Subgroups — C₅×#79453 #14418963

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5128	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5111	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4828	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4730	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4718	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4718	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4701	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2965	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₄	1	1	yes	characteristic
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
22	C₄×C₅×#67	C₂²	1	1	yes	characteristic
23	C₄×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
29	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
30	C₅×#892	C₄	1	1	yes	characteristic
31	C₅×#887	C₄	1	1	yes	characteristic
32	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
33	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
34	C₅×#877	C₄	1	1	yes	characteristic
35	C₅×#877	C₄	1	1	yes	characteristic
36	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
37	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×C₅×#97	C₂²	1	1	yes	characteristic
42	C₅×#830	C₂²	1	1	yes	characteristic
43	C₅×#830	C₂²	1	1	yes	characteristic
44	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×#815	C₂²	1	1	yes	characteristic
47	C₅×#815	C₂²	1	1	yes	characteristic
48	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
57	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
58	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
59	C₅×#803	C₂²	1	1	yes	characteristic
60	#79453	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₄×C₅×#41	—	3	1	no	—
62	C₅×#446	—	3	1	no	—
63	C₅×#446	—	3	1	no	—
64	C₅×#436	—	3	1	no	—
65	C₅×#436	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	C₅×#435	—	3	1	no	—
68	C₅×#435	—	3	1	no	—
69	C₅×#435	D₃	1	1	yes	characteristic, complemented
70	C₅×#431	—	3	1	no	—
71	C₅×#431	—	3	1	no	—
72	C₅×#431	—	3	1	no	—
73	C₄×C₅×M₁₆	—	3	1	no	—
74	C₄×C₅×M₁₆	—	3	1	no	—
75	C₂×C₄×C₅×C₈	—	3	1	no	—
76	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
80	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
85	C₅×#237	—	2	4	no	—
86	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
90	C₃×C₅×M₁₆	—	2	2	no	—
91	C₂×C₃×C₅×C₈	—	2	2	no	—
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#217	C₂×C₄	1	1	yes	characteristic
101	C₅×#217	C₂×C₄	1	1	yes	characteristic
102	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
105	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
110	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
111	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
112	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
113	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
114	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
117	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
118	C₅×#208	—	2	2	no	—
119	C₂×C₅×C₃⋊C₈	—	2	2	no	—
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
125	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
126	C₄×#237	C₂×C₅	1	1	yes	characteristic
127	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
128	#5128	C₂×C₅	1	1	yes	characteristic, complemented
129	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
130	#5111	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
132	#5011	C₂×C₅	1	1	yes	characteristic, complemented
133	#4833	C₂×C₅	1	1	yes	characteristic, complemented
134	#4828	C₂×C₅	1	1	yes	characteristic, complemented
135	#4730	C₂×C₅	1	1	yes	characteristic, complemented
136	#4729	C₂×C₅	1	1	yes	characteristic, complemented
137	#4718	C₂×C₅	1	1	yes	characteristic, complemented
138	#4718	C₂×C₅	1	1	yes	characteristic, complemented
139	#4707	C₂×C₅	1	1	yes	characteristic, complemented
140	#4701	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₅×#41	—	3	1	no	—
142	C₂×C₅×M₁₆	—	3	1	no	—
143	C₂×C₅×M₁₆	—	3	1	no	—
144	C₂×C₅×M₁₆	—	3	1	no	—
145	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
146	C₂²×C₅×C₈	—	3	1	no	—
147	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
148	C₄×C₅×Q₈	—	3	1	no	—
149	C₄×C₅×Q₈	—	3	1	no	—
150	C₄×C₅×D₄	—	3	1	no	—
151	C₄×C₅×D₄	—	3	1	no	—
152	C₄×C₅×D₄	—	3	1	no	—
153	C₄×C₅×D₄	—	3	1	no	—
154	C₄×C₅×D₄	—	3	1	no	—
155	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
156	C₅×#117	—	3	1	no	—
157	C₅×#117	—	3	1	no	—
158	C₅×#117	—	3	1	no	—
159	C₂×C₄²×C₅	—	3	1	no	—
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₂×C₄²×C₅	—	3	1	no	—
162	C₅×C₄⋊C₈	—	3	1	no	—
163	C₅×C₄⋊C₈	—	3	1	no	—
164	C₅×C₄⋊C₈	—	3	1	no	—
165	C₅×C₄⋊C₈	—	3	1	no	—
166	C₅×C₄⋊C₈	—	3	1	no	—
167	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
168	C₅×C₂²⋊C₈	—	3	1	no	—
169	C₅×C₂²⋊C₈	—	3	1	no	—
170	C₅×C₂²⋊C₈	—	3	1	no	—
171	C₅×C₂²⋊C₈	—	3	1	no	—
172	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
173	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
174	C₅×#97	—	3	1	no	—
175	C₅×#97	—	3	1	no	—
176	C₅×#97	—	3	1	no	—
177	C₅×#97	C₂×D₃	1	1	yes	characteristic
178	C₄×C₅×C₈	—	3	1	no	—
179	C₄×C₅×C₈	—	3	1	no	—
180	C₄×C₅×C₈	—	3	1	no	—
181	C₄×C₅×C₈	—	3	1	no	—
182	C₄×C₅×C₈	—	3	1	no	—
183	C₄×C₅×C₈	—	3	1	no	—
184	#2965	—	3	1	no	Sylow
185	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
188	C₃×C₅×D₄	—	2	2	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₅×#67	—	2	2	no	—
199	C₅×#67	—	2	2	no	—
200	C₂×C₅×Dic₃	—	2	2	no	—
201	C₂×C₅×Dic₃	—	2	2	no	—
202	C₂×C₅×Dic₃	—	2	2	no	—
203	C₂×C₅×Dic₃	M₁₆	1	4	yes	complemented
204	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
211	C₄×C₅×D₃	—	2	1	no	—
212	C₄×C₅×D₃	—	2	1	no	—
213	C₄×C₅×D₃	—	2	2	no	—
214	C₄×C₅×D₃	—	2	2	no	—
215	C₅×Dic₆	—	2	2	no	—
216	C₃×C₅×C₈	—	2	1	no	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₃×C₅×C₈	—	2	1	no	—
219	C₃×C₅×C₈	#41	1	2	yes	complemented
220	C₅×C₃⋊C₈	—	2	1	no	—
221	C₅×C₃⋊C₈	—	2	1	no	—
222	C₅×C₃⋊C₈	—	2	1	no	—
223	C₅×C₃⋊C₈	#41	1	2	yes	complemented
224	C₂×#237	C₄×C₅	1	1	yes	characteristic
225	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
227	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
228	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
229	C₄×#67	C₂²×C₅	1	1	yes	characteristic
230	C₄×#67	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
233	C₂×#208	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
236	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
237	#892	C₄×C₅	1	1	yes	characteristic
238	#887	C₄×C₅	1	1	yes	characteristic
239	#67⋊C₄	C₄×C₅	1	1	yes	characteristic
240	#67⋊C₄	C₄×C₅	1	1	yes	characteristic
241	#877	C₄×C₅	1	1	yes	characteristic
242	#877	C₄×C₅	1	1	yes	characteristic
243	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
244	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
246	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₃×#97	C₂²×C₅	1	1	yes	characteristic
249	#830	C₂²×C₅	1	1	yes	characteristic
250	#830	C₂²×C₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	#815	C₂²×C₅	1	1	yes	characteristic
254	#815	C₂²×C₅	1	1	yes	characteristic
255	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
258	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
260	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
261	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
262	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
263	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
264	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
265	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
266	#803	C₂²×C₅	1	1	yes	characteristic
267	C₅×#41	—	6	4	no	—
268	C₂×C₅×Q₈	—	3	1	no	—
269	C₂×C₅×D₄	—	3	1	no	—
270	C₂×C₅×D₄	—	3	1	no	—
271	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
272	C₂²×C₄×C₅	—	3	1	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	3	1	no	—
275	C₂²×C₄×C₅	—	3	1	no	—
276	C₂²×C₄×C₅	—	3	1	no	—
277	C₂²×C₄×C₅	—	3	1	no	—
278	C₂²×C₄×C₅	—	3	1	no	—
279	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
281	C₅×M₁₆	—	2	2	no	—
282	C₅×M₁₆	—	6	2	no	—
283	C₅×M₁₆	—	6	2	no	—
284	C₅×M₁₆	—	6	2	no	—
285	C₂×C₅×C₈	—	2	2	no	—
286	C₂×C₅×C₈	—	3	1	no	—
287	C₂×C₅×C₈	—	3	1	no	—
288	C₂×C₅×C₈	—	3	1	no	—
289	C₂×C₅×C₈	—	3	1	no	—
290	C₂×C₅×C₈	—	6	2	no	—
291	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	—	3	1	no	—
296	C₅×C₄⋊C₄	—	3	1	no	—
297	C₅×C₄⋊C₄	—	3	1	no	—
298	C₅×C₄⋊C₄	—	3	1	no	—
299	C₅×C₄⋊C₄	—	3	1	no	—
300	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
301	C₅×C₂²⋊C₄	—	3	1	no	—
302	C₅×C₂²⋊C₄	—	3	1	no	—
303	C₅×C₂²⋊C₄	—	3	1	no	—
304	C₅×C₂²⋊C₄	—	3	1	no	—
305	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
306	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
307	C₄²×C₅	—	3	1	no	—
308	C₄²×C₅	—	3	1	no	—
309	C₄²×C₅	—	3	1	no	—
310	C₄²×C₅	—	3	1	no	—
311	C₄²×C₅	—	3	1	no	—
312	C₄²×C₅	—	3	1	no	—
313	C₄²×C₅	—	3	1	no	—
314	C₄²×C₅	—	3	1	no	—
315	C₄²×C₅	—	3	1	no	—
316	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
317	C₄×#41	—	3	1	no	—
318	#446	—	3	1	no	—
319	#446	—	3	1	no	—
320	#436	—	3	1	no	—
321	#436	—	3	1	no	—
322	#435	—	3	1	no	—
323	#435	—	3	1	no	—
324	#435	—	3	1	no	—
325	#435	C₅×D₃	1	1	yes	characteristic, complemented
326	#431	—	3	1	no	—
327	#431	—	3	1	no	—
328	#431	—	3	1	no	—
329	C₄×M₁₆	—	3	1	no	—
330	C₄×M₁₆	—	3	1	no	—
331	C₂×C₄×C₈	—	3	1	no	—
332	C₂²×C₃×C₅	—	2	1	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	2	1	no	—
336	C₂²×C₃×C₅	—	2	1	no	—
337	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
338	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₅×D₃	—	2	1	no	—
340	C₂×C₅×D₃	—	2	1	no	—
341	C₂×C₅×D₃	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
347	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₅×Dic₃	—	2	1	no	—
349	C₅×Dic₃	—	2	1	no	—
350	C₅×Dic₃	—	2	1	no	—
351	C₅×Dic₃	—	2	1	no	—
352	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
353	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
354	C₅×Dic₃	#131	1	2	yes	—
355	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
359	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
362	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
363	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
364	#237	—	2	4	no	—
365	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
366	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
367	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
368	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
369	C₃×M₁₆	—	2	2	no	—
370	C₂×C₃×C₈	—	2	2	no	—
371	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
376	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
377	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
378	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
379	#217	C₂×C₄×C₅	1	1	yes	characteristic
380	#217	C₂×C₄×C₅	1	1	yes	characteristic
381	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
382	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
384	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
385	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
386	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
387	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
388	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
389	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
390	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
391	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
392	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
393	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
394	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
395	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
396	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
397	#208	—	2	2	no	—
398	C₂×C₃⋊C₈	—	2	2	no	—
399	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
403	ΓL(1,𝔽₂₅)	—	2	2	no	—
404	ΓL(1,𝔽₂₅)	—	2	2	no	—
405	C₂³×C₅	—	3	1	no	—
406	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
407	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
408	C₅×Q₈	—	6	2	no	—
409	C₅×D₄	—	2	2	no	—
410	C₅×D₄	—	6	2	no	—
411	C₅×D₄	—	6	2	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	3	4	no	—
417	C₂×C₄×C₅	—	3	1	no	—
418	C₂×C₄×C₅	—	3	1	no	—
419	C₂×C₄×C₅	—	3	1	no	—
420	C₂×C₄×C₅	—	3	1	no	—
421	C₂×C₄×C₅	—	3	1	no	—
422	C₂×C₄×C₅	—	3	1	no	—
423	C₂×C₄×C₅	—	3	1	no	—
424	C₂×C₄×C₅	—	6	2	no	—
425	C₂×C₄×C₅	—	6	2	no	—
426	C₂×C₄×C₅	—	6	2	no	—
427	C₂×C₄×C₅	—	6	2	no	—
428	C₂×C₄×C₅	—	6	2	no	—
429	C₂×C₄×C₅	—	6	1	no	—
430	C₂×C₄×C₅	—	6	1	no	—
431	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
432	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
433	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
434	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
435	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
436	C₅×C₈	—	2	1	no	—
437	C₅×C₈	—	2	1	no	—
438	C₅×C₈	—	2	1	no	—
439	C₅×C₈	—	3	2	no	—
440	C₅×C₈	—	6	1	no	—
441	C₅×C₈	—	6	1	no	—
442	C₅×C₈	—	6	1	no	—
443	C₅×C₈	#237	1	2	yes	complemented
444	C₂×#41	—	3	1	no	—
445	C₂×M₁₆	—	3	1	no	—
446	C₂×M₁₆	—	3	1	no	—
447	C₂×M₁₆	—	3	1	no	—
448	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
449	C₂²×C₈	—	3	1	no	—
450	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
451	C₄×Q₈	—	3	1	no	—
452	C₄×Q₈	—	3	1	no	—
453	C₄×D₄	—	3	1	no	—
454	C₄×D₄	—	3	1	no	—
455	C₄×D₄	—	3	1	no	—
456	C₄×D₄	—	3	1	no	—
457	C₄×D₄	—	3	1	no	—
458	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
459	#117	—	3	1	no	—
460	#117	—	3	1	no	—
461	#117	—	3	1	no	—
462	C₂×C₄²	—	3	1	no	—
463	C₂×C₄²	—	3	1	no	—
464	C₂×C₄²	—	3	1	no	—
465	C₄⋊C₈	—	3	1	no	—
466	C₄⋊C₈	—	3	1	no	—
467	C₄⋊C₈	—	3	1	no	—
468	C₄⋊C₈	—	3	1	no	—
469	C₄⋊C₈	—	3	1	no	—
470	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
471	C₂²⋊C₈	—	3	1	no	—
472	C₂²⋊C₈	—	3	1	no	—
473	C₂²⋊C₈	—	3	1	no	—
474	C₂²⋊C₈	—	3	1	no	—
475	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
476	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
477	#97	—	3	1	no	—
478	#97	—	3	1	no	—
479	#97	—	3	1	no	—
480	#97	C₂×C₅×D₃	1	1	yes	characteristic
481	C₄×C₈	—	3	1	no	—
482	C₄×C₈	—	3	1	no	—
483	C₄×C₈	—	3	1	no	—
484	C₄×C₈	—	3	1	no	—
485	C₄×C₈	—	3	1	no	—
486	C₄×C₈	—	3	1	no	—
487	C₂×C₃×C₅	—	2	2	no	—
488	C₂×C₃×C₅	—	4	1	no	—
489	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
490	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
491	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
492	C₅×D₃	—	4	1	no	—
493	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
494	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
495	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₃×D₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
503	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
506	#67	—	2	2	no	—
507	#67	—	2	2	no	—
508	C₂×Dic₃	—	2	2	no	—
509	C₂×Dic₃	—	2	2	no	—
510	C₂×Dic₃	—	2	2	no	—
511	C₂×Dic₃	C₅×M₁₆	1	4	yes	complemented
512	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
513	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
514	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
515	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
516	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
517	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
518	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
519	C₄×D₃	—	2	1	no	—
520	C₄×D₃	—	2	1	no	—
521	C₄×D₃	—	2	2	no	—
522	C₄×D₃	—	2	2	no	—
523	Dic₆	—	2	2	no	—
524	C₃×C₈	—	2	1	no	—
525	C₃×C₈	—	2	1	no	—
526	C₃×C₈	—	2	1	no	—
527	C₃×C₈	C₅×#41	1	2	yes	complemented
528	C₃⋊C₈	—	2	1	no	—
529	C₃⋊C₈	—	2	1	no	—
530	C₃⋊C₈	—	2	1	no	—
531	C₃⋊C₈	C₅×#41	1	2	yes	complemented
532	C₂²×C₅	—	2	1	no	—
533	C₂²×C₅	—	2	1	no	—
534	C₂²×C₅	—	2	1	no	—
535	C₂²×C₅	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	6	1	no	—
538	C₂²×C₅	—	6	1	no	—
539	C₂²×C₅	—	6	1	no	—
540	C₂²×C₅	D₃×M₁₆	1	2	yes	—
541	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
542	C₄×C₅	—	2	1	no	—
543	C₄×C₅	—	2	1	no	—
544	C₄×C₅	—	2	1	no	—
545	C₄×C₅	—	2	1	no	—
546	C₄×C₅	—	3	2	no	—
547	C₄×C₅	—	3	2	no	—
548	C₄×C₅	—	3	2	no	—
549	C₄×C₅	—	6	1	no	—
550	C₄×C₅	—	6	1	no	—
551	C₄×C₅	—	6	1	no	—
552	C₄×C₅	—	6	1	no	—
553	C₄×C₅	C₂×#237	1	1	yes	characteristic
554	C₄×C₅	D₃×#41	1	1	yes	characteristic
555	#41	—	6	4	no	—
556	C₂×Q₈	—	3	1	no	—
557	C₂×D₄	—	3	1	no	—
558	C₂×D₄	—	3	1	no	—
559	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
560	C₂²×C₄	—	3	1	no	—
561	C₂²×C₄	—	3	1	no	—
562	C₂²×C₄	—	3	1	no	—
563	C₂²×C₄	—	3	1	no	—
564	C₂²×C₄	—	3	1	no	—
565	C₂²×C₄	—	3	1	no	—
566	C₂²×C₄	—	3	1	no	—
567	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
569	M₁₆	—	2	2	no	—
570	M₁₆	—	6	2	no	—
571	M₁₆	—	6	2	no	—
572	M₁₆	—	6	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	3	1	no	—
575	C₂×C₈	—	3	1	no	—
576	C₂×C₈	—	3	1	no	—
577	C₂×C₈	—	3	1	no	—
578	C₂×C₈	—	6	2	no	—
579	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
580	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
581	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
582	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
583	C₄⋊C₄	—	3	1	no	—
584	C₄⋊C₄	—	3	1	no	—
585	C₄⋊C₄	—	3	1	no	—
586	C₄⋊C₄	—	3	1	no	—
587	C₄⋊C₄	—	3	1	no	—
588	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
589	C₂²⋊C₄	—	3	1	no	—
590	C₂²⋊C₄	—	3	1	no	—
591	C₂²⋊C₄	—	3	1	no	—
592	C₂²⋊C₄	—	3	1	no	—
593	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
594	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
595	C₄²	—	3	1	no	—
596	C₄²	—	3	1	no	—
597	C₄²	—	3	1	no	—
598	C₄²	—	3	1	no	—
599	C₄²	—	3	1	no	—
600	C₄²	—	3	1	no	—
601	C₄²	—	3	1	no	—
602	C₄²	—	3	1	no	—
603	C₄²	—	3	1	no	—
604	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
605	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	2	1	no	—
610	C₂²×C₃	—	2	1	no	—
611	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
612	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
613	C₂×D₃	—	2	1	no	—
614	C₂×D₃	—	2	1	no	—
615	C₂×D₃	—	2	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	2	1	no	—
619	C₃×C₄	—	2	1	no	—
620	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
621	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
622	Dic₃	—	2	1	no	—
623	Dic₃	—	2	1	no	—
624	Dic₃	—	2	1	no	—
625	Dic₃	—	2	1	no	—
626	Dic₃	C₂×C₅×M₁₆	1	2	yes	—
627	Dic₃	C₂×C₅×M₁₆	1	2	yes	—
628	Dic₃	C₅×#131	1	2	yes	—
629	C₂×C₅	—	2	2	no	—
630	C₂×C₅	—	4	1	no	—
631	C₂×C₅	—	12	1	no	—
632	C₂×C₅	C₄×#237	1	1	yes	characteristic
633	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
634	C₂×C₅	D₃×#131	1	1	yes	characteristic
635	C₂³	—	3	1	no	—
636	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
637	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
638	Q₈	—	6	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	6	2	no	—
641	D₄	—	6	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	3	4	no	—
647	C₂×C₄	—	3	1	no	—
648	C₂×C₄	—	3	1	no	—
649	C₂×C₄	—	3	1	no	—
650	C₂×C₄	—	3	1	no	—
651	C₂×C₄	—	3	1	no	—
652	C₂×C₄	—	3	1	no	—
653	C₂×C₄	—	3	1	no	—
654	C₂×C₄	—	6	2	no	—
655	C₂×C₄	—	6	2	no	—
656	C₂×C₄	—	6	2	no	—
657	C₂×C₄	—	6	2	no	—
658	C₂×C₄	—	6	2	no	—
659	C₂×C₄	—	6	1	no	—
660	C₂×C₄	—	6	1	no	—
661	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
662	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
663	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
664	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
666	C₈	—	2	1	no	—
667	C₈	—	2	1	no	—
668	C₈	—	2	1	no	—
669	C₈	—	3	2	no	—
670	C₈	—	6	1	no	—
671	C₈	—	6	1	no	—
672	C₈	—	6	1	no	—
673	C₈	C₅×#237	1	2	yes	complemented
674	C₂×C₃	—	2	2	no	—
675	C₂×C₃	—	4	1	no	—
676	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
677	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
678	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
679	D₃	—	4	1	no	—
680	C₅	#79453	1	1	yes	characteristic, direct product factor, Sylow
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	6	1	no	—
687	C₂²	—	6	1	no	—
688	C₂²	—	6	1	no	—
689	C₂²	C₅×D₃×M₁₆	1	2	yes	—
690	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	3	2	no	—
696	C₄	—	3	2	no	—
697	C₄	—	3	2	no	—
698	C₄	—	6	1	no	—
699	C₄	—	6	1	no	—
700	C₄	—	6	1	no	—
701	C₄	—	6	1	no	—
702	C₄	C₂×C₅×#237	1	1	yes	characteristic
703	C₄	C₅×D₃×#41	1	1	yes	characteristic
704	C₃	C₅×#2965	1	1	yes	characteristic, complemented, Sylow
705	C₂	—	2	2	no	—
706	C₂	—	4	1	no	—
707	C₂	—	12	1	no	—
708	C₂	C₄×C₅×#237	1	1	yes	characteristic
709	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
710	C₂	C₅×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#435	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#237	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#435	D₃
hypocenter	C₃	C₅×#2965
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#435

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#435	C₂	semidirect
3. C₅×#5128	C₂	semidirect
4. C₅×Dic₃×M₁₆	C₂	semidirect
5. C₅×#5111	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
7. C₅×#5011	C₂	semidirect
8. C₅×#4833	C₂	semidirect
9. C₅×#4828	C₂	semidirect
10. C₅×#4730	C₂	semidirect
11. C₅×#4729	C₂	semidirect
12. C₅×#4718	C₂	semidirect
13. C₅×#4718	C₂	semidirect
14. C₅×#4707	C₂	semidirect
15. C₅×#4701	C₂	semidirect
60. #79453	C₅	direct (N × H)
69. C₅×#435	D₃	semidirect
127. C₃×#435	C₂×C₅	semidirect
128. #5128	C₂×C₅	semidirect
129. Dic₃×M₁₆	C₂×C₅	semidirect
130. #5111	C₂×C₅	semidirect
131. C₂×C₈×Dic₃	C₂×C₅	semidirect
132. #5011	C₂×C₅	semidirect
133. #4833	C₂×C₅	semidirect
134. #4828	C₂×C₅	semidirect
135. #4730	C₂×C₅	semidirect
136. #4729	C₂×C₅	semidirect
137. #4718	C₂×C₅	semidirect
138. #4718	C₂×C₅	semidirect
139. #4707	C₂×C₅	semidirect
140. #4701	C₂×C₅	semidirect
203. C₂×C₅×Dic₃	M₁₆	semidirect
219. C₃×C₅×C₈	#41	semidirect
223. C₅×C₃⋊C₈	#41	semidirect
325. #435	C₅×D₃	semidirect
443. C₅×C₈	#237	semidirect
511. C₂×Dic₃	C₅×M₁₆	semidirect
527. C₃×C₈	C₅×#41	semidirect
531. C₃⋊C₈	C₅×#41	semidirect
605. C₃×C₅	#2965	semidirect
673. C₈	C₅×#237	semidirect
680. C₅	#79453	direct (N × H)
704. C₃	C₅×#2965	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#237	2
C₃×C₅×#435	2
C₅×#5128	2
C₅×Dic₃×M₁₆	2
C₅×#5111	2
C₂×C₅×C₈×Dic₃	2
C₅×#5011	2
C₅×#4833	2
C₅×#4828	2
C₅×#4730	2
C₅×#4729	2
C₅×#4718	2
C₅×#4707	2
C₅×#4701	2
C₅×#2965	3
#79453	5

Subgroups — C5×#79453 #14418963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79453 #14418963