Finite Group Databasebeta

← #14289859

Subgroups — #14289859

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×#65918C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11746923C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745855C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10601950—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4092—21no—
12C3×#4044—22no—
13C3×#4038—21no—
14C3×#4021—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10—21no—
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×#835—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90986—21no—
24#90972—22no—
25#90964—21no—
26#71932—51nomaximal, Hall
27#65918D311yescharacteristic
28C5×#477—31no—
29#65373—31no—
30#65370—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×#685—22no—
49C3×#685—22no—
50C3×#685—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D412yes—
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×C4×Dic5—22no—
56C3×#556—51no—
57#5093—51no—
58#5021D511yescharacteristic, complemented
59#5008—51no—
60#4547—51no—
61#4535—51no—
62D4⋊(C3⋊C8)—51no—
63C5×C4⋊Q8—31no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—21no—
66#4044—22no—
67#4038—21no—
68#4021—21no—
69C4×D20C2×D311yescharacteristic
70#4015C2×D311yescharacteristic
71C4×Dic10—21no—
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—62no—
76#3941—61no—
77#3940—61no—
78C4⋊#168—31no—
79C4×#168—31no—
80#1638—151noSylow
81C22×C3×D5—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C5×Dic3—41no—
90C5×Dic6—42no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—22no—
93C3×D20—21no—
94C3×D20—21no—
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×#126—102no—
104C3×#124—101no—
105C3×C22⋊Q8—101no—
106C3×C4×Q8—101no—
107C3×C4×Q8C2×D511yescharacteristic
108C3×C4×D4—51no—
109C3×#117—101no—
110#869C2×D511yescharacteristic
111#835—21no—
112#832—101no—
113#810—102no—
114#808—101no—
115#807—21no—
116C4⋊(C3⋊C8)—51no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4×C3⋊C8—51no—
119C2×C5×Q8—61no—
120C2×C5×Q8#6711yescharacteristic
121C2×D20#6711yescharacteristic
122C2×C4×D5—21no—
123C2×Dic10—21no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4#6711yescharacteristic
129C42×C5—21no—
130C42×C5C22×D311yescharacteristic
131#685—22no—
132#685—22no—
133#685—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5#6711yescharacteristic
136C4⋊Dic5#6712yes—
137#683—22no—
138C4×Dic5—22no—
139C2×#168—61no—
140C2×#168—61no—
141#556—51no—
142#487—151no—
143#477—31no—
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—41no—
154C3×C4×C5—41no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×Dic5—42no—
160C3×Dic5—41no—
161C5×Dic3—81no—
162C2×C3×Q8—101no—
163C2×C3×Q8C22⋊D511yescharacteristic
164C2×C3×D4—51no—
165C22×C3×C4—101no—
166C2×Dic6—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—51no—
169C3×C4⋊C4—52no—
170C3×C4⋊C4—102no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4C22⋊D511yescharacteristic
173C3×C22⋊C4—102no—
174C3×C22⋊C4—102no—
175C3×C22⋊C4—101no—
176C3×C42—21no—
177C3×C42—102no—
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—21no—
186C5×Q8—21no—
187C5×Q8—122no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—121no—
191C2×C4×C5C2×#6711yescharacteristic
192C2×C4×C5C2×#6711yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—21no—
195C2×Dic5—22no—
196D20—21no—
197D20—21no—
198C4×D5—41no—
199C4×D5—41no—
200Dic10—41no—
201Dic10—41no—
202C5×C8—121no—
203#168—121no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—51no—
207#126—102no—
208#124—101no—
209C22⋊Q8—101no—
210C4×Q8—101no—
211C4×Q8D3×D511yescharacteristic
212C4×D4—51no—
213#117—101no—
214#107—61no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—151no—
218#103—61no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C3×D5—81no—
226C23×C3—101no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—201no—
230C3×Q8—201no—
231C3×D4—101no—
232C3×D4—101no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—101no—
236C2×C3×C4—102no—
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—41no—
253C4×C5—41no—
254C4×C5—241no—
255C4×C5#95011yescharacteristic
256C4×C5#95011yescharacteristic
257C4×C5#95111yescharacteristic
258C4×C5#95111yescharacteristic
259Dic5—42no—
260Dic5—41no—
261C2×Q8—61no—
262C2×Q8—101no—
263C2×Q8#120111yescharacteristic
264C2×D4—51no—
265C22×C4—101no—
266C2×C8—61no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—52no—
271C4⋊C4—51no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—102no—
275C4⋊C4—101no—
276C4⋊C4#120111yescharacteristic
277C22⋊C4—102no—
278C22⋊C4—102no—
279C22⋊C4—101no—
280C42—21no—
281C42—102no—
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—41no—
290C3×C4—41no—
291C3×C4—201no—
292C3×C4—202no—
293C3×C4#406411yescharacteristic
294C3×C4#406511yescharacteristic
295C3×C4#408811yescharacteristic
296C3×C4#409611yescharacteristic
297Dic3—81no—
298C2×C5#523911yescharacteristic
299C2×C5#523911yescharacteristic
300C2×C5#524511yescharacteristic
301D5—81no—
302C23—101no—
303Q8—21no—
304Q8—21no—
305Q8—122no—
306Q8—201no—
307Q8—201no—
308D4—101no—
309D4—101no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—101no—
313C2×C4—102no—
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#6533611yescharacteristic
325C2×C3#6547611yescharacteristic
326C2×C3#6549011yescharacteristic
327C5#7193211yescharacteristic, complemented, Sylow
328C22—201no—
329C22—201no—
330C22—201no—
331C22#9156311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—202no—
336C4—201no—
337C4—241no—
338C4#9129711yescharacteristic
339C4#9130711yescharacteristic
340C4#9150811yescharacteristic
341C4#9151611yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—401no—
344C2#1174852811yescharacteristic
345C2#1174929411yescharacteristic
346C2#1174945611yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×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×#5021C2semidirect
3. #11746923C2semidirect
5. #11746356C2semidirect
6. #11745855C2semidirect
58. #5021D5semidirect
283. C3×C5#1638semidirect
327. C5#71932semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
C3×#659182
C5×#50212
#117469232
#117468802
#117463562
#117458552
#117458342
#106019503
#719325