Finite Group Databasebeta

← #14290578

Subgroups — #14290578

Order 1920.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756491C211yesmaximal, characteristic
2#11751179C211yesmaximal, characteristic, complemented
3#11750952C211yesmaximal, characteristic, complemented
4#11750942C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic
8#10599230—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91836—21no—
11Q8×Dic15—21no—
12C2×#6706—21no—
13#91787—22no—
14#91786—21no—
15#91781—21no—
16C4×D60C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21#91101—21no—
22#91100—21no—
23#91100—21no—
24#91091—22no—
25C4×C3⋊#168C2211yescharacteristic
26#68437—51nomaximal, Hall
27#66066—31no—
28#65367—31no—
29#65140—31no—
30#65130—31no—
31C5×#332D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D412yes—
43C3×C42×C5C2311yescharacteristic
44#6714—22no—
45#6714—22no—
46#6714—21no—
47C4⋊Dic15—22no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D411yescharacteristic
52#6712—21no—
53C4×Dic15—22no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56#6706—42no—
57#5732—51no—
58#5078—51no—
59#4851—51no—
60#4841—51no—
61C3×#332D511yescharacteristic, complemented
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65#4093—61no—
66Q8×Dic5—61no—
67C2×#677—61no—
68#4044—62no—
69#4043—61no—
70#4038—61no—
71C4×D20—31no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C5×C4⋊C8C2×D311yescharacteristic
76#3949—61no—
77#3948—61no—
78#3948—61no—
79#3939—62no—
80C4×#168—31no—
81#1650—151noSylow
82C22×D15—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—41no—
93D60—21no—
94D60—21no—
95C4×D15—41no—
96C4×D15—41no—
97Dic30—21no—
98Dic30—21no—
99Dic30—41no—
100Dic30—41no—
101C3×C5×C8—41no—
102C3×C5×C8—41no—
103C3⋊#168—22no—
104C3×C4⋊Q8C2×D511yescharacteristic
105#947—101no—
106Q8×Dic3—101no—
107C2×#204—101no—
108#898—102no—
109#897—101no—
110#892—101no—
111C4×D12—51no—
112#869—51no—
113C4×Dic6—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×C4⋊C8C2×D511yescharacteristic
116#817—101no—
117#816—101no—
118#816—101no—
119#807—102no—
120C4×C3⋊C8—51no—
121C2×C5×Q8—21no—
122C2×D20—31no—
123C2×C4×D5—61no—
124C2×Dic10—31no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4D1212yes—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136C4⋊Dic5—62no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—61no—
140C4×Dic5—62no—
141C4×Dic5—61no—
142C2×#168—61no—
143#677—122no—
144#556—151no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332D1511yescharacteristic, complemented
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—42no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—41no—
162Dic15—41no—
163Dic15—41no—
164Dic15—81no—
165C2×C3×Q8—21no—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×Dic6—51no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4D2012yes—
174C3×C42C22×D511yescharacteristic
175(C2×D3)⋊C4—102no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—101no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—102no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—101no—
184C4×Dic3—102no—
185C4×Dic3—101no—
186C2×C3⋊C8—101no—
187#204—202no—
188C22×D5—61no—
189C5×Q8—41no—
190C5×Q8—41no—
191C2×C4×C5—22no—
192C2×C4×C5C2×D1211yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×Dic5—61no—
196C2×Dic5—61no—
197C2×Dic5—61no—
198C2×Dic5—121no—
199D20—61no—
200D20—61no—
201C4×D5—121no—
202C4×D5—121no—
203Dic10—61no—
204Dic10—61no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—41no—
208C5×C8—41no—
209#168—62no—
210C2×SD16—301no—
211C4⋊Q8—151no—
212C4⋊Q8C2×D1511yescharacteristic
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—151no—
217C4×Q8—301no—
218C4×D4—151no—
219#117—301no—
220#107—302no—
221#106—301no—
222C4⋊C8C2×D1511yescharacteristic
223C4⋊C8C2×D1511yescharacteristic
224#103—301no—
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—41no—
233C3×Q8—41no—
234C2×C3×C4—22no—
235C2×C3×C4C2×D2011yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×Dic3—101no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241C2×Dic3—201no—
242D12—101no—
243D12—101no—
244C4×D3—201no—
245C4×D3—201no—
246Dic6—101no—
247Dic6—101no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—41no—
251C3×C8—41no—
252C3⋊C8—102no—
253C22×C5#88211yescharacteristic
254C2×D5—121no—
255C2×D5—121no—
256C2×D5—121no—
257C4×C5—21no—
258C4×C5—42no—
259C4×C5#91111yescharacteristic
260C4×C5#91611yescharacteristic
261C4×C5#91611yescharacteristic
262C4×C5#91811yescharacteristic
263Dic5—121no—
264Dic5—121no—
265Dic5—121no—
266Dic5—241no—
267C2×Q8—21no—
268C2×Q8—151no—
269C2×Q8—301no—
270C2×D4—151no—
271C22×C4—301no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—151no—
278C4⋊C4—151no—
279C4⋊C4—302no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4D6012yes—
284C22⋊C4—302no—
285C22⋊C4—302no—
286C22⋊C4—301no—
287C42—302no—
288C42—301no—
289C42C22×D1511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#402811yescharacteristic
292C2×D3—201no—
293C2×D3—201no—
294C2×D3—201no—
295C3×C4—21no—
296C3×C4—42no—
297C3×C4#405711yescharacteristic
298C3×C4#406211yescharacteristic
299C3×C4#406211yescharacteristic
300C3×C4#406411yescharacteristic
301Dic3—201no—
302Dic3—201no—
303Dic3—201no—
304Dic3—401no—
305C2×C5#475211yescharacteristic
306C2×C5#478111yescharacteristic
307C2×C5#480811yescharacteristic
308D5—241no—
309C23—301no—
310Q8—41no—
311Q8—41no—
312Q8—301no—
313Q8—301no—
314Q8—601no—
315Q8—601no—
316D4—301no—
317D4—301no—
318C2×C4—22no—
319C2×C4—301no—
320C2×C4—301no—
321C2×C4—301no—
322C2×C4—601no—
323C2×C4—601no—
324C2×C4—601no—
325C2×C4C2×D6011yescharacteristic
326C2×C4D4×D1511yescharacteristic
327C2×C4D4×D1511yescharacteristic
328C8—41no—
329C8—41no—
330C8—302no—
331C2×C3#6504111yescharacteristic
332C2×C3#6507011yescharacteristic
333C2×C3#6509911yescharacteristic
334D3—401no—
335C5#6843711yescharacteristic, complemented, Sylow
336C22—601no—
337C22—601no—
338C22—601no—
339C22#9177111yescharacteristic
340C4—21no—
341C4—42no—
342C4—601no—
343C4—601no—
344C4—601no—
345C4—1201no—
346C4#9180011yescharacteristic
347C4#9180511yescharacteristic
348C4#9180511yescharacteristic
349C4#9180711yescharacteristic
350C3#1059923011yescharacteristic, complemented, Sylow
351C2—1201no—
352C2#1175085311yescharacteristic
353C2#1175088211yescharacteristic
354C2#1175090911yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#332D15
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #11751179C2semidirect
3. #11750952C2semidirect
5. C3×C5×#332C2semidirect
6. #11746305C2semidirect
31. C5×#332D3semidirect
61. C3×#332D5semidirect
148. #332D15semidirect
290. C3×C5#1650semidirect
335. C5#68437semidirect
350. C3#10599230semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117511792
#117509522
#117509422
C3×C5×#3322
#117463052
#117463042
#105992303
#684375