Finite Group Databasebeta

← #14289833

Subgroups — #14289833

Order 1920.

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

normal subgroups only

This group has 388 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
2#11751185C211yesmaximal, characteristic
3C5×#5091C211yesmaximal, characteristic, complemented
4C3×#65370C211yesmaximal, characteristic, complemented
5#11745855C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10601950—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×D60C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91383—21no—
14#91374—21no—
15#91347—21no—
16#91345—22no—
17Dic3×Dic10—21no—
18#91093—21no—
19#91092—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#810—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3967—22no—
25C3×C4×#168C2211yescharacteristic
26#71229—51nomaximal, Hall
27#65918—31no—
28C5×#477—31no—
29#65373—31no—
30#65370D311yescharacteristic, complemented
31Q8⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6714—21no—
43C4⋊Dic15D411yescharacteristic
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—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#5732—51no—
57C3×#487—51no—
58#5091D511yescharacteristic, complemented
59#5084—51no—
60#4547—51no—
61#4459—51no—
62#4456—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64C4×C5×Q8—31no—
65#4092—61no—
66#4044—62no—
67#4038—61no—
68#4021—61no—
69C4×D20—31no—
70#4015C2×D311yescharacteristic
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—22no—
76#3941—61no—
77#3940—61no—
78C4⋊#168—31no—
79C4×#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×D15—21no—
82C3×C5×Q8—42no—
83C2×C3×C4×C5—41no—
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—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C2×C3×Dic5—22no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3⋊#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8—51no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#947—101no—
105Q8×Dic3—101no—
106#898—102no—
107#897—101no—
108#892—101no—
109C4×D12—51no—
110C4×Dic6C2×D511yescharacteristic
111C3×#103—102no—
112C3×C4×C8—51no—
113#810—21no—
114#809—101no—
115#808—101no—
116#807—21no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—21no—
120C2×C5×Q8—31no—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—21no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C42×C5—61no—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—21no—
135C4⋊Dic5—31no—
136C4⋊Dic5#6712yes—
137#683—62no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—61no—
141#556—151no—
142#487—51no—
143#477—31no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—41no—
152C3×C4×C5—21no—
153C3×C4×C5—81no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—41no—
159C3×Dic5—42no—
160C5×Dic3—41no—
161C5×Dic3—41no—
162C2×C3×Q8—21no—
163C2×C3×Q8—101no—
164C2×D12—51no—
165C2×C4×D3—101no—
166C2×Dic6C22⋊D511yescharacteristic
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—101no—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—101no—
176C4⋊Dic3—51no—
177C4⋊Dic3—102no—
178C4⋊Dic3C22⋊D511yescharacteristic
179Dic3⋊C4—21no—
180C4×Dic3—21no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—101no—
184C22×D5—61no—
185C5×Q8—42no—
186C5×Q8—61no—
187C5×Q8—61no—
188C2×C4×C5—41no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—61no—
196D20—61no—
197D20—61no—
198C4×D5—121no—
199C4×D5—121no—
200Dic10—41no—
201Dic10—41no—
202C5×C8—121no—
203#168—41no—
204#168—121no—
205C4⋊Q8—51no—
206C4⋊Q8D3×D511yescharacteristic
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—31no—
211C4×Q8—301no—
212C4×D4—151no—
213#117—301no—
214#107—61no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—151no—
218#103—61no—
219#103—102no—
220#102—301no—
221C4×C8—51no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—42no—
228C3×Q8—201no—
229C3×Q8—201no—
230C2×C3×C4—41no—
231C2×C3×C4—102no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—101no—
238D12—101no—
239D12—101no—
240C4×D3—201no—
241C4×D3—201no—
242Dic6—21no—
243Dic6—21no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—201no—
247C22×C5#93711yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—81no—
253C4×C5—121no—
254C4×C5—121no—
255C4×C5#91511yescharacteristic
256C4×C5#91611yescharacteristic
257C4×C5#91811yescharacteristic
258C4×C5#91911yescharacteristic
259Dic5—42no—
260Dic5—121no—
261C2×Q8—21no—
262C2×Q8—31no—
263C2×Q8—101no—
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—61no—
267C2×C8—101no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—31no—
272C4⋊C4—52no—
273C4⋊C4—61no—
274C4⋊C4—101no—
275C4⋊C4—151no—
276C4⋊C4—302no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—61no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—81no—
290C3×C4—202no—
291C3×C4#406411yescharacteristic
292C3×C4#406511yescharacteristic
293C3×C4#408811yescharacteristic
294C3×C4#409611yescharacteristic
295Dic3—41no—
296Dic3—41no—
297Dic3—201no—
298C2×C5#506211yescharacteristic
299C2×C5#517311yescharacteristic
300C2×C5#518711yescharacteristic
301D5—241no—
302C23—301no—
303Q8—42no—
304Q8—61no—
305Q8—61no—
306Q8—201no—
307Q8—201no—
308D4—301no—
309D4—301no—
310C2×C4—41no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—102no—
314C2×C4—301no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D5×#6711yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C2×C4#679011yescharacteristic
320C8—121no—
321C8—201no—
322C8—601no—
323C2×C3#6533611yescharacteristic
324C2×C3#6547611yescharacteristic
325C2×C3#6549011yescharacteristic
326D3—401no—
327C5#7122911yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9157711yescharacteristic
332C4—21no—
333C4—81no—
334C4—121no—
335C4—121no—
336C4—202no—
337C4—601no—
338C4#9151911yescharacteristic
339C4#9152011yescharacteristic
340C4#9152111yescharacteristic
341C4#9152211yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174916811yescharacteristic
345C2#1174940411yescharacteristic
346C2#1174940811yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C5×#5091C2semidirect
4. C3×#65370C2semidirect
5. #11745855C2semidirect
6. #11745843C2semidirect
30. #65370D3semidirect
58. #5091D5semidirect
283. C3×C5#1638semidirect
327. C5#71229semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
#117524832
#117511852
C5×#50912
C3×#653702
#117458552
#117458432
#117458392
#106019503
#712295