Subgroups — C₅×#83999 #14418020

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	2	yes	maximal, complemented
3	C₅×#5236	C₂	1	2	yes	maximal, complemented
4	C₅×#5197	C₂	1	4	yes	maximal, complemented
5	C₅×#5196	C₂	1	4	yes	maximal, complemented
6	C₅×#5125	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2955	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₃×C₅×#137	C₄	1	4	yes	complemented
11	C₃×C₅×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
12	C₃×C₅×#135	C₂²	1	4	yes	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₅×#948	—	2	2	no	—
15	C₅×#948	—	2	2	no	—
16	C₅×#948	C₂²	1	4	yes	complemented
17	C₅×#948	C₂²	1	4	yes	complemented
18	C₅×#926	C₂²	1	1	yes	characteristic
19	C₂×C₅×#208	—	2	2	no	—
20	C₂×C₅×#208	C₂²	1	2	yes	—
21	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
22	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₅×#837	C₂²	1	8	yes	complemented
24	C₅×#819	C₂²	1	4	yes	complemented
25	C₅×#815	C₂²	1	2	yes	complemented
26	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
27	#83999	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#575	D₃	1	1	yes	characteristic
29	C₂×C₅×#131	—	3	2	no	—
30	C₅×#444	—	3	4	no	—
31	C₅×#443	—	3	4	no	—
32	C₅×#430	—	3	1	no	—
33	C₅×#421	—	3	2	no	—
34	C₅×#405	—	3	1	no	—
35	C₃×C₅×#41	—	2	2	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	C₂×C₄	1	4	yes	—
38	C₃×C₅×#41	C₂³	1	4	yes	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	—
45	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	—
46	C₃×C₅×D₈	C₂×C₄	1	4	yes	—
47	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₅×#217	—	2	1	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₄×C₅×Dic₃	C₂³	1	2	yes	—
52	C₅×#208	—	2	2	no	—
53	C₅×#208	—	2	4	no	—
54	C₅×#208	—	2	4	no	—
55	C₅×#208	C₂³	1	4	yes	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₃×#575	C₂×C₅	1	1	yes	characteristic
64	C₂×#948	C₂×C₅	1	2	yes	complemented
65	#5236	C₂×C₅	1	2	yes	complemented
66	#5197	C₂×C₅	1	4	yes	complemented
67	#5196	C₂×C₅	1	4	yes	complemented
68	#5125	C₂×C₅	1	1	yes	characteristic, complemented
69	#5122	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₅×#41	C₂×D₃	1	2	yes	—
71	C₅×#137	Dic₃	1	4	yes	complemented
72	C₅×AGL(1,ℤ/8)	Dic₃	1	4	yes	complemented
73	C₅×#135	C₂×D₃	1	4	yes	—
74	C₅×#131	—	3	4	no	—
75	C₅×#131	—	3	4	no	—
76	C₅×#131	—	6	2	no	—
77	C₅×#131	—	6	2	no	—
78	C₂×C₅×M₁₆	—	3	2	no	—
79	C₂×C₅×M₁₆	—	6	2	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂²×C₅×C₈	—	6	2	no	—
83	C₅×#117	—	3	1	no	—
84	C₅×#108	—	3	4	no	—
85	C₅×#104	—	3	8	no	—
86	C₅×#97	—	3	2	no	—
87	C₄×C₅×C₈	—	3	2	no	—
88	#2955	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	2	no	—
92	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	4	no	—
95	C₃×C₅×D₄	—	2	2	no	—
96	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
106	C₅×C₃⋊C₈	—	2	4	no	—
107	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
108	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
109	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
111	C₃×#137	C₄×C₅	1	4	yes	complemented
112	C₃×AGL(1,ℤ/8)	C₄×C₅	1	4	yes	complemented
113	C₃×#135	C₂²×C₅	1	4	yes	—
114	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
115	#948	—	2	2	no	—
116	#948	—	2	2	no	—
117	#948	C₂²×C₅	1	4	yes	complemented
118	#948	C₂²×C₅	1	4	yes	complemented
119	#926	C₂²×C₅	1	1	yes	characteristic
120	C₂×#208	—	2	2	no	—
121	C₂×#208	C₂²×C₅	1	2	yes	—
122	C₂²×C₃⋊C₈	—	2	2	no	—
123	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	#837	C₂²×C₅	1	8	yes	complemented
125	#819	C₂²×C₅	1	4	yes	complemented
126	#815	C₂²×C₅	1	2	yes	complemented
127	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
128	C₅×#41	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	C₂×Dic₃	1	4	yes	—
131	C₅×#41	C₂²×D₃	1	4	yes	—
132	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₅×Q₁₆	C₂×Dic₃	1	4	yes	—
138	C₅×SD₁₆	C₂×Dic₃	1	8	yes	—
139	C₅×D₈	C₂×Dic₃	1	4	yes	—
140	C₅×M₁₆	—	3	4	no	—
141	C₅×M₁₆	—	6	4	no	—
142	C₅×M₁₆	—	6	4	no	—
143	C₅×M₁₆	—	6	2	no	—
144	C₅×M₁₆	C₂×Dic₃	1	4	yes	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	3	2	no	—
147	C₂×C₅×C₈	—	3	1	no	—
148	C₂×C₅×C₈	—	3	1	no	—
149	C₂×C₅×C₈	—	6	4	no	—
150	C₂×C₅×C₈	—	6	4	no	—
151	C₂×C₅×C₈	—	6	2	no	—
152	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
153	C₅×C₄⋊C₄	—	6	1	no	—
154	C₅×C₂²⋊C₄	—	6	1	no	—
155	C₄²×C₅	—	3	2	no	—
156	#575	C₅×D₃	1	1	yes	characteristic
157	C₂×#131	—	3	2	no	—
158	#444	—	3	4	no	—
159	#443	—	3	4	no	—
160	#430	—	3	1	no	—
161	#421	—	3	2	no	—
162	#405	—	3	1	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	4	1	no	—
165	C₂²×C₃×C₅	—	4	4	no	—
166	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
167	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
168	C₃×C₄×C₅	—	2	4	no	—
169	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₅×Dic₃	—	4	2	no	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	2	2	no	—
175	C₃×#41	C₂×C₄×C₅	1	4	yes	—
176	C₃×#41	C₂³×C₅	1	4	yes	—
177	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
178	C₂×C₃×D₄	—	2	2	no	—
179	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	—
183	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	—
184	C₃×D₈	C₂×C₄×C₅	1	4	yes	—
185	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
186	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
187	#217	—	2	1	no	—
188	C₄⋊Dic₃	—	2	1	no	—
189	C₄×Dic₃	C₂³×C₅	1	2	yes	—
190	#208	—	2	2	no	—
191	#208	—	2	4	no	—
192	#208	—	2	4	no	—
193	#208	C₂³×C₅	1	4	yes	—
194	C₂×C₃⋊C₈	—	2	2	no	—
195	C₂×C₃⋊C₈	—	2	4	no	—
196	C₂×C₃⋊C₈	—	2	4	no	—
197	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
198	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
199	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
200	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	#237	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	2	4	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	C₂²×Dic₃	1	4	yes	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	6	2	no	—
213	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	#237	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
216	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
217	C₅×C₈	—	3	1	no	—
218	C₅×C₈	—	3	2	no	—
219	C₅×C₈	—	3	1	no	—
220	C₅×C₈	—	6	4	no	—
221	C₅×C₈	C₂²×Dic₃	1	4	yes	—
222	C₂×#41	C₂×C₅×D₃	1	2	yes	—
223	#137	C₅×Dic₃	1	4	yes	complemented
224	AGL(1,ℤ/8)	C₅×Dic₃	1	4	yes	complemented
225	#135	C₂×C₅×D₃	1	4	yes	—
226	#131	—	3	4	no	—
227	#131	—	3	4	no	—
228	#131	—	6	2	no	—
229	#131	—	6	2	no	—
230	C₂×M₁₆	—	3	2	no	—
231	C₂×M₁₆	—	6	2	no	—
232	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
233	C₂²×C₈	—	3	1	no	—
234	C₂²×C₈	—	6	2	no	—
235	#117	—	3	1	no	—
236	#108	—	3	4	no	—
237	#104	—	3	8	no	—
238	#97	—	3	2	no	—
239	C₄×C₈	—	3	2	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	—	4	4	no	—
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	C₅×#41	1	1	yes	characteristic
246	C₃×Q₈	—	2	2	no	—
247	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
248	C₃×D₄	—	2	4	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	C₂×Dic₃	—	2	2	no	—
260	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
261	C₃⋊C₈	—	2	4	no	—
262	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
263	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
264	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₅	—	2	4	no	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	D₄×Dic₃	1	2	yes	—
269	C₂²×C₅	C₂×#237	1	1	yes	characteristic
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	—	12	2	no	—
272	C₄×C₅	D₄×Dic₃	1	2	yes	—
273	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
274	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	C₂×C₅×Dic₃	1	4	yes	—
278	#41	C₂²×C₅×D₃	1	4	yes	—
279	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
284	Q₁₆	C₂×C₅×Dic₃	1	4	yes	—
285	SD₁₆	C₂×C₅×Dic₃	1	8	yes	—
286	D₈	C₂×C₅×Dic₃	1	4	yes	—
287	M₁₆	—	3	4	no	—
288	M₁₆	—	6	4	no	—
289	M₁₆	—	6	4	no	—
290	M₁₆	—	6	2	no	—
291	M₁₆	C₂×C₅×Dic₃	1	4	yes	—
292	C₂×C₈	—	3	2	no	—
293	C₂×C₈	—	3	2	no	—
294	C₂×C₈	—	3	1	no	—
295	C₂×C₈	—	3	1	no	—
296	C₂×C₈	—	6	4	no	—
297	C₂×C₈	—	6	4	no	—
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
300	C₄⋊C₄	—	6	1	no	—
301	C₂²⋊C₄	—	6	1	no	—
302	C₄²	—	3	2	no	—
303	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	4	no	—
307	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
308	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
311	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
312	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
313	Dic₃	—	4	2	no	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	4	4	no	—
317	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	C₅×#237	1	1	yes	characteristic
320	Q₈	—	2	2	no	—
321	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
322	D₄	—	2	4	no	—
323	D₄	—	2	4	no	—
324	D₄	—	2	2	no	—
325	D₄	C₂²×C₅×Dic₃	1	4	yes	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	6	2	no	—
330	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
331	C₂×C₄	C₅×#237	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
333	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
334	C₈	—	3	1	no	—
335	C₈	—	3	2	no	—
336	C₈	—	3	1	no	—
337	C₈	—	6	4	no	—
338	C₈	C₂²×C₅×Dic₃	1	4	yes	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	4	4	no	—
342	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
343	C₅	#83999	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	4	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	4	no	—
347	C₂²	C₅×D₄×Dic₃	1	2	yes	—
348	C₂²	C₂×C₅×#237	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	12	2	no	—
351	C₄	C₅×D₄×Dic₃	1	2	yes	—
352	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
353	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
354	C₃	C₅×#2955	1	1	yes	characteristic, complemented, Sylow
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	4	no	—
358	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₃×C₅×#575	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#575	D₃
hypocenter	C₃	C₅×#2955
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#575

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₅×#5236	C₂	semidirect
4. C₅×#5197	C₂	semidirect
5. C₅×#5196	C₂	semidirect
6. C₅×#5125	C₂	semidirect
7. C₅×#5122	C₂	semidirect
10. C₃×C₅×#137	C₄	semidirect
11. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
16. C₅×#948	C₂²	semidirect
17. C₅×#948	C₂²	semidirect
23. C₅×#837	C₂²	semidirect
24. C₅×#819	C₂²	semidirect
25. C₅×#815	C₂²	semidirect
26. C₅×C₈×Dic₃	C₂²	semidirect
27. #83999	C₅	direct (N × H)
64. C₂×#948	C₂×C₅	semidirect
65. #5236	C₂×C₅	semidirect
66. #5197	C₂×C₅	semidirect
67. #5196	C₂×C₅	semidirect
68. #5125	C₂×C₅	semidirect
69. #5122	C₂×C₅	semidirect
71. C₅×#137	Dic₃	semidirect
72. C₅×AGL(1,ℤ/8)	Dic₃	semidirect
111. C₃×#137	C₄×C₅	semidirect
112. C₃×AGL(1,ℤ/8)	C₄×C₅	semidirect
117. #948	C₂²×C₅	semidirect
118. #948	C₂²×C₅	semidirect
124. #837	C₂²×C₅	semidirect
125. #819	C₂²×C₅	semidirect
126. #815	C₂²×C₅	semidirect
127. C₈×Dic₃	C₂²×C₅	semidirect
223. #137	C₅×Dic₃	semidirect
224. AGL(1,ℤ/8)	C₅×Dic₃	semidirect
303. C₃×C₅	#2955	semidirect
343. C₅	#83999	direct (N × H)
354. C₃	C₅×#2955	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#575	2
C₂×C₅×#948	2
C₅×#5236	2
C₅×#5197	2
C₅×#5196	2
C₅×#5125	2
C₅×#5122	2
C₅×#2955	3
#83999	5

Subgroups — C5×#83999 #14418020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83999 #14418020