Finite Group Databasebeta

← #14303102

Subgroups — #14303102

Order 1920.

616 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 148 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#11756584C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic
3C5×#5237C211yesmaximal, characteristic
4C2×#90963C212yesmaximal, complemented
5#11745990C212yesmaximal, complemented
6#10600931—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×Dic30C2211yescharacteristic
9#91833—21no—
10#91825—21no—
11#91824C414yes—
12#91815C2211yescharacteristic
13#91813—22no—
14C2×C5×#208C2212yes—
15C3×#4094—24no—
16C2×C3×#681—22no—
17C2×C3×#681C2212yes—
18C5×#836—21no—
19C5×#833—21no—
20#90963—24no—
21#72031—51nomaximal, Hall
22#66159—31no—
23#66153D311yescharacteristic
24C5×#413—31no—
25C2×#3956—32no—
26#64776—32no—
27C3×C5×#41—22no—
28C3×C5×#41—22no—
29C2×C3×C5×Q8D411yescharacteristic
30C2×C3×C5×D4C2×C412yes—
31C2×C3×C5×D4D411yescharacteristic
32C22×C3×C4×C5D412yes—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15C2×C412yes—
35C2×Dic30—22no—
36C2×Dic30—21no—
37C2×Dic30—21no—
38C2×Dic30—22no—
39#6719—24no—
40#6719C2×C412yes—
41C4⋊Dic15—21no—
42#6712—24no—
43C4×Dic15—21no—
44C5×#208—22no—
45C5×#208—22no—
46C2×C5×C3⋊C8—22no—
47C3×#681—24no—
48C3×#681—22no—
49C3×#681D414yes—
50C2×C3×#168—24no—
51C2×C3×#168—22no—
52C3×#568—51no—
53#5825—51no—
54#5237D511yescharacteristic
55C2×#824—52no—
56#4559—52no—
57C2×C5×#41C2×D311yescharacteristic
58C22×Dic10—31no—
59C2×C5×M16—32no—
60#4094—24no—
61#4090—61no—
62#4082—61no—
63#4081—34no—
64#4072—31no—
65#4070—62no—
66C2×#681—22no—
67C2×#681C2×D312yes—
68C5×#101—61no—
69C5×#100—61no—
70#3956—64no—
71#1915—151noSylow
72C23×C3×C5C22⋊C412yes—
73C23×C3×C5C22×C411yescharacteristic
74C3×C5×Q8—22no—
75C3×C5×D4—24no—
76C3×C5×D4—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5C22⋊C412yes—
80C2×C3×C4×C5C2×D412yes—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4112yes—
84C2×Dic15—22no—
85C2×Dic15—22no—
86C2×Dic15—24no—
87Dic30—41no—
88Dic30—42no—
89Dic30—41no—
90C3×#168—24no—
91C5×C3⋊C8—42no—
92C2×C3×#41C2×D511yescharacteristic
93C22×Dic6—51no—
94C3×#131—104no—
95C2×C3×M16—52no—
96C2×C3×M16—102no—
97#944—101no—
98#936—101no—
99#935—54no—
100#926—51no—
101#924—102no—
102C2×#208C2×D512yes—
103#836—21no—
104#833—21no—
105#824—104no—
106C5×#41—22no—
107C5×#41—22no—
108C2×C5×Q8D1211yescharacteristic
109C2×C5×D4C4×D312yes—
110C2×C5×D4D1211yescharacteristic
111C22×C4×C5#6712yes—
112C22×C4×C5C22×D311yescharacteristic
113C22×Dic5—32no—
114C2×Dic10—61no—
115C2×Dic10—62no—
116C2×Dic10—62no—
117C2×Dic10—61no—
118C5×M16—62no—
119C5×M16—62no—
120C2×C5×C8—62no—
121C22⋊Dic5—32no—
122C22⋊Dic5—64no—
123C4⋊Dic5—61no—
124#683—64no—
125C4×Dic5—61no—
126#681—24no—
127#681—22no—
128#681#6714yes—
129C2×#168—24no—
130C2×#168—22no—
131#568—51no—
132#536—151no—
133#413—31no—
134C2×#101—152no—
135#344—152no—
136C22×C3×C5—22no—
137C22×C3×C5—41no—
138C22×C3×C5—42no—
139C22×C3×C5C2×C22⋊C411yescharacteristic
140C22×C3×C5C4×D412yes—
141C3×C4×C5—22no—
142C3×C4×C5#12011yescharacteristic
143C3×C4×C5#12112yes—
144C3×C4×C5#12311yescharacteristic
145Dic15—42no—
146Dic15—42no—
147C3×#41—22no—
148C3×#41—22no—
149C2×C3×Q8C22⋊D511yescharacteristic
150C2×C3×D4C4×D512yes—
151C2×C3×D4C22⋊D511yescharacteristic
152C22×C3×C4D2012yes—
153C22×C3×C4C22×D511yescharacteristic
154C22×Dic3—52no—
155C2×Dic6—101no—
156C2×Dic6—102no—
157C2×Dic6—102no—
158C2×Dic6—101no—
159C3×M16—54no—
160C3×M16—104no—
161C3×M16—102no—
162C2×C3×C8—104no—
163C2×C3×C8—102no—
164#217—52no—
165#217—104no—
166C4⋊Dic3—101no—
167Dic3⋊C4—104no—
168C4×Dic3—101no—
169#208—22no—
170#208—22no—
171C2×C3⋊C8—22no—
172C23×C5(C2×D3)⋊C412yes—
173C23×C5C2×C4×D311yescharacteristic
174C5×Q8—22no—
175C5×D4—24no—
176C5×D4—22no—
177C2×C4×C5—22no—
178C2×C4×C5—22no—
179C2×C4×C5(C2×D3)⋊C412yes—
180C2×C4×C5C2×D1211yescharacteristic
181C2×C4×C5#23512yes—
182C2×C4×C5C2×#6711yescharacteristic
183C2×C4×C5C2×#6712yes—
184C2×Dic5—62no—
185C2×Dic5—62no—
186C2×Dic5—64no—
187Dic10—121no—
188Dic10—122no—
189Dic10—121no—
190C5×C8—122no—
191#168—24no—
192C2×#41D3×D511yescharacteristic
193C22×Q8—151no—
194#131—104no—
195C2×M16—32no—
196C2×M16—52no—
197C2×M16—102no—
198C4⋊Q8—301no—
199#124—301no—
200#123—154no—
201C22⋊Q8—302no—
202#117—151no—
203#101—61no—
204#101—304no—
205#100—61no—
206C2×C3×C5—21no—
207C2×C3×C5—22no—
208C2×C3×C5—42no—
209C2×C3×C5#38611yescharacteristic
210C23×C3#68512yes—
211C23×C3C2×C4×D511yescharacteristic
212C3×Q8—22no—
213C3×D4—24no—
214C3×D4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4#68512yes—
218C2×C3×C4C2×D2011yescharacteristic
219C2×C3×C4D4×D512yes—
220C2×C3×C4#71112yes—
221C2×C3×C4C2×C22⋊D511yescharacteristic
222C2×Dic3—104no—
223C2×Dic3—102no—
224C2×Dic3—102no—
225Dic6—201no—
226Dic6—201no—
227Dic6—202no—
228C3×C8—104no—
229C3⋊C8—42no—
230C22×C5—22no—
231C22×C5—41no—
232C22×C5—42no—
233C22×C5C2×(C2×D3)⋊C411yescharacteristic
234C22×C5C4×#6712yes—
235C4×C5—22no—
236C4×C5#92911yescharacteristic
237C4×C5#93012yes—
238C4×C5#95311yescharacteristic
239Dic5—122no—
240Dic5—122no—
241#41—22no—
242#41—22no—
243C2×Q8—302no—
244C2×Q8—301no—
245C2×Q8—301no—
246C2×Q8—302no—
247C2×Q8#120311yescharacteristic
248C2×D4#120012yes—
249C2×D4#120311yescharacteristic
250C22×C4—152no—
251C22×C4#120212yes—
252C22×C4C2×D3×D511yescharacteristic
253M16—54no—
254M16—62no—
255M16—62no—
256M16—104no—
257M16—102no—
258C2×C8—62no—
259C2×C8—104no—
260C2×C8—102no—
261C4⋊C4—304no—
262C4⋊C4—301no—
263C22⋊C4—152no—
264C22⋊C4—304no—
265C42—301no—
266C3×C5#191511yescharacteristic, complemented, Hall
267C22×C3—22no—
268C22×C3—41no—
269C22×C3—42no—
270C22×C3#402712yes—
271C22×C3C2×#68511yescharacteristic
272C3×C4—22no—
273C3×C4#402811yescharacteristic
274C3×C4#403211yescharacteristic
275C3×C4#408512yes—
276Dic3—202no—
277Dic3—202no—
278C2×C5—21no—
279C2×C5—22no—
280C2×C5—42no—
281C2×C5#521311yescharacteristic
282C23#666712yes—
283C23C2×#120011yescharacteristic
284Q8—22no—
285Q8—601no—
286Q8—601no—
287Q8—602no—
288D4—24no—
289D4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—302no—
293C2×C4—302no—
294C2×C4—304no—
295C2×C4#666712yes—
296C2×C4#678212yes—
297C2×C4C2×#120211yescharacteristic
298C2×C4C2×#120311yescharacteristic
299C2×C4D5×#6712yes—
300C8—104no—
301C8—122no—
302C2×C3—21no—
303C2×C3—22no—
304C2×C3—42no—
305C2×C3#6524711yescharacteristic
306C5#7203111yescharacteristic, complemented, Sylow
307C22—22no—
308C22—41no—
309C22—42no—
310C22C2×#666711yescharacteristic
311C22#9155212yes—
312C4—22no—
313C4—602no—
314C4—602no—
315C4#9154611yescharacteristic
316C4#9156411yescharacteristic
317C4#9156612yes—
318C3#1060093111yescharacteristic, complemented, Sylow
319C2—21no—
320C2—22no—
321C2—42no—
322C2#1174949411yescharacteristic
subgroupG/H
centerC2#11749494
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC2×C3×C5#386
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#90963C2semidirect
5. #11745990C2semidirect
266. C3×C5#1915semidirect
306. C5#72031semidirect
318. C3#10600931semidirect

Maximal subgroups

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

subgroupindex
#117565842
C3×#661532
C5×#52372
C2×#909632
#117459902
#106009313
#720315