Finite Group Databasebeta

← #14316345

Subgroups — #14316345

Order 1920.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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×#575C211yesmaximal, characteristic
2#11751296C212yesmaximal, complemented
3#11751238C211yesmaximal, characteristic, complemented
4#11746387C212yesmaximal, complemented
5#11746374C211yesmaximal, characteristic, complemented
6#10602906—31nomaximal, Hall
7C2×C3×C5×#41—21no—
8C3×C5×#137—22no—
9C3×C5×AGL(1,ℤ/8)—22no—
10C3×C5×#135—21no—
11C3×C5×#135C2212yes—
12C2×C3×C5×M16C2211yescharacteristic
13#91813—21no—
14C2×Dic60C2211yescharacteristic, complemented
15#91113—22no—
16#91111—22no—
17#91101C2211yescharacteristic, complemented
18#91100—21no—
19#91096C2212yescomplemented
20#72113—51nomaximal, Hall
21C5×#575D311yescharacteristic
22#65484—32no—
23#65426—31no—
24#64786—32no—
25#64773—31no—
26C3×C5×#41—22no—
27C3×C5×#41—22no—
28C3×C5×#41—41no—
29C3×C5×#41—41no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—41no—
33C22×C3×C4×C5—41no—
34C22×C3×C4×C5D411yescharacteristic
35C2×Dic30—21no—
36C3×C5×Q16—21no—
37C3×C5×Q16D412yes—
38C3×C5×SD16—22no—
39C3×C5×SD16—22no—
40C3×C5×D8—21no—
41C3×C5×D8D412yes—
42C3×C5×M16—22no—
43C2×C3×C5×C8D411yescharacteristic
44C2×C3×C5×C8C2311yescharacteristic
45#6719—41no—
46C4⋊Dic15—21no—
47#6712—41no—
48Dic60—22no—
49C3⋊#672—22no—
50C3×#575D511yescharacteristic
51#5195—52no—
52#5137—51no—
53#4566—52no—
54#4553—51no—
55C2×C5×#41—21no—
56C5×#137—22no—
57C5×AGL(1,ℤ/8)—22no—
58C5×#135—21no—
59C5×#135C2×D312yes—
60C2×C5×M16C2×D311yescharacteristic
61#4070—61no—
62C2×Dic20—31no—
63#3961—62no—
64#3959—62no—
65#3949—31no—
66#3948—61no—
67#3944—32no—
68#2191—151noSylow
69C23×C3×C5—41no—
70C23×C3×C5D811yescharacteristic
71C3×C5×Q8—22no—
72C3×C5×Q8—41no—
73C3×C5×D4—22no—
74C3×C5×D4—41no—
75C3×C5×D4—42no—
76C3×C5×D4—42no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5D811yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×Dic15—41no—
85C2×Dic15—41no—
86Dic30—41no—
87Dic30—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×C3×#41—21no—
91C3×#137—22no—
92C3×AGL(1,ℤ/8)—22no—
93C3×#135—21no—
94C3×#135C2×D512yes—
95C2×C3×M16C2×D511yescharacteristic
96#924—101no—
97C2×Dic12—51no—
98#829—102no—
99#827—102no—
100#817—51no—
101#816—101no—
102#812—52no—
103C5×#41—22no—
104C5×#41—22no—
105C5×#41—41no—
106C5×#41—41no—
107C2×C5×Q8—21no—
108C2×C5×D4—21no—
109C2×C5×D4—41no—
110C22×C4×C5—41no—
111C22×C4×C5#6711yescharacteristic
112C2×Dic10—61no—
113C5×Q16—21no—
114C5×Q16#6712yes—
115C5×SD16—22no—
116C5×SD16—22no—
117C5×D8—21no—
118C5×D8#6712yes—
119C5×M16—22no—
120C2×C5×C8#6711yescharacteristic
121C2×C5×C8C22×D311yescharacteristic
122C22⋊Dic5—121no—
123C4⋊Dic5—61no—
124#683—121no—
125Dic20—62no—
126#672—62no—
127#575D1511yescharacteristic
128#510—152no—
129#470—151no—
130#360—152no—
131#349—151no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5—42no—
135C22×C3×C5—82no—
136C22×C3×C5C2×D811yescharacteristic
137C3×C4×C5—21no—
138C3×C4×C5—42no—
139C3×C4×C5#12011yescharacteristic
140C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
141Dic15—81no—
142Dic15—81no—
143C3×#41—22no—
144C3×#41—22no—
145C3×#41—41no—
146C3×#41—41no—
147C2×C3×Q8—21no—
148C2×C3×D4—21no—
149C2×C3×D4—41no—
150C22×C3×C4—41no—
151C22×C3×C4C22⋊D511yescharacteristic
152C2×Dic6—101no—
153C3×Q16—21no—
154C3×Q16C22⋊D512yes—
155C3×SD16—22no—
156C3×SD16—22no—
157C3×D8—21no—
158C3×D8C22⋊D512yes—
159C3×M16—22no—
160C2×C3×C8C22⋊D511yescharacteristic
161C2×C3×C8C22×D511yescharacteristic
162#217—201no—
163C4⋊Dic3—101no—
164Dic3⋊C4—201no—
165Dic12—102no—
166C3⋊C16—102no—
167C23×C5—41no—
168C23×C5#21311yescharacteristic
169C5×Q8—22no—
170C5×Q8—41no—
171C5×D4—22no—
172C5×D4—41no—
173C5×D4—42no—
174C5×D4—42no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5#21311yescharacteristic
181C2×C4×C5C2×#6711yescharacteristic
182C2×Dic5—121no—
183C2×Dic5—121no—
184Dic10—121no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8C2×#6712yes—
188C2×#41—21no—
189#137—22no—
190AGL(1,ℤ/8)—22no—
191#135—21no—
192#135C2×D1512yes—
193C2×Q16—151no—
194C2×M16C2×D1511yescharacteristic
195C22⋊Q8—301no—
196Q32—302no—
197SD32—302no—
198M32—152no—
199#106—151no—
200#103—301no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5—82no—
204C2×C3×C5#44711yescharacteristic
205C23×C3—41no—
206C23×C3#68611yescharacteristic
207C3×Q8—22no—
208C3×Q8—41no—
209C3×D4—22no—
210C3×D4—41no—
211C3×D4—42no—
212C3×D4—42no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—42no—
218C2×C3×C4#68611yescharacteristic
219C2×C3×C4C2×C22⋊D511yescharacteristic
220C2×Dic3—201no—
221C2×Dic3—201no—
222Dic6—201no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8C2×C22⋊D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5C2×#21311yescharacteristic
231C4×C5—21no—
232C4×C5—42no—
233C4×C5#93211yescharacteristic
234C4×C5#95311yescharacteristic
235Dic5—241no—
236Dic5—241no—
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241C2×Q8—21no—
242C2×Q8—301no—
243C2×D4—21no—
244C2×D4—41no—
245C22×C4—41no—
246C22×C4#122011yescharacteristic
247Q16—21no—
248Q16—302no—
249Q16#122012yes—
250SD16—22no—
251SD16—22no—
252D8—21no—
253D8#122012yes—
254M16—22no—
255C2×C8#122011yescharacteristic
256C2×C8C22×D1511yescharacteristic
257C4⋊C4—301no—
258C4⋊C4—601no—
259C22⋊C4—601no—
260C16—302no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3—42no—
265C22×C3—82no—
266C22×C3C2×#68611yescharacteristic
267C3×C4—21no—
268C3×C4—42no—
269C3×C4#407811yescharacteristic
270C3×C4#409911yescharacteristic
271Dic3—401no—
272Dic3—401no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5—82no—
276C2×C5#521711yescharacteristic
277C23—41no—
278C23#671511yescharacteristic
279Q8—22no—
280Q8—41no—
281Q8—601no—
282Q8—601no—
283D4—22no—
284D4—41no—
285D4—42no—
286D4—42no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—601no—
293C2×C4—601no—
294C2×C4#671511yescharacteristic
295C2×C4C2×#122011yescharacteristic
296C8—21no—
297C8C2×#122012yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3—82no—
301C2×C3#6550611yescharacteristic
302C5#7211311yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—42no—
306C22—82no—
307C22C2×#671511yescharacteristic
308C4—21no—
309C4—42no—
310C4—1201no—
311C4—1201no—
312C4#9182111yescharacteristic
313C4#9184211yescharacteristic
314C3#1060290611yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—82no—
318C2#1175131811yescharacteristic
subgroupG/H
centerC2#11751318
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
Fitting, prime radicalC3×C5×#575C2
socleC2×C3×C5#447
hypercenter#575D15
hypocenterC3×C5#2191
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
2. #11751296C2semidirect
3. #11751238C2semidirect
4. #11746387C2semidirect
5. #11746374C2semidirect
14. C2×Dic60C22semidirect
17. #91101C22semidirect
19. #91096C22semidirect
261. C3×C5#2191semidirect
302. C5#72113semidirect
314. C3#10602906semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5752
#117512962
#117512382
#117463872
#117463742
#106029063
#721135