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—32no—
137C5×C4⋊C4—62no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4#6711yescharacteristic
140C5×C22⋊C4—21no—
141C5×C22⋊C4—62no—
142C5×C22⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144C4⋊Dic5—21no—
145C4⋊Dic5—21no—
146C2×#168—21no—
147C2×#168—61no—
148C2×#168—61no—
149#547—31no—
150#487—151no—
151#476—51no—
152#476—151no—
153#332—151no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×C5×D3—41no—
161C2×C5×D3—41no—
162C2×C5×D3—41no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169C3×Dic5—81no—
170C5×Dic3—42no—
171C5×Dic3—41no—
172C2×C3×Q8—101no—
173C2×C3×D4C22⋊D511yescharacteristic
174C22×C3×C4—21no—
175C2×#67—22no—
176C22×Dic3—22no—
177#237—42no—
178#237—42no—
179C2×D12C22⋊D511yescharacteristic
180C2×C4×D3—21no—
181C2×Dic6—21no—
182C2×C3×C8—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C22⋊C4—21no—
187C3×C42C22×D511yescharacteristic
188(C2×D3)⋊C4—22no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3—22no—
191C4⋊Dic3—21no—
192C4⋊Dic3C22⋊D511yescharacteristic
193C4⋊Dic3C22⋊D512yes—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C23×C5—61no—
198C5×Q8—121no—
199C5×Q8—121no—
200C5×D4—21no—
201C5×D4—61no—
202C5×D4—61no—
203C5×D4—124no—
204C5×D4#21512yes—
205C2×C4×C5—21no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—61no—
209C2×C4×C5—62no—
210C2×C4×C5—124no—
211C2×C4×C5—121no—
212C2×C4×C5—121no—
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×Dic5—41no—
217Dic10—42no—
218#168—41no—
219#168—121no—
220#168—121no—
221C2×#41—61no—
222C4⋊Q8—31no—
223C4⋊Q8—51no—
224#123—62no—
225C22⋊Q8—61no—
226#121—61no—
227C4×D4—31no—
228C4×D4D3×D511yescharacteristic
229C2×C4⋊C4—61no—
230#106—101no—
231#106—301no—
232C4⋊C8—51no—
233C4⋊C8—151no—
234#103—302no—
235#102—101no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5—42no—
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45211yescharacteristic
241C2×C3×C5#45411yescharacteristic
242C5×D3—81no—
243C23×C3—21no—
244C22×D3—21no—
245C3×Q8—202no—
246C3×D4—21no—
247C3×D4#68712yes—
248C2×C3×C4—21no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—201no—
252C2×C3×C4C2×C22⋊D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255#67—44no—
256C2×Dic3—22no—
257C2×Dic3—21no—
258C2×Dic3—44no—
259D12—21no—
260D12—21no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—41no—
264Dic6—41no—
265C3×C8—201no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5—121no—
272C22×C5—121no—
273C22×C5—121no—
274C22×C5#93711yescharacteristic
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—121no—
278C4×C5—122no—
279C4×C5#91511yescharacteristic
280C4×C5#91611yescharacteristic
281C4×C5C2×#21511yescharacteristic
282C4×C5#94911yescharacteristic
283Dic5—81no—
284#41—122no—
285#41—122no—
286C2×Q8—61no—
287C2×Q8—101no—
288C2×D4—31no—
289C2×D4—62no—
290C2×D4#120111yescharacteristic
291C22×C4—21no—
292C22×C4—62no—
293C22×C4—61no—
294C2×C8—101no—
295C2×C8—301no—
296C2×C8—301no—
297C4⋊C4—32no—
298C4⋊C4—31no—
299C4⋊C4—62no—
300C4⋊C4—61no—
301C4⋊C4—101no—
302C4⋊C4—101no—
303C4⋊C4#120111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—62no—
306C22⋊C4—61no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3#409911yescharacteristic
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—401no—
319C3×C4#407811yescharacteristic
320C3×C4C2×#68711yescharacteristic
321C3×C4#409611yescharacteristic
322C3×C4#409711yescharacteristic
323Dic3—42no—
324Dic3—41no—
325C2×C5—42no—
326C2×C5—241no—
327C2×C5#504611yescharacteristic
328C2×C5#517311yescharacteristic
329C2×C5#520111yescharacteristic
330C23—21no—
331C23—61no—
332Q8—121no—
333Q8—121no—
334Q8—202no—
335D4—21no—
336D4—61no—
337D4—61no—
338D4—124no—
339D4#665612yes—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—61no—
344C2×C4—62no—
345C2×C4—124no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—201no—
349C2×C4C2×#120111yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4D3×C22⋊D511yescharacteristic
352C8—201no—
353C8—601no—
354C8—601no—
355C2×C3—42no—
356C2×C3#6550711yescharacteristic
357C2×C3#6552811yescharacteristic
358C2×C3#6553411yescharacteristic
359D3—81no—
360C5#7114611yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—121no—
365C22—121no—
366C22—121no—
367C22#9156811yescharacteristic
368C4—21no—
369C4—41no—
370C4—121no—
371C4—122no—
372C4—401no—
373C4#9129911yescharacteristic
374C4C2×#665611yescharacteristic
375C4#9148611yescharacteristic
376C4#9149511yescharacteristic
377C3#1060270411yescharacteristic, complemented, Sylow
378C2—42no—
379C2—241no—
380C2#1174853711yescharacteristic
381C2#1174905911yescharacteristic
382C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC5×#5555C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65297C2semidirect
3. #11746924C2semidirect
4. #11746882C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745858C2semidirect
7. #11745836C2semidirect
30. #65297D3semidirect
308. C3×C5#1635semidirect
360. C5#71146semidirect
377. C3#10602704semidirect

Maximal subgroups

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

subgroupindex
C5×#55552
C3×#652972
#117469242
#117468822
D4⋊(C3⋊#168)2
#117458582
#117458362
#106027043
#711465