Finite Group Databasebeta

← #14316920

Subgroups — #14316920

Order 1920.

496 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 68 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×#66017C211yesmaximal, characteristic, complemented
2C5×#5062C211yesmaximal, characteristic, complemented
3#11749386C212yesmaximal, complemented
4#11746363C211yesmaximal, characteristic, complemented
5#11746012C212yesmaximal, complemented
6#10601780—31nomaximal, Hall
7C5×#1007C2211yescharacteristic, complemented
8C3×C5×#124C2211yescharacteristic
9C5×#932—21no—
10C3×#4093C2212yes—
11C3×#4083—21no—
12C3×#4031—22no—
13C3×#4028—22no—
14C3×#4021—21no—
15#91298—22no—
16#91120C2212yescomplemented
17C5×#836C2211yescharacteristic, complemented
18C5×#805—21no—
19#90979—22no—
20#71951—51nomaximal, Hall
21#66017D311yescharacteristic, complemented
22C5×#454—31no—
23#65534—32no—
24#64762—31no—
25#64697—32no—
26C23×C3×D5—21no—
27C2×C3×C5×Q8C2311yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C5×#239—41no—
30C5×D3×Q8—41no—
31C5×#235—21no—
32C5×#235—22no—
33C2×C3×C22⋊D5—22no—
34C2×C3×D20—21no—
35C2×C3×D20D412yes—
36C2×C3×Dic10—21no—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5D411yescharacteristic
39#6710—22no—
40C5×#214—41no—
41C5×#213—41no—
42C5×#208—21no—
43C3×C22⋊Dic5—21no—
44C3×#685—22no—
45C3×#685—22no—
46C3×#685—22no—
47C3×C4×Dic5D412yes—
48#6655—42no—
49#6652—42no—
50C3×H(3,𝔽4)—51no—
51#5062—52no—
52#5062D511yescharacteristic, complemented
53#4542—51no—
54#4542—52no—
55C5×2−1+4—31no—
56C5×AGL(1,ℤ/8)—61no—
57C5×#124C2×D311yescharacteristic
58#4095—62no—
59#4093C2×D312yes—
60#4083—21no—
61#4031—22no—
62#4028—22no—
63#4021—21no—
64C5×#104—61no—
65C5×#101—31no—
66#3969—62no—
67#3968—32no—
68#2202—151noSylow
69C23×C3×C5—21no—
70C22×C3×D5—22no—
71C22×C3×D5—82no—
72C22×C3×D5—81no—
73C3×C5×Q8—41no—
74C3×C5×D4—41no—
75C2×C3×C4×C5—21no—
76C2×C3×C4×C5C2×D412yes—
77C2×C3×C4×C5C2×D411yescharacteristic
78C5×#67—41no—
79C5×D12—21no—
80C5×D12—22no—
81C4×C5×D3—41no—
82C4×C5×D3—42no—
83C5×Dic6—21no—
84C5×Dic6—22no—
85C3×C22⋊D5—82no—
86C2×C3×Dic5—22no—
87C3×D20—42no—
88C3×D20—81no—
89C3×Dic10—81no—
90C3⋊#168—42no—
91C5×C3⋊C8—41no—
92#1007C2×D511yescharacteristic, complemented
93C3×#124—52no—
94C3×#124—102no—
95C3×#124—101no—
96C3×#124C2×D511yescharacteristic
97C3×#120—102no—
98C3×#120—101no—
99#932—21no—
100#932—102no—
101#836—52no—
102#836C2×D511yescharacteristic, complemented
103#805—21no—
104#805—102no—
105C23×D5—21no—
106C5×#41—61no—
107C5×#41—62no—
108C5×#41—121no—
109C2×C5×Q8—121no—
110C2×C5×Q8C22×D311yescharacteristic
111C2×C5×D4#6711yescharacteristic
112C2×C22⋊D5—22no—
113C2×D20—21no—
114C2×D20#6712yes—
115C2×Dic10—21no—
116C5×SD16—121no—
117C5×D8—121no—
118C5×M16—61no—
119C5×C22⋊C4—22no—
120C42×C5#6711yescharacteristic
121C22⋊Dic5—21no—
122#688—122no—
123#686—122no—
124#685—22no—
125#685—22no—
126#685—22no—
127C4×Dic5#6712yes—
128#681—62no—
129H(3,𝔽4)—51no—
130#454—31no—
131#454—152no—
132#355—152no—
133#355—151no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5#12011yescharacteristic
137C2×C5×D3—41no—
138C2×C3×D5—42no—
139C2×C3×D5—42no—
140C2×C3×D5—42no—
141C2×C3×D5—84no—
142C3×C4×C5—21no—
143C3×C4×C5—22no—
144C3×C4×C5—41no—
145C3×Dic5—42no—
146C5×Dic3—41no—
147C24×C3—101no—
148C2×C3×Q8—101no—
149C2×C3×Q8C22×D511yescharacteristic
150C2×C3×D4—52no—
151C2×C3×D4—101no—
152C2×C3×D4—102no—
153C2×C3×D4C22⋊D511yescharacteristic
154#239—41no—
155D3×Q8—41no—
156#235—22no—
157#235—21no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—102no—
160C3×C22⋊C4—101no—
161C3×C22⋊C4—102no—
162C3×C22⋊C4—102no—
163C3×C42—52no—
164C3×C42C22⋊D511yescharacteristic
165#214—41no—
166#214—202no—
167#213—41no—
168#213—202no—
169#208—21no—
170#208—102no—
171C23×C5—21no—
172C22×D5—22no—
173C22×D5—82no—
174C22×D5—81no—
175C5×Q8—41no—
176C5×Q8—62no—
177C5×Q8—61no—
178C5×D4—41no—
179C5×D4—62no—
180C5×D4—61no—
181C5×D4—121no—
182C2×C4×C5—21no—
183C2×C4×C5—122no—
184C2×C4×C5—121no—
185C2×C4×C5C2×#6711yescharacteristic
186C2×C4×C5C2×#6712yes—
187C22⋊D5—82no—
188C2×Dic5—22no—
189D20—42no—
190D20—81no—
191Dic10—81no—
192C5×C8—121no—
193#168—122no—
1942−1+4—31no—
195AGL(1,ℤ/8)—61no—
196AGL(1,ℤ/8)—302no—
197#124—52no—
198#124—102no—
199#124—101no—
200#124D3×D511yescharacteristic
201#120—102no—
202#120—101no—
203#104—61no—
204#104—302no—
205#101—31no—
206#101—152no—
207C2×C3×C5—21no—
208C2×C3×C5—81no—
209C2×C3×C5B(4,𝔽2)11yescharacteristic
210C3×D5—82no—
211C5×D3—81no—
212C23×C3—21no—
213C23×C3—102no—
214C23×C3—402no—
215C23×C3—401no—
216C3×Q8—41no—
217C3×Q8—401no—
218C3×D4—41no—
219C3×D4—202no—
220C3×D4—401no—
221C3×D4—402no—
222C2×C3×C4—21no—
223C2×C3×C4—102no—
224C2×C3×C4D4×D512yes—
225C2×C3×C4C2×C22⋊D511yescharacteristic
226#67—41no—
227D12—21no—
228D12—22no—
229C4×D3—41no—
230C4×D3—42no—
231Dic6—21no—
232Dic6—22no—
233C3⋊C8—41no—
234C3⋊C8—202no—
235C22×C5—42no—
236C22×C5—41no—
237C22×C5—121no—
238C22×C5#95311yescharacteristic
239C2×D5—42no—
240C2×D5—42no—
241C2×D5—42no—
242C2×D5—84no—
243C4×C5—22no—
244C4×C5—21no—
245C4×C5—41no—
246C4×C5—121no—
247Dic5—42no—
248C24—101no—
249#41—61no—
250#41—62no—
251#41—121no—
252C2×Q8—101no—
253C2×Q8—121no—
254C2×Q8C2×D3×D511yescharacteristic
255C2×D4—52no—
256C2×D4—101no—
257C2×D4—102no—
258C2×D4#120111yescharacteristic
259SD16—121no—
260SD16—602no—
261D8—121no—
262D8—602no—
263M16—61no—
264M16—302no—
265C22⋊C4—22no—
266C22⋊C4—102no—
267C22⋊C4—101no—
268C22⋊C4—102no—
269C22⋊C4—102no—
270C42—52no—
271C42#120111yescharacteristic
272C3×C5#220211yescharacteristic, complemented, Hall
273C22×C3—42no—
274C22×C3—41no—
275C22×C3—202no—
276C22×C3—202no—
277C22×C3—202no—
278C22×C3—404no—
279C22×C3#408311yescharacteristic
280C2×D3—41no—
281C3×C4—21no—
282C3×C4—22no—
283C3×C4—41no—
284C3×C4—202no—
285Dic3—41no—
286C2×C5—21no—
287C2×C5—81no—
288C2×C5—241no—
289C2×C5#524411yescharacteristic
290D5—82no—
291C23—21no—
292C23—102no—
293C23—402no—
294C23—401no—
295Q8—41no—
296Q8—61no—
297Q8—62no—
298Q8—401no—
299D4—41no—
300D4—61no—
301D4—62no—
302D4—121no—
303D4—202no—
304D4—401no—
305D4—402no—
306C2×C4—21no—
307C2×C4—102no—
308C2×C4—121no—
309C2×C4—122no—
310C2×C4C2×#120111yescharacteristic
311C2×C4D5×#6712yes—
312C8—121no—
313C8—602no—
314C2×C3—21no—
315C2×C3—81no—
316C2×C3—402no—
317C2×C3#6532111yescharacteristic
318D3—81no—
319C5#7195111yescharacteristic, complemented, Sylow
320C22—42no—
321C22—41no—
322C22—121no—
323C22—202no—
324C22—202no—
325C22—202no—
326C22—404no—
327C22#9156311yescharacteristic
328C4—21no—
329C4—22no—
330C4—41no—
331C4—121no—
332C4—202no—
333C3#1060178011yescharacteristic, complemented, Sylow
334C2—21no—
335C2—81no—
336C2—241no—
337C2—402no—
338C2#1174917511yescharacteristic
subgroupG/H
centerC2#11749175
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5B(4,𝔽2)
hypercenter#124D3×D5
hypocenterC3×C5#2202
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#66017C2semidirect
2. C5×#5062C2semidirect
3. #11749386C2semidirect
4. #11746363C2semidirect
5. #11746012C2semidirect
7. C5×#1007C22semidirect
16. #91120C22semidirect
17. C5×#836C22semidirect
21. #66017D3semidirect
52. #5062D5semidirect
92. #1007C2×D5semidirect
102. #836C2×D5semidirect
272. C3×C5#2202semidirect
319. C5#71951semidirect
333. C3#10601780semidirect

Maximal subgroups

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

subgroupindex
C3×#660172
C5×#50622
#117493862
#117463632
#117460122
#106017803
#719515