Finite Group Databasebeta

← #14290625

Subgroups — #14290625

Order 1920.

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

normal subgroups only

This group has 400 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#11752483C211yesmaximal, characteristic
2C5×#4851C211yesmaximal, characteristic, complemented
3#11747087C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601919—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18C2×#6660—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#817—21no—
22C5×#816—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90989—22no—
25#90973—21no—
26#68437—51nomaximal, Hall
27#65918—31no—
28C5×#475—31no—
29#65372—31no—
30#65367—31no—
31Q8⋊#168—31no—
32#64706D311yescharacteristic, complemented
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42C4⋊Dic15D411yescharacteristic
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D412yes—
51C2×C3×#168—21no—
52#6668—22no—
53#6667—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#6660—42no—
57#5732—51no—
58#5078—51no—
59#4851D511yescharacteristic, complemented
60#4841—51no—
61C3×#332—51no—
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8—31no—
66#4092—61no—
67C2×#688—61no—
68#4044—62no—
69#4038—61no—
70#4021—61no—
71C4×D20—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10—61no—
74C5×#106—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—61no—
77#3967—61no—
78#3939—62no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1650—151noSylow
82C22×D15—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87D60—21no—
88D60—21no—
89C4×D15—41no—
90C4×D15—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—41no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C2×C3×Dic5—22no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—41no—
102C3⋊#168—22no—
103C3×#168—41no—
104C3×C4⋊Q8—51no—
105#947—101no—
106Q8×Dic3—101no—
107C2×#204—101no—
108#898—102no—
109#897—101no—
110#892—101no—
111C4×D12—51no—
112#869C2×D511yescharacteristic
113C4×Dic6C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116#817—21no—
117#816—21no—
118#816—101no—
119#807—102no—
120C4×C3⋊C8—51no—
121C2×C5×Q8—31no—
122C2×C5×Q8—61no—
123C2×D20—31no—
124C2×C4×D5—61no—
125C2×Dic10—21no—
126C2×C5×C8—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5—61no—
132C42×C5C22×D311yescharacteristic
133#688—122no—
134#685—62no—
135#685—62no—
136#685—61no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139C4⋊Dic5D1212yes—
140#683—62no—
141C4×Dic5—62no—
142C2×#168—21no—
143C2×#168—61no—
144#556—151no—
145#500—151no—
146#475—31no—
147#461—151no—
148#332—51no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C3×C4×C5—21no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161C3×Dic5—42no—
162C5×Dic3—41no—
163C5×Dic3—41no—
164C5×Dic3—81no—
165C2×C3×Q8—101no—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×Dic6—21no—
169C2×Dic6C22⋊D511yescharacteristic
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—52no—
173C3×C4⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175(C2×D3)⋊C4—102no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—21no—
184C4×Dic3—21no—
185C4×Dic3—102no—
186C2×C3⋊C8—101no—
187#204—202no—
188C22×D5—61no—
189C5×Q8—61no—
190C5×Q8—61no—
191C5×Q8—121no—
192C5×Q8—121no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5—121no—
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×Dic5—22no—
200C2×Dic5—61no—
201D20—61no—
202D20—61no—
203C4×D5—121no—
204C4×D5—121no—
205Dic10—41no—
206Dic10—41no—
207C5×C8—41no—
208#168—41no—
209#168—62no—
210C2×SD16—301no—
211C4⋊Q8—31no—
212C4⋊Q8—51no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—31no—
217C4×Q8—301no—
218C4×D4—151no—
219#117—301no—
220#107—302no—
221#106—61no—
222C4⋊C8—51no—
223C4⋊C8D3×D511yescharacteristic
224#103—61no—
225#103—301no—
226C4×C8—151no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230D15—81no—
231C22×D3—101no—
232C3×Q8—201no—
233C3×Q8—201no—
234C2×C3×C4—102no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—41no—
241C2×Dic3—101no—
242D12—101no—
243D12—101no—
244C4×D3—201no—
245C4×D3—201no—
246Dic6—21no—
247Dic6—21no—
248Dic6—41no—
249Dic6—41no—
250C3×C8—41no—
251C3×C8—201no—
252C3⋊C8—102no—
253C22×C5#88211yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—121no—
259C4×C5—121no—
260C4×C5—241no—
261C4×C5#91111yescharacteristic
262C4×C5#91611yescharacteristic
263C4×C5#91611yescharacteristic
264C4×C5#91811yescharacteristic
265Dic5—42no—
266Dic5—121no—
267C2×Q8—31no—
268C2×Q8—61no—
269C2×Q8—101no—
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—31no—
277C4⋊C4—52no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—101no—
282C4⋊C4—151no—
283C4⋊C4—302no—
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—61no—
288C42—302no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#408311yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—202no—
297C3×C4#406011yescharacteristic
298C3×C4#406211yescharacteristic
299C3×C4#408811yescharacteristic
300C3×C4#409611yescharacteristic
301Dic3—41no—
302Dic3—41no—
303Dic3—81no—
304Dic3—201no—
305C2×C5#475211yescharacteristic
306C2×C5#478111yescharacteristic
307C2×C5#480811yescharacteristic
308D5—241no—
309C23—301no—
310Q8—61no—
311Q8—61no—
312Q8—121no—
313Q8—121no—
314Q8—201no—
315Q8—201no—
316D4—301no—
317D4—301no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—102no—
321C2×C4—121no—
322C2×C4—301no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4D5×D1211yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—41no—
329C8—201no—
330C8—302no—
331C2×C3#6533611yescharacteristic
332C2×C3#6546111yescharacteristic
333C2×C3#6549411yescharacteristic
334D3—401no—
335C5#6843711yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9147511yescharacteristic
340C4—21no—
341C4—121no—
342C4—121no—
343C4—202no—
344C4—241no—
345C4—601no—
346C4#9125811yescharacteristic
347C4#9127611yescharacteristic
348C4#9149511yescharacteristic
349C4#9152011yescharacteristic
350C3#1060191911yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1174751611yescharacteristic
353C2#1174815311yescharacteristic
354C2#1174825811yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1650
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. C5×#4851C2semidirect
4. #11746962C2semidirect
6. C3×#64706C2semidirect
7. #11745842C2semidirect
32. #64706D3semidirect
59. #4851D5semidirect
290. C3×C5#1650semidirect
335. C5#68437semidirect
350. C3#10601919semidirect

Maximal subgroups

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

subgroupindex
#117524832
C5×#48512
#117470872
#117469622
#117463042
C3×#647062
#117458422
#106019193
#684375