Finite Group Databasebeta

← #14289835

Subgroups — #14289835

Order 1920.

388 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#66066C211yesmaximal, characteristic
2C5×#5093C211yesmaximal, characteristic, complemented
3#11746954C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10602022—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4093—21no—
12C3×Q8×Dic5—21no—
13C3×#4044—22no—
14C3×#4043—21no—
15C3×#4038—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×#810—22no—
21C4×C5×C3⋊C8C2211yescharacteristic
22#90989—21no—
23#90986—21no—
24#90970—21no—
25#90964—21no—
26#71932—51nomaximal, Hall
27#66066D311yescharacteristic
28C5×#487—31no—
29#65380—31no—
30#65373—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×C5×Dic6—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10D411yescharacteristic
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D412yes—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C2×C5×C3⋊C8—21no—
47C3×#685—22no—
48C3×#685—22no—
49C3×#685—21no—
50C3×C4⋊Dic5—22no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56C3×#556—51no—
57#5093D511yescharacteristic, complemented
58#5021—51no—
59#5008—51no—
60#4547—51no—
61#4535—51no—
62D4⋊(C3⋊C8)—51no—
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4093—21no—
66Q8×Dic5—21no—
67#4044—22no—
68#4043—21no—
69#4038—21no—
70C4×D20C2×D311yescharacteristic
71C4×Dic10C2×D311yescharacteristic
72C5×#103—62no—
73C4×C5×C8—31no—
74#3942—61no—
75#3941—61no—
76#3940—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
80#1638—151noSylow
81C22×C3×D5—21no—
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C5×Dic3—41no—
89C5×Dic6—42no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—21no—
94C3×D20—21no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103C3×#126—102no—
104C3×#124—101no—
105C3×C22⋊Q8—101no—
106C3×C4×Q8—51no—
107C3×C4×Q8—101no—
108C3×C4×D4—51no—
109C3×#117—101no—
110#869C2×D511yescharacteristic
111#835—101no—
112#832—101no—
113#810—22no—
114#808—101no—
115#807—101no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8C2×D511yescharacteristic
119C2×C5×Q8—21no—
120C2×C5×Q8—61no—
121C2×D20#6711yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10#6711yescharacteristic
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4#6712yes—
129C42×C5C22×D311yescharacteristic
130#685—22no—
131#685—22no—
132#685—21no—
133C4⋊Dic5—22no—
134C4⋊Dic5#6711yescharacteristic
135C4⋊Dic5#6711yescharacteristic
136#683—21no—
137C4×Dic5—22no—
138C4×Dic5—21no—
139C2×#168—61no—
140C2×#168—61no—
141#556—51no—
142#487—31no—
143#477—151no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×C3×D5—41no—
150C2×C3×D5—41no—
151C2×C3×D5—41no—
152C3×C4×C5—21no—
153C3×C4×C5—42no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×Dic5—41no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C5×Dic3—81no—
162C2×C3×Q8—21no—
163C2×C3×Q8—51no—
164C2×C3×D4—51no—
165C22×C3×C4—101no—
166C2×Dic6—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4C22⋊D512yes—
173C3×C22⋊C4—102no—
174C3×C22⋊C4—102no—
175C3×C22⋊C4—101no—
176C3×C42—102no—
177C3×C42—101no—
178C3×C42C22×D511yescharacteristic
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C22×D5—21no—
185C5×Q8—41no—
186C5×Q8—41no—
187C5×Q8—122no—
188C2×C4×C5—22no—
189C2×C4×C5—121no—
190C2×C4×C5C2×#6711yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—21no—
196D20—21no—
197D20—21no—
198C4×D5—41no—
199C4×D5—41no—
200Dic10—21no—
201Dic10—21no—
202C5×C8—121no—
203#168—121no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8D3×D511yescharacteristic
207#126—102no—
208#124—101no—
209C22⋊Q8—101no—
210C4×Q8—51no—
211C4×Q8—101no—
212C4×D4—51no—
213#117—101no—
214#107—301no—
215#106—301no—
216C4⋊C8—151no—
217C4⋊C8—151no—
218#103—62no—
219#103—301no—
220#102—301no—
221C4×C8—31no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—101no—
230C3×Q8—101no—
231C3×D4—101no—
232C3×D4—101no—
233C2×C3×C4—22no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4—201no—
238C2×C3×C4—201no—
239C2×C3×C4D4×D511yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×Dic3—41no—
243Dic6—42no—
244C3⋊C8—41no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5#95311yescharacteristic
248C2×D5—41no—
249C2×D5—41no—
250C2×D5—41no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5—241no—
254C4×C5#95011yescharacteristic
255C4×C5#95011yescharacteristic
256C4×C5#95111yescharacteristic
257C4×C5#95111yescharacteristic
258Dic5—41no—
259Dic5—41no—
260Dic5—41no—
261C2×Q8—21no—
262C2×Q8—51no—
263C2×Q8—61no—
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—61no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—51no—
271C4⋊C4—51no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—102no—
275C4⋊C4—101no—
276C4⋊C4#120112yes—
277C22⋊C4—102no—
278C22⋊C4—102no—
279C22⋊C4—101no—
280C42—102no—
281C42—101no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—201no—
285C22×C3—201no—
286C22×C3—201no—
287C22×C3#408311yescharacteristic
288C3×C4—21no—
289C3×C4—42no—
290C3×C4—201no—
291C3×C4—201no—
292C3×C4—201no—
293C3×C4#406111yescharacteristic
294C3×C4#406211yescharacteristic
295C3×C4#406411yescharacteristic
296C3×C4#406511yescharacteristic
297Dic3—81no—
298C2×C5#523911yescharacteristic
299C2×C5#523911yescharacteristic
300C2×C5#524511yescharacteristic
301D5—81no—
302C23—101no—
303Q8—41no—
304Q8—41no—
305Q8—101no—
306Q8—101no—
307Q8—122no—
308D4—101no—
309D4—101no—
310C2×C4—22no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—101no—
314C2×C4—121no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4C2×#120111yescharacteristic
318C2×C4D5×#6711yescharacteristic
319C2×C4D5×#6711yescharacteristic
320C8—121no—
321C8—601no—
322C8—601no—
323C2×C3—401no—
324C2×C3#6535111yescharacteristic
325C2×C3#6546211yescharacteristic
326C2×C3#6547611yescharacteristic
327C5#7193211yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9156311yescharacteristic
332C4—21no—
333C4—42no—
334C4—201no—
335C4—201no—
336C4—201no—
337C4—241no—
338C4#9148411yescharacteristic
339C4#9149211yescharacteristic
340C4#9150811yescharacteristic
341C4#9151611yescharacteristic
342C3#1060202211yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174904711yescharacteristic
345C2#1174929411yescharacteristic
346C2#1174938311yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1638
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
2. C5×#5093C2semidirect
3. #11746954C2semidirect
5. #11746368C2semidirect
6. #11745841C2semidirect
57. #5093D5semidirect
283. C3×C5#1638semidirect
327. C5#71932semidirect
342. C3#10602022semidirect

Maximal subgroups

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

subgroupindex
C3×#660662
C5×#50932
#117469542
#117468802
#117463682
#117458412
#117458352
#106020223
#719325