Finite Group Databasebeta

← #14289495

Subgroups — #14289495

Order 1920.

428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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#11756302C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic, complemented
4#11750800C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6#11746302C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598995—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10D4×Dic15—21no—
11C2×C4⋊Dic15—21no—
12#91813—21no—
13C2×Dic60—22no—
14#91779—21no—
15#91767—22no—
16#91758C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91116—21no—
22#91102—21no—
23#91100—21no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68202—51nomaximal, Hall
27#65877—31no—
28#65297—31no—
29#65139—31no—
30#64988—31no—
31C5×D4⋊C8D311yescharacteristic
32#64701—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×Dic15—22no—
37C2×Dic30—21no—
38C2×Dic30D411yescharacteristic
39C2×Dic30D412yes—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6719—22no—
46C4⋊Dic15—22no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15D411yescharacteristic
52#6712—22no—
53#6712—21no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56Dic60—44no—
57#5543—51no—
58#5008—51no—
59#4850—51no—
60#4699—51no—
61C3×D4⋊C8D511yescharacteristic
62#4481—51no—
63#4456—51no—
64C4×C5×D4C2×D311yescharacteristic
65D4×Dic5—61no—
66C2×C4⋊Dic5—61no—
67#4070—61no—
68C2×Dic20—62no—
69#4036—61no—
70#4024—62no—
71#4015—31no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3950—61no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
81#1632—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4Q1612yescomplemented
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—22no—
94C2×Dic15—41no—
95C2×Dic15—82no—
96Dic30—21no—
97Dic30—21no—
98Dic30—42no—
99Dic30—42no—
100C3×C5×C8—22no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C3×C4×D4C2×D511yescharacteristic
104D4×Dic3—101no—
105C2×C4⋊Dic3—101no—
106#924—101no—
107C2×Dic12—102no—
108#890—101no—
109#878—102no—
110#869—51no—
111#869—51no—
112C4×Dic6—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C4×C8C2×D511yescharacteristic
115#832—101no—
116#818—101no—
117#816—101no—
118#808—101no—
119C4⋊(C3⋊C8)—51no—
120C2×C5×D4D1211yescharacteristic
121C22×C4×C5—21no—
122C22×Dic5—62no—
123C2×Dic10—31no—
124C2×Dic10—32no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4D1211yescharacteristic
129C5×C22⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—62no—
132C4⋊Dic5—31no—
133C4⋊Dic5—62no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138#683—62no—
139#683—61no—
140C4×Dic5—61no—
141C2×#168—61no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8D1511yescharacteristic
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161Dic15—42no—
162Dic15—41no—
163Dic15—81no—
164C2×C3×D4D2011yescharacteristic
165C22×C3×C4—21no—
166C22×Dic3—102no—
167C2×Dic6—51no—
168C2×Dic6—52no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4D2011yescharacteristic
173C3×C22⋊C4—21no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176C4⋊Dic3—51no—
177C4⋊Dic3—102no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182Dic3⋊C4—102no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—101no—
186Dic12—204no—
187C23×C5—21no—
188C5×D4—21no—
189C5×D4Dic1212yescomplemented
190C2×C4×C5—21no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5C2×D1211yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×Dic5—61no—
197C2×Dic5—61no—
198C2×Dic5—62no—
199C2×Dic5—121no—
200C2×Dic5—242no—
201Dic10—61no—
202Dic10—61no—
203Dic10—122no—
204Dic10—122no—
205C5×C8—22no—
206C5×C8—41no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—151no—
215C4×D4—301no—
216C4×D4C2×D1511yescharacteristic
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8C2×D1511yescharacteristic
222#103—301no—
223#102—301no—
224C4×C8C2×D1511yescharacteristic
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×D4—21no—
231C3×D4Dic2012yescomplemented
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4C2×D2011yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×Dic3—101no—
239C2×Dic3—101no—
240C2×Dic3—102no—
241C2×Dic3—201no—
242C2×Dic3—402no—
243Dic6—101no—
244Dic6—101no—
245Dic6—202no—
246Dic6—202no—
247C3×C8—22no—
248C3×C8—41no—
249C3⋊C8—201no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#88211yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5C2×Dic1211yescharacteristic
257C4×C5#90911yescharacteristic
258C4×C5#91211yescharacteristic
259C4×C5#91511yescharacteristic
260Dic5—121no—
261Dic5—122no—
262Dic5—121no—
263Dic5—241no—
264C2×Q8—151no—
265C2×Q8—152no—
266C2×Q8—301no—
267C2×D4D6011yescharacteristic
268C22×C4—21no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—301no—
274C4⋊C4—151no—
275C4⋊C4—302no—
276C4⋊C4—302no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4D6011yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—302no—
285C42—301no—
286C42C22×D1511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3#402811yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4C2×Dic2011yescharacteristic
295C3×C4#405511yescharacteristic
296C3×C4#405811yescharacteristic
297C3×C4#406111yescharacteristic
298Dic3—201no—
299Dic3—202no—
300Dic3—201no—
301Dic3—401no—
302C2×C5—42no—
303C2×C5#473911yescharacteristic
304C2×C5#478311yescharacteristic
305C2×C5#482211yescharacteristic
306C23—21no—
307Q8—301no—
308Q8—301no—
309Q8—602no—
310Q8—602no—
311D4—21no—
312D4Dic6012yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—302no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×D6011yescharacteristic
322C2×C4D4×D1511yescharacteristic
323C2×C4D4×D1511yescharacteristic
324C8—22no—
325C8—41no—
326C8—601no—
327C2×C3—42no—
328C2×C3#6502811yescharacteristic
329C2×C3#6507211yescharacteristic
330C2×C3#6511111yescharacteristic
331C5#6820211yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22#9177111yescharacteristic
336C4—21no—
337C4—41no—
338C4—601no—
339C4—602no—
340C4—601no—
341C4—1201no—
342C4C2×Dic6011yescharacteristic
343C4#9179811yescharacteristic
344C4#9180111yescharacteristic
345C4#9180411yescharacteristic
346C3#1059899511yescharacteristic, complemented, Sylow
347C2—42no—
348C2#1175084011yescharacteristic
349C2#1175088411yescharacteristic
350C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterD4⋊C8D15
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11750951C2semidirect
4. #11750800C2semidirect
6. #11746302C2semidirect
7. #11746277C2semidirect
84. C3×C5×D4Q16semidirect
189. C5×D4Dic12semidirect
231. C3×D4Dic20semidirect
287. C3×C5#1632semidirect
312. D4Dic60semidirect
331. C5#68202semidirect
346. C3#10598995semidirect

Maximal subgroups

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

subgroupindex
#117563022
#117511092
#117509512
#117508002
C3×C5×D4⋊C82
#117463022
#117462772
#105989953
#682025