Finite Group Databasebeta

← #14316115

Subgroups — #14316115

Order 1920.

460 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 82 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×#91270C211yesmaximal, characteristic, complemented
2C2×#91111C211yesmaximal, characteristic, complemented
3C2×C5×#826C211yesmaximal, characteristic, complemented
4C3×#65446C211yesmaximal, characteristic, complemented
5#11745901C211yesmaximal, characteristic, complemented
6#11745893C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10602261—31nomaximal, Hall
9C2×#6772—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×Dic60C2211yescharacteristic
12C2×C5×D24C2211yescharacteristic
13C3×#4084—21no—
14C2×C3×C8×D5C2211yescharacteristic
15C2×#6659—21no—
16#91270—22no—
17#91270—22no—
18#91111—22no—
19C2×C3⋊#672C2211yescharacteristic
20C5×#826—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22C3×#3964—21no—
23C3×#3950C2211yescharacteristic
24#71076—51nomaximal, Hall
25C2×#4058—31no—
26C2×C5×D16—31no—
27#65446D311yescharacteristic, complemented
28C2×#3959—31no—
29#64782—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×D4—21no—
33C2×Dic30—21no—
34C2×C5×D12—21no—
35C2×C3×C22⋊D5—41no—
36C2×C3×C4×D5D411yescharacteristic
37C2×#1201—41no—
38C2×D3×Dic5—41no—
39#6772—24no—
40#6772—42no—
41C3×C5×D8—21no—
42C3×C5×D8—21no—
43C2×C3×C5×C8C2311yescharacteristic
44Dic60—21no—
45Dic60D412yescomplemented
46C5×D24—21no—
47C5×D24D412yescomplemented
48C3×C22⋊Dic5—41no—
49C3×C4⋊Dic5—21no—
50C2×C3×#168D411yescharacteristic
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6659—24no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C2×#904—51no—
57C3×#466—51no—
58C2×#827—51no—
59C2×#826D511yescharacteristic, complemented
60#4549—51no—
61#4492—51no—
62#4491—51no—
63C2×#711—61no—
64C2×C5×D8—31no—
65C2×C5×D8C2×D311yescharacteristic
66#4084—21no—
67C2×#687—61no—
68#4058—62no—
69#4058—62no—
70C2×Dic20—31no—
71C2×C8×D5C2×D311yescharacteristic
72C5×D16—62no—
73C2×C5×C16—31no—
74#3964—21no—
75#3959—62no—
76#3950C2×D311yescharacteristic
77C2×#672—31no—
78#2186—151noSylow
79C23×C3×C5—41no—
80C22×C5×D3—41no—
81C22×C3×D5D811yescharacteristic
82C3×C5×D4—41no—
83C3×C5×D4—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—41no—
86Dic30—22no—
87Dic30—41no—
88C5×D12—22no—
89C5×D12—41no—
90C3×C22⋊D5—82no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5D811yescharacteristic
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95#1201—44no—
96D3×Dic5—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C2×#235—101no—
101C2×C3×D8C2×D511yescharacteristic
102C22×C3×C8—51no—
103C3×#121—101no—
104C2×Dic12—51no—
105#904—102no—
106#904—102no—
107C2×D24C2×D511yescharacteristic
108C2×#204—101no—
109C3×#107—51no—
110C3×#102—101no—
111#827—102no—
112#826—22no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×D4—21no—
116C2×C5×D4—61no—
117C2×C22⋊D5—41no—
118C2×C22⋊D5—121no—
119C22×Dic5—121no—
120#711—64no—
121#711—122no—
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—61no—
124C5×D8—21no—
125C5×D8—21no—
126C5×D8—32no—
127C5×D8—61no—
128C2×C5×C8C22×D311yescharacteristic
129C22⋊Dic5—41no—
130#687—64no—
131C4⋊Dic5—21no—
132C2×#168#6711yescharacteristic
133Dic20—32no—
134Dic20—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C2×#135—151no—
140C2×SD32—151no—
141C2×D16—31no—
142#466—51no—
143#358—151no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5—81no—
147C22×C3×C5—81no—
148C22×C3×C5—81no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C5×D3—42no—
151C2×C5×D3—81no—
152C2×C5×D3—81no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C3×C4×C5#12011yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158Dic15—42no—
159C3×Dic5—21no—
160C3×Dic5—81no—
161C2×C3×D4—21no—
162C2×C3×D4—201no—
163C22×C3×C4—51no—
164C2×#67—201no—
165#235—104no—
166#235—202no—
167C2×D12—21no—
168C2×C4×D3—201no—
169C2×Dic6—101no—
170C3×D8—21no—
171C3×D8—21no—
172C2×C3×C8—51no—
173C2×C3×C8—101no—
174C2×C3×C8—101no—
175C2×C3×C8C22×D511yescharacteristic
176C3×C4⋊C4—101no—
177C3×C22⋊C4—201no—
178Dic12—52no—
179Dic12—101no—
180D24—21no—
181D24C22⋊D512yescomplemented
182#204—104no—
183C3⋊C16—21no—
184C3⋊C16—101no—
185C23×C5—41no—
186C23×C5—121no—
187C22×D5#21311yescharacteristic
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—62no—
191C5×D4—121no—
192C2×C4×C5C2×#6711yescharacteristic
193C22⋊D5—82no—
194C22⋊D5—124no—
195C2×Dic5—41no—
196C2×Dic5—124no—
197C2×Dic5—121no—
198C2×Dic5#21311yescharacteristic
199C4×D5—21no—
200C4×D5—21no—
201Dic10—62no—
202Dic10—121no—
203C5×C8D3×D411yescharacteristic
204C5×C8D3×D411yescharacteristic
205#168—21no—
206C2×#41—301no—
207#135—302no—
208#135—302no—
209C2×Q16—151no—
210C2×SD16—301no—
211C2×D8—31no—
212C2×D8D3×D511yescharacteristic
213C22×C8—51no—
214#121—101no—
215SD32—302no—
216D16—62no—
217C2×C16—31no—
218C2×C16—151no—
219#107—51no—
220#102—101no—
221C2×C3×C5—161no—
222C2×C3×C5#44711yescharacteristic
223C2×C3×C5#50811yescharacteristic
224C2×C3×C5#50911yescharacteristic
225C3×D5—41no—
226C5×D3—82no—
227C23×C3—41no—
228C23×C3—51no—
229C22×D3—41no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—402no—
233C2×C3×C4—51no—
234C2×C3×C4—101no—
235C2×C3×C4—101no—
236C2×C3×C4—201no—
237C2×C3×C4D4×D511yescharacteristic
238#67—204no—
239C2×Dic3—201no—
240D12—22no—
241D12—41no—
242C4×D3—204no—
243Dic6—102no—
244Dic6—201no—
245C3×C8—101no—
246C3×C8D4×D511yescharacteristic
247C3×C8C2×C22⋊D511yescharacteristic
248C22×C5—81no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5—122no—
252C22×C5—241no—
253C22×C5—241no—
254C22×C5C2×#21311yescharacteristic
255C2×D5—21no—
256C2×D5—21no—
257C2×D5—21no—
258C4×C5#93711yescharacteristic
259C4×C5#94911yescharacteristic
260Dic5—21no—
261Dic5—81no—
262Dic5—122no—
263#41—304no—
264#41—602no—
265C2×Q8—301no—
266C2×D4—21no—
267C2×D4—61no—
268C2×D4—201no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—601no—
272Q16—152no—
273Q16—301no—
274SD16—304no—
275D8—21no—
276D8—21no—
277D8—32no—
278D8—61no—
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—101no—
284C22⋊C4—201no—
285C16—61no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—81no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3D5×D811yescharacteristic
295C2×D3—42no—
296C2×D3—81no—
297C2×D3—81no—
298C3×C4—101no—
299C3×C4—401no—
300C3×C4#405711yescharacteristic
301C3×C4#408311yescharacteristic
302Dic3—202no—
303C2×C5—161no—
304C2×C5—242no—
305C2×C5#503611yescharacteristic
306C2×C5#514711yescharacteristic
307C2×C5#519411yescharacteristic
308D5—41no—
309C23—41no—
310C23—51no—
311C23—121no—
312Q8—302no—
313Q8—601no—
314D4—41no—
315D4—41no—
316D4—62no—
317D4—121no—
318D4—402no—
319D4—604no—
320C2×C4—51no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—201no—
324C2×C4—604no—
325C2×C4—601no—
326C2×C4D5×#6711yescharacteristic
327C8—101no—
328C8D3×C22⋊D511yescharacteristic
329C8#679011yescharacteristic
330C2×C3—161no—
331C2×C3—201no—
332C2×C3#6520011yescharacteristic
333C2×C3#6520111yescharacteristic
334C2×C3#6544511yescharacteristic
335D3—82no—
336C5#7107611yescharacteristic, complemented, Sylow
337C22—81no—
338C22—81no—
339C22—81no—
340C22—101no—
341C22—101no—
342C22—101no—
343C22—122no—
344C22—241no—
345C22—241no—
346C22D5×#21311yescharacteristic
347C4—101no—
348C4—401no—
349C4—602no—
350C4#9147811yescharacteristic
351C4#9157711yescharacteristic
352C3#1060226111yescharacteristic, complemented, Sylow
353C2—161no—
354C2—201no—
355C2—242no—
356C2#1174827611yescharacteristic
357C2#1174827711yescharacteristic
358C2#1174915111yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
hypercenterC2×D8D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#91270C2semidirect
2. C2×#91111C2semidirect
3. C2×C5×#826C2semidirect
4. C3×#65446C2semidirect
5. #11745901C2semidirect
6. #11745893C2semidirect
7. #11745879C2semidirect
27. #65446D3semidirect
45. Dic60D4semidirect
47. C5×D24D4semidirect
59. C2×#826D5semidirect
181. D24C22⋊D5semidirect
287. C3×C5#2186semidirect
336. C5#71076semidirect
352. C3#10602261semidirect

Maximal subgroups

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

subgroupindex
C2×#912702
C2×#911112
C2×C5×#8262
C3×#654462
#117459012
#117458932
#117458792
#106022613
#710765