Finite Group Databasebeta

← #14289486

Subgroups — #14289486

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#11756338C211yesmaximal, characteristic
2C3×C5×#477C211yesmaximal, characteristic, complemented
3#11751193C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic
7#11746302C211yesmaximal, characteristic, complemented
8#10601949—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8C2211yescharacteristic
11#91835—21no—
12C2×#6718—22no—
13#91785—22no—
14C4⋊C4×D15—21no—
15C4×D60—21no—
16C4×D60C2211yescharacteristic
17#91759—21no—
18#91758C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22#91093—21no—
23#91092—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71156—51nomaximal, Hall
27#65913—31no—
28C5×#477D311yescharacteristic, complemented
29#65381—31no—
30#65373—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×C4×D15—22no—
39C2×Dic30D412yes—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6718—44no—
48#6714—22no—
49#6714—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53#6712—22no—
54#6712—22no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57#5579—51no—
58C3×#477D511yescharacteristic, complemented
59#5092—51no—
60#5084—51no—
61#4535—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×Q8C2×D311yescharacteristic
66#4092—61no—
67C2×#689—62no—
68#4042—62no—
69D5×C4⋊C4—61no—
70C4×D20—31no—
71C4×D20—61no—
72#4016—61no—
73#4015—31no—
74C5×#107—21no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—21no—
77#3941—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1632—151noSylow
82C22×D15—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8—42no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—22no—
94D60—21no—
95D60Q1612yescomplemented
96C4×D15—41no—
97C4×D15—41no—
98C4×D15—82no—
99Dic30—42no—
100C3×C5×C8—41no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×C4×Q8C2×D511yescharacteristic
105#946—101no—
106C2×#216—102no—
107#896—102no—
108D3×C4⋊C4—101no—
109C4×D12—51no—
110C4×D12—101no—
111#870—101no—
112#869—51no—
113C3×#107—21no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×#103—21no—
116#809—101no—
117#808—101no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—21no—
121C2×C5×Q8#6711yescharacteristic
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×C4×D5—62no—
125C2×Dic10—32no—
126C2×C5×C8—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4#6711yescharacteristic
131C42×C5—21no—
132C42×C5C22×D311yescharacteristic
133#689—124no—
134#685—62no—
135#685—61no—
136C4⋊Dic5—31no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—62no—
141C2×#168—61no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477D1511yescharacteristic, complemented
146#476—151no—
147#333—151no—
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—41no—
156C3×C4×C5—41no—
157C3×C4×C5—81no—
158C3×C4×C5C2×Q1611yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—42no—
164C2×C3×Q8—21no—
165C2×C3×Q8C22⋊D511yescharacteristic
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×C4×D3—102no—
169C2×Dic6—52no—
170C2×C3×C8—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C42—21no—
176C3×C42C22×D511yescharacteristic
177#216—204no—
178(C2×D3)⋊C4—102no—
179(C2×D3)⋊C4—101no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C22×D5—61no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—42no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—61no—
198C2×Dic5—62no—
199D20—32no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203C4×D5—242no—
204Dic10—122no—
205C5×C8—41no—
206#168—62no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8C2×D1511yescharacteristic
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8C2×D1511yescharacteristic
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—21no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8C2×D1511yescharacteristic
222#103—21no—
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—21no—
231C3×Q8—21no—
232C3×Q8—42no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239C2×Dic3—101no—
240C2×Dic3—102no—
241D12—52no—
242D12—101no—
243C4×D3—201no—
244C4×D3—201no—
245C4×D3—402no—
246Dic6—202no—
247C3×C8—41no—
248C3⋊C8—102no—
249C3⋊C8—201no—
250C22×C5#93711yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—81no—
258C4×C5D3×Q1611yescharacteristic
259C4×C5#91811yescharacteristic
260C4×C5#94211yescharacteristic
261C4×C5#95011yescharacteristic
262Dic5—122no—
263Dic5—121no—
264C2×Q8—21no—
265C2×Q8—152no—
266C2×Q8#122011yescharacteristic
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—151no—
278C4⋊C4—302no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4#122011yescharacteristic
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—21no—
286C42C22×D1511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#408311yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—81no—
296C3×C4D5×Q1611yescharacteristic
297C3×C4#406411yescharacteristic
298C3×C4#408811yescharacteristic
299C3×C4#409611yescharacteristic
300Dic3—201no—
301Dic3—202no—
302C2×C5#504711yescharacteristic
303C2×C5#518611yescharacteristic
304C2×C5#519811yescharacteristic
305D5—122no—
306C23—301no—
307Q8—21no—
308Q8—21no—
309Q8—42no—
310Q8—602no—
311D4—152no—
312D4—301no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—301no—
317C2×C4—302no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4D4×D1511yescharacteristic
322C2×C4D4×D1511yescharacteristic
323C2×C4C2×#122011yescharacteristic
324C8—41no—
325C8—302no—
326C8—601no—
327C2×C3#6533611yescharacteristic
328C2×C3#6547511yescharacteristic
329C2×C3#6548711yescharacteristic
330D3—202no—
331C5#7115611yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9182611yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—602no—
341C4—601no—
342C4Q16×D1511yescharacteristic
343C4#9180711yescharacteristic
344C4#9183111yescharacteristic
345C4#9183911yescharacteristic
346C3#1060194911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1175114811yescharacteristic
349C2#1175128711yescharacteristic
350C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#477C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#477D15
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. C3×C5×#477C2semidirect
3. #11751193C2semidirect
5. #11746356C2semidirect
7. #11746302C2semidirect
28. C5×#477D3semidirect
58. C3×#477D5semidirect
95. D60Q16semidirect
145. #477D15semidirect
287. C3×C5#1632semidirect
331. C5#71156semidirect
346. C3#10601949semidirect

Maximal subgroups

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

subgroupindex
#117563382
C3×C5×#4772
#117511932
#117511852
#117463562
#117463042
#117463022
#106019493
#711565