Finite Group Databasebeta

← #14316099

Subgroups — #14316099

Order 1920.

460 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#91793C211yesmaximal, characteristic, complemented
2C3×C5×#466C211yesmaximal, characteristic, complemented
3C2×#91111C211yesmaximal, characteristic, complemented
4C2×#91110C211yesmaximal, characteristic, complemented
5#11746370C211yesmaximal, characteristic, complemented
6#11746313C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic, complemented
8#10601869—31nomaximal, Hall
9C2×#6817—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C3×C5×#121—21no—
13C2×Dic60C2211yescharacteristic
14#91793—22no—
15#91793—22no—
16C2×D120C2211yescharacteristic
17C2×#6706—21no—
18C3×C5×#107C2211yescharacteristic
19C3×C5×#102—21no—
20#91111—22no—
21#91110—22no—
22C2×C3⋊#672C2211yescharacteristic
23C2×C3⋊#672C2211yescharacteristic
24#71076—51nomaximal, Hall
25C2×#4050—31no—
26C5×#466D311yescharacteristic, complemented
27C2×#3959—31no—
28C2×#3958—31no—
29C22⋊#672—31no—
30#64712—31no—
31#64711—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—41no—
34C22×C3×C4×C5D411yescharacteristic
35C2×#1220—41no—
36#6817—24no—
37#6817—42no—
38C2×D60—21no—
39C2×C4×D15—41no—
40C2×Dic30—21no—
41C3×C5×D8—21no—
42C3×C5×D8—21no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8D411yescharacteristic
46C2×C3×C5×C8C2311yescharacteristic
47C3×C5×C4⋊C4—21no—
48C3×C5×C22⋊C4—41no—
49Dic60—21no—
50Dic60D412yescomplemented
51D120—21no—
52D120D412yescomplemented
53#6706—24no—
54C3⋊#672—21no—
55C3⋊#672—21no—
56C2×#904—51no—
57C3×#466D511yescharacteristic, complemented
58C2×#827—51no—
59C2×#826—51no—
60#4549—51no—
61#4492—51no—
62#4491—51no—
63C2×#709—61no—
64C2×C5×D8C2×D311yescharacteristic
65C22×C5×C8C2×D311yescharacteristic
66C5×#121—21no—
67C2×Dic20—31no—
68#4050—62no—
69#4050—62no—
70C2×D40—31no—
71C2×#677—61no—
72C5×#107C2×D311yescharacteristic
73C5×#102—21no—
74#3959—62no—
75#3958—62no—
76C2×#672—31no—
77C2×#672—31no—
78#2186—151noSylow
79C23×C3×C5—41no—
80C23×C3×C5D811yescharacteristic
81C22×D15—41no—
82C3×C5×D4—41no—
83C3×C5×D4—41no—
84C3×C5×D4—82no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5D811yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90#1220—44no—
91C2×Dic15—41no—
92D60—22no—
93D60—41no—
94C4×D15—44no—
95Dic30—22no—
96Dic30—41no—
97C3×C5×C8—21no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C2×#235—101no—
101C2×C3×D8C2×D511yescharacteristic
102C22×C3×C8C2×D511yescharacteristic
103C3×#121—21no—
104C2×Dic12—51no—
105#904—102no—
106#904—102no—
107C2×D24—51no—
108C2×#204—101no—
109C3×#107C2×D511yescharacteristic
110C3×#102—21no—
111#827—102no—
112#826—102no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16—51no—
115C2×C5×D4—21no—
116C2×C5×D4—41no—
117C22×C4×C5#6711yescharacteristic
118C2×C22⋊D5—121no—
119#709—64no—
120#709—122no—
121C2×D20—61no—
122C2×C4×D5—121no—
123C2×Dic10—61no—
124C5×D8—21no—
125C5×D8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C2×C5×C8#6711yescharacteristic
129C2×C5×C8C22×D311yescharacteristic
130C5×C4⋊C4—21no—
131C5×C22⋊C4—41no—
132Dic20—32no—
133Dic20—61no—
134D40—32no—
135D40—61no—
136#677—64no—
137#672—61no—
138#672—61no—
139C2×#135—151no—
140C2×SD32—151no—
141C2×D16—151no—
142#466D1511yescharacteristic, complemented
143#358—151no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5—81no—
152C22×C3×C5C2×D811yescharacteristic
153C2×D15—42no—
154C2×D15—81no—
155C2×D15—81no—
156C3×C4×C5—21no—
157C3×C4×C5—81no—
158C3×C4×C5#12011yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160Dic15—42no—
161C2×C3×D4—21no—
162C2×C3×D4—41no—
163C22×C3×C4C22⋊D511yescharacteristic
164C2×#67—201no—
165#235—104no—
166#235—202no—
167C2×D12—101no—
168C2×C4×D3—201no—
169C2×Dic6—101no—
170C3×D8—21no—
171C3×D8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8C22⋊D511yescharacteristic
175C2×C3×C8C22×D511yescharacteristic
176C3×C4⋊C4—21no—
177C3×C22⋊C4—41no—
178Dic12—52no—
179Dic12—101no—
180D24—52no—
181D24—101no—
182#204—104no—
183C3⋊C16—101no—
184C3⋊C16—101no—
185C23×C5—41no—
186C23×C5#21311yescharacteristic
187C22×D5—121no—
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—82no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5#21311yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C22⋊D5—124no—
197C2×Dic5—121no—
198D20—62no—
199D20—121no—
200C4×D5—124no—
201Dic10—62no—
202Dic10—121no—
203C5×C8—21no—
204C5×C8D3×D411yescharacteristic
205C5×C8D3×D411yescharacteristic
206C2×#41—301no—
207#135—302no—
208#135—302no—
209C2×Q16—151no—
210C2×SD16—301no—
211C2×D8—151no—
212C2×D8C2×D1511yescharacteristic
213C22×C8C2×D1511yescharacteristic
214#121—21no—
215SD32—302no—
216D16—302no—
217C2×C16—151no—
218C2×C16—151no—
219#107C2×D1511yescharacteristic
220#102—21no—
221C2×C3×C5—41no—
222C2×C3×C5—161no—
223C2×C3×C5#44711yescharacteristic
224C2×C3×C5#50811yescharacteristic
225C2×C3×C5#50911yescharacteristic
226D15—82no—
227C23×C3—41no—
228C23×C3#68611yescharacteristic
229C22×D3—201no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—82no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4#68611yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238#67—204no—
239C2×Dic3—201no—
240D12—102no—
241D12—201no—
242C4×D3—204no—
243Dic6—102no—
244Dic6—201no—
245C3×C8—21no—
246C3×C8D4×D511yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—81no—
252C22×C5—81no—
253C22×C5—81no—
254C22×C5C2×#21311yescharacteristic
255C2×D5—122no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—21no—
259C4×C5—81no—
260C4×C5#93711yescharacteristic
261C4×C5#94911yescharacteristic
262Dic5—122no—
263#41—304no—
264#41—602no—
265C2×Q8—301no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—301no—
269C2×D4—601no—
270C22×C4—601no—
271C22×C4#122011yescharacteristic
272Q16—152no—
273Q16—301no—
274SD16—304no—
275D8—21no—
276D8—21no—
277D8—152no—
278D8—301no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8#122011yescharacteristic
282C2×C8C22×D1511yescharacteristic
283C4⋊C4—21no—
284C22⋊C4—41no—
285C16—301no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—81no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3C2×#68611yescharacteristic
295C2×D3—202no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—21no—
299C3×C4—81no—
300C3×C4#408311yescharacteristic
301C3×C4#409511yescharacteristic
302Dic3—202no—
303C2×C5—41no—
304C2×C5—161no—
305C2×C5#503611yescharacteristic
306C2×C5#514711yescharacteristic
307C2×C5#519411yescharacteristic
308D5—242no—
309C23—41no—
310C23—601no—
311C23#671511yescharacteristic
312Q8—302no—
313Q8—601no—
314D4—41no—
315D4—41no—
316D4—82no—
317D4—302no—
318D4—604no—
319D4—601no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—604no—
324C2×C4—601no—
325C2×C4#671511yescharacteristic
326C2×C4C2×#122011yescharacteristic
327C8—21no—
328C8D4×D1511yescharacteristic
329C8D4×D1511yescharacteristic
330C2×C3—41no—
331C2×C3—161no—
332C2×C3#6532511yescharacteristic
333C2×C3#6543611yescharacteristic
334C2×C3#6548311yescharacteristic
335D3—402no—
336C5#7107611yescharacteristic, complemented, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—602no—
344C22—1201no—
345C22—1201no—
346C22C2×#671511yescharacteristic
347C4—21no—
348C4—81no—
349C4—602no—
350C4#9182611yescharacteristic
351C4#9183811yescharacteristic
352C3#1060186911yescharacteristic, complemented, Sylow
353C2—41no—
354C2—161no—
355C2—1202no—
356C2#1175113711yescharacteristic
357C2#1175124811yescharacteristic
358C2#1175129511yescharacteristic
subgroupG/H
centerC22C2×#6715
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#466C2
socleC22×C3×C5C2×D8
hypercenter#466D15
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#91793C2semidirect
2. C3×C5×#466C2semidirect
3. C2×#91111C2semidirect
4. C2×#91110C2semidirect
5. #11746370C2semidirect
6. #11746313C2semidirect
7. #11746312C2semidirect
26. C5×#466D3semidirect
50. Dic60D4semidirect
52. D120D4semidirect
57. C3×#466D5semidirect
142. #466D15semidirect
287. C3×C5#2186semidirect
336. C5#71076semidirect
352. C3#10601869semidirect

Maximal subgroups

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

subgroupindex
C2×#917932
C3×C5×#4662
C2×#911112
C2×#911102
#117463702
#117463132
#117463122
#106018693
#710765