Finite Group Databasebeta

← #14289539

Subgroups — #14289539

Order 1920.

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

normal subgroups only

This group has 428 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
1#11752645C211yesmaximal, characteristic
2C5×#4850C211yesmaximal, characteristic, complemented
3#11747103C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5#11746304C211yesmaximal, characteristic
6C3×#64701C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601949—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91437—21no—
14#91428—21no—
15#91411—22no—
16#91383—21no—
17#91381—21no—
18C2×#6661—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#818—21no—
22C5×#816—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90985—21no—
25#90969—21no—
26#68492—51nomaximal, Hall
27#65913—31no—
28C5×#477—31no—
29#65381—31no—
30#65373—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64701D311yescharacteristic, complemented
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10D412yes—
39C2×#1200—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42#6714—21no—
43C4⋊Dic15D411yescharacteristic
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C2×C3×#168—21no—
53#6669—22no—
54#6668—22no—
55#6667—22no—
56#6661—44no—
57#5730—51no—
58#5092—51no—
59#4850D511yescharacteristic, complemented
60#4842—51no—
61C3×#333—51no—
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8—31no—
66#4092—61no—
67C2×#689—62no—
68#4042—62no—
69D5×C4⋊C4—61no—
70C4×D20—31no—
71C4×D20—61no—
72#4016—61no—
73#4015C2×D311yescharacteristic
74C5×#107—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1632—151noSylow
82C22×D15—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87D60—21no—
88D60Q1612yescomplemented
89C4×D15—41no—
90C4×D15—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—41no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—42no—
97C2×C3×Dic5—22no—
98C3×Dic10—42no—
99#1200—82no—
100C3×C5×C8—41no—
101C3⋊#168—22no—
102C3×#168—41no—
103C3×C4⋊Q8—51no—
104#946—102no—
105C2×#216—102no—
106#897—101no—
107#893—101no—
108D3×C4⋊C4—101no—
109#890—101no—
110C4×D12—51no—
111#869C2×D511yescharacteristic
112C4×Dic6C2×D511yescharacteristic
113C3×C4⋊C8—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115#821—101no—
116#818—21no—
117#817—101no—
118#816—21no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—31no—
121C2×C5×Q8—61no—
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×C4×D5—62no—
125C2×Dic10D1212yes—
126C2×C5×C8—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5—61no—
132C42×C5C22×D311yescharacteristic
133#689—124no—
134#685—62no—
135#685—61no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139#683—62no—
140#683—62no—
141C2×#168—21no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477—31no—
146#476—151no—
147#333—51no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160C3×Dic5—42no—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C5×Dic3—81no—
164C2×C3×Q8—52no—
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×C4×D3—102no—
168C2×Dic6—21no—
169C2×Dic6C22⋊D511yescharacteristic
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175#216—204no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—102no—
185C4×Dic3—21no—
186C2×C3⋊C8—101no—
187C22×D5—61no—
188C5×Q8—61no—
189C5×Q8—61no—
190C5×Q8—122no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5—121no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—22no—
198C2×Dic5—61no—
199D20—32no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203C4×D5—242no—
204Dic10—42no—
205C5×C8—41no—
206#168—41no—
207#168—62no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—31no—
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—61no—
219#106—301no—
220C4⋊C8—51no—
221C4⋊C8D3×D511yescharacteristic
222#103—61no—
223#102—301no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—202no—
231C2×C3×C4—102no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—41no—
238C2×Dic3—101no—
239D12—52no—
240D12—101no—
241C4×D3—201no—
242C4×D3—201no—
243C4×D3—402no—
244Dic6—21no—
245Dic6—21no—
246Dic6—42no—
247C3×C8—41no—
248C3×C8—201no—
249C3⋊C8—102no—
250C22×C5#88211yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257C4×C5—241no—
258C4×C5#91511yescharacteristic
259C4×C5#91611yescharacteristic
260C4×C5D3×Q1611yescharacteristic
261C4×C5#91811yescharacteristic
262Dic5—42no—
263Dic5—121no—
264C2×Q8—31no—
265C2×Q8—52no—
266C2×Q8—61no—
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—151no—
281C4⋊C4—302no—
282C4⋊C4—302no—
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—61no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#408311yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—202no—
294C3×C4D5×Q1611yescharacteristic
295C3×C4#406411yescharacteristic
296C3×C4#408811yescharacteristic
297C3×C4#409611yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—81no—
301Dic3—201no—
302C2×C5#474711yescharacteristic
303C2×C5#480811yescharacteristic
304C2×C5#480911yescharacteristic
305D5—122no—
306C23—301no—
307Q8—61no—
308Q8—61no—
309Q8—122no—
310Q8—202no—
311D4—152no—
312D4—301no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—102no—
316C2×C4—121no—
317C2×C4—301no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4D5×D1211yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—41no—
325C8—201no—
326C8—302no—
327C2×C3#6533611yescharacteristic
328C2×C3#6547511yescharacteristic
329C2×C3#6548711yescharacteristic
330D3—202no—
331C5#6849211yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9147511yescharacteristic
336C4—21no—
337C4—121no—
338C4—121no—
339C4—202no—
340C4—241no—
341C4—601no—
342C4#9126411yescharacteristic
343C4#9127811yescharacteristic
344C4#9149511yescharacteristic
345C4#9152011yescharacteristic
346C3#1060194911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1174751611yescharacteristic
349C2#1174813111yescharacteristic
350C2#1174824611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4850C2semidirect
3. #11747103C2semidirect
6. C3×#64701C2semidirect
7. #11745842C2semidirect
33. #64701D3semidirect
59. #4850D5semidirect
88. D60Q16semidirect
287. C3×C5#1632semidirect
331. C5#68492semidirect
346. C3#10601949semidirect

Maximal subgroups

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

subgroupindex
#117526452
C5×#48502
#117471032
#117468852
#117463042
C3×#647012
#117458422
#106019493
#684925