Finite Group Databasebeta

← #14316150

Subgroups — #14316150

Order 1920.

460 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 88 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×C3×#4065C211yesmaximal, characteristic, complemented
2C2×#91112C211yesmaximal, characteristic, complemented
3#11747899C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic, complemented
5C5×#4564C211yesmaximal, characteristic, complemented
6#11745891C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10600017—31nomaximal, Hall
9C2×C3×#713—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×D120C2211yescharacteristic
12C2×C3×#688—21no—
13C3×#4065—22no—
14C3×#4065—22no—
15C2×C3×D40C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91450—21no—
18#91112—22no—
19C2×C3⋊#672C2211yescharacteristic
20C5×#818C2211yescharacteristic
21C2×C5×C3⋊C16C2211yescharacteristic
22#90969—21no—
23#90938—22no—
24#72082—51nomaximal, Hall
25C2×#4065D311yescharacteristic, complemented
26C2×#3960—31no—
27C2×D80—31no—
28#65172—31no—
29C5×#358—31no—
30#64727—31no—
31#64711—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C3×#713—24no—
35C3×#713—42no—
36C2×C3×D20—21no—
37C2×C3×D20—41no—
38C2×C3×C4×D5—41no—
39C2×C3×C4×D5D411yescharacteristic
40C2×#1202—41no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44D120—21no—
45D120—21no—
46C5×C4⋊Dic3—21no—
47C3×#688—24no—
48C2×C3×#168D411yescharacteristic
49C3×D40—21no—
50C3×D40D412yescomplemented
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6667—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C2×C3×#135—51no—
57C2×#828—51no—
58C2×#826—51no—
59#5115—51no—
60#4564D511yescharacteristic, complemented
61#4562—51no—
62#4549—51no—
63C2×#713—21no—
64C2×C5×Q16C2×D311yescharacteristic
65C2×#688—21no—
66#4065—22no—
67#4065—22no—
68C2×D40—31no—
69C2×D40C2×D311yescharacteristic
70C2×C8×D5C2×D311yescharacteristic
71#4041—61no—
72C2×C5×C16—31no—
73C5×#107—31no—
74#3960—62no—
75C2×#672—31no—
76#3941—61no—
77D80—62no—
78#2186—151noSylow
79C22×D15—41no—
80C22×C3×D5—41no—
81C22×C3×D5D811yescharacteristic
82C3×C5×Q8—22no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86D60—41no—
87D60—41no—
88C2×C5×Dic3—41no—
89C2×C3×Dic5D811yescharacteristic
90C3×D20—22no—
91C3×D20—44no—
92C3×D20—41no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95C3×C4×D5—44no—
96#1202—82no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C2×C3×#41—101no—
101C3×#135—102no—
102C3×#135—102no—
103C2×C3×Q16C2×D511yescharacteristic
104C2×C3×SD16—101no—
105C2×C3×D8—51no—
106C22×C3×C8—51no—
107#930—101no—
108C2×D24—51no—
109#828—102no—
110#826—102no—
111#821—101no—
112#818C2×D511yescharacteristic
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—21no—
116#713—24no—
117#713—42no—
118C2×D20—21no—
119C2×D20—41no—
120C2×D20—61no—
121C2×D20—121no—
122C2×C4×D5—41no—
123C2×C4×D5#6711yescharacteristic
124C5×Q16—21no—
125C5×Q16#6712yescomplemented
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—61no—
128#688—24no—
129#685—121no—
130C2×#168#6711yescharacteristic
131D40—21no—
132D40—61no—
133D40—61no—
134D40#6712yescomplemented
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C2×#135—51no—
140C2×SD32—151no—
141C2×D16—151no—
142#466—151no—
143#358—31no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×D15—81no—
148C2×D15—81no—
149C2×D15—81no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—42no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—42no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5—21no—
160C5×Dic3—81no—
161C3×#41—104no—
162C3×#41—202no—
163C2×C3×Q8—21no—
164C2×C3×D4—101no—
165C2×C3×D4—201no—
166C22×C3×C4—51no—
167C22×C3×C4—201no—
168C2×#67—201no—
169C2×D12—101no—
170C3×Q16—21no—
171C3×Q16D2012yescomplemented
172C3×SD16—104no—
173C3×D8—52no—
174C3×D8—101no—
175C2×C3×C8—51no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C2×C3×C8C22×D511yescharacteristic
179(C2×D3)⋊C4—201no—
180C4⋊Dic3—21no—
181D24—101no—
182D24—101no—
183C3⋊C16—21no—
184C3⋊C16—101no—
185C22×D5—41no—
186C22×D5—121no—
187C22×D5#21311yescharacteristic
188C5×Q8—22no—
189C5×Q8—41no—
190C2×C4×C5—41no—
191C2×C4×C5—121no—
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5#21311yescharacteristic
194D20—22no—
195D20—44no—
196D20—41no—
197D20—121no—
198D20—121no—
199D20—242no—
200C4×D5—21no—
201C4×D5—21no—
202C4×D5—44no—
203C5×C8C2×#6711yescharacteristic
204C5×C8C2×#6711yescharacteristic
205#168—21no—
206C2×#41—101no—
207#135—102no—
208#135—102no—
209C2×Q16D3×D511yescharacteristic
210C2×SD16—101no—
211C2×D8—51no—
212C2×D8—151no—
213C22×C8—51no—
214#121—301no—
215SD32—302no—
216D16—302no—
217C2×C16—31no—
218C2×C16—151no—
219#107—31no—
220#102—301no—
221C2×C3×C5#44711yescharacteristic
222C2×C3×C5#50811yescharacteristic
223C2×C3×C5#50911yescharacteristic
224D15—161no—
225C3×D5—41no—
226C3×D5—82no—
227C23×C3—51no—
228C23×C3—201no—
229C22×D3—201no—
230C3×Q8—22no—
231C3×Q8—41no—
232C3×D4—102no—
233C3×D4—204no—
234C3×D4—201no—
235C2×C3×C4—41no—
236C2×C3×C4—51no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—204no—
240C2×C3×C4D4×D511yescharacteristic
241#67—402no—
242C2×Dic3—41no—
243D12—201no—
244D12—201no—
245C3×C8—101no—
246C3×C8C2×D2011yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5C2×#21311yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—42no—
253C2×D5—81no—
254C2×D5—81no—
255C2×D5—241no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—42no—
259C4×C5—241no—
260C4×C5#93211yescharacteristic
261C4×C5#95311yescharacteristic
262Dic5—21no—
263#41—104no—
264#41—202no—
265C2×Q8—21no—
266C2×D4—101no—
267C2×D4—201no—
268C2×D4—301no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—201no—
272Q16—21no—
273Q16#120212yescomplemented
274SD16—104no—
275D8—52no—
276D8—101no—
277D8—301no—
278D8—301no—
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—61no—
284C22⋊C4—601no—
285C16—61no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—101no—
289C22×C3—101no—
290C22×C3—101no—
291C22×C3—202no—
292C22×C3—401no—
293C22×C3—401no—
294C22×C3D5×D811yescharacteristic
295C2×D3—401no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—42no—
299C3×C4—101no—
300C3×C4#402811yescharacteristic
301C3×C4#406011yescharacteristic
302Dic3—81no—
303C2×C5#519311yescharacteristic
304C2×C5#519411yescharacteristic
305C2×C5#521711yescharacteristic
306D5—41no—
307D5—82no—
308D5—481no—
309C23—51no—
310C23—201no—
311C23—601no—
312Q8—22no—
313Q8—41no—
314D4—102no—
315D4—204no—
316D4—201no—
317D4—601no—
318D4—601no—
319D4—1202no—
320C2×C4—41no—
321C2×C4—51no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—121no—
325C2×C4—204no—
326C2×C4D5×#6711yescharacteristic
327C8—101no—
328C8C2×#120211yescharacteristic
329C8D5×#6711yescharacteristic
330C2×C3—201no—
331C2×C3—402no—
332C2×C3#6506211yescharacteristic
333C2×C3#6520311yescharacteristic
334C2×C3#6520811yescharacteristic
335D3—801no—
336C5#7208211yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—202no—
341C22—401no—
342C22—401no—
343C22—1201no—
344C22—1201no—
345C22—1201no—
346C22D5×#21311yescharacteristic
347C4—42no—
348C4—101no—
349C4—241no—
350C4#9149111yescharacteristic
351C4#9156411yescharacteristic
352C3#1060001711yescharacteristic, complemented, Sylow
353C2—201no—
354C2—402no—
355C2—2401no—
356C2#1174828911yescharacteristic
357C2#1174830311yescharacteristic
358C2#1174902211yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4065C2semidirect
2. C2×#91112C2semidirect
3. #11747899C2semidirect
4. C2×#90938C2semidirect
5. C5×#4564C2semidirect
6. #11745891C2semidirect
7. #11745879C2semidirect
25. C2×#4065D3semidirect
42. C3×C5×Q16D4semidirect
50. C3×D40D4semidirect
60. #4564D5semidirect
125. C5×Q16#67semidirect
134. D40#67semidirect
171. C3×Q16D20semidirect
273. Q16#1202semidirect
287. C3×C5#2186semidirect
336. C5#72082semidirect
352. C3#10600017semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40652
C2×#911122
#117478992
C2×#909382
C5×#45642
#117458912
#117458792
#106000173
#720825