Subgroups — C₅×#79938 #14418978

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4838	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4836	C₂	1	2	yes	maximal, complemented
6	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4833	C₂	1	2	yes	maximal, complemented
8	C₅×#4707	C₂	1	2	yes	maximal, complemented
9	C₅×#4706	C₂	1	2	yes	maximal, complemented
10	C₅×#4688	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2965	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
20	C₅×#893	C₄	1	2	yes	—
21	C₅×#893	C₄	1	1	yes	characteristic
22	C₅×#892	C₄	1	2	yes	—
23	C₅×#892	C₄	1	1	yes	characteristic
24	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₄×C₅×D₁₂	C₂²	1	2	yes	—
26	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₄²×C₅×D₃	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×#97	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
34	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
35	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
36	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
37	C₅×C₈×Dic₃	C₂²	1	2	yes	—
38	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
39	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	2	yes	—
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#79938	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₄×C₅×#41	—	3	1	no	—
44	C₅×#446	—	3	1	no	—
45	C₅×#446	D₃	1	1	yes	characteristic, complemented
46	C₅×#436	—	3	1	no	—
47	C₅×#436	—	3	1	no	—
48	C₅×#435	—	3	2	no	—
49	C₅×#435	—	3	2	no	—
50	C₅×#431	—	3	1	no	—
51	C₅×#431	—	3	2	no	—
52	C₄×C₅×M₁₆	—	3	2	no	—
53	C₂×C₄×C₅×C₈	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#239	—	2	4	no	—
56	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂³	1	2	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
75	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
78	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
85	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
86	C₅×D₃×C₈	—	2	2	no	—
87	C₅×D₃×C₈	—	2	2	no	—
88	C₄×#239	C₂×C₅	1	1	yes	characteristic
89	C₃×#446	C₂×C₅	1	1	yes	characteristic, complemented
90	#5024	C₂×C₅	1	1	yes	characteristic, complemented
91	#4838	C₂×C₅	1	1	yes	characteristic, complemented
92	#4836	C₂×C₅	1	2	yes	complemented
93	#4833	C₂×C₅	1	1	yes	characteristic, complemented
94	#4833	C₂×C₅	1	2	yes	complemented
95	#4707	C₂×C₅	1	2	yes	complemented
96	#4706	C₂×C₅	1	2	yes	complemented
97	#4688	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₅×#41	—	3	1	no	—
100	C₂×C₅×M₁₆	—	3	2	no	—
101	C₂×C₅×M₁₆	—	3	2	no	—
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₂²×C₅×C₈	—	3	1	no	—
104	C₄×C₅×Q₈	—	3	1	no	—
105	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
106	C₄×C₅×D₄	—	3	2	no	—
107	C₄×C₅×D₄	—	3	1	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	3	1	no	—
110	C₅×#117	—	3	1	no	—
111	C₅×#117	—	3	2	no	—
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	2	no	—
114	C₅×C₄⋊C₈	—	3	2	no	—
115	C₅×C₄⋊C₈	—	3	1	no	—
116	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
117	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
118	C₅×C₂²⋊C₈	—	3	2	no	—
119	C₅×C₂²⋊C₈	—	3	2	no	—
120	C₅×C₂²⋊C₈	—	3	2	no	—
121	C₅×#97	—	3	2	no	—
122	C₅×#97	C₂×D₃	1	2	yes	—
123	C₄×C₅×C₈	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
128	#2965	—	3	1	no	Sylow
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
141	C₅×D₁₂	—	2	4	no	—
142	C₅×D₁₂	—	2	2	no	—
143	C₄×C₅×D₃	—	2	1	no	—
144	C₄×C₅×D₃	—	2	1	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₄×C₅×D₃	—	2	4	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	2	4	no	—
150	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	#41	1	2	yes	complemented
154	C₅×C₃⋊C₈	—	2	1	no	—
155	C₅×C₃⋊C₈	—	2	2	no	—
156	C₅×C₃⋊C₈	#41	1	2	yes	complemented
157	C₂×#239	C₄×C₅	1	1	yes	characteristic
158	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
159	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
160	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
161	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
162	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
164	#893	C₄×C₅	1	2	yes	—
165	#893	C₄×C₅	1	1	yes	characteristic
166	#892	C₄×C₅	1	2	yes	—
167	#892	C₄×C₅	1	1	yes	characteristic
168	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
169	C₄×D₁₂	C₂²×C₅	1	2	yes	—
170	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
171	C₄²×D₃	C₂²×C₅	1	2	yes	—
172	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
173	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×#97	C₂²×C₅	1	2	yes	—
175	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
176	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
177	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
178	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
179	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
181	C₈×Dic₃	C₂²×C₅	1	2	yes	—
182	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
183	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
184	#803	C₂²×C₅	1	2	yes	—
185	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₅×#41	—	6	4	no	—
187	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
188	C₂×C₅×D₄	—	3	2	no	—
189	C₂×C₅×D₄	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₂²×C₄×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	2	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	—	3	2	no	—
196	C₅×M₁₆	—	6	4	no	—
197	C₅×M₁₆	—	6	4	no	—
198	C₂×C₅×C₈	—	3	1	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	3	2	no	—
201	C₂×C₅×C₈	—	6	2	no	—
202	C₂×C₅×C₈	—	6	2	no	—
203	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
205	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
206	C₅×C₄⋊C₄	—	3	2	no	—
207	C₅×C₄⋊C₄	—	3	1	no	—
208	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
209	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	3	2	no	—
211	C₅×C₂²⋊C₄	—	3	2	no	—
212	C₅×C₂²⋊C₄	—	3	2	no	—
213	C₄²×C₅	—	3	1	no	—
214	C₄²×C₅	—	3	2	no	—
215	C₄²×C₅	—	3	2	no	—
216	C₄²×C₅	—	3	1	no	—
217	C₄²×C₅	—	3	1	no	—
218	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₄²×C₅	C₂²×D₃	1	2	yes	—
220	C₄×#41	—	3	1	no	—
221	#446	—	3	1	no	—
222	#446	C₅×D₃	1	1	yes	characteristic, complemented
223	#436	—	3	1	no	—
224	#436	—	3	1	no	—
225	#435	—	3	2	no	—
226	#435	—	3	2	no	—
227	#431	—	3	2	no	—
228	#431	—	3	1	no	—
229	C₄×M₁₆	—	3	2	no	—
230	C₂×C₄×C₈	—	3	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₅×D₃	—	2	1	no	—
233	C₂×C₅×D₃	—	2	1	no	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	—	2	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₅×Dic₃	—	2	1	no	—
245	C₅×Dic₃	—	2	2	no	—
246	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
247	C₅×Dic₃	#131	1	2	yes	—
248	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
249	#239	—	2	4	no	—
250	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
251	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
253	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
254	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
258	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
260	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
262	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
263	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
264	C₃×C₄²	C₂³×C₅	1	2	yes	—
265	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
267	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
268	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
269	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
270	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
271	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
272	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
273	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
274	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
277	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
278	ΓL(1,𝔽₂₅)	—	2	4	no	—
279	ΓL(1,𝔽₂₅)	—	2	4	no	—
280	D₃×C₈	—	2	2	no	—
281	D₃×C₈	—	2	2	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂³×C₅	—	3	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×D₄	—	6	4	no	—
286	C₅×D₄	—	6	2	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	—	3	4	no	—
290	C₂×C₄×C₅	—	3	1	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	6	4	no	—
294	C₂×C₄×C₅	—	6	4	no	—
295	C₂×C₄×C₅	—	6	1	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	1	no	—
298	C₂×C₄×C₅	—	6	2	no	—
299	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	—	3	2	no	—
307	C₅×C₈	—	6	1	no	—
308	C₅×C₈	—	6	2	no	—
309	C₅×C₈	#239	1	2	yes	complemented
310	C₂×#41	—	3	1	no	—
311	C₂×M₁₆	—	3	2	no	—
312	C₂×M₁₆	—	3	2	no	—
313	C₂²×C₈	—	3	1	no	—
314	C₂²×C₈	—	3	1	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	#117	—	3	1	no	—
322	#117	—	3	2	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	3	2	no	—
325	C₄⋊C₈	—	3	2	no	—
326	C₄⋊C₈	—	3	1	no	—
327	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
328	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
329	C₂²⋊C₈	—	3	2	no	—
330	C₂²⋊C₈	—	3	2	no	—
331	C₂²⋊C₈	—	3	2	no	—
332	#97	—	3	2	no	—
333	#97	C₂×C₅×D₃	1	2	yes	—
334	C₄×C₈	—	3	1	no	—
335	C₄×C₈	—	3	1	no	—
336	C₄×C₈	—	3	2	no	—
337	C₄×C₈	—	3	1	no	—
338	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	C₅×D₃	—	2	2	no	—
343	C₅×D₃	—	4	2	no	—
344	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
345	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₃×Q₈	—	2	2	no	—
347	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
348	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
352	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
353	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
354	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
355	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
356	D₁₂	—	2	4	no	—
357	D₁₂	—	2	2	no	—
358	C₄×D₃	—	2	1	no	—
359	C₄×D₃	—	2	1	no	—
360	C₄×D₃	—	2	2	no	—
361	C₄×D₃	—	2	2	no	—
362	C₄×D₃	—	2	4	no	—
363	C₄×D₃	—	2	2	no	—
364	C₄×D₃	—	2	4	no	—
365	C₄×D₃	C₅×M₁₆	1	4	yes	complemented
366	C₃×C₈	—	2	1	no	—
367	C₃×C₈	—	2	2	no	—
368	C₃×C₈	C₅×#41	1	2	yes	complemented
369	C₃⋊C₈	—	2	1	no	—
370	C₃⋊C₈	—	2	2	no	—
371	C₃⋊C₈	C₅×#41	1	2	yes	complemented
372	C₂²×C₅	—	3	2	no	—
373	C₂²×C₅	—	6	1	no	—
374	C₂²×C₅	—	6	1	no	—
375	C₂²×C₅	—	6	2	no	—
376	C₂²×C₅	—	6	2	no	—
377	C₂²×C₅	—	6	2	no	—
378	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	3	2	no	—
383	C₄×C₅	—	3	2	no	—
384	C₄×C₅	—	6	1	no	—
385	C₄×C₅	—	6	2	no	—
386	C₄×C₅	D₃×M₁₆	1	2	yes	—
387	C₄×C₅	C₂×#239	1	1	yes	characteristic
388	C₄×C₅	D₃×#41	1	1	yes	characteristic
389	#41	—	6	4	no	—
390	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
391	C₂×D₄	—	3	2	no	—
392	C₂×D₄	—	3	1	no	—
393	C₂²×C₄	—	3	1	no	—
394	C₂²×C₄	—	3	2	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	3	2	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	3	2	no	—
399	M₁₆	—	6	4	no	—
400	M₁₆	—	6	4	no	—
401	C₂×C₈	—	3	1	no	—
402	C₂×C₈	—	3	1	no	—
403	C₂×C₈	—	3	2	no	—
404	C₂×C₈	—	6	2	no	—
405	C₂×C₈	—	6	2	no	—
406	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
408	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
409	C₄⋊C₄	—	3	2	no	—
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
412	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
413	C₂²⋊C₄	—	3	2	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	3	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	3	2	no	—
418	C₄²	—	3	2	no	—
419	C₄²	—	3	1	no	—
420	C₄²	—	3	1	no	—
421	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₄²	C₂²×C₅×D₃	1	2	yes	—
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
425	C₂×D₃	—	2	1	no	—
426	C₂×D₃	—	2	1	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	2	2	no	—
430	C₂×D₃	C₂×C₅×M₁₆	1	2	yes	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	C₂×C₅×M₁₆	1	2	yes	—
435	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
437	Dic₃	—	2	1	no	—
438	Dic₃	—	2	2	no	—
439	Dic₃	C₂×C₅×M₁₆	1	2	yes	—
440	Dic₃	C₅×#131	1	2	yes	—
441	C₂×C₅	—	6	2	no	—
442	C₂×C₅	—	12	2	no	—
443	C₂×C₅	C₄×#239	1	1	yes	characteristic
444	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
445	C₂×C₅	D₃×#131	1	1	yes	characteristic
446	C₂³	—	3	1	no	—
447	C₂³	—	3	2	no	—
448	Q₈	—	2	2	no	—
449	D₄	—	6	4	no	—
450	D₄	—	6	2	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	6	4	no	—
457	C₂×C₄	—	6	2	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	—	6	1	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
465	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
466	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
467	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	2	no	—
470	C₈	—	3	2	no	—
471	C₈	—	6	1	no	—
472	C₈	—	6	2	no	—
473	C₈	C₅×#239	1	2	yes	complemented
474	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
475	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
476	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
477	D₃	—	2	2	no	—
478	D₃	—	4	2	no	—
479	C₅	#79938	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	3	2	no	—
481	C₂²	—	6	1	no	—
482	C₂²	—	6	1	no	—
483	C₂²	—	6	2	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	6	2	no	—
486	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	3	2	no	—
491	C₄	—	3	2	no	—
492	C₄	—	6	1	no	—
493	C₄	—	6	2	no	—
494	C₄	C₅×D₃×M₁₆	1	2	yes	—
495	C₄	C₂×C₅×#239	1	1	yes	characteristic
496	C₄	C₅×D₃×#41	1	1	yes	characteristic
497	C₃	C₅×#2965	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	6	2	no	—
499	C₂	—	12	2	no	—
500	C₂	C₄×C₅×#239	1	1	yes	characteristic
501	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
502	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×#446	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#239	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#446	D₃
hypocenter	C₃	C₅×#2965
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. C₅×#5024	C₂	semidirect
4. C₅×#4838	C₂	semidirect
5. C₅×#4836	C₂	semidirect
6. C₅×#4833	C₂	semidirect
7. C₅×#4833	C₂	semidirect
8. C₅×#4707	C₂	semidirect
9. C₅×#4706	C₂	semidirect
10. C₅×#4688	C₂	semidirect
11. C₄×C₅×D₃×C₈	C₂	semidirect
42. #79938	C₅	direct (N × H)
45. C₅×#446	D₃	semidirect
89. C₃×#446	C₂×C₅	semidirect
90. #5024	C₂×C₅	semidirect
91. #4838	C₂×C₅	semidirect
92. #4836	C₂×C₅	semidirect
93. #4833	C₂×C₅	semidirect
94. #4833	C₂×C₅	semidirect
95. #4707	C₂×C₅	semidirect
96. #4706	C₂×C₅	semidirect
97. #4688	C₂×C₅	semidirect
98. C₄×D₃×C₈	C₂×C₅	semidirect
150. C₄×C₅×D₃	M₁₆	semidirect
153. C₃×C₅×C₈	#41	semidirect
156. C₅×C₃⋊C₈	#41	semidirect
222. #446	C₅×D₃	semidirect
309. C₅×C₈	#239	semidirect
365. C₄×D₃	C₅×M₁₆	semidirect
368. C₃×C₈	C₅×#41	semidirect
371. C₃⋊C₈	C₅×#41	semidirect
423. C₃×C₅	#2965	semidirect
473. C₈	C₅×#239	semidirect
479. C₅	#79938	direct (N × H)
497. 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×#239	2
C₃×C₅×#446	2
C₅×#5024	2
C₅×#4838	2
C₅×#4836	2
C₅×#4833	2
C₅×#4707	2
C₅×#4706	2
C₅×#4688	2
C₄×C₅×D₃×C₈	2
C₅×#2965	3
#79938	5

Subgroups — C5×#79938 #14418978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79938 #14418978