Finite Group Databasebeta

← #14289522

Subgroups — #14289522

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752657C211yesmaximal, characteristic
2#11750800C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic
5C5×#4456C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7#11745863C211yesmaximal, characteristic, complemented
8#10599039—31nomaximal, Hall
9C2×Dic60—22no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91431—22no—
15Dic3×D20—21no—
16D5×C4⋊Dic3—21no—
17#91381—21no—
18#91359—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90987—21no—
24#90973—21no—
25#90965—21no—
26#68202—51nomaximal, Hall
27#65913—31no—
28#65310—31no—
29#65131—31no—
30#64988—31no—
31C5×Q8⋊C8—31no—
32#64701—31no—
33#64679D311yescharacteristic
34C2×Dic30—21no—
35C2×Dic30D412yes—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×D5×Dic3—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46Dic60—44no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54#6669—22no—
55#6668—22no—
56#6665—22no—
57#5543—51no—
58#5008—51no—
59#4850—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4456D511yescharacteristic, complemented
64C4×C5×Q8—31no—
65#4092—61no—
66C2×Dic20—62no—
67#4042—62no—
68D5×C4⋊C4—61no—
69C4×D20—61no—
70C4×D20C2×D311yescharacteristic
71#4016—61no—
72#4015—31no—
73#4015—31no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—61no—
78#3949—61no—
79#3939—61no—
80C4⋊#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×C3×D5—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87C2×Dic15—41no—
88Dic30—42no—
89Dic30—42no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×Dic6—21no—
93C5×Dic6—21no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20Q1612yescomplemented
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99D5×Dic3—82no—
100C3×C5×C8—22no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4×D4—51no—
104D4×Dic3—101no—
105C2×C4⋊Dic3—101no—
106#924—101no—
107C2×Dic12—102no—
108#890—101no—
109#878—102no—
110#869—51no—
111#869—51no—
112C4×Dic6C2×D511yescharacteristic
113C3×C4⋊C8—51no—
114C3×C4×C8C2×D511yescharacteristic
115#832—101no—
116#818—101no—
117#816—101no—
118#808—101no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—31no—
121C2×D20D1211yescharacteristic
122C2×C4×D5—21no—
123C2×C4×D5—62no—
124C2×Dic10—32no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C42×C5—61no—
131C42×C5C22×D311yescharacteristic
132#685—21no—
133#685—62no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5D1211yescharacteristic
139#683—62no—
140#683—62no—
141C2×#168—21no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8—31no—
149D4⋊C8—51no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—42no—
160Dic15—81no—
161C3×Dic5—41no—
162C5×Dic3—41no—
163C5×Dic3—41no—
164C2×C3×D4—51no—
165C22×C3×C4—101no—
166C22×Dic3—102no—
167C2×Dic6—52no—
168C2×Dic6—101no—
169C2×Dic6D2011yescharacteristic
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—51no—
173C3×C22⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176C4⋊Dic3—102no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3D2011yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184C4×Dic3—21no—
185C2×C3⋊C8—21no—
186Dic12—204no—
187C22×D5—21no—
188C5×Q8—61no—
189C5×Q8—61no—
190C2×C4×C5—61no—
191C2×C4×C5—61no—
192C2×C4×C5C2×D1211yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—62no—
197C2×Dic5—121no—
198D20—21no—
199D20Dic1212yescomplemented
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—242no—
203Dic10—122no—
204Dic10—122no—
205C5×C8—22no—
206C5×C8—121no—
207#168—41no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—31no—
215C4×D4—51no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222#103—301no—
223#102—301no—
224C4×C8D3×D511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×D4—52no—
231C3×D4—101no—
232C2×C3×C4—101no—
233C2×C3×C4—201no—
234C2×C3×C4—201no—
235C2×C3×C4C2×D2011yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—102no—
241C2×Dic3—201no—
242C2×Dic3—402no—
243Dic6—21no—
244Dic6—21no—
245Dic6—202no—
246Dic6—202no—
247C3×C8—22no—
248C3×C8—201no—
249C3⋊C8—41no—
250C22×C5#88211yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257C4×C5C2×Dic1211yescharacteristic
258C4×C5#90911yescharacteristic
259C4×C5#91211yescharacteristic
260C4×C5#91511yescharacteristic
261Dic5—41no—
262Dic5—122no—
263Dic5—241no—
264C2×Q8—31no—
265C2×Q8—152no—
266C2×Q8—301no—
267C2×D4—51no—
268C22×C4—101no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—101no—
274C4⋊C4—31no—
275C4⋊C4—51no—
276C4⋊C4—61no—
277C4⋊C4—302no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—101no—
284C22⋊C4—302no—
285C42—61no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—102no—
289C22×C3—201no—
290C22×C3—201no—
291C22×C3#402811yescharacteristic
292C3×C4—21no—
293C3×C4—201no—
294C3×C4#405011yescharacteristic
295C3×C4#405511yescharacteristic
296C3×C4#406111yescharacteristic
297C3×C4D5×Q1611yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—202no—
301Dic3—401no—
302C2×C5#473911yescharacteristic
303C2×C5#478311yescharacteristic
304C2×C5#482211yescharacteristic
305D5—42no—
306C23—101no—
307Q8—61no—
308Q8—61no—
309Q8—602no—
310Q8—602no—
311D4—52no—
312D4—101no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—101no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4—302no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4D5×D1211yescharacteristic
322C2×C4D3×D2011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—22no—
325C8—121no—
326C8—201no—
327C2×C3—202no—
328C2×C3#6502211yescharacteristic
329C2×C3#6509711yescharacteristic
330C2×C3#6511111yescharacteristic
331C5#6820211yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9147611yescharacteristic
336C4—21no—
337C4—121no—
338C4—121no—
339C4—201no—
340C4—602no—
341C4—1201no—
342C4D5×Dic1211yescharacteristic
343C4#9126011yescharacteristic
344C4#9127311yescharacteristic
345C4#9127411yescharacteristic
346C3#1059903911yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174711811yescharacteristic
349C2#1174813011yescharacteristic
350C2#1174816211yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
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. #11750800C2semidirect
3. #11746961C2semidirect
5. C5×#4456C2semidirect
7. #11745863C2semidirect
63. #4456D5semidirect
96. C3×D20Q16semidirect
199. D20Dic12semidirect
287. C3×C5#1632semidirect
331. C5#68202semidirect
346. C3#10599039semidirect

Maximal subgroups

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

subgroupindex
#117526572
#117508002
#117469612
#117468812
C5×#44562
C3×#646792
#117458632
#105990393
#682025