Finite Group Databasebeta

← #14290607

Subgroups — #14290607

Order 1920.

400 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752483C211yesmaximal, characteristic
2C3×#64971C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic
4#11746927C211yesmaximal, characteristic, complemented
5#11746280C211yesmaximal, characteristic
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599043—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18C2×#6658—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3950—22no—
23#90986—21no—
24#90972—21no—
25#90971—21no—
26#71370—51nomaximal, Hall
27#65918—31no—
28#65309—31no—
29#65130—31no—
30#64971D311yescharacteristic, complemented
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10—21no—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3D411yescharacteristic
45C5×Dic3⋊C4—21no—
46C4×C5×Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52#6668—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#6658—42no—
57#5732—51no—
58C3×#500—51no—
59#5094—51no—
60#5083—51no—
61#4547—51no—
62#4459—51no—
63#4456D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4092—61no—
66C2×#677—61no—
67#4044—62no—
68#4038—61no—
69#4021—61no—
70C4×D20—31no—
71#4015C2×D311yescharacteristic
72#4015C2×D311yescharacteristic
73C4×Dic10—61no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3950—22no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×D15—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87D60—21no—
88D60—21no—
89C4×D15—41no—
90C4×D15—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×Dic6—21no—
94C5×Dic6—21no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—41no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—22no—
102C3⋊#168—41no—
103C5×C3⋊C8—41no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8—51no—
106#947—101no—
107Q8×Dic3—101no—
108C2×#215—101no—
109#898—102no—
110#897—101no—
111#892—101no—
112C4×D12—51no—
113C4×Dic6C2×D511yescharacteristic
114C3×#107—102no—
115C3×C4×C8C2×D511yescharacteristic
116#835—101no—
117#810—101no—
118#808—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C2×C5×Q8—31no—
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×Dic10—21no—
125C2×Dic10—21no—
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C42×C5—61no—
131C42×C5C22×D311yescharacteristic
132#685—62no—
133#685—62no—
134#685—61no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139C4⋊Dic5#6712yes—
140#683—62no—
141C4×Dic5—62no—
142C2×#168—61no—
143#677—122no—
144#556—151no—
145#500—51no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—31no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C3×C4×C5—21no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161C3×Dic5—42no—
162C3×Dic5—81no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—101no—
166C2×C3×Q8—101no—
167C2×D12—51no—
168C2×C4×D3—101no—
169C2×Dic6D2011yescharacteristic
170C2×C3×C8—21no—
171C3×C4⋊C4—52no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C42C22×D511yescharacteristic
176#215—202no—
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—102no—
179(C2×D3)⋊C4—101no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182C4⋊Dic3D2011yescharacteristic
183Dic3⋊C4—21no—
184C4×Dic3—21no—
185C4×Dic3—102no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C22×D5—61no—
189C5×Q8—61no—
190C5×Q8—61no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—22no—
197C2×Dic5—41no—
198C2×Dic5—61no—
199D20—61no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203Dic10—41no—
204Dic10—41no—
205Dic10—41no—
206Dic10—41no—
207C5×C8—22no—
208C5×C8—121no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—51no—
212C4⋊Q8—51no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—31no—
217C4×Q8—301no—
218C4×D4—151no—
219#117—301no—
220#107—102no—
221#106—301no—
222C4⋊C8—31no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8D3×D511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230D15—81no—
231C22×D3—101no—
232C3×Q8—201no—
233C3×Q8—201no—
234C3×Q8—201no—
235C3×Q8—201no—
236C2×C3×C4—102no—
237C2×C3×C4—201no—
238C2×C3×C4C2×D2011yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—101no—
244D12—101no—
245D12—101no—
246C4×D3—201no—
247C4×D3—201no—
248Dic6—21no—
249Dic6—21no—
250C3×C8—22no—
251C3⋊C8—41no—
252C3⋊C8—201no—
253C22×C5#93711yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—121no—
259C4×C5—121no—
260C4×C5#91111yescharacteristic
261C4×C5#91211yescharacteristic
262C4×C5#91811yescharacteristic
263C4×C5#91911yescharacteristic
264Dic5—42no—
265Dic5—81no—
266Dic5—121no—
267C2×Q8—31no—
268C2×Q8—101no—
269C2×Q8—101no—
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—61no—
275C2×C8—301no—
276C4⋊C4—31no—
277C4⋊C4—52no—
278C4⋊C4—61no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4—151no—
283C4⋊C4—302no—
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—61no—
288C42—302no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#402811yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—202no—
297C3×C4—401no—
298C3×C4#405011yescharacteristic
299C3×C4#405511yescharacteristic
300C3×C4#406011yescharacteristic
301C3×C4#406511yescharacteristic
302Dic3—41no—
303Dic3—41no—
304Dic3—201no—
305C2×C5#509511yescharacteristic
306C2×C5#515811yescharacteristic
307C2×C5#518711yescharacteristic
308D5—241no—
309C23—301no—
310Q8—61no—
311Q8—61no—
312Q8—201no—
313Q8—201no—
314Q8—201no—
315Q8—201no—
316D4—301no—
317D4—301no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—102no—
321C2×C4—201no—
322C2×C4—301no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4D3×D2011yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—22no—
329C8—121no—
330C8—601no—
331C2×C3#6502211yescharacteristic
332C2×C3#6510011yescharacteristic
333C2×C3#6511511yescharacteristic
334D3—401no—
335C5#7137011yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9147411yescharacteristic
340C4—21no—
341C4—121no—
342C4—121no—
343C4—202no—
344C4—401no—
345C4—601no—
346C4#9125811yescharacteristic
347C4#9126311yescharacteristic
348C4#9127511yescharacteristic
349C4#9127711yescharacteristic
350C3#1059904311yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1174712011yescharacteristic
353C2#1174815011yescharacteristic
354C2#1174815211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#64971C2semidirect
4. #11746927C2semidirect
6. C5×#4456C2semidirect
7. #11745856C2semidirect
30. #64971D3semidirect
63. #4456D5semidirect
290. C3×C5#1650semidirect
335. C5#71370semidirect
350. C3#10599043semidirect

Maximal subgroups

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

subgroupindex
#117524832
C3×#649712
#117470852
#117469272
#117462802
C5×#44562
#117458562
#105990433
#713705