Finite Group Databasebeta

← #14279099

Subgroups — #14279099

Order 1920.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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#11752436C211yesmaximal, characteristic
2#11752434C211yesmaximal, characteristic
3C3×#65034C211yesmaximal, characteristic
4#10598574—31nomaximal, Hall
5C2×C3×#711C2211yescharacteristic
6C2×#6762—21no—
7C2×#6762C411yescharacteristic
8C22×C3⋊#170C411yescharacteristic
9C3×D5×M16—21no—
10#91242C412yes—
11#91241—21no—
12#91234—21no—
13#91232—21no—
14C3×C5×#100C411yescharacteristic
15C3×#3965C411yescharacteristic
16C3×#3956—21no—
17#67700—51nomaximal, Hall
18#65777—31no—
19#65775—31no—
20#65034D311yescharacteristic
21C2×C3×C5×D4C2×C411yescharacteristic
22C2×C3×C22⋊D5C2×C411yescharacteristic
23C2×C3×C22⋊D5Q811yescharacteristic
24C22×C3×Dic5C2×C411yescharacteristic
25C22×C3×Dic5D411yescharacteristic
26C3×#711—41no—
27C3×#711—41no—
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×Dic10D411yescharacteristic
30#6762—22no—
31#6762—41no—
32#6762—41no—
33C2×C3⋊#170—21no—
34C2×C3⋊#170—21no—
35C2×C3⋊#170—41no—
36C2×C3⋊#170—41no—
37C3×C5×M16—21no—
38C3×#681—21no—
39C3×#676—41no—
40C3×C8×D5—41no—
41C3×#413—51no—
42#5237—51no—
43#5234—51no—
44C2×#711C2×D311yescharacteristic
45C2×#704—31no—
46C2×#704—61no—
47C22×#170—31no—
48D5×M16—21no—
49#4013—32no—
50C22⋊#170—61no—
51#4005—61no—
52#4003—61no—
53C5×#100Dic311yescharacteristic
54#3965Dic311yescharacteristic
55#3956—21no—
56#1392—151noSylow
57C23×C3×C5C4211yescharacteristic
58C23×C3×C5C4⋊C411yescharacteristic
59C22×C3×D5C4⋊C411yescharacteristic
60C3×C5×D4—41no—
61C2×C3×C4×C5C22⋊C411yescharacteristic
62C3×C22⋊D5—41no—
63C3×C22⋊D5—41no—
64C2×C3×Dic5—21no—
65C2×C3×Dic5—21no—
66C2×C3×Dic5—21no—
67C2×C3×Dic5—21no—
68C2×C3×Dic5C22⋊C411yescharacteristic
69C2×C3×Dic5C22⋊C411yescharacteristic
70C2×C3×Dic5C4⋊C411yescharacteristic
71C3×C4×D5—21no—
72C3×C4×D5—21no—
73C3×Dic10—41no—
74C3⋊#170—42no—
75C3⋊#170—41no—
76C3⋊#170—41no—
77C3×C5×C8—41no—
78C3×#168—41no—
79C2×C3×#41—51no—
80C2×C3×M16—101no—
81C2×#208—51no—
82C2×#208—101no—
83C22×C3⋊C8—51no—
84C3×#101—101no—
85C3×#100—51no—
86C3×#100AGL(1,𝔽5)11yescharacteristic
87#836—101no—
88#833—52no—
89#830—101no—
90#830—101no—
91C2×C5×D4C2×Dic311yescharacteristic
92C2×C22⋊D5Dic611yescharacteristic
93C2×C22⋊D5C4×D311yescharacteristic
94C22×Dic5C4×D311yescharacteristic
95C22×Dic5D1211yescharacteristic
96#711—41no—
97#711—41no—
98C2×C4×D5#6711yescharacteristic
99C2×Dic10#6711yescharacteristic
100#704—62no—
101#704—121no—
102#704—121no—
103C2×#170—61no—
104C2×#170—61no—
105C2×#170—121no—
106C2×#170—121no—
107C5×M16—21no—
108#681—21no—
109#676—41no—
110C8×D5—41no—
111#413—51no—
112#413—151no—
113#408—151no—
114C22×C3×C5—21no—
115C22×C3×C5—21no—
116C22×C3×C5—41no—
117C22×C3×C5—41no—
118C22×C3×C5#9511yescharacteristic
119C2×C3×D5—21no—
120C2×C3×D5—41no—
121C3×C4×C5—21no—
122C3×Dic5—21no—
123C3×Dic5—21no—
124C3×Dic5#9911yescharacteristic
125C3×Dic5#9911yescharacteristic
126C3×#41—201no—
127C3×#41—201no—
128C2×C3×Q8—51no—
129C2×C3×D4—51no—
130C2×C3×D4—51no—
131C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
132C22×C3×C4—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C3×M16—21no—
136C3×M16—101no—
137C3×M16—201no—
138C2×C3×C8—201no—
139#208—102no—
140#208—201no—
141#208—201no—
142C2×C3⋊C8—101no—
143C2×C3⋊C8—101no—
144C2×C3⋊C8—201no—
145C2×C3⋊C8—201no—
146C23×C5C4×Dic311yescharacteristic
147C23×C5C4⋊Dic311yescharacteristic
148C22×D5Dic3⋊C411yescharacteristic
149C5×D4—41no—
150C2×C4×C5#21711yescharacteristic
151C22⋊D5—41no—
152C22⋊D5—41no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5Dic3⋊C411yescharacteristic
158C2×Dic5(C2×D3)⋊C411yescharacteristic
159C2×Dic5(C2×D3)⋊C411yescharacteristic
160C4×D5—21no—
161C4×D5—21no—
162Dic10—41no—
163#170—122no—
164#170—121no—
165#170—121no—
166C5×C8—41no—
167#168—41no—
168C2×#41—51no—
169C2×M16—101no—
170C2×M16—151no—
171C2×M16—301no—
172C22×C8—151no—
173#101—101no—
174#101—301no—
175#100—51no—
176#100—152no—
177#100ΓL(1,𝔽16)11yescharacteristic
178C22⋊C8—301no—
179C22⋊C8—301no—
180C2×C3×C5—21no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C5#34211yescharacteristic
184C3×D5—41no—
185C23×C3—51no—
186C23×C3C4×AGL(1,𝔽5)11yescharacteristic
187C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
188C3×Q8—201no—
189C3×D4—41no—
190C3×D4—201no—
191C3×D4—201no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—101no—
196C2×C3×C4—101no—
197C2×C3×C4—101no—
198C2×C3×C4—101no—
199C2×C3×C4—101no—
200C2×C3×C4—101no—
201C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
202C3×C8—41no—
203C3×C8—201no—
204C3⋊C8—201no—
205C3⋊C8—201no—
206C3⋊C8—202no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5C3⋊#9511yescharacteristic
212C2×D5—21no—
213C2×D5—41no—
214C4×C5—21no—
215Dic5—21no—
216Dic5—21no—
217Dic5#80611yescharacteristic
218Dic5#80611yescharacteristic
219#41—201no—
220#41—201no—
221C2×Q8—51no—
222C2×D4—51no—
223C2×D4—51no—
224C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
225C22×C4—51no—
226C22×C4—51no—
227C22×C4—51no—
228M16—21no—
229M16—101no—
230M16—201no—
231M16—302no—
232M16—601no—
233M16—601no—
234C2×C8—201no—
235C2×C8—301no—
236C2×C8—301no—
237C2×C8—601no—
238C2×C8—601no—
239C3×C5#139211yescharacteristic, complemented, Hall
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—101no—
245C22×C3—201no—
246C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
247C3×C4—21no—
248C3×C4—51no—
249C3×C4—51no—
250C3×C4—101no—
251C3×C4—101no—
252C2×C5—21no—
253C2×C5—41no—
254C2×C5—41no—
255C2×C5#452711yescharacteristic
256D5—41no—
257C23—51no—
258C23C4×ΓL(1,𝔽16)11yescharacteristic
259C23C4⋊ΓL(1,𝔽16)11yescharacteristic
260Q8—201no—
261D4—41no—
262D4—201no—
263D4—201no—
264C2×C4—51no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—101no—
268C2×C4—101no—
269C2×C4—101no—
270C2×C4—101no—
271C2×C4—101no—
272C2×C4—101no—
273C2×C4#676311yescharacteristic
274C8—41no—
275C8—201no—
276C8—601no—
277C8—601no—
278C8—602no—
279C2×C3—21no—
280C2×C3—41no—
281C2×C3—41no—
282C2×C3—201no—
283C2×C3#6486611yescharacteristic
284C5#6770011yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—101no—
290C22—201no—
291C22#9123511yescharacteristic
292C4—21no—
293C4—51no—
294C4—51no—
295C4—101no—
296C4—101no—
297C3#1059857411yescharacteristic, complemented, Sylow
298C2—21no—
299C2—41no—
300C2—41no—
301C2—201no—
302C2#1174673711yescharacteristic
subgroupG/H
centerC2#11746737
commutatorC23×C3×C5C42
FrattiniC2×D4C2×ΓL(1,𝔽16)
FittingC3×C5×#100C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#711C22
hypercenter#100ΓL(1,𝔽16)
hypocenterC3×C5#1392
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
239. C3×C5#1392semidirect
284. C5#67700semidirect
297. C3#10598574semidirect

Maximal subgroups

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

subgroupindex
#117524362
#117524342
C3×#650342
#105985743
#677005