Finite Group Databasebeta

← #14292347

Subgroups — #14292347

Order 1920.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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×C5×#492C211yesmaximal, characteristic, complemented
2#11751188C211yesmaximal, characteristic, complemented
3#11751173C211yesmaximal, characteristic
4#11750789C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746365C211yesmaximal, characteristic, complemented
7#11746279C211yesmaximal, characteristic, complemented
8#10602061—31nomaximal, Hall
9C2×C3×C5×SD16—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#127C2211yescharacteristic
13C2×#6715—21no—
14C2×#6705—21no—
15C4×D60C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17#91116—21no—
18#91104—21no—
19#91093—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4⋊(C3⋊#168)C2211yescharacteristic
24#71268—51nomaximal, Hall
25C5×#492D311yescharacteristic, complemented
26#65376—31no—
27#65361—31no—
28#64977—31no—
29#64767—31no—
30#64764—31no—
31#64678—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C3×C5×SD16—42no—
39C3×C5×SD16—42no—
40C2×C3×C5×C8D411yescharacteristic
41C2×C3×C5×C8D411yescharacteristic
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6715—42no—
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C2×C3⋊#168—21no—
51#6705—42no—
52C3×#492D511yescharacteristic, complemented
53#5087—51no—
54#5072—51no—
55#4688—51no—
56#4547—51no—
57#4544—51no—
58#4458—51no—
59C2×C5×SD16—21no—
60C2×C5×SD16—21no—
61C5×C4⋊Q8C2×D311yescharacteristic
62C5×#127C2×D311yescharacteristic
63C2×#686—61no—
64C2×#676—61no—
65C4×D20—31no—
66C4×C5×C8C2×D311yescharacteristic
67#3964—61no—
68#3952—61no—
69#3941—61no—
70#3939—61no—
71C4⋊#168—31no—
72C4⋊#168—31no—
73C4⋊#168—31no—
74#1685—151noSylow
75C23×C3×C5—41no—
76C22×D15—21no—
77C3×C5×Q8—41no—
78C3×C5×Q8—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C2×Dic15—21no—
89D60—21no—
90D60—21no—
91C4×D15—41no—
92C4×D15—41no—
93C3×C5×C8—21no—
94C3×C5×C8D812yescomplemented
95C3⋊#168—41no—
96C3⋊#168—41no—
97C3⋊#168—41no—
98C2×C3×SD16—21no—
99C2×C3×SD16—21no—
100C3×C4⋊Q8C2×D511yescharacteristic
101C3×#127C2×D511yescharacteristic
102C2×#213—101no—
103C2×ΓL(1,𝔽25)—101no—
104C4×D12—51no—
105C3×C4×C8C2×D511yescharacteristic
106#832—101no—
107(C2×D3)⋊C8—101no—
108#809—101no—
109#807—101no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)—51no—
112C4⋊(C3⋊C8)—51no—
113C2×C5×Q8—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×D20—31no—
118C2×C4×D5—61no—
119C5×SD16—42no—
120C5×SD16—42no—
121C2×C5×C8#6711yescharacteristic
122C2×C5×C8#6711yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C42×C5C22×D311yescharacteristic
126#686—122no—
127#685—61no—
128C4⋊Dic5—31no—
129C2×#168—61no—
130C2×#168—61no—
131C2×#168—61no—
132#676—122no—
133#492D1511yescharacteristic, complemented
134#474—151no—
135#459—151no—
136#436—151no—
137#335—151no—
138#332—151no—
139#331—151no—
140C22×C3×C5—81no—
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5#12111yescharacteristic
144C2×D15—41no—
145C2×D15—41no—
146C2×D15—41no—
147C3×C4×C5—21no—
148C3×C4×C5—81no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
152C3×C4×C5#13711yescharacteristic
153Dic15—41no—
154C2×C3×Q8—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×D12—51no—
159C2×C4×D3—101no—
160C3×SD16—42no—
161C3×SD16—42no—
162C2×C3×C8C22⋊D511yescharacteristic
163C2×C3×C8C22⋊D511yescharacteristic
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C42C22×D511yescharacteristic
167#213—202no—
168(C2×D3)⋊C4—101no—
169C4⋊Dic3—51no—
170C2×C3⋊C8—101no—
171C2×C3⋊C8—101no—
172C2×C3⋊C8—101no—
173ΓL(1,𝔽25)—202no—
174C23×C5—41no—
175C22×D5—61no—
176C5×Q8—41no—
177C5×Q8—41no—
178C5×D4—41no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—81no—
183C2×C4×C5—41no—
184C2×C4×C5D3×D411yescharacteristic
185C2×C4×C5#23711yescharacteristic
186C2×C4×C5C2×#6711yescharacteristic
187C2×Dic5—61no—
188D20—61no—
189D20—61no—
190C4×D5—121no—
191C4×D5—121no—
192C5×C8—21no—
193C5×C8#21312yescomplemented
194#168—121no—
195#168—121no—
196#168—121no—
197C2×SD16—21no—
198C2×SD16—21no—
199C2×D8—301no—
200C2×M16—301no—
201C4⋊Q8C2×D1511yescharacteristic
202#127C2×D1511yescharacteristic
203C4×D4—151no—
204#107—301no—
205C4⋊C8—151no—
206C4⋊C8—151no—
207C4⋊C8—151no—
208#102—301no—
209#102—301no—
210C22⋊C8—301no—
211C4×C8C2×D1511yescharacteristic
212C2×C3×C5—161no—
213C2×C3×C5#45911yescharacteristic
214C2×C3×C5#46811yescharacteristic
215C2×C3×C5#47111yescharacteristic
216D15—81no—
217C23×C3—41no—
218C22×D3—101no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—81no—
226C2×C3×C4—41no—
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4#71111yescharacteristic
229C2×C3×C4C2×C22⋊D511yescharacteristic
230C2×Dic3—101no—
231D12—101no—
232D12—101no—
233C4×D3—201no—
234C4×D3—201no—
235C3×C8—21no—
236C3×C8#68612yescomplemented
237C3⋊C8—201no—
238C3⋊C8—201no—
239C3⋊C8—201no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5—81no—
243C22×C5#93811yescharacteristic
244C2×D5—121no—
245C2×D5—121no—
246C2×D5—121no—
247C4×C5—21no—
248C4×C5—81no—
249C4×C5#91411yescharacteristic
250C4×C5#91511yescharacteristic
251C4×C5C2×#21311yescharacteristic
252C4×C5#93211yescharacteristic
253Dic5—121no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—151no—
259C22×C4—301no—
260SD16—42no—
261SD16—42no—
262D8—602no—
263M16—602no—
264C2×C8—301no—
265C2×C8—301no—
266C2×C8—301no—
267C2×C8#122011yescharacteristic
268C2×C8#122011yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—151no—
272C22⋊C4—301no—
273C42C22×D1511yescharacteristic
274C3×C5#168511yescharacteristic, complemented, Hall
275C22×C3—81no—
276C22×C3—81no—
277C22×C3—81no—
278C22×C3#408411yescharacteristic
279C2×D3—201no—
280C2×D3—201no—
281C2×D3—201no—
282C3×C4—21no—
283C3×C4—81no—
284C3×C4#406011yescharacteristic
285C3×C4#406111yescharacteristic
286C3×C4C2×#68611yescharacteristic
287C3×C4#407811yescharacteristic
288Dic3—201no—
289C2×C5—161no—
290C2×C5#507211yescharacteristic
291C2×C5#517411yescharacteristic
292C2×C5#517711yescharacteristic
293D5—241no—
294C23—41no—
295C23—301no—
296Q8—41no—
297Q8—41no—
298D4—41no—
299D4—41no—
300D4—41no—
301D4—41no—
302D4—81no—
303D4—301no—
304D4—301no—
305C2×C4—41no—
306C2×C4—301no—
307C2×C4—601no—
308C2×C4—601no—
309C2×C4D4×D1511yescharacteristic
310C2×C4#681911yescharacteristic
311C2×C4C2×#122011yescharacteristic
312C8—21no—
313C8—601no—
314C8—601no—
315C8—601no—
316C8#671512yescomplemented
317C2×C3—161no—
318C2×C3#6536111yescharacteristic
319C2×C3#6546311yescharacteristic
320C2×C3#6546611yescharacteristic
321D3—401no—
322C5#7126811yescharacteristic, complemented, Sylow
323C22—81no—
324C22—81no—
325C22—81no—
326C22—601no—
327C22—601no—
328C22—601no—
329C22#9182711yescharacteristic
330C4—21no—
331C4—81no—
332C4—601no—
333C4#9180311yescharacteristic
334C4#9180411yescharacteristic
335C4C2×#671511yescharacteristic
336C4#9182111yescharacteristic
337C3#1060206111yescharacteristic, complemented, Sylow
338C2—161no—
339C2—1201no—
340C2#1175117311yescharacteristic
341C2#1175127511yescharacteristic
342C2#1175127811yescharacteristic
subgroupG/H
centerC22#91827
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#121
prime radical#11751173C2
hypercenter#492D15
hypocenterC3×C5#1685
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C3×C5×#492C2semidirect
2. #11751188C2semidirect
4. #11750789C2semidirect
5. #11746368C2semidirect
6. #11746365C2semidirect
7. #11746279C2semidirect
25. C5×#492D3semidirect
52. C3×#492D5semidirect
94. C3×C5×C8D8semidirect
133. #492D15semidirect
193. C5×C8#213semidirect
236. C3×C8#686semidirect
274. C3×C5#1685semidirect
316. C8#6715semidirect
322. C5#71268semidirect
337. C3#10602061semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4922
#117511882
#117511732
#117507892
#117463682
#117463652
#117462792
#106020613
#712685