Finite Group Databasebeta

← #14289521

Subgroups — #14289521

Order 1920.

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

normal subgroups only

This group has 428 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
1#11752645C211yesmaximal, characteristic
2C3×#64988C211yesmaximal, characteristic, complemented
3#11746959C211yesmaximal, characteristic, complemented
4#11746942C211yesmaximal, characteristic
5#11746280C211yesmaximal, characteristic
6C5×#4456C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10599039—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C2×C3×Dic20—22no—
12C3×#4015C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91437—21no—
15#91428—21no—
16#91411—22no—
17#91383—21no—
18#91381—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90989—21no—
23#90987—21no—
24#90972—21no—
25#90968—21no—
26#71303—51nomaximal, Hall
27#65913—31no—
28#65310—31no—
29#65131—31no—
30#64988D311yescharacteristic, complemented
31C5×Q8⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×Dic10—21no—
38C2×C3×Dic10D412yes—
39C2×#1200—22no—
40C2×C3×C5×C8—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⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×Dic20—44no—
54#6669—22no—
55#6668—22no—
56#6667—22no—
57#5730—51no—
58C3×#494—51no—
59#5091—51no—
60#5084—51no—
61#4546—51no—
62#4459—51no—
63#4456D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4092—61no—
66C2×Dic20—22no—
67#4042—62no—
68D5×C4⋊C4—61no—
69C4×D20—31no—
70C4×D20—61no—
71#4016—61no—
72#4015C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—61no—
78#3949—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1632—151noSylow
82C22×D15—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87D60—21no—
88D60Q1612yescomplemented
89C4×D15—41no—
90C4×D15—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C5×Dic6—21no—
94C5×Dic6—21no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—41no—
97C3×Dic10—42no—
98C3×Dic10—42no—
99#1200—82no—
100C3×C5×C8—22no—
101C3⋊#168—41no—
102C5×C3⋊C8—41no—
103C2×C3×Q16—102no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8—51no—
106#946—102no—
107#897—101no—
108#893—101no—
109D3×C4⋊C4—101no—
110#890—101no—
111C4×D12—51no—
112C4×Dic6C2×D511yescharacteristic
113C3×C4×C8C2×D511yescharacteristic
114#810—101no—
115#809—101no—
116#808—101no—
117#807—101no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—31no—
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×C4×D5—62no—
124C2×Dic10—21no—
125C2×Dic10#6712yes—
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C42×C5—61no—
131C42×C5C22×D311yescharacteristic
132#685—62no—
133#685—61no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—31no—
139#683—62no—
140#683—62no—
141C2×#168—61no—
142Dic20—44no—
143#554—151no—
144#494—51no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8—31no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×D15—22no—
152C2×D15—41no—
153C2×D15—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160C3×Dic5—42no—
161C3×Dic5—81no—
162C5×Dic3—41no—
163C5×Dic3—41no—
164C2×C3×Q8—52no—
165C2×C3×Q8—101no—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×C4×D3—102no—
169C2×Dic6D2011yescharacteristic
170C3×Q16—204no—
171C2×C3×C8—21no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C42C22×D511yescharacteristic
177(C2×D3)⋊C4—102no—
178(C2×D3)⋊C4—101no—
179C4⋊Dic3—51no—
180C4⋊Dic3—102no—
181C4⋊Dic3D2011yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184C4×Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C22×D5—61no—
188C5×Q8—61no—
189C5×Q8—61no—
190C2×C4×C5—61no—
191C2×C4×C5—61no—
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—22no—
196C2×Dic5—41no—
197C2×Dic5—61no—
198D20—32no—
199D20—61no—
200C4×D5—121no—
201C4×D5—121no—
202C4×D5—242no—
203Dic10—42no—
204Dic10—42no—
205C5×C8—22no—
206C5×C8—121no—
207#168—121no—
208C2×Q16—102no—
209C4⋊Q8—51no—
210C4⋊Q8—51no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—31no—
215C4×D4—151no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—151no—
222#103—301no—
223#102—301no—
224C4×C8D3×D511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228D15—42no—
229C22×D3—101no—
230C3×Q8—202no—
231C3×Q8—202no—
232C2×C3×C4—102no—
233C2×C3×C4—201no—
234C2×C3×C4C2×D2011yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—101no—
240D12—52no—
241D12—101no—
242C4×D3—201no—
243C4×D3—201no—
244C4×D3—402no—
245Dic6—21no—
246Dic6—21no—
247C3×C8—22no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5#93711yescharacteristic
251C2×D5—62no—
252C2×D5—121no—
253C2×D5—121no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257C4×C5D3×Q1611yescharacteristic
258C4×C5#91811yescharacteristic
259C4×C5#91811yescharacteristic
260C4×C5#91911yescharacteristic
261Dic5—42no—
262Dic5—81no—
263Dic5—121no—
264C2×Q8—31no—
265C2×Q8—52no—
266C2×Q8—101no—
267C2×D4—151no—
268C22×C4—302no—
269C22×C4—301no—
270Q16—204no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—61no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—151no—
281C4⋊C4—302no—
282C4⋊C4—302no—
283C22⋊C4—302no—
284C22⋊C4—301no—
285C42—61no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—102no—
290C2×D3—201no—
291C2×D3—201no—
292C3×C4—21no—
293C3×C4—202no—
294C3×C4—401no—
295C3×C4#405011yescharacteristic
296C3×C4#405511yescharacteristic
297C3×C4#406111yescharacteristic
298C3×C4D5×Q1611yescharacteristic
299Dic3—41no—
300Dic3—41no—
301Dic3—201no—
302C2×C5#507711yescharacteristic
303C2×C5#518611yescharacteristic
304C2×C5#518711yescharacteristic
305D5—122no—
306C23—301no—
307Q8—61no—
308Q8—61no—
309Q8—202no—
310Q8—202no—
311D4—152no—
312D4—301no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—102no—
316C2×C4—201no—
317C2×C4—301no—
318C2×C4—601no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4D3×D2011yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—22no—
325C8—121no—
326C8—601no—
327C2×C3#6502211yescharacteristic
328C2×C3#6509711yescharacteristic
329C2×C3#6511111yescharacteristic
330D3—202no—
331C5#7130311yescharacteristic, complemented, Sylow
332C22—302no—
333C22—601no—
334C22—601no—
335C22#9147411yescharacteristic
336C4—21no—
337C4—121no—
338C4—121no—
339C4—202no—
340C4—401no—
341C4—601no—
342C4#9126311yescharacteristic
343C4#9126411yescharacteristic
344C4#9127511yescharacteristic
345C4#9128011yescharacteristic
346C3#1059903911yescharacteristic, complemented, Sylow
347C2—602no—
348C2#1174711411yescharacteristic
349C2#1174812611yescharacteristic
350C2#1174815211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1632
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. #11746959C2semidirect
6. C5×#4456C2semidirect
7. #11745861C2semidirect
30. #64988D3semidirect
63. #4456D5semidirect
88. D60Q16semidirect
287. C3×C5#1632semidirect
331. C5#71303semidirect
346. C3#10599039semidirect

Maximal subgroups

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

subgroupindex
#117526452
C3×#649882
#117469592
#117469422
#117462802
C5×#44562
#117458612
#105990393
#713035