Finite Group Databasebeta

← #14292095

Subgroups — #14292095

Order 1920.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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×#486C211yesmaximal, characteristic, complemented
2#11751184C211yesmaximal, characteristic, complemented
3#11751173C211yesmaximal, characteristic
4C8×D60C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6#11746365C211yesmaximal, characteristic, complemented
7#11746279C211yesmaximal, characteristic, complemented
8#10601994—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×#6717—21no—
12C2×#6715—21no—
13C2×C8×D15—21no—
14C4×D60C2211yescharacteristic
15C3×C5×#102—21no—
16C3×C5×#102—21no—
17C3×C4×C5×C8C2211yescharacteristic
18#91119—21no—
19#91116—21no—
20#91104—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4⋊(C3⋊#168)C2211yescharacteristic
24#71201—51nomaximal, Hall
25C5×#486D311yescharacteristic, complemented
26#65372—31no—
27#65361—31no—
28C8×D20—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—
38C2×C3×C5×C8D411yescharacteristic
39C2×C3×C5×C8D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6717—42no—
44#6715—42no—
45#6714—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C8×D15—42no—
51C3×#486D511yescharacteristic, complemented
52#5083—51no—
53#5072—51no—
54C8×D12—51no—
55#4547—51no—
56#4544—51no—
57#4458—51no—
58C5×C4⋊Q8C2×D311yescharacteristic
59C5×#127C2×D311yescharacteristic
60C2×#688—61no—
61C2×#686—61no—
62C2×C8×D5—61no—
63C4×D20—31no—
64C5×#102—21no—
65C5×#102—21no—
66C4×C5×C8C2×D311yescharacteristic
67#3967—61no—
68#3964—61no—
69#3952—61no—
70C4⋊#168—31no—
71C4⋊#168—31no—
72C4⋊#168—31no—
73#1681—151noSylow
74C23×C3×C5—41no—
75C22×D15—21no—
76C3×C5×Q8—41no—
77C3×C5×Q8—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—81no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×Dic15—21no—
88D60—21no—
89D60D812yes—
90C4×D15—41no—
91C4×D15—41no—
92C3×C5×C8—21no—
93C3×C5×C8—21no—
94C3⋊#168—41no—
95C3⋊#168—41no—
96C3⋊#168—41no—
97C3×C4⋊Q8C2×D511yescharacteristic
98C3×#127C2×D511yescharacteristic
99C2×#215—101no—
100C2×#213—101no—
101C2×D3×C8—101no—
102C4×D12—51no—
103C3×#102—21no—
104C3×#102—21no—
105C3×C4×C8C2×D511yescharacteristic
106#835—101no—
107#832—101no—
108(C2×D3)⋊C8—101no—
109C4⋊(C3⋊C8)—51no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)—51no—
112C2×C5×Q8—21no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×C5×D4—21no—
116C2×D20—31no—
117C2×C4×D5—61no—
118C2×C5×C8#6711yescharacteristic
119C2×C5×C8#6711yescharacteristic
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C42×C5C22×D311yescharacteristic
123#688—122no—
124#686—122no—
125#685—61no—
126C4⋊Dic5—31no—
127C2×#168—61no—
128C2×#168—61no—
129C2×#168—61no—
130C8×D5—122no—
131#486D1511yescharacteristic, complemented
132#461—151no—
133#459—151no—
134C8×D4—151no—
135#335—151no—
136#332—151no—
137#331—151no—
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C2×D15—22no—
143C2×D15—41no—
144C2×D15—41no—
145C3×C4×C5—21no—
146C3×C4×C5—81no—
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151Dic15—41no—
152C2×C3×Q8—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×D12—51no—
157C2×C4×D3—101no—
158C2×C3×C8C22⋊D511yescharacteristic
159C2×C3×C8C22⋊D511yescharacteristic
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C42C22×D511yescharacteristic
163#215—202no—
164#213—202no—
165(C2×D3)⋊C4—101no—
166C4⋊Dic3—51no—
167C2×C3⋊C8—101no—
168C2×C3⋊C8—101no—
169C2×C3⋊C8—101no—
170D3×C8—202no—
171C23×C5—41no—
172C22×D5—61no—
173C5×Q8—41no—
174C5×Q8—41no—
175C5×D4—41no—
176C5×D4—41no—
177C5×D4—41no—
178C5×D4—41no—
179C5×D4—81no—
180C2×C4×C5—41no—
181C2×C4×C5D3×D411yescharacteristic
182C2×C4×C5#23711yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C2×Dic5—61no—
185D20—32no—
186D20—61no—
187C4×D5—121no—
188C4×D5—121no—
189C5×C8—21no—
190C5×C8—21no—
191#168—121no—
192#168—121no—
193#168—121no—
194C2×SD16—301no—
195C2×D8—301no—
196C22×C8—301no—
197C4⋊Q8C2×D1511yescharacteristic
198#127C2×D1511yescharacteristic
199C4×D4—151no—
200C4⋊C8—151no—
201C4⋊C8—151no—
202C4⋊C8—151no—
203#103—301no—
204#102—21no—
205#102—21no—
206#102—301no—
207C22⋊C8—301no—
208C4×C8C2×D1511yescharacteristic
209C2×C3×C5—161no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213D15—42no—
214C23×C3—41no—
215C22×D3—101no—
216C3×Q8—41no—
217C3×Q8—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—81no—
223C2×C3×C4—41no—
224C2×C3×C4D4×D511yescharacteristic
225C2×C3×C4#71111yescharacteristic
226C2×C3×C4C2×C22⋊D511yescharacteristic
227C2×Dic3—101no—
228D12—52no—
229D12—101no—
230C4×D3—201no—
231C4×D3—201no—
232C3×C8—21no—
233C3×C8—21no—
234C3⋊C8—201no—
235C3⋊C8—201no—
236C3⋊C8—201no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5#93811yescharacteristic
241C2×D5—62no—
242C2×D5—121no—
243C2×D5—121no—
244C4×C5—21no—
245C4×C5—81no—
246C4×C5D3×D811yescharacteristic
247C4×C5#91211yescharacteristic
248C4×C5#94911yescharacteristic
249C4×C5#95011yescharacteristic
250Dic5—121no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—151no—
256C22×C4—301no—
257SD16—602no—
258D8—602no—
259C2×C8—301no—
260C2×C8—301no—
261C2×C8—301no—
262C2×C8—602no—
263C2×C8#122011yescharacteristic
264C2×C8#122011yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—151no—
268C22⋊C4—301no—
269C42C22×D1511yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3#408411yescharacteristic
275C2×D3—102no—
276C2×D3—201no—
277C2×D3—201no—
278C3×C4—21no—
279C3×C4—81no—
280C3×C4D5×D811yescharacteristic
281C3×C4#405811yescharacteristic
282C3×C4#409511yescharacteristic
283C3×C4#409611yescharacteristic
284Dic3—201no—
285C2×C5—161no—
286C2×C5#505711yescharacteristic
287C2×C5#515711yescharacteristic
288C2×C5#517711yescharacteristic
289D5—122no—
290C23—41no—
291C23—301no—
292Q8—41no—
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—81no—
299D4—152no—
300D4—301no—
301C2×C4—41no—
302C2×C4—301no—
303C2×C4—601no—
304C2×C4—601no—
305C2×C4D4×D1511yescharacteristic
306C2×C4#681911yescharacteristic
307C2×C4C2×#122011yescharacteristic
308C8—21no—
309C8—21no—
310C8—601no—
311C8—601no—
312C8—601no—
313C2×C3—161no—
314C2×C3#6534611yescharacteristic
315C2×C3#6544611yescharacteristic
316C2×C3#6546611yescharacteristic
317D3—202no—
318C5#7120111yescharacteristic, complemented, Sylow
319C22—81no—
320C22—81no—
321C22—81no—
322C22—302no—
323C22—601no—
324C22—601no—
325C22#9182711yescharacteristic
326C4—21no—
327C4—81no—
328C4—601no—
329C4D8×D1511yescharacteristic
330C4#9180111yescharacteristic
331C4#9183811yescharacteristic
332C4#9183911yescharacteristic
333C3#1060199411yescharacteristic, complemented, Sylow
334C2—161no—
335C2—602no—
336C2#1175115811yescharacteristic
337C2#1175125811yescharacteristic
338C2#1175127811yescharacteristic
subgroupG/H
centerC22#91827
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#121
prime radical#11751173C2
hypercenter#486D15
hypocenterC3×C5#1681
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C3×C5×#486C2semidirect
2. #11751184C2semidirect
4. C8×D60C2semidirect
5. #11746368C2semidirect
6. #11746365C2semidirect
7. #11746279C2semidirect
25. C5×#486D3semidirect
51. C3×#486D5semidirect
131. #486D15semidirect
270. C3×C5#1681semidirect
318. C5#71201semidirect
333. C3#10601994semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4862
#117511842
#117511732
C8×D602
#117463682
#117463652
#117462792
#106019943
#712015