Finite Group Databasebeta

← #14289492

Subgroups — #14289492

Order 1920.

428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756489C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3#11750951C211yesmaximal, characteristic, complemented
4#11750943C211yesmaximal, characteristic
5C3×C5×#333C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic
8#10599285—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—22no—
11C2×#6718—22no—
12#91786—21no—
13#91782—21no—
14C4⋊C4×D15—21no—
15#91779—21no—
16C4×D60C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21#91105—21no—
22#91102—21no—
23#91101—21no—
24#91100—21no—
25C4×C3⋊#168C2211yescharacteristic
26#68492—51nomaximal, Hall
27#66064—31no—
28#65381—31no—
29#65139—31no—
30#65131—31no—
31C5×#333D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8D412yes—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30—21no—
39C2×Dic30D411yescharacteristic
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6718—44no—
46#6714—22no—
47#6714—21no—
48C4⋊Dic15—22no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15D411yescharacteristic
52C4⋊Dic15D411yescharacteristic
53#6712—22no—
54#6712—21no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57#5730—51no—
58#5092—51no—
59#4850—51no—
60#4842—51no—
61C3×#333D511yescharacteristic, complemented
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4092—62no—
66C2×#689—62no—
67#4043—61no—
68#4039—61no—
69D5×C4⋊C4—61no—
70#4036—61no—
71C4×D20—31no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C5×C4⋊C8C2×D311yescharacteristic
76#3953—61no—
77#3950—61no—
78#3949—61no—
79#3948—61no—
80C4×#168—31no—
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—41no—
92D60—21no—
93D60Q1612yescomplemented
94C4×D15—41no—
95C4×D15—41no—
96C4×D15—82no—
97Dic30—21no—
98Dic30—21no—
99Dic30—42no—
100C3×C5×C8—41no—
101C3×C5×C8—41no—
102C3⋊#168—22no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#946—102no—
105C2×#216—102no—
106#897—101no—
107#893—101no—
108D3×C4⋊C4—101no—
109#890—101no—
110C4×D12—51no—
111#869—51no—
112C4×Dic6—51no—
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C4⋊C8C2×D511yescharacteristic
115#821—101no—
116#818—101no—
117#817—101no—
118#816—101no—
119C4×C3⋊C8—51no—
120C2×C5×Q8D1212yes—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×C4×D5—62no—
124C2×Dic10—31no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131#689—124no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136C4⋊Dic5—62no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—61no—
141C4×Dic5—61no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333D1511yescharacteristic, complemented
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×C5—42no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161Dic15—41no—
162Dic15—41no—
163Dic15—81no—
164C2×C3×Q8D2012yes—
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×C4×D3—102no—
168C2×Dic6—51no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C42C22×D511yescharacteristic
175#216—204no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—102no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—101no—
185C4×Dic3—101no—
186C2×C3⋊C8—101no—
187C22×D5—61no—
188C5×Q8—42no—
189C2×C4×C5—22no—
190C2×C4×C5C2×D1211yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5—61no—
196C2×Dic5—121no—
197D20—32no—
198D20—61no—
199C4×D5—121no—
200C4×D5—121no—
201C4×D5—242no—
202Dic10—61no—
203Dic10—61no—
204Dic10—122no—
205C5×C8—41no—
206C5×C8—41no—
207#168—62no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8C2×D1511yescharacteristic
211#125—301no—
212C22⋊Q8—301no—
213C22⋊Q8—302no—
214C4×Q8—151no—
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8C2×D1511yescharacteristic
221C4⋊C8C2×D1511yescharacteristic
222#103—301no—
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—42no—
231C2×C3×C4—22no—
232C2×C3×C4C2×D2011yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—101no—
236C2×Dic3—101no—
237C2×Dic3—101no—
238C2×Dic3—201no—
239D12—52no—
240D12—101no—
241C4×D3—201no—
242C4×D3—201no—
243C4×D3—402no—
244Dic6—101no—
245Dic6—101no—
246Dic6—202no—
247C3×C8—41no—
248C3×C8—41no—
249C3⋊C8—102no—
250C22×C5#88211yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5#91511yescharacteristic
257C4×C5#91611yescharacteristic
258C4×C5D3×Q1611yescharacteristic
259C4×C5#91811yescharacteristic
260Dic5—121no—
261Dic5—121no—
262Dic5—121no—
263Dic5—241no—
264C2×Q8—151no—
265C2×Q8—301no—
266C2×Q8D6012yes—
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—151no—
277C4⋊C4—151no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—301no—
286C42C22×D1511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—42no—
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4D5×Q1611yescharacteristic
297C3×C4#406411yescharacteristic
298Dic3—201no—
299Dic3—201no—
300Dic3—201no—
301Dic3—401no—
302C2×C5#474711yescharacteristic
303C2×C5#480811yescharacteristic
304C2×C5#480911yescharacteristic
305D5—122no—
306C23—301no—
307Q8—42no—
308Q8—301no—
309Q8—301no—
310Q8—602no—
311D4—152no—
312D4—301no—
313C2×C4—22no—
314C2×C4—301no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4—601no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4C2×D6011yescharacteristic
322C2×C4D4×D1511yescharacteristic
323C2×C4D4×D1511yescharacteristic
324C8—41no—
325C8—41no—
326C8—302no—
327C2×C3#6503611yescharacteristic
328C2×C3#6509711yescharacteristic
329C2×C3#6509911yescharacteristic
330D3—202no—
331C5#6849211yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9177111yescharacteristic
336C4—21no—
337C4—42no—
338C4—601no—
339C4—601no—
340C4—601no—
341C4—1201no—
342C4#9180411yescharacteristic
343C4#9180511yescharacteristic
344C4Q16×D1511yescharacteristic
345C4#9180711yescharacteristic
346C3#1059928511yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1175084811yescharacteristic
349C2#1175090911yescharacteristic
350C2#1175091011yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#333D15
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #11751193C2semidirect
3. #11750951C2semidirect
5. C3×C5×#333C2semidirect
6. #11746305C2semidirect
31. C5×#333D3semidirect
61. C3×#333D5semidirect
93. D60Q16semidirect
147. #333D15semidirect
287. C3×C5#1632semidirect
331. C5#68492semidirect
346. C3#10599285semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117511932
#117509512
#117509432
C3×C5×#3332
#117463052
#117463042
#105992853
#684925