Finite Group Databasebeta

← #14316145

Subgroups — #14316145

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×C5×#828C211yesmaximal, characteristic, complemented
3#11747898C211yesmaximal, characteristic, complemented
4C2×#90937C211yesmaximal, characteristic, complemented
5#11746385C211yesmaximal, characteristic, complemented
6#11745892C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10602277—31nomaximal, Hall
9C2×C3×#713—21no—
10C2×C3×C5×Q16C2211yescharacteristic
11C2×C5×D24C2211yescharacteristic
12C2×C3×#688—21no—
13C3×#4065—22no—
14C3×#4065—22no—
15C2×C3×D40C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91449—21no—
18#91102C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C5×#828—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22#90967—21no—
23#90937—22no—
24#72082—51nomaximal, Hall
25C2×#4065D311yescharacteristic, complemented
26C2×C5×SD32—31no—
27#65446—31no—
28C2×#3958—31no—
29#64784—31no—
30#64729—31no—
31#64727—31no—
32C2×C3×C5×Q8—21no—
33C2×C5×D12—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×#1201—41no—
41C3×C5×Q16—21no—
42C3×C5×Q16D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44C4⋊Dic15—21no—
45C5×D24—21no—
46C5×D24—21no—
47C3×#688—24no—
48C2×C3×#168D411yescharacteristic
49C3×D40—21no—
50C3×D40D412yescomplemented
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53(C2×D3)⋊Dic5—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C2×C3×#135—51no—
57C2×#828D511yescharacteristic, complemented
58C2×#826—51no—
59#5115—51no—
60#4564—51no—
61#4562—51no—
62#4549—51no—
63C2×#713—21no—
64C2×C5×Q16C2×D311yescharacteristic
65C2×C5×D8—31no—
66C2×#688—21no—
67#4084—61no—
68#4065—22no—
69#4065—22no—
70C2×D40C2×D311yescharacteristic
71C2×C8×D5C2×D311yescharacteristic
72C5×SD32—62no—
73C2×C5×C16—31no—
74#3964—61no—
75#3958—62no—
76#3950—31no—
77C2×#672—31no—
78#2186—151noSylow
79C22×C5×D3—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
86C2×Dic15—41no—
87C5×D12—41no—
88C5×D12—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#1201—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×D24C2×D511yescharacteristic
109#828—22no—
110#826—102no—
111#821—101no—
112#818—51no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—21no—
116C2×C5×D4—61no—
117C2×C22⋊D5—121no—
118#713—24no—
119#713—42no—
120C2×D20—21no—
121C2×D20—41no—
122C2×C4×D5—41no—
123C2×C4×D5#6711yescharacteristic
124C5×Q16—21no—
125C5×Q16#6712yescomplemented
126C5×D8—61no—
127C5×D8—61no—
128C2×C5×C8C22×D311yescharacteristic
129C22⋊Dic5—121no—
130#688—24no—
131C4⋊Dic5—61no—
132C2×#168#6711yescharacteristic
133D40—21no—
134D40#6712yescomplemented
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C2×#135—51no—
140C2×SD32—31no—
141C2×D16—151no—
142#466—151no—
143#358—151no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×C5×D3—81no—
148C2×C5×D3—81no—
149C2×C5×D3—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
159Dic15—81no—
160C3×Dic5—21no—
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—21no—
170C3×Q16—21no—
171C3×Q16C22⋊D512yescomplemented
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—101no—
181D24—21no—
182D24—21no—
183C3⋊C16—21no—
184C3⋊C16—101no—
185C23×C5—121no—
186C22×D5—41no—
187C22×D5#21311yescharacteristic
188C5×Q8—22no—
189C5×Q8—41no—
190C5×D4—121no—
191C5×D4—121no—
192C2×C4×C5—41no—
193C2×C4×C5C2×#6711yescharacteristic
194C22⋊D5—242no—
195C2×Dic5—121no—
196C2×Dic5#21311yescharacteristic
197D20—22no—
198D20—44no—
199D20—41no—
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—31no—
212C2×D8—51no—
213C22×C8—51no—
214#121—301no—
215SD32—62no—
216D16—302no—
217C2×C16—31no—
218C2×C16—151no—
219#107—151no—
220#102—301no—
221C2×C3×C5#44711yescharacteristic
222C2×C3×C5#50811yescharacteristic
223C2×C3×C5#50911yescharacteristic
224C3×D5—41no—
225C3×D5—82no—
226C5×D3—161no—
227C23×C3—51no—
228C23×C3—201no—
229C22×D3—41no—
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—201no—
243D12—41no—
244D12—41no—
245C3×C8—101no—
246C3×C8D4×D511yescharacteristic
247C3×C8C2×C22⋊D511yescharacteristic
248C22×C5—241no—
249C22×C5—241no—
250C22×C5—241no—
251C22×C5C2×#21311yescharacteristic
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C2×D5—42no—
256C2×D5—81no—
257C2×D5—81no—
258C4×C5—42no—
259C4×C5#93211yescharacteristic
260C4×C5#95311yescharacteristic
261Dic5—21no—
262Dic5—241no—
263#41—104no—
264#41—202no—
265C2×Q8—21no—
266C2×D4—61no—
267C2×D4—101no—
268C2×D4—201no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—201no—
272Q16—21no—
273Q16#120112yescomplemented
274SD16—104no—
275D8—52no—
276D8—61no—
277D8—61no—
278D8—101no—
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—301no—
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—81no—
296C2×D3—81no—
297C2×D3—81no—
298C3×C4—42no—
299C3×C4—101no—
300C3×C4#405711yescharacteristic
301C3×C4#408311yescharacteristic
302Dic3—401no—
303C2×C5—481no—
304C2×C5#519311yescharacteristic
305C2×C5#519411yescharacteristic
306C2×C5#521711yescharacteristic
307D5—41no—
308D5—82no—
309C23—51no—
310C23—121no—
311C23—201no—
312Q8—22no—
313Q8—41no—
314D4—102no—
315D4—121no—
316D4—121no—
317D4—204no—
318D4—201no—
319D4—1202no—
320C2×C4—41no—
321C2×C4—51no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—204no—
325C2×C4—601no—
326C2×C4D5×#6711yescharacteristic
327C8—101no—
328C8C2×#120111yescharacteristic
329C8D5×#6711yescharacteristic
330C2×C3—201no—
331C2×C3—402no—
332C2×C3#6520311yescharacteristic
333C2×C3#6520511yescharacteristic
334C2×C3#6544511yescharacteristic
335D3—161no—
336C5#7208211yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—202no—
341C22—241no—
342C22—241no—
343C22—241no—
344C22—401no—
345C22—401no—
346C22D5×#21311yescharacteristic
347C4—42no—
348C4—101no—
349C4—1201no—
350C4#9148911yescharacteristic
351C4#9156311yescharacteristic
352C3#1060227711yescharacteristic, complemented, Sylow
353C2—201no—
354C2—402no—
355C2—481no—
356C2#1174828911yescharacteristic
357C2#1174830111yescharacteristic
358C2#1174902111yescharacteristic
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×C5×#828C2semidirect
3. #11747898C2semidirect
4. C2×#90937C2semidirect
5. #11746385C2semidirect
6. #11745892C2semidirect
7. #11745879C2semidirect
25. C2×#4065D3semidirect
42. C3×C5×Q16D4semidirect
50. C3×D40D4semidirect
57. C2×#828D5semidirect
125. C5×Q16#67semidirect
134. D40#67semidirect
171. C3×Q16C22⋊D5semidirect
273. Q16#1201semidirect
287. C3×C5#2186semidirect
336. C5#72082semidirect
352. C3#10602277semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40652
C2×C5×#8282
#117478982
C2×#909372
#117463852
#117458922
#117458792
#106022773
#720825