Finite Group Databasebeta

← #14292389

Subgroups — #14292389

Order 1920.

364 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 84 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#11751186C211yesmaximal, characteristic, complemented
2C3×#65376C211yesmaximal, characteristic, complemented
3#11747028C211yesmaximal, characteristic
4#11747013C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745868C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic, complemented
8#10599241—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6717—21no—
11C2×#6717—21no—
12#91763C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14C2×#6653—21no—
15C2×#6649—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3941—21no—
20C3×#3939—21no—
21C3×C4⋊#168C2211yescharacteristic
22#90968—21no—
23#90955—21no—
24#71104—51nomaximal, Hall
25#65376D311yescharacteristic, complemented
26#65374—31no—
27#65132—31no—
28#65127—31no—
29C5×#332—31no—
30#64705—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41#6717—42no—
42#6717—42no—
43C2×C3⋊#168D411yescharacteristic
44C2×C3⋊#168D411yescharacteristic
45C2×C5×C3⋊C8—21no—
46C2×C5×C3⋊C8—21no—
47C3×#685—21no—
48C3×C4⋊Dic5D411yescharacteristic
49C2×C3×#168—21no—
50#6653—42no—
51#6649—42no—
52C3×#474—51no—
53#5085—51no—
54#5015—51no—
55#5012—51no—
56#4547D511yescharacteristic, complemented
57#4485—51no—
58#4479—51no—
59C5×C4⋊Q8C2×D311yescharacteristic
60C2×#688—61no—
61C2×#688—61no—
62C2×D40—61no—
63C2×#676—61no—
64#4020—31no—
65C4×D20C2×D311yescharacteristic
66C5×C4⋊C8—31no—
67C5×C4⋊C8—31no—
68#3953—61no—
69#3952—61no—
70#3941—21no—
71#3939—21no—
72C4⋊#168C2×D311yescharacteristic
73C4×#168—31no—
74#1685—151noSylow
75C22×D15—41no—
76C22×C3×D5—21no—
77C3×C5×Q8—41no—
78C3×C5×Q8—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5#4111yescharacteristic
83D60—41no—
84D60—41no—
85D60—41no—
86D60—41no—
87D60—81no—
88C2×C3×Dic5—21no—
89C3×D20—21no—
90C3×D20—21no—
91C3×C4×D5—41no—
92C3×C4×D5—41no—
93C3⋊#168—21no—
94C3⋊#168D812yescomplemented
95C3×#168—41no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8—41no—
98C3×C4⋊Q8C2×D511yescharacteristic
99C3×C4×D4—51no—
100C2×#215—101no—
101C2×#215—101no—
102C2×#213—101no—
103C2×#208—101no—
104#874—51no—
105C3×#107—101no—
106C3×C4⋊C8—51no—
107C3×#102—101no—
108#830—101no—
109#809—101no—
110C4⋊(C3⋊C8)C2×D511yescharacteristic
111C4⋊(C3⋊C8)C2×D511yescharacteristic
112C4×C3⋊C8—51no—
113C2×C5×Q8—21no—
114C2×D20—61no—
115C2×D20—61no—
116C2×D20—61no—
117C2×D20#6711yescharacteristic
118C2×C4×D5—21no—
119C2×C5×C8—61no—
120C2×C5×C8—61no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—21no—
123C42×C5C22×D311yescharacteristic
124#688—122no—
125#688—122no—
126#685—21no—
127C4⋊Dic5#6711yescharacteristic
128C2×#168—21no—
129C2×#168—31no—
130C2×#168—31no—
131D40—122no—
132#676—122no—
133#492—151no—
134#474—51no—
135#459—151no—
136#436—151no—
137#335—151no—
138#332—31no—
139#331—151no—
140C22×C3×C5#12111yescharacteristic
141C2×D15—81no—
142C2×D15—81no—
143C2×D15—81no—
144C2×C3×D5—41no—
145C2×C3×D5—41no—
146C2×C3×D5—41no—
147C3×C4×C5—21no—
148C3×C4×C5—81no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×Dic5—41no—
154C2×C3×Q8—21no—
155C2×C3×D4—51no—
156C22×C3×C4—101no—
157C2×D12—101no—
158C2×D12—101no—
159C2×D12—101no—
160C2×C3×C8—101no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—51no—
164C3×C22⋊C4—101no—
165C3×C42C22×D511yescharacteristic
166#215—202no—
167#215—202no—
168#213—202no—
169#208—202no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—51no—
173C2×C3⋊C8—51no—
174C22×D5—21no—
175C22×D5—121no—
176C5×Q8—41no—
177C5×Q8—41no—
178C2×C4×C5—41no—
179C2×C4×C5D3×D411yescharacteristic
180C2×C4×C5#23711yescharacteristic
181C2×C4×C5C2×#6711yescharacteristic
182C2×Dic5—21no—
183D20—21no—
184D20—21no—
185D20—121no—
186D20—121no—
187D20—121no—
188D20—121no—
189D20—241no—
190C4×D5—41no—
191C4×D5—41no—
192C5×C8—121no—
193C5×C8—121no—
194#168—32no—
195#168—41no—
196#168—61no—
197C2×SD16—301no—
198C2×SD16—301no—
199C2×D8—301no—
200C2×M16—301no—
201C4⋊Q8D3×D511yescharacteristic
202#127—151no—
203C4×D4—51no—
204#107—101no—
205C4⋊C8—31no—
206C4⋊C8—31no—
207C4⋊C8—51no—
208#102—101no—
209#102—301no—
210C22⋊C8—301no—
211C4×C8—151no—
212C2×C3×C5#45911yescharacteristic
213C2×C3×C5#46811yescharacteristic
214C2×C3×C5#47111yescharacteristic
215D15—161no—
216C3×D5—81no—
217C23×C3—101no—
218C22×D3—201no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×D4—101no—
222C3×D4—101no—
223C2×C3×C4—41no—
224C2×C3×C4—101no—
225C2×C3×C4—201no—
226C2×C3×C4—201no—
227C2×C3×C4#70911yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×C3×C4D4×D511yescharacteristic
230D12—201no—
231D12—201no—
232D12—201no—
233D12—201no—
234D12—401no—
235C3×C8—201no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C3⋊C8—52no—
239C3⋊C8—101no—
240C22×C5#93911yescharacteristic
241C2×D5—41no—
242C2×D5—41no—
243C2×D5—41no—
244C2×D5—241no—
245C2×D5—241no—
246C2×D5—241no—
247C4×C5—21no—
248C4×C5—81no—
249C4×C5D3×D811yescharacteristic
250C4×C5#91111yescharacteristic
251C4×C5#94211yescharacteristic
252C4×C5#94911yescharacteristic
253Dic5—41no—
254C2×Q8—21no—
255C2×D4—51no—
256C2×D4—301no—
257C2×D4—301no—
258C2×D4—301no—
259C22×C4—101no—
260SD16—602no—
261SD16—602no—
262D8—602no—
263M16—602no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—101no—
267C2×C8—151no—
268C2×C8—151no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—51no—
272C22⋊C4—101no—
273C42C2×D3×D511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—201no—
276C22×C3—201no—
277C22×C3—201no—
278C22×C3#403011yescharacteristic
279C2×D3—401no—
280C2×D3—401no—
281C2×D3—401no—
282C3×C4—21no—
283C3×C4—81no—
284C3×C4—201no—
285C3×C4D5×D811yescharacteristic
286C3×C4#406011yescharacteristic
287C3×C4#406011yescharacteristic
288C3×C4#406411yescharacteristic
289C2×C5#504911yescharacteristic
290C2×C5#515011yescharacteristic
291C2×C5#520311yescharacteristic
292D5—81no—
293D5—481no—
294C23—101no—
295C23—601no—
296Q8—41no—
297Q8—41no—
298D4—101no—
299D4—101no—
300D4—601no—
301D4—601no—
302D4—601no—
303D4—601no—
304D4—1201no—
305C2×C4—41no—
306C2×C4—101no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4#677911yescharacteristic
310C2×C4D5×#6711yescharacteristic
311C2×C4#679011yescharacteristic
312C8—121no—
313C8—121no—
314C8—152no—
315C8—201no—
316C8—301no—
317C2×C3—401no—
318C2×C3#6504311yescharacteristic
319C2×C3#6507511yescharacteristic
320C2×C3#6510111yescharacteristic
321D3—801no—
322C5#7110411yescharacteristic, complemented, Sylow
323C22—201no—
324C22—201no—
325C22—201no—
326C22—1201no—
327C22—1201no—
328C22—1201no—
329C22#9155011yescharacteristic
330C4—21no—
331C4—81no—
332C4—201no—
333C4#9148111yescharacteristic
334C4#9149811yescharacteristic
335C4#9150211yescharacteristic
336C4#9151511yescharacteristic
337C3#1059924111yescharacteristic, complemented, Sylow
338C2—401no—
339C2—2401no—
340C2#1174898311yescharacteristic
341C2#1174927311yescharacteristic
342C2#1174937711yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#121
prime radical#11747028C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1685
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11751186C2semidirect
2. C3×#65376C2semidirect
4. #11747013C2semidirect
5. C5×#4547C2semidirect
6. #11745868C2semidirect
7. #11745854C2semidirect
25. #65376D3semidirect
56. #4547D5semidirect
94. C3⋊#168D8semidirect
274. C3×C5#1685semidirect
322. C5#71104semidirect
337. C3#10599241semidirect

Maximal subgroups

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

subgroupindex
#117511862
C3×#653762
#117470282
#117470132
C5×#45472
#117458682
#117458542
#105992413
#711045