Finite Group Databasebeta

← #14289611

Subgroups — #14289611

Order 1920.

436 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752710C211yesmaximal, characteristic
2C3×#64988C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic, complemented
5#11746280C211yesmaximal, characteristic, complemented
6C5×#4459C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10598996—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C2×C3×Dic20—22no—
12C3×#4015C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91466—21no—
15#91460—21no—
16#91347—21no—
17#91338—21no—
18#91326—22no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90987—21no—
23#90986—21no—
24#90968—21no—
25#90966—21no—
26#71304—51nomaximal, Hall
27#65897—31no—
28#65297—31no—
29#65131—31no—
30#64988D311yescharacteristic, complemented
31C5×D4⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D412yes—
40C2×#1203—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15D411yescharacteristic
45C2×C3⋊#168—21no—
46C5×(C2×D3)⋊C4—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×Dic20—44no—
54#6667—22no—
55(C2×D3)⋊Dic5—22no—
56Dic3×Dic5—22no—
57#5734—51no—
58C3×#494—51no—
59#5084—51no—
60#5084—51no—
61#4546—51no—
62#4459—51no—
63#4459D511yescharacteristic, complemented
64C4×C5×D4—31no—
65#4084—61no—
66#4076—61no—
67#4072—61no—
68C2×Dic20—22no—
69#4038—61no—
70#4031—62no—
71C4×D20—31no—
72#4015C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3953—61no—
78#3949—61no—
79#3940—61no—
80C4⋊#168—31no—
81#1634—151noSylow
82C22×D15—21no—
83C22×C5×D3—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88D60—21no—
89D60—21no—
90C4×D15—41no—
91C4×D15—41no—
92C2×C5×Dic3—21no—
93C5×D12—21no—
94C5×D12—21no—
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5—41no—
99C3×Dic10—42no—
100C3×Dic10—42no—
101#1203—82no—
102C3×C5×C8—22no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C2×C3×Q16—102no—
106C3×C4⋊Q8—51no—
107C3×C4⋊Q8—51no—
108#947—102no—
109#895—101no—
110#895—101no—
111#892—101no—
112#892—101no—
113C4×D12—51no—
114C4×D12C2×D511yescharacteristic
115C3×C4×C8C2×D511yescharacteristic
116#809—101no—
117#809—101no—
118#808—101no—
119#808—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×D4—31no—
123C22×C4×C5—61no—
124C2×C22⋊D5—62no—
125C2×D20—31no—
126C2×C4×D5—61no—
127C2×Dic10—21no—
128C2×Dic10#6712yes—
129C2×C5×C8—21no—
130C2×C5×C8—61no—
131C5×C4⋊C4—31no—
132C5×C22⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135#685—62no—
136#685—61no—
137C4⋊Dic5—21no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4×Dic5—62no—
143C2×#168—61no—
144Dic20—44no—
145#555—151no—
146#494—51no—
147#476—151no—
148#476—151no—
149#333—151no—
150D4⋊C8—31no—
151D4⋊C8—151no—
152C22×C3×C5#12011yescharacteristic
153C2×D15—41no—
154C2×D15—41no—
155C2×D15—41no—
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C3×C4×C5—21no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13711yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165C3×Dic5—42no—
166C3×Dic5—81no—
167C5×Dic3—41no—
168C2×C3×Q8—52no—
169C2×C3×Q8—101no—
170C2×D12—51no—
171C2×D12—102no—
172C2×D12D2011yescharacteristic
173C2×C4×D3—21no—
174C2×C4×D3—101no—
175C3×Q16—204no—
176C2×C3×C8—21no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3D2011yescharacteristic
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C23×C5—61no—
192C22×D5—61no—
193C5×D4—61no—
194C5×D4—61no—
195C2×C4×C5—61no—
196C2×C4×C5—121no—
197C2×C4×C5—121no—
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C22⋊D5—242no—
202C2×Dic5—22no—
203C2×Dic5—41no—
204C2×Dic5—61no—
205D20—61no—
206D20—61no—
207C4×D5—121no—
208C4×D5—121no—
209Dic10—42no—
210Dic10—42no—
211C5×C8—22no—
212C5×C8—121no—
213#168—121no—
214C2×Q16—102no—
215C4⋊Q8—51no—
216C4⋊Q8—51no—
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—31no—
221C4×D4—151no—
222#117—301no—
223#117—301no—
224#106—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—151no—
228#102—301no—
229#102—301no—
230C4×C8D3×D511yescharacteristic
231C2×C3×C5#45211yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45311yescharacteristic
234D15—81no—
235C5×D3—81no—
236C22×D3—21no—
237C22×D3—101no—
238C3×Q8—202no—
239C3×Q8—202no—
240C2×C3×C4—102no—
241C2×C3×C4—201no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—101no—
247D12—21no—
248D12—21no—
249D12—101no—
250D12—101no—
251D12—402no—
252C4×D3—41no—
253C4×D3—41no—
254C4×D3—201no—
255C4×D3—201no—
256C3×C8—22no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5—121no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#93711yescharacteristic
263C2×D5—121no—
264C2×D5—121no—
265C2×D5—121no—
266C4×C5—21no—
267C4×C5—121no—
268C4×C5#91811yescharacteristic
269C4×C5#91811yescharacteristic
270C4×C5#91911yescharacteristic
271C4×C5#91911yescharacteristic
272Dic5—42no—
273Dic5—81no—
274Dic5—121no—
275C2×Q8—52no—
276C2×Q8—101no—
277C2×D4—31no—
278C2×D4—151no—
279C2×D4—302no—
280C22×C4—61no—
281C22×C4—301no—
282Q16—204no—
283C2×C8—21no—
284C2×C8—61no—
285C2×C8—301no—
286C4⋊C4—31no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4—151no—
292C22⋊C4—61no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—301no—
296C42—302no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3#402811yescharacteristic
300C2×D3—41no—
301C2×D3—41no—
302C2×D3—41no—
303C2×D3—201no—
304C2×D3—201no—
305C2×D3—201no—
306C3×C4—21no—
307C3×C4—202no—
308C3×C4—401no—
309C3×C4#405011yescharacteristic
310C3×C4#405511yescharacteristic
311C3×C4#405811yescharacteristic
312C3×C4#406111yescharacteristic
313Dic3—41no—
314Dic3—201no—
315C2×C5—241no—
316C2×C5#507711yescharacteristic
317C2×C5#518711yescharacteristic
318C2×C5#518711yescharacteristic
319D5—241no—
320C23—61no—
321C23—301no—
322Q8—202no—
323Q8—202no—
324D4—61no—
325D4—61no—
326D4—301no—
327D4—301no—
328D4—1202no—
329C2×C4—61no—
330C2×C4—102no—
331C2×C4—121no—
332C2×C4—121no—
333C2×C4—201no—
334C2×C4—301no—
335C2×C4—601no—
336C2×C4—601no—
337C2×C4D3×D2011yescharacteristic
338C2×C4#677711yescharacteristic
339C2×C4D5×#6711yescharacteristic
340C8—22no—
341C8—121no—
342C8—601no—
343C2×C3#6502211yescharacteristic
344C2×C3#6507211yescharacteristic
345C2×C3#6511111yescharacteristic
346D3—81no—
347D3—401no—
348C5#7130411yescharacteristic, complemented, Sylow
349C22—121no—
350C22—121no—
351C22—121no—
352C22—601no—
353C22—601no—
354C22—601no—
355C22#9147411yescharacteristic
356C4—21no—
357C4—121no—
358C4—202no—
359C4—401no—
360C4—601no—
361C4#9126311yescharacteristic
362C4#9127511yescharacteristic
363C4#9127911yescharacteristic
364C4#9128011yescharacteristic
365C3#1059899611yescharacteristic, complemented, Sylow
366C2—241no—
367C2—1201no—
368C2#1174711411yescharacteristic
369C2#1174815111yescharacteristic
370C2#1174815211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752710C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#64988C2semidirect
3. #11746942C2semidirect
4. #11746882C2semidirect
5. #11746280C2semidirect
6. C5×#4459C2semidirect
7. #11745861C2semidirect
30. #64988D3semidirect
63. #4459D5semidirect
298. C3×C5#1634semidirect
348. C5#71304semidirect
365. C3#10598996semidirect

Maximal subgroups

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

subgroupindex
#117527102
C3×#649882
#117469422
#117468822
#117462802
C5×#44592
#117458612
#105989963
#713045