Finite Group Databasebeta

← #14289162

Subgroups — #14289162

Order 1920.

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

normal subgroups only

This group has 420 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#11756480C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic
3#11750949C211yesmaximal, characteristic
4#11750949C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746305C211yesmaximal, characteristic, complemented
8#10599249—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10Q8×Dic15—21no—
11#91833—21no—
12C2×#6706—21no—
13C2×#6706—21no—
14#91779—21no—
15#91778—22no—
16#91776—21no—
17#91763C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22#91105—21no—
23#91105—21no—
24#91093—22no—
25C4×C3⋊#168C2211yescharacteristic
26#68456—51nomaximal, Hall
27#66055—31no—
28#65377—31no—
29#65137—31no—
30#65137—31no—
31C5×#332D311yescharacteristic, complemented
32#64704—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×Dic30D411yescharacteristic
39C2×Dic30D411yescharacteristic
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D412yes—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—22no—
46C4⋊Dic15D411yescharacteristic
47C4⋊Dic15D411yescharacteristic
48#6712—22no—
49#6712—22no—
50#6712—21no—
51#6712—21no—
52C4×Dic15—22no—
53C4×Dic15—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56#6706—42no—
57#6706—42no—
58#5721—51no—
59#5088—51no—
60#4848—51no—
61#4848—51no—
62C3×#332D511yescharacteristic, complemented
63#4484—51no—
64#4484—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66Q8×Dic5—61no—
67#4090—61no—
68C2×#677—61no—
69C2×#677—61no—
70#4036—61no—
71#4035—62no—
72#4033—61no—
73#4020—31no—
74C4×Dic10—31no—
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×C4⋊C8C2×D311yescharacteristic
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
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94D60—42no—
95D60—41no—
96D60—41no—
97D60—41no—
98D60—41no—
99Dic30—21no—
100Dic30—21no—
101Dic30—21no—
102Dic30SD1612yescomplemented
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C3×C4⋊Q8C2×D511yescharacteristic
107Q8×Dic3—101no—
108#944—101no—
109C2×#204—101no—
110C2×#204—101no—
111#890—101no—
112#889—102no—
113#887—101no—
114#874—51no—
115C4×Dic6—51no—
116C4×Dic6—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4⋊C8C2×D511yescharacteristic
119#821—101no—
120#821—101no—
121#809—102no—
122C4×C3⋊C8—51no—
123C2×C5×Q8—21no—
124C2×D20—61no—
125C2×D20—61no—
126C2×D20—61no—
127C2×Dic10—31no—
128C2×Dic10—31no—
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4D1212yes—
133C42×C5C22×D311yescharacteristic
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136C4⋊Dic5—62no—
137#683—62no—
138#683—62no—
139#683—61no—
140#683—61no—
141C4×Dic5—62no—
142C4×Dic5—61no—
143C4×Dic5—61no—
144C2×#168—61no—
145#677—122no—
146#677—122no—
147#557—151no—
148#486—151no—
149#460—151no—
150#460—151no—
151#332D1511yescharacteristic, complemented
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
164Dic15—22no—
165Dic15—41no—
166Dic15—41no—
167Dic15—41no—
168C2×C3×Q8—21no—
169C2×D12—101no—
170C2×D12—101no—
171C2×D12—101no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4D2012yes—
178C3×C42C22×D511yescharacteristic
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182Dic3⋊C4—102no—
183Dic3⋊C4—102no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186C4×Dic3—102no—
187C4×Dic3—101no—
188C4×Dic3—101no—
189C2×C3⋊C8—101no—
190#204—202no—
191#204—202no—
192C22×D5—121no—
193C5×Q8—41no—
194C5×Q8—41no—
195C2×C4×C5—22no—
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×Dic5—61no—
200C2×Dic5—61no—
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208Dic10—32no—
209Dic10—61no—
210Dic10—61no—
211Dic10—61no—
212C5×C8—41no—
213C5×C8—41no—
214#168—121no—
215C2×SD16—301no—
216C2×SD16—301no—
217C4⋊Q8—301no—
218C4⋊Q8C2×D1511yescharacteristic
219#127—151no—
220#125—301no—
221#125—302no—
222C4×Q8—151no—
223C4×Q8—151no—
224C4×Q8—301no—
225C4×Q8—301no—
226C4⋊C8C2×D1511yescharacteristic
227C4⋊C8C2×D1511yescharacteristic
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—
239C2×C3×C4—22no—
240C2×C3×C4C2×D2011yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×Dic3—101no—
244C2×Dic3—101no—
245C2×Dic3—101no—
246C2×Dic3—101no—
247D12—202no—
248D12—201no—
249D12—201no—
250D12—201no—
251D12—201no—
252Dic6—52no—
253Dic6—101no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—41no—
257C3×C8—41no—
258C3⋊C8—201no—
259C22×C5#88211yescharacteristic
260C2×D5—241no—
261C2×D5—241no—
262C2×D5—241no—
263C4×C5—21no—
264C4×C5—42no—
265C4×C5#91111yescharacteristic
266C4×C5D3×SD1611yescharacteristic
267C4×C5#91611yescharacteristic
268C4×C5#91811yescharacteristic
269Dic5—62no—
270Dic5—121no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—151no—
275C2×Q8—151no—
276C2×D4—301no—
277C2×D4—301no—
278C2×D4—301no—
279SD16—602no—
280SD16—602no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—301no—
284C4⋊C4—21no—
285C4⋊C4—151no—
286C4⋊C4—151no—
287C4⋊C4—302no—
288C4⋊C4—302no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4D6012yes—
293C42—302no—
294C42—301no—
295C42—301no—
296C42C22×D1511yescharacteristic
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#405711yescharacteristic
305C3×C4D5×SD1611yescharacteristic
306C3×C4#406211yescharacteristic
307C3×C4#406411yescharacteristic
308Dic3—102no—
309Dic3—201no—
310Dic3—201no—
311Dic3—201no—
312C2×C5#475311yescharacteristic
313C2×C5#478111yescharacteristic
314C2×C5#480611yescharacteristic
315D5—481no—
316C23—601no—
317Q8—41no—
318Q8—41no—
319Q8—152no—
320Q8—301no—
321Q8—301no—
322Q8—301no—
323D4—602no—
324D4—601no—
325D4—601no—
326D4—601no—
327D4—601no—
328C2×C4—22no—
329C2×C4—301no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—301no—
333C2×C4C2×D6011yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C8—41no—
337C8—41no—
338C8—601no—
339C2×C3#6504211yescharacteristic
340C2×C3#6507011yescharacteristic
341C2×C3#6509511yescharacteristic
342D3—801no—
343C5#6845611yescharacteristic, complemented, Sylow
344C22—1201no—
345C22—1201no—
346C22—1201no—
347C22#9177111yescharacteristic
348C4—21no—
349C4—42no—
350C4—302no—
351C4—601no—
352C4—601no—
353C4—601no—
354C4#9180011yescharacteristic
355C4SD16×D1511yescharacteristic
356C4#9180511yescharacteristic
357C4#9180711yescharacteristic
358C3#1059924911yescharacteristic, complemented, Sylow
359C2—2401no—
360C2#1175085411yescharacteristic
361C2#1175088211yescharacteristic
362C2#1175090711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenter#332D15
hypocenterC3×C5#1626
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #11756480C2semidirect
5. C3×C5×#332C2semidirect
6. #11746305C2semidirect
7. #11746305C2semidirect
31. C5×#332D3semidirect
62. C3×#332D5semidirect
102. Dic30SD16semidirect
151. #332D15semidirect
297. C3×C5#1626semidirect
343. C5#68456semidirect
358. C3#10599249semidirect

Maximal subgroups

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

subgroupindex
#117564802
#117511892
#117509492
C3×C5×#3322
#117463052
#105992493
#684565