Finite Group Databasebeta

← #14316121

Subgroups — #14316121

Order 1920.

460 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 88 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×C3×#4058C211yesmaximal, characteristic, complemented
2C2×C5×#826C211yesmaximal, characteristic, complemented
3#11747898C211yesmaximal, characteristic, complemented
4C2×#90941C211yesmaximal, characteristic, complemented
5#11746383C211yesmaximal, characteristic, complemented
6#11745898C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10602261—31nomaximal, Hall
9C2×C3×#711—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×C5×D24C2211yescharacteristic
12C2×C3×#687—21no—
13C3×#4058—22no—
14C3×#4058—22no—
15C2×C3×Dic20C2211yescharacteristic
16C2×C3×C8×D5C2211yescharacteristic
17#91449—21no—
18#91102C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C5×#826—22no—
21C2×C5×C3⋊C16C2211yescharacteristic
22#90967—21no—
23#90941—22no—
24#72082—51nomaximal, Hall
25C2×#4058D311yescharacteristic, complemented
26C2×C5×D16—31no—
27#65446—31no—
28C2×#3959—31no—
29#64782—31no—
30#64727—31no—
31#64723—31no—
32C2×C3×C5×D4—21no—
33C2×C5×D12—21no—
34C2×C3×C22⋊D5—41no—
35C22×C3×Dic5—41no—
36C3×#711—24no—
37C3×#711—42no—
38C2×C3×C4×D5D411yescharacteristic
39C2×C3×Dic10—21no—
40C2×#1201—41no—
41C3×C5×D8—21no—
42C3×C5×D8D412yescomplemented
43C2×C3×C5×C8C2311yescharacteristic
44C4⋊Dic15—21no—
45C5×D24—21no—
46C5×D24—21no—
47C3×#687—24no—
48C2×C3×#168D411yescharacteristic
49C3×Dic20—21no—
50C3×Dic20D412yescomplemented
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53(C2×D3)⋊Dic5—41no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C2×C3×#135—51no—
57C2×#828—51no—
58C2×#826D511yescharacteristic, complemented
59#5115—51no—
60#4564—51no—
61#4562—51no—
62#4549—51no—
63C2×#711—21no—
64C2×C5×D8—31no—
65C2×C5×D8C2×D311yescharacteristic
66#4084—61no—
67C2×#687—21no—
68#4058—22no—
69#4058—22no—
70C2×Dic20C2×D311yescharacteristic
71C2×C8×D5C2×D311yescharacteristic
72C5×D16—62no—
73C2×C5×C16—31no—
74#3964—61no—
75#3959—62no—
76#3950—31no—
77C2×#672—31no—
78#2186—151noSylow
79C23×C3×C5—41no—
80C22×C5×D3—41no—
81C22×C3×D5D811yescharacteristic
82C3×C5×D4—22no—
83C3×C5×D4—41no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—41no—
86C5×D12—41no—
87C5×D12—41no—
88C3×C22⋊D5—44no—
89C2×C3×Dic5—44no—
90C2×C3×Dic5—41no—
91C2×C3×Dic5D811yescharacteristic
92C3×C4×D5—21no—
93C3×C4×D5—21no—
94C3×Dic10—22no—
95C3×Dic10—41no—
96#1201—82no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C2×C3×#41—101no—
101C3×#135—102no—
102C3×#135—102no—
103C2×C3×Q16—51no—
104C2×C3×SD16—101no—
105C2×C3×D8C2×D511yescharacteristic
106C22×C3×C8—51no—
107#930—101no—
108C2×D24C2×D511yescharacteristic
109#828—102no—
110#826—22no—
111#821—101no—
112#818—51no—
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—41no—
120#711—24no—
121#711—42no—
122C2×C4×D5#6711yescharacteristic
123C2×Dic10—21no—
124C5×D8—21no—
125C5×D8—61no—
126C5×D8—61no—
127C5×D8#6712yescomplemented
128C2×C5×C8C22×D311yescharacteristic
129C22⋊Dic5—121no—
130#687—24no—
131C4⋊Dic5—61no—
132C2×#168#6711yescharacteristic
133Dic20—21no—
134Dic20#6712yescomplemented
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C2×#135—51no—
140C2×SD32—151no—
141C2×D16—31no—
142#466—151no—
143#358—151no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5—42no—
147C22×C3×C5—81no—
148C22×C3×C5—81no—
149C22×C3×C5C2×D811yescharacteristic
150C2×C5×D3—81no—
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—81no—
159C3×Dic5—21no—
160C3×Dic5—42no—
161C3×#41—104no—
162C3×#41—202no—
163C2×C3×Q8—101no—
164C2×C3×D4—21no—
165C2×C3×D4—201no—
166C22×C3×C4—51no—
167C22×C3×C4—201no—
168C2×#67—201no—
169C2×D12—21no—
170C3×Q16—52no—
171C3×Q16—101no—
172C3×SD16—104no—
173C3×D8—21no—
174C3×D8C22⋊D512yescomplemented
175C2×C3×C8—51no—
176C2×C3×C8—101no—
177C2×C3×C8—101no—
178C2×C3×C8C22×D511yescharacteristic
179(C2×D3)⋊C4—201no—
180C4⋊Dic3—101no—
181D24—21no—
182D24—21no—
183C3⋊C16—21no—
184C3⋊C16—101no—
185C23×C5—41no—
186C23×C5—121no—
187C22×D5#21311yescharacteristic
188C5×D4—22no—
189C5×D4—41no—
190C5×D4—121no—
191C5×D4—121no—
192C2×C4×C5C2×#6711yescharacteristic
193C22⋊D5—44no—
194C22⋊D5—242no—
195C2×Dic5—44no—
196C2×Dic5—41no—
197C2×Dic5—121no—
198C2×Dic5#21311yescharacteristic
199C4×D5—21no—
200C4×D5—21no—
201Dic10—22no—
202Dic10—41no—
203C5×C8C2×#6711yescharacteristic
204C5×C8C2×#6711yescharacteristic
205#168—21no—
206C2×#41—101no—
207#135—102no—
208#135—102no—
209C2×Q16—51no—
210C2×SD16—101no—
211C2×D8—31no—
212C2×D8D3×D511yescharacteristic
213C22×C8—51no—
214#121—301no—
215SD32—302no—
216D16—62no—
217C2×C16—31no—
218C2×C16—151no—
219#107—151no—
220#102—301no—
221C2×C3×C5—82no—
222C2×C3×C5#44711yescharacteristic
223C2×C3×C5#50811yescharacteristic
224C2×C3×C5#50911yescharacteristic
225C3×D5—41no—
226C5×D3—161no—
227C23×C3—41no—
228C23×C3—51no—
229C22×D3—41no—
230C3×Q8—102no—
231C3×Q8—201no—
232C3×D4—22no—
233C3×D4—41no—
234C3×D4—204no—
235C2×C3×C4—51no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—204no—
239C2×C3×C4—201no—
240C2×C3×C4D4×D511yescharacteristic
241#67—402no—
242C2×Dic3—201no—
243D12—41no—
244D12—41no—
245C3×C8—101no—
246C3×C8D4×D511yescharacteristic
247C3×C8C2×C22⋊D511yescharacteristic
248C22×C5—42no—
249C22×C5—81no—
250C22×C5—81no—
251C22×C5—241no—
252C22×C5—241no—
253C22×C5—241no—
254C22×C5C2×#21311yescharacteristic
255C2×D5—21no—
256C2×D5—21no—
257C2×D5—21no—
258C4×C5#93211yescharacteristic
259C4×C5#95311yescharacteristic
260Dic5—21no—
261Dic5—42no—
262Dic5—241no—
263#41—104no—
264#41—202no—
265C2×Q8—101no—
266C2×D4—21no—
267C2×D4—61no—
268C2×D4—201no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—201no—
272Q16—52no—
273Q16—101no—
274SD16—104no—
275D8—21no—
276D8—61no—
277D8—61no—
278D8#120112yescomplemented
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—301no—
284C22⋊C4—601no—
285C16—61no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—42no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3—101no—
292C22×C3—101no—
293C22×C3—101no—
294C22×C3D5×D811yescharacteristic
295C2×D3—81no—
296C2×D3—81no—
297C2×D3—81no—
298C3×C4—101no—
299C3×C4—202no—
300C3×C4#405711yescharacteristic
301C3×C4#408311yescharacteristic
302Dic3—401no—
303C2×C5—82no—
304C2×C5—481no—
305C2×C5#519311yescharacteristic
306C2×C5#519411yescharacteristic
307C2×C5#521711yescharacteristic
308D5—41no—
309C23—41no—
310C23—51no—
311C23—121no—
312Q8—102no—
313Q8—201no—
314D4—22no—
315D4—41no—
316D4—121no—
317D4—121no—
318D4—204no—
319D4—1202no—
320C2×C4—51no—
321C2×C4—101no—
322C2×C4—101no—
323C2×C4—204no—
324C2×C4—201no—
325C2×C4—601no—
326C2×C4D5×#6711yescharacteristic
327C8—101no—
328C8C2×#120111yescharacteristic
329C8D5×#6711yescharacteristic
330C2×C3—82no—
331C2×C3—201no—
332C2×C3#6520011yescharacteristic
333C2×C3#6520111yescharacteristic
334C2×C3#6544511yescharacteristic
335D3—161no—
336C5#7208211yescharacteristic, complemented, Sylow
337C22—42no—
338C22—81no—
339C22—81no—
340C22—101no—
341C22—101no—
342C22—101no—
343C22—241no—
344C22—241no—
345C22—241no—
346C22D5×#21311yescharacteristic
347C4—101no—
348C4—202no—
349C4—1201no—
350C4#9148911yescharacteristic
351C4#9156311yescharacteristic
352C3#1060226111yescharacteristic, complemented, Sylow
353C2—82no—
354C2—201no—
355C2—481no—
356C2#1174826511yescharacteristic
357C2#1174827711yescharacteristic
358C2#1174902111yescharacteristic
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×C3×#4058C2semidirect
2. C2×C5×#826C2semidirect
3. #11747898C2semidirect
4. C2×#90941C2semidirect
5. #11746383C2semidirect
6. #11745898C2semidirect
7. #11745879C2semidirect
25. C2×#4058D3semidirect
42. C3×C5×D8D4semidirect
50. C3×Dic20D4semidirect
58. C2×#826D5semidirect
127. C5×D8#67semidirect
134. Dic20#67semidirect
174. C3×D8C22⋊D5semidirect
278. D8#1201semidirect
287. C3×C5#2186semidirect
336. C5#72082semidirect
352. C3#10602261semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40582
C2×C5×#8262
#117478982
C2×#909412
#117463832
#117458982
#117458792
#106022613
#720825