Finite Group Databasebeta

← C5×C3⋊(C5⋊#64424) #36348037

Subgroups — C5×C3⋊(C5⋊#64424) #36348037

Order 22050.

480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×C52×#3861C211yesmaximal, characteristic, complemented, Hall
2C5×C3⋊(C5⋊(C7⋊D7))C311yesmaximal, characteristic, complemented
3C5×C5⋊#64424—31nomaximal
4C3⋊(C5⋊#64424)C511yesmaximal, characteristic, direct product factor
5C5×C3⋊#64424—51nomaximal
6C52×#3861—21no—
7C52×#3861D311yescharacteristic, complemented
8C3×C52×C72C2×C311yescharacteristic, complemented
9C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
10C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
11C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
12C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
13C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
14C5×C3⋊(C5⋊AGL(1,𝔽7))—71nomaximal
15C5×C3⋊(C5⋊AGL(1,𝔽7))—72nomaximal
16C5×C5⋊(C7⋊D7)—31noHall
17C3×C5×#3861—22no—
18C3×C5×#3861D511yescharacteristic, complemented
19C3×C5×#3861C2×C511yescharacteristic, complemented
20C3×C52×ΓL(1,𝔽8)—71no—
21C3×C52×ΓL(1,𝔽8)—141no—
22C3×C52×ΓL(1,𝔽8)—141no—
23C3×C52×ΓL(1,𝔽8)—141no—
24C3×C52×ΓL(1,𝔽8)—141no—
25C3×C52×ΓL(1,𝔽8)—141no—
26C3×C52×ΓL(1,𝔽8)—142no—
27C3⋊(C5⋊(C7⋊D7))C3×C511yescharacteristic, complemented
28C5×C3⋊(C7⋊D7)—51no—
29C5⋊#64424—31no—
30C5×#64424—151no—
31C52×C72C3×D311yescharacteristic, complemented, Hall
32C5×D105—71no—
33C5×D105—71no—
34C5×D105—71no—
35C5×D105—71no—
36C5×D105—71no—
37C5×D105—71no—
38C5×D105—72no—
39C5×C5⋊AGL(1,𝔽7)—211no—
40C5×C5⋊AGL(1,𝔽7)—211no—
41C5×C5⋊AGL(1,𝔽7)—211no—
42C5×C5⋊AGL(1,𝔽7)—211no—
43C5×C5⋊AGL(1,𝔽7)—211no—
44C5×C5⋊AGL(1,𝔽7)—211no—
45C5×C5⋊AGL(1,𝔽7)—212no—
46C3⋊#64424—51noHall
47C3×C5×C72—22no—
48C3×C5×C72C3×D511yescharacteristic, complemented
49C3×C5×C72C2×C3×C511yescharacteristic, complemented
50C5×#3861—24no—
51C5×#3861—22no—
52C5×#3861—21no—
53C5×#3861—21no—
54C5×#3861C5×D311yescharacteristic, complemented
55C5×#3861D1511yescharacteristic, complemented
56C3⋊(C5⋊AGL(1,𝔽7))—71no—
57C3⋊(C5⋊AGL(1,𝔽7))—71no—
58C3⋊(C5⋊AGL(1,𝔽7))—71no—
59C3⋊(C5⋊AGL(1,𝔽7))—71no—
60C3⋊(C5⋊AGL(1,𝔽7))—71no—
61C3⋊(C5⋊AGL(1,𝔽7))—71no—
62C3⋊(C5⋊AGL(1,𝔽7))—72no—
63C5×C3⋊AGL(1,𝔽7)—351no—
64C5×C3⋊AGL(1,𝔽7)—351no—
65C5×C3⋊AGL(1,𝔽7)—351no—
66C5×C3⋊AGL(1,𝔽7)—351no—
67C5×C3⋊AGL(1,𝔽7)—351no—
68C5×C3⋊AGL(1,𝔽7)—351no—
69C5×C3⋊AGL(1,𝔽7)—352no—
70C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
71C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
72C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
73C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
74C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
75C3×C52×C7AGL(1,𝔽7)11yescharacteristic, complemented
76C3×C52×C7AGL(1,𝔽7)12yescomplemented
77C52×ΓL(1,𝔽8)—71no—
78C52×ΓL(1,𝔽8)—141no—
79C52×ΓL(1,𝔽8)—141no—
80C52×ΓL(1,𝔽8)—141no—
81C52×ΓL(1,𝔽8)—141no—
82C52×ΓL(1,𝔽8)—141no—
83C52×ΓL(1,𝔽8)—141no—
84C52×ΓL(1,𝔽8)—141no—
85C52×ΓL(1,𝔽8)—141no—
86C52×ΓL(1,𝔽8)—141no—
87C52×ΓL(1,𝔽8)—142no—
88C52×ΓL(1,𝔽8)—141no—
89C52×ΓL(1,𝔽8)—141no—
90C52×ΓL(1,𝔽8)—142no—
91C5⋊(C7⋊D7)—31no—
92C5×C7⋊D7—151no—
93C3×C5×D15—491noHall
94C3×#3861C5×D511yescharacteristic, complemented, Hall
95C5×D35—211no—
96C5×D35—211no—
97C5×D35—211no—
98C5×D35—211no—
99C5×D35—211no—
100C5×D35—211no—
101C5×D35—212no—
102C3×C5×ΓL(1,𝔽8)—71no—
103C3×C5×ΓL(1,𝔽8)—71no—
104C3×C5×ΓL(1,𝔽8)—71no—
105C3×C5×ΓL(1,𝔽8)—71no—
106C3×C5×ΓL(1,𝔽8)—141no—
107C3×C5×ΓL(1,𝔽8)—141no—
108C3×C5×ΓL(1,𝔽8)—142no—
109C3×C5×ΓL(1,𝔽8)—142no—
110C3×C5×ΓL(1,𝔽8)—142no—
111C3×C5×ΓL(1,𝔽8)—142no—
112C3×C5×ΓL(1,𝔽8)—142no—
113C3×C5×ΓL(1,𝔽8)—142no—
114C3×C5×ΓL(1,𝔽8)—144no—
115C3×C5×ΓL(1,𝔽8)—141no—
116C3×C5×ΓL(1,𝔽8)—141no—
117C3×C5×ΓL(1,𝔽8)—141no—
118C3×C5×ΓL(1,𝔽8)—142no—
119C3×C5×ΓL(1,𝔽8)—141no—
120C3×C5×ΓL(1,𝔽8)—141no—
121C3×C5×ΓL(1,𝔽8)—141no—
122C3×C5×ΓL(1,𝔽8)—142no—
123C3⋊(C7⋊D7)—51no—
124#64424—151no—
125C5×C72—22no—
126C5×C72C3×C5×D311yescharacteristic, complemented
127C5×C72C3×D1511yescharacteristic, complemented
128C32×C52—981noHall
129D105—71no—
130D105—71no—
131D105—71no—
132D105—71no—
133D105—71no—
134D105—71no—
135D105—72no—
136C5×D21—351no—
137C5×D21—351no—
138C5×D21—351no—
139C5×D21—351no—
140C5×D21—351no—
141C5×D21—351no—
142C5×D21—352no—
143C5⋊AGL(1,𝔽7)—211no—
144C5⋊AGL(1,𝔽7)—211no—
145C5⋊AGL(1,𝔽7)—211no—
146C5⋊AGL(1,𝔽7)—211no—
147C5⋊AGL(1,𝔽7)—211no—
148C5⋊AGL(1,𝔽7)—211no—
149C5⋊AGL(1,𝔽7)—212no—
150C5×AGL(1,𝔽7)—1051no—
151C5×AGL(1,𝔽7)—1051no—
152C5×AGL(1,𝔽7)—1051no—
153C5×AGL(1,𝔽7)—1051no—
154C5×AGL(1,𝔽7)—1051no—
155C5×AGL(1,𝔽7)—1051no—
156C5×AGL(1,𝔽7)—1052no—
157C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
158C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
159C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
160C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
161C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
162C52×C7C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
163C52×C7C3⋊AGL(1,𝔽7)12yescomplemented
164C5×D15—491no—
165C3×C5×D5—1471no—
166C3×C72C3×C5×D511yescharacteristic, complemented
167#3861—21no—
168#3861C5×D1511yescharacteristic, complemented
169C3⋊AGL(1,𝔽7)—351no—
170C3⋊AGL(1,𝔽7)—351no—
171C3⋊AGL(1,𝔽7)—351no—
172C3⋊AGL(1,𝔽7)—351no—
173C3⋊AGL(1,𝔽7)—351no—
174C3⋊AGL(1,𝔽7)—351no—
175C3⋊AGL(1,𝔽7)—352no—
176C3×C5×C7—22no—
177C3×C5×C7—22no—
178C3×C5×C7—22no—
179C3×C5×C7—22no—
180C3×C5×C7—22no—
181C3×C5×C7—22no—
182C3×C5×C7—24no—
183C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
184C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
185C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
186C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
187C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
188C3×C5×C7C5×AGL(1,𝔽7)11yescharacteristic, complemented
189C3×C5×C7C5×AGL(1,𝔽7)12yescomplemented
190C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
191C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
192C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
193C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
194C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
195C3×C5×C7C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
196C3×C5×C7C5⋊AGL(1,𝔽7)12yescomplemented
197C5×ΓL(1,𝔽8)—71no—
198C5×ΓL(1,𝔽8)—71no—
199C5×ΓL(1,𝔽8)—71no—
200C5×ΓL(1,𝔽8)—142no—
201C5×ΓL(1,𝔽8)—141no—
202C5×ΓL(1,𝔽8)—141no—
203C5×ΓL(1,𝔽8)—144no—
204C5×ΓL(1,𝔽8)—144no—
205C5×ΓL(1,𝔽8)—144no—
206C5×ΓL(1,𝔽8)—144no—
207C5×ΓL(1,𝔽8)—144no—
208C5×ΓL(1,𝔽8)—144no—
209C5×ΓL(1,𝔽8)—148no—
210C5×ΓL(1,𝔽8)—142no—
211C5×ΓL(1,𝔽8)—142no—
212C5×ΓL(1,𝔽8)—142no—
213C5×ΓL(1,𝔽8)—142no—
214C5×ΓL(1,𝔽8)—142no—
215C5×ΓL(1,𝔽8)—144no—
216C5×ΓL(1,𝔽8)—141no—
217C5×ΓL(1,𝔽8)—141no—
218C5×ΓL(1,𝔽8)—141no—
219C5×ΓL(1,𝔽8)—141no—
220C5×ΓL(1,𝔽8)—142no—
221C5×ΓL(1,𝔽8)—141no—
222C5×ΓL(1,𝔽8)—141no—
223C5×ΓL(1,𝔽8)—141no—
224C5×ΓL(1,𝔽8)—141no—
225C5×ΓL(1,𝔽8)—141no—
226C5×ΓL(1,𝔽8)—141no—
227C5×ΓL(1,𝔽8)—142no—
228C5×ΓL(1,𝔽8)—141no—
229C5×ΓL(1,𝔽8)—141no—
230C5×ΓL(1,𝔽8)—141no—
231C5×ΓL(1,𝔽8)—141no—
232C5×ΓL(1,𝔽8)—141no—
233C5×ΓL(1,𝔽8)—141no—
234C5×ΓL(1,𝔽8)—141no—
235C5×ΓL(1,𝔽8)—142no—
236C5×ΓL(1,𝔽8)—141no—
237C5×ΓL(1,𝔽8)—141no—
238C5×ΓL(1,𝔽8)—142no—
239C7⋊D7—151noHall
240C3×D15—491no—
241C3×C5×D3—2451no—
242C3×C52—981no—
243C3×C52—981no—
244C3×C52#6442411yescharacteristic, complemented
245D35—211no—
246D35—211no—
247D35—211no—
248D35—211no—
249D35—211no—
250D35—211no—
251D35—212no—
252C5×D7—1051no—
253C5×D7—1051no—
254C5×D7—1051no—
255C5×D7—1051no—
256C5×D7—1051no—
257C5×D7—1051no—
258C5×D7—1052no—
259C3×ΓL(1,𝔽8)—71no—
260C3×ΓL(1,𝔽8)—71no—
261C3×ΓL(1,𝔽8)—141no—
262C3×ΓL(1,𝔽8)—141no—
263C3×ΓL(1,𝔽8)—141no—
264C3×ΓL(1,𝔽8)—141no—
265C3×ΓL(1,𝔽8)—142no—
266C5×D5—1471noHall
267C72C3×C5×D1511yescharacteristic, complemented, Sylow
268C32×C5—982no—
269C32×C5—981no—
270C32×C5—981no—
271D21—351no—
272D21—351no—
273D21—351no—
274D21—351no—
275D21—351no—
276D21—351no—
277D21—352no—
278AGL(1,𝔽7)—1051no—
279AGL(1,𝔽7)—1051no—
280AGL(1,𝔽7)—1051no—
281AGL(1,𝔽7)—1051no—
282AGL(1,𝔽7)—1051no—
283AGL(1,𝔽7)—1051no—
284AGL(1,𝔽7)—1052no—
285C5×C7—22no—
286C5×C7—22no—
287C5×C7—22no—
288C5×C7—22no—
289C5×C7—22no—
290C5×C7—22no—
291C5×C7—24no—
292C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
293C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
294C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
295C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
296C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
297C5×C7C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
298C5×C7C5×C3⋊AGL(1,𝔽7)12yescomplemented
299C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
300C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
301C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
302C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
303C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
304C5×C7C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
305C5×C7C3⋊(C5⋊AGL(1,𝔽7))12yescomplemented
306C2×C3×C5—7351no—
307D15—491no—
308C3×D5—1471no—
309C5×D3—2451no—
310C52C3⋊#6442411yescharacteristic, complemented, Sylow
311C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
312C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
313C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
314C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
315C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
316C3×C7C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
317C3×C7C5×C5⋊AGL(1,𝔽7)12yescomplemented
318ΓL(1,𝔽8)—71no—
319ΓL(1,𝔽8)—141no—
320ΓL(1,𝔽8)—141no—
321ΓL(1,𝔽8)—141no—
322ΓL(1,𝔽8)—141no—
323ΓL(1,𝔽8)—141no—
324ΓL(1,𝔽8)—141no—
325ΓL(1,𝔽8)—142no—
326ΓL(1,𝔽8)—141no—
327ΓL(1,𝔽8)—141no—
328ΓL(1,𝔽8)—141no—
329ΓL(1,𝔽8)—141no—
330ΓL(1,𝔽8)—141no—
331ΓL(1,𝔽8)—142no—
332C3×D3—2451noHall
333C3×C5—22no—
334C3×C5—982no—
335C3×C5—984no—
336C3×C5—981no—
337C3×C5—981no—
338C3×C5—981no—
339C3×C5—981no—
340C3×C5C5×#6442411yescharacteristic, complemented
341C3×C5C5⋊#6442411yescharacteristic, complemented
342D7—1051no—
343D7—1051no—
344D7—1051no—
345D7—1051no—
346D7—1051no—
347D7—1051no—
348D7—1052no—
349C2×C5—7351no—
350D5—1471no—
351C32—981noSylow
352C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
353C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
354C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
355C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
356C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
357C7C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
358C7C5×C3⋊(C5⋊AGL(1,𝔽7))12yescomplemented
359C2×C3—7351no—
360D3—2451no—
361C5—22no—
362C5C5×C3⋊#6442411yescharacteristic, complemented
363C5C3⋊(C5⋊#64424)11yescharacteristic, direct product factor
364C3—981no—
365C3—981no—
366C3C5×C5⋊#6442411yescharacteristic, complemented
367C2—7351noSylow
subgroupG/H
center, hypercenterC5C3⋊(C5⋊#64424)
commutator, cosocle, hypocenterC3×C5×C72C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C3×C5×C72
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×#3861C2semidirect
2. C5×C3⋊(C5⋊(C7⋊D7))C3semidirect
4. C3⋊(C5⋊#64424)C5direct (N × H)
7. C52×#3861D3semidirect
8. C3×C52×C72C2×C3semidirect
18. C3×C5×#3861D5semidirect
19. C3×C5×#3861C2×C5semidirect
27. C3⋊(C5⋊(C7⋊D7))C3×C5semidirect
31. C52×C72C3×D3semidirect
48. C3×C5×C72C3×D5semidirect
49. C3×C5×C72C2×C3×C5semidirect
54. C5×#3861C5×D3semidirect
55. C5×#3861D15semidirect
70. C3×C52×C7AGL(1,𝔽7)semidirect
71. C3×C52×C7AGL(1,𝔽7)semidirect
72. C3×C52×C7AGL(1,𝔽7)semidirect
73. C3×C52×C7AGL(1,𝔽7)semidirect
74. C3×C52×C7AGL(1,𝔽7)semidirect
75. C3×C52×C7AGL(1,𝔽7)semidirect
76. C3×C52×C7AGL(1,𝔽7)semidirect
94. C3×#3861C5×D5semidirect
126. C5×C72C3×C5×D3semidirect
127. C5×C72C3×D15semidirect
157. C52×C7C3⋊AGL(1,𝔽7)semidirect
158. C52×C7C3⋊AGL(1,𝔽7)semidirect
159. C52×C7C3⋊AGL(1,𝔽7)semidirect
160. C52×C7C3⋊AGL(1,𝔽7)semidirect
161. C52×C7C3⋊AGL(1,𝔽7)semidirect
162. C52×C7C3⋊AGL(1,𝔽7)semidirect
163. C52×C7C3⋊AGL(1,𝔽7)semidirect
166. C3×C72C3×C5×D5semidirect
168. #3861C5×D15semidirect
183. C3×C5×C7C5×AGL(1,𝔽7)semidirect
184. C3×C5×C7C5×AGL(1,𝔽7)semidirect
185. C3×C5×C7C5×AGL(1,𝔽7)semidirect
186. C3×C5×C7C5×AGL(1,𝔽7)semidirect
187. C3×C5×C7C5×AGL(1,𝔽7)semidirect
188. C3×C5×C7C5×AGL(1,𝔽7)semidirect
189. C3×C5×C7C5×AGL(1,𝔽7)semidirect
190. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
191. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
192. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
193. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
194. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
195. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
196. C3×C5×C7C5⋊AGL(1,𝔽7)semidirect
244. C3×C52#64424semidirect
267. C72C3×C5×D15semidirect
292. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
293. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
294. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
295. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
296. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
297. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
298. C5×C7C5×C3⋊AGL(1,𝔽7)semidirect
299. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
300. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
301. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
302. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
303. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
304. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
305. C5×C7C3⋊(C5⋊AGL(1,𝔽7))semidirect
310. C52C3⋊#64424semidirect
311. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
312. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
313. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
314. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
315. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
316. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
317. C3×C7C5×C5⋊AGL(1,𝔽7)semidirect
340. C3×C5C5×#64424semidirect
341. C3×C5C5⋊#64424semidirect
352. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
353. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
354. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
355. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
356. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
357. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
358. C7C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
362. C5C5×C3⋊#64424semidirect
363. C5C3⋊(C5⋊#64424)direct (N × H)
366. C3C5×C5⋊#64424semidirect

Maximal subgroups

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

subgroupindex
C3×C52×#38612
C5×C3⋊(C5⋊(C7⋊D7))3
C5×C5⋊#644243
C3⋊(C5⋊#64424)5
C5×C3⋊#644245
C5×C3⋊(C5⋊AGL(1,𝔽7))7