Finite Group Databasebeta

← #14289203

Subgroups — #14289203

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
1#11756329C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic
3#11747083C211yesmaximal, characteristic
4#11746890C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745859C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10599045—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10Q8×Dic15—21no—
11#91779—21no—
12#91779—22no—
13#91758—21no—
14#91758C2211yescharacteristic
15C4×Dic30—21no—
16C4×Dic30C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6657—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3941—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90965—21no—
25#90965—22no—
26#71030—51nomaximal, Hall
27#65904—31no—
28#65316D311yescharacteristic
29#65137—31no—
30#64983—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×Dic30D411yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15—22no—
45C4⋊Dic15—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15D411yescharacteristic
48C4⋊Dic15D412yes—
49#6712—22no—
50#6712—21no—
51C4×Dic15—22no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6657—42no—
58#5570—51no—
59C3×#460—51no—
60#5075—51no—
61#5070—51no—
62#4535D511yescharacteristic, complemented
63#4486—51no—
64#4484—51no—
65C4×C5×Q8C2×D311yescharacteristic
66Q8×Dic5—61no—
67C2×#688—21no—
68C2×#677—61no—
69#4036—62no—
70#4036—61no—
71#4020C2×D311yescharacteristic
72#4015—31no—
73#4015—61no—
74C4×Dic10—31no—
75C4×Dic10—61no—
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3953—61no—
79#3953—62no—
80#3941—21no—
81C4⋊#168C2×D311yescharacteristic
82#1626—151noSylow
83C22×C3×D5—41no—
84C3×C5×Q8—21no—
85C3×C5×Q8SD1612yescomplemented
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—22no—
94Dic30—21no—
95Dic30—21no—
96Dic30—41no—
97Dic30—41no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C2×C3×SD16—101no—
107C3×#127—51no—
108C3×C4×Q8C2×D511yescharacteristic
109Q8×Dic3—101no—
110C2×#214—101no—
111#890—102no—
112#890—101no—
113#869—51no—
114#869—101no—
115C4×Dic6—51no—
116C4×Dic6—101no—
117C3×C4⋊C8—51no—
118C3×#102—101no—
119#832—102no—
120#832—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8#6711yescharacteristic
124C2×D20—21no—
125C2×D20—21no—
126C2×D20—21no—
127C2×Dic10—31no—
128C2×Dic10—61no—
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4#6711yescharacteristic
133C42×C5—21no—
134C42×C5C22×D311yescharacteristic
135#688—42no—
136C4⋊Dic5—31no—
137C4⋊Dic5—32no—
138C4⋊Dic5—62no—
139C4⋊Dic5—62no—
140C4⋊Dic5—61no—
141#683—62no—
142#683—61no—
143C4×Dic5—62no—
144C4×Dic5—61no—
145C2×#168—21no—
146#677—122no—
147#557—151no—
148#486—151no—
149#460—51no—
150#460—151no—
151#332—151no—
152Q8⋊C8—31no—
153Q8⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—81no—
156C2×C3×D5—81no—
157C2×C3×D5—81no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—42no—
167Dic15—41no—
168C2×C3×Q8D2011yescharacteristic
169C2×C3×D4—101no—
170C2×C3×D4—101no—
171C2×C3×D4—101no—
172C2×Dic6—51no—
173C2×Dic6—101no—
174C3×SD16—202no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4D2011yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180#214—202no—
181C4⋊Dic3—51no—
182C4⋊Dic3—52no—
183C4⋊Dic3—102no—
184C4⋊Dic3—102no—
185C4⋊Dic3—101no—
186Dic3⋊C4—102no—
187Dic3⋊C4—101no—
188C4×Dic3—102no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C22×D5—41no—
193C5×Q8—21no—
194C5×Q8#21412yescomplemented
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—61no—
201C2×Dic5—62no—
202C2×Dic5—61no—
203D20—42no—
204D20—41no—
205D20—41no—
206D20—41no—
207D20—41no—
208Dic10—61no—
209Dic10—61no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213C5×C8—121no—
214#168—41no—
215C2×SD16—101no—
216C2×SD16—301no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219#127—51no—
220#125—302no—
221#125—301no—
222C4×Q8—151no—
223C4×Q8—301no—
224C4×Q8—301no—
225C4×Q8D3×D511yescharacteristic
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—101no—
229#102—301no—
230#102—302no—
231C4×C8—31no—
232C2×C3×C5#44811yescharacteristic
233C2×C3×C5#44911yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—161no—
236C23×C3—201no—
237C3×Q8—21no—
238C3×Q8#67712yescomplemented
239C3×D4—202no—
240C3×D4—201no—
241C3×D4—201no—
242C3×D4—201no—
243C3×D4—201no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4C2×D2011yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×Dic3—101no—
250C2×Dic3—102no—
251C2×Dic3—101no—
252Dic6—101no—
253Dic6—101no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5#93711yescharacteristic
260C2×D5—81no—
261C2×D5—81no—
262C2×D5—81no—
263C4×C5—21no—
264C4×C5—22no—
265C4×C5—41no—
266C4×C5#91411yescharacteristic
267C4×C5#91611yescharacteristic
268C4×C5C2×#21411yescharacteristic
269C4×C5#95111yescharacteristic
270Dic5—121no—
271Dic5—122no—
272Dic5—121no—
273C2×Q8—151no—
274C2×Q8—301no—
275C2×Q8#120211yescharacteristic
276C2×D4—101no—
277C2×D4—101no—
278C2×D4—101no—
279SD16—202no—
280SD16—602no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—151no—
286C4⋊C4—152no—
287C4⋊C4—302no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4#120211yescharacteristic
293C42—21no—
294C42—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#162611yescharacteristic, complemented, Hall
298C22×C3—401no—
299C22×C3—401no—
300C22×C3—401no—
301C22×C3#402811yescharacteristic
302C3×C4—22no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4C2×#67711yescharacteristic
306C3×C4#405511yescharacteristic
307C3×C4#406011yescharacteristic
308C3×C4#406511yescharacteristic
309Dic3—201no—
310Dic3—202no—
311Dic3—201no—
312C2×C5#504011yescharacteristic
313C2×C5#517211yescharacteristic
314C2×C5#520111yescharacteristic
315D5—161no—
316C23—201no—
317Q8—21no—
318Q8—301no—
319Q8—301no—
320Q8—601no—
321Q8—601no—
322Q8#665712yescomplemented
323D4—202no—
324D4—201no—
325D4—201no—
326D4—201no—
327D4—201no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—301no—
331C2×C4—302no—
332C2×C4—301no—
333C2×C4C2×#120211yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—121no—
338C8—201no—
339C2×C3—801no—
340C2×C3#6502711yescharacteristic
341C2×C3#6510011yescharacteristic
342C2×C3#6511611yescharacteristic
343C5#7103011yescharacteristic, complemented, Sylow
344C22—401no—
345C22—401no—
346C22—401no—
347C22#9157211yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—601no—
352C4—601no—
353C4—602no—
354C4C2×#665711yescharacteristic
355C4#9131311yescharacteristic
356C4#9150611yescharacteristic
357C4#9152111yescharacteristic
358C3#1059904511yescharacteristic, complemented, Sylow
359C2—801no—
360C2#1174854911yescharacteristic
361C2#1174928811yescharacteristic
362C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
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. #11756329C2semidirect
5. C5×#4535C2semidirect
6. #11745859C2semidirect
7. #11745844C2semidirect
62. #4535D5semidirect
85. C3×C5×Q8SD16semidirect
194. C5×Q8#214semidirect
238. C3×Q8#677semidirect
297. C3×C5#1626semidirect
322. Q8#6657semidirect
343. C5#71030semidirect
358. C3#10599045semidirect

Maximal subgroups

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

subgroupindex
#117563292
C3×#653162
#117470832
#117468902
C5×#45352
#117458592
#117458442
#105990453
#710305