Finite Group Databasebeta

← #14297620

Subgroups — #14297620

Order 1920.

544 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#91331C211yesmaximal, characteristic
2C2×#91234C211yesmaximal, characteristic
3C2×C3×#4005C211yesmaximal, characteristic
4#11752012C212yesmaximal
5#11746574C212yesmaximal
6#10604336—31nomaximal, Hall
7C22×C3×Dic10C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C2212yes—
10C2×C4×Dic15C411yescharacteristic
11C2×C5×C4⋊Dic3C411yescharacteristic
12C2×#6668C411yescharacteristic
13C2×#6668C2211yescharacteristic
14C2×Dic3×Dic5C411yescharacteristic
15C2×Dic3×Dic5C2211yescharacteristic
16#91331—22no—
17#91331—22no—
18#91234—22no—
19C3×#4005—22no—
20#91177—22no—
21Dic3⋊#170—22no—
22#70097—51nomaximal, Hall
23C2×#4033—31no—
24C2×#4005—31no—
25C2×#4005D311yescharacteristic
26#65758—32no—
27#64919—32no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×Dic15C2×C411yescharacteristic
30C22×Dic15C2×C411yescharacteristic
31C22×C5×Dic3C2×C411yescharacteristic
32C22×C5×Dic3C2×C411yescharacteristic
33C22×C3×Dic5C2×C411yescharacteristic
34C22×C3×Dic5C2311yescharacteristic
35C2×C3×Dic10—22no—
36C2×C3×Dic10—22no—
37C2×C3×Dic10D412yes—
38C2×C3×Dic10Q812yes—
39#6762—22no—
40#6762—22no—
41C2×C3⋊#170—22no—
42C3×#704—22no—
43C3×#704—22no—
44C2×C3×#170—22no—
45C4×Dic15—21no—
46C4×Dic15—21no—
47C5×C4⋊Dic3—22no—
48#6668—22no—
49#6668—22no—
50Dic3×Dic5—21no—
51Dic3×Dic5—21no—
52Dic3×Dic5D412yes—
53Dic3×Dic5D412yes—
54C2×Q8×Dic3—51no—
55C2×C3×#101—51no—
56C2×#836—51no—
57#5118—52no—
58#4554—52no—
59C22×Dic10C2×D311yescharacteristic
60C2×#704—32no—
61C2×#704C2×D312yes—
62C2×C5×C4⋊C4—31no—
63C2×#683—31no—
64C2×#683—31no—
65C2×C4×Dic5—31no—
66C2×C4×Dic5—31no—
67C2×C4×Dic5—31no—
68#4033—62no—
69#4033—62no—
70#4005—22no—
71#4005—62no—
72#4004—62no—
73C4⋊#170—62no—
74#1801—151noSylow
75C23×C3×C5C22×C411yescharacteristic
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5C4⋊C412yes—
79C2×Dic15—22no—
80C2×Dic15—21no—
81C2×Dic15—41no—
82C2×Dic15C22⋊C411yescharacteristic
83C2×Dic15C22⋊C411yescharacteristic
84C2×C5×Dic3—21no—
85C2×C5×Dic3—41no—
86C2×C5×Dic3—41no—
87C2×C5×Dic3C22⋊C412yes—
88C2×C3×Dic5—21no—
89C2×C3×Dic5—21no—
90C2×C3×Dic5C4⋊C412yes—
91C2×C3×Dic5C2×D411yescharacteristic
92C2×C3×Dic5C2×D412yes—
93C2×C3×Dic5C2×Q811yescharacteristic
94C2×C3×Dic5#4112yes—
95C3×Dic10—24no—
96C3×Dic10—24no—
97C3⋊#170—42no—
98C3×#170—42no—
99C22×C3×Q8—51no—
100C2×C3×M16—52no—
101Q8×Dic3—102no—
102Q8×Dic3—102no—
103C2×C4⋊Dic3—51no—
104C2×C4⋊Dic3—51no—
105C2×C4⋊Dic3AGL(1,𝔽5)11yescharacteristic
106C2×C4×Dic3—51no—
107C2×C4×Dic3—51no—
108C2×C4×Dic3—51no—
109C2×#208—52no—
110C3×#101—102no—
111#836—102no—
112Dic3⋊C8—102no—
113Dic3⋊C8—102no—
114C22×C4×C5—31no—
115C22×C4×C5—31no—
116C22×C4×C5C4×D311yescharacteristic
117C22×Dic5—31no—
118C22×Dic5—31no—
119C22×Dic5C4×D311yescharacteristic
120C22×Dic5C22×D311yescharacteristic
121C2×Dic10—22no—
122C2×Dic10—22no—
123C2×Dic10Dic612yes—
124C2×Dic10#6712yes—
125#704—22no—
126#704—22no—
127#704—62no—
128#704—62no—
129C2×#170—22no—
130C2×#170—62no—
131C5×C4⋊C4—62no—
132#683—62no—
133#683—62no—
134C4×Dic5—32no—
135C4×Dic5—32no—
136C4×Dic5—61no—
137C4×Dic5—61no—
138C4×Dic5—61no—
139C4×Dic5—61no—
140C2×C4×Q8—151no—
141#423—152no—
142C2×#101—51no—
143C2×#101—151no—
144#343—152no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C22×C3×C5C2×C4⋊C411yescharacteristic
149C22×C3×C5#11711yescharacteristic
150C3×C4×C5—22no—
151Dic15—21no—
152Dic15—41no—
153Dic15#10112yescomplemented
154C3×Dic5—22no—
155C3×Dic5#12112yes—
156C3×Dic5C22⋊Q812yes—
157C5×Dic3—22no—
158C5×Dic3—41no—
159C2×C3×Q8—52no—
160C2×C3×Q8—52no—
161C2×C3×Q8—102no—
162C2×C3×Q8—102no—
163C22×C3×C4—51no—
164C22×C3×C4—51no—
165C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
166C22×Dic3—51no—
167C22×Dic3—51no—
168C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
169C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
170C3×M16—102no—
171C3×M16—102no—
172C2×C3×C8—102no—
173C4⋊Dic3—22no—
174C4⋊Dic3—102no—
175C4⋊Dic3—102no—
176C4×Dic3—52no—
177C4×Dic3—52no—
178C4×Dic3—101no—
179C4×Dic3—101no—
180C4×Dic3—101no—
181C4×Dic3—101no—
182#208—102no—
183#208—102no—
184C2×C3⋊C8—102no—
185C23×C5C2×C4×D311yescharacteristic
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—32no—
189C2×C4×C5—61no—
190C2×C4×C5—121no—
191C2×C4×C5—121no—
192C2×C4×C5Dic3⋊C412yes—
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—31no—
196C2×Dic5—31no—
197C2×Dic5—62no—
198C2×Dic5—61no—
199C2×Dic5—121no—
200C2×Dic5Dic3⋊C412yes—
201C2×Dic5C2×Dic611yescharacteristic
202C2×Dic5D3×D412yes—
203C2×Dic5#23712yes—
204C2×Dic5C2×#6711yescharacteristic
205Dic10—24no—
206Dic10—24no—
207#170—42no—
208#170—122no—
209C22×Q8—51no—
210C2×M16—52no—
211C2×M16—152no—
212C4×Q8—302no—
213C4×Q8—302no—
214C2×C4⋊C4—31no—
215C2×C4⋊C4—151no—
216C2×C4⋊C4—151no—
217C2×C42—151no—
218C2×C42—151no—
219C2×C42—151no—
220C4⋊C8—302no—
221C4⋊C8—302no—
222#101—102no—
223#101—302no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5#38011yescharacteristic
227C2×C3×C5C2×#10111yescharacteristic
228C2×C3×C5#41311yescharacteristic
229C23×C3C22×AGL(1,𝔽5)11yescharacteristic
230C3×Q8—104no—
231C3×Q8—104no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—51no—
235C2×C3×C4—51no—
236C2×C3×C4—52no—
237C2×C3×C4—52no—
238C2×C3×C4—52no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4C4⋊AGL(1,𝔽5)12yes—
242C2×Dic3—21no—
243C2×Dic3—41no—
244C2×Dic3—41no—
245C2×Dic3—51no—
246C2×Dic3—51no—
247C2×Dic3—102no—
248C2×Dic3—101no—
249C2×Dic3—201no—
250C2×Dic3C22⋊AGL(1,𝔽5)12yes—
251C3×C8—202no—
252C3⋊C8—202no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5#87711yescharacteristic
256C22×C5D3×C22⋊C411yescharacteristic
257C22×C5C2×Dic3⋊C411yescharacteristic
258C4×C5—22no—
259C4×C5—62no—
260C4×C5—121no—
261Dic5—22no—
262Dic5—32no—
263Dic5—61no—
264Dic5—121no—
265Dic5#87812yes—
266Dic5#93912yes—
267C2×Q8—52no—
268C2×Q8—52no—
269C2×Q8—102no—
270C2×Q8—102no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—151no—
276C22×C4—151no—
277C22×C4D3×AGL(1,𝔽5)11yescharacteristic
278M16—102no—
279M16—102no—
280M16—302no—
281M16—302no—
282C2×C8—102no—
283C2×C8—302no—
284C4⋊C4—62no—
285C4⋊C4—302no—
286C4⋊C4—302no—
287C42—152no—
288C42—152no—
289C42—301no—
290C42—301no—
291C42—301no—
292C42—301no—
293C3×C5#180111yescharacteristic, complemented, Hall
294C22×C3—21no—
295C22×C3—21no—
296C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
297C22×C3#413011yescharacteristic
298C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
299C3×C4—22no—
300C3×C4—52no—
301C3×C4—52no—
302C3×C4—102no—
303Dic3—22no—
304Dic3—41no—
305Dic3—52no—
306Dic3—101no—
307Dic3—201no—
308C2×C5—21no—
309C2×C5—21no—
310C2×C5D3×#10111yescharacteristic
311C2×C5#475111yescharacteristic
312C2×C5#494211yescharacteristic
313C23C2×D3×AGL(1,𝔽5)11yescharacteristic
314Q8—104no—
315Q8—104no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—32no—
319C2×C4—52no—
320C2×C4—51no—
321C2×C4—51no—
322C2×C4—52no—
323C2×C4—52no—
324C2×C4—61no—
325C2×C4—101no—
326C2×C4—101no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4—151no—
330C2×C4—151no—
331C2×C4—302no—
332C2×C4—301no—
333C2×C4—601no—
334C2×C4Dic3⋊AGL(1,𝔽5)12yes—
335C8—202no—
336C8—602no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3#6576511yescharacteristic
340C2×C3#6577711yescharacteristic
341C2×C3D5⋊#10111yescharacteristic
342C5#7009711yescharacteristic, complemented, Sylow
343C22—21no—
344C22—21no—
345C22#9192311yescharacteristic
346C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
347C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
348C4—22no—
349C4—52no—
350C4—52no—
351C4—62no—
352C4—102no—
353C4—121no—
354C4—152no—
355C4—301no—
356C4—601no—
357C3#1060433611yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2#1175191611yescharacteristic
361C2#1175191811yescharacteristic
362C2#1175202811yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutator, prime radicalC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1801
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
153. Dic15#101semidirect
293. C3×C5#1801semidirect
342. C5#70097semidirect
357. C3#10604336semidirect

Maximal subgroups

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

subgroupindex
C2×#913312
C2×#912342
C2×C3×#40052
#117520122
#117465742
#106043363
#700975