Finite Group Databasebeta

← #14289180

Subgroups — #14289180

Order 1920.

420 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#66055C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic
3#11747064C211yesmaximal, characteristic
4#11747064C211yesmaximal, characteristic
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745840C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599249—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91763C2211yescharacteristic
11C3×Q8×Dic5—21no—
12C3×#4090—21no—
13C3×#4036—21no—
14C3×#4035—22no—
15C3×#4033—21no—
16C3×C4×Dic10C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6658—21no—
19C2×#6658—21no—
20#91093—22no—
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90968—21no—
25#90968—21no—
26#71935—51nomaximal, Hall
27#66055D311yescharacteristic, complemented
28#65377—31no—
29#65137—31no—
30#65137—31no—
31C5×#332—31no—
32#64704—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D412yes—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C5×C3⋊C8—21no—
45C2×C5×C3⋊C8—21no—
46C3×C4⋊Dic5—22no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—22no—
50C3×#683—22no—
51C3×#683—21no—
52C3×#683—21no—
53C3×C4×Dic5—22no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5—21no—
56#6658—42no—
57#6658—42no—
58C3×#557—51no—
59#5088—51no—
60#5027—51no—
61#5027—51no—
62#4547D511yescharacteristic, complemented
63#4535—51no—
64#4535—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66Q8×Dic5—21no—
67#4090—21no—
68C2×#677—61no—
69C2×#677—61no—
70#4036—21no—
71#4035—22no—
72#4033—21no—
73#4020—31no—
74C4×Dic10C2×D311yescharacteristic
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8—31no—
78#3953—61no—
79#3953—61no—
80#3941—62no—
81C4×#168—31no—
82#1626—151noSylow
83C22×D15—41no—
84C3×C5×Q8—41no—
85C3×C5×Q8—41no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90D60—42no—
91D60—41no—
92D60—41no—
93D60—41no—
94D60—41no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C3×C4⋊Q8—101no—
107C3×C4⋊Q8C2×D511yescharacteristic
108C3×#125—101no—
109C3×#125—102no—
110C3×C4×Q8—51no—
111C3×C4×Q8—51no—
112C3×C4×Q8—101no—
113C3×C4×Q8—101no—
114C2×#215—101no—
115C2×#215—101no—
116#874—51no—
117#809—101no—
118#809—101no—
119#809—102no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—21no—
124C2×D20—61no—
125C2×D20—61no—
126C2×D20—61no—
127C2×Dic10#6711yescharacteristic
128C2×Dic10#6711yescharacteristic
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4#6712yes—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—22no—
135C4⋊Dic5#6711yescharacteristic
136C4⋊Dic5#6711yescharacteristic
137#683—22no—
138#683—22no—
139#683—21no—
140#683—21no—
141C4×Dic5—22no—
142C4×Dic5—21no—
143C4×Dic5—21no—
144C2×#168—61no—
145#677—122no—
146#677—122no—
147#557—51no—
148#486—151no—
149#460—151no—
150#460—151no—
151#332—31no—
152Q8⋊C8—151no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—81no—
156C2×D15—81no—
157C2×D15—81no—
158C3×C4×C5—21no—
159C3×C4×C5—42no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—22no—
165C3×Dic5—41no—
166C3×Dic5—41no—
167C3×Dic5—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8—51no—
170C2×C3×Q8—51no—
171C2×D12—101no—
172C2×D12—101no—
173C2×D12—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—102no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4D2012yes—
183C3×C42—102no—
184C3×C42—101no—
185C3×C42—101no—
186C3×C42C22×D511yescharacteristic
187#215—202no—
188#215—202no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—121no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—22no—
196C2×C4×C5C2×#6711yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208Dic10—21no—
209Dic10—21no—
210Dic10—21no—
211Dic10#21512yescomplemented
212C5×C8—121no—
213C5×C8—121no—
214#168—121no—
215C2×SD16—301no—
216C2×SD16—301no—
217C4⋊Q8—101no—
218C4⋊Q8D3×D511yescharacteristic
219#127—151no—
220#125—101no—
221#125—102no—
222C4×Q8—51no—
223C4×Q8—51no—
224C4×Q8—101no—
225C4×Q8—101no—
226C4⋊C8—31no—
227C4⋊C8—31no—
228#102—301no—
229#102—301no—
230#102—302no—
231C4×C8—151no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—161no—
236C22×D3—201no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—52no—
240C3×Q8—101no—
241C3×Q8—101no—
242C3×Q8—101no—
243C2×C3×C4—22no—
244C2×C3×C4—101no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4—101no—
248C2×C3×C4C2×D2011yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251D12—202no—
252D12—201no—
253D12—201no—
254D12—201no—
255D12—201no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#95311yescharacteristic
260C2×D5—241no—
261C2×D5—241no—
262C2×D5—241no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5C2×#21511yescharacteristic
266C4×C5#94211yescharacteristic
267C4×C5#94911yescharacteristic
268C4×C5#95011yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—41no—
272Dic5—41no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8—51no—
276C2×D4—301no—
277C2×D4—301no—
278C2×D4—301no—
279SD16—602no—
280SD16—602no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—102no—
288C4⋊C4—102no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4#120212yes—
293C42—102no—
294C42—101no—
295C42—101no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—401no—
300C2×D3—401no—
301C2×D3—401no—
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—102no—
305C3×C4—201no—
306C3×C4—201no—
307C3×C4—201no—
308C3×C4#405711yescharacteristic
309C3×C4D5×SD1611yescharacteristic
310C3×C4#406211yescharacteristic
311C3×C4#406411yescharacteristic
312C2×C5#522711yescharacteristic
313C2×C5#523811yescharacteristic
314C2×C5#524511yescharacteristic
315D5—481no—
316C23—601no—
317Q8—41no—
318Q8—41no—
319Q8—52no—
320Q8—101no—
321Q8—101no—
322Q8—101no—
323D4—602no—
324D4—601no—
325D4—601no—
326D4—601no—
327D4—601no—
328C2×C4—22no—
329C2×C4—101no—
330C2×C4—101no—
331C2×C4—101no—
332C2×C4—101no—
333C2×C4C2×#120211yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—121no—
337C8—121no—
338C8—601no—
339C2×C3#6504211yescharacteristic
340C2×C3#6507011yescharacteristic
341C2×C3#6509511yescharacteristic
342D3—801no—
343C5#7193511yescharacteristic, complemented, Sylow
344C22—1201no—
345C22—1201no—
346C22—1201no—
347C22#9156411yescharacteristic
348C4—21no—
349C4—42no—
350C4—102no—
351C4—201no—
352C4—201no—
353C4—201no—
354C4#9147811yescharacteristic
355C4#9149211yescharacteristic
356C4D5×#21511yescharacteristic
357C4#9151511yescharacteristic
358C3#1059924911yescharacteristic, complemented, Sylow
359C2—2401no—
360C2#1174902611yescharacteristic
361C2#1174926811yescharacteristic
362C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66055C2semidirect
5. C5×#4547C2semidirect
6. #11745840C2semidirect
7. #11745840C2semidirect
27. #66055D3semidirect
62. #4547D5semidirect
102. C3×Dic10SD16semidirect
211. Dic10#215semidirect
297. C3×C5#1626semidirect
343. C5#71935semidirect
358. C3#10599249semidirect

Maximal subgroups

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

subgroupindex
C3×#660552
#117511892
#117470642
C5×#45472
#117458402
#105992493
#719355